I

I
I

I

71-23,158
ASHTON, Peter Geoffrey, 19*4-0RECREATIONAL BOATING CARRYING CAPACITY:
A PRELIMINARY STUDY OF THREE HEAVILY USED
LAKES IN SOUTHEASTERN MICHIGAN.
Michigan State University, Ph.D., 1971
Environmental Sciences

U niversity Microfilms, A XEROXC om pany , A nn A rbor, M ichigan

RECREATIONAL BOATING CARRYING CAPACITY:

A

PRELIMINARY STUDY OF THREE HEAVILY USED
LAKES IN SOUTHEASTERN MICHIGAN
By
Peter Geoffrey Ashton

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Resource Development
1971

PLEASE NOTE:

Some pages have small
and Indistinct type.
Filmed as received.
University Microfilms

ABSTRACT
RECREATIONAL BOATING CARRYING CAPACITY:
A
PRELIMINARY STUDY OF THREE HEAVILY USED
LAKES IN SOUTHEASTERN MICHIGAN
By
Peter Geoffrey Ashton

The tremendous growth of participation in recre­
ational boating has focused attention on the ability of
surface waters to support different types of water-based
recreation under intensive use.

Many recreation resource

planners believe that both the environment and the quality
of the experience deteriorate when water is used too in­
tensively.

If state agencies responsible for controlling

the access to and use of .water are to follow a policy of
maintaining high quality water-oriented recreation,

ade­

quate methods for doing so must be adopted.
In order to regulate usage of a water surface,

the

basic relationship of users to the physical resource and
the ways in which satisfaction may change with different
amounts of use must be known.

The position of this r e ­

search is that water carrying capacity is a combination
of both these relationships.

Peter Geoffrey Ashton
These relationships were investigated during the
summer of 1969 on Union, Cass,

and Orchard Lakes in O a k ­

land County, M i c h i g a n using attitude responses and aerial
photography.

The m a j o r thrust of the research was to:

(1) investigate the attitudes of water-oriented user
groups during times of intense use,

(2) develop a measure

of the level of boating activity intensity,

(3) relate

boater attitudes to levels of boating activity intensity
in order to develop a method of expressing boating ca r r y ­
ing capacity quantitatively,

and

(4) determine if a

significant difference exists between the selected socio­
economic characteristics of boaters indicating unfavorable
conditions of use and the characteristics of those indi­
cating favorable conditions of use.
The analysis was divided into three successive
phases.

In the first phase,

a least squares stepwise

deletion analysis technique was used to examine various
methods of measuring the amount of boating taking place.
The dispersion and consumption by boating activities on
the water surface were used as coefficients for describing
the intensity of boating usage.

These coefficients were

investigated for possible relationships individually and
in combination.

In the second phase, a deletion analysis

technique was again used to:

(1) compare the attitudes

toward boating experiences with the level of boating
activity intensity, and

<2) compare the number of acres

per boat with the level of boating activity intensity.

Peter Geoffrey Ashton
T h e a t t i t u d e of u s e r s was d e f i n e d in terms of a n i n d e x
c a l c u l a t e d by d i v i d i n g the n u m b e r of u n f a v o r a b l e r e s p o n s e s
b y b o a t e r s b y the total n u m b e r of r e s p o n s e s
time, period,

a n d place.

for a g i v e n

T h e n u m b e r o f acres p e r b o a t

w a s d e t e r m i n e d b y d i v i d i n g the a r e a of e a c h lake z o n e b y
the t otal n u m b e r of b o a t s i n v o l v e d in all a c t i v i t i e s .

The

c o m b i n a t i o n of the two r e l a t i o n s h i p s was u s e d to d e v e l o p a
m e t h o d of d e t e r m i n i n g b o a t i n g c a r r y i n g capacity.
t h i r d phase,

In the

c h i - s q u a r e anal y s i s w a s u s e d to d e t e r m i n e if

s i g n i f i c a n t d i f f e r e n c e s in s e l e c t e d s o c i o - e c o n o m i c c h a r a c ­
t e r i s t i c s e x i s t e d b e t w e e n boa t e r s

indicating unfavorable

c o n d i t i o n s of use and those i n d i c a t i n g f a v o r a b l e c o n d i t i o n s
of use.
T h e s t u d y res u l t s

in P h a s e X s h o w that

"the s p a c e

c o n s u m p t i o n s a f e t y c o e f f i c i e n t p r o c e d u r e " SCSC-P, w h i c h
computes

the t o t a l sur f a c e w a t e r space u s e d b y all a c t i v i ­

ties and d i v i d e s by the area of the lake in w h i c h a c t i v i ­
ties t o o k place,

a d e q u a t e l y m e a s u r e s the level o f b o a t i n g

a c t i v i t y intensity.
(1)

T h e results in P h a s e II indicate:

that a s i g n i f i c a n t r e l a t i o n s h i p ex i s t s b e t w e e n the

u s e r a t t i t u d e in d e x UAI and the space c o n s u m p t i o n s a f e t y
c o e f f i c i e n t SCSC,

and

(2)

the n u m b e r of acres p e r b o a t

an d the space c o n s u m p t i o n safety c o e f f i c i e n t .

A method

for d e t e r m i n i n g a b o a t i n g c a r r y i n g c a p a c i t y r a n g e for
c o m b i n e d a c t i v i t i e s in terms of n u m b e r of a c r e s p e r b o a t
wa s d e v e l o p e d u s i n g the above r e l a t i o n s h i p s .

T h e P h a s e III

Peter Geoffrey Ashton
results demonstrated that there is a significant differ­
ence in the socio-economic characteristics of boaters
responding to unfavorable conditions and those responding
to favorable conditions of use at the same point in time
and at the same location.

To my one-year-old son, Geoffrey, who
diligently and enthusiastically tore
into this dissertation as I did.

ACKNOWLEDGMENTS

I w o u l d like -to a c k n o w l e d g e the e n c o u r a g e m e n t and
p r o f e s s i o n a l d i r e c t i o n g i v e n to me by the m e m b e r s of m y
g u i d a n c e committee:

Dr. R. B a r l o w e ,

R. Marty, Dr. S. Romberger,

Dr.

a n d Dr. M.

C. H u m p h r y s , Dr.

Stei n m u e l l e r .

P a r t i c u l a r a c k n o w l e d g m e n t is g i v e n to Dr. M. Chubb, w h o
h as s e r v e d as the c h a i r m a n o f this d i s s e r t a t i o n c o m m i t t e e
and has b e e n of i n v a l u a b l e a s s i s t a n c e as the m a j o r a d v i s o r
for this research.
p e r s i s tence,

It has b e e n t h r o u g h his patience,

under s t a n d i n g ,

a n d i n s i g h t s t h a t this p r o j e c t

has r e a c h e d its c o n c l usion.
T o Dr. C. H u m p h r y s

for his guidance,

direct i o n ,

and s up p o r t as c h a i r m a n of m y c o m m i t t e e , I give m y t h a n k s .
To Mr. W. A l l a r d and Mr. J. Teeter, A p p l i c a t i o n
Programming,

C o m p u t e r Center, M i c h i g a n S t a t e U n i v e r s i t y

for t heir v a l u a b l e a s s i s t a n c e in w o r k i n g o u t the t e c h n i c a l
de t a i l s of p r o c e d u r e and s t a t i s t i c a l analysis.
To Dr. D. Gilliland,
Probability,

D e p a r t m e n t of S t a t i s t i c s and

I w i s h to e x p r e s s a s p e c i a l note of thanks.

I, as do o t h e r g r a d u a t e s t u d e n t s a s s o c i a t e d w i t h the
D e p a r t m e n t of P a r k and R e c r e a t i o n R e s o u r c e s , owe h i m a
d e b t w h i c h ca n n o t b e repaid.

He h a s m a d e us p r o u d of our

association with the Department of Park and Recreation
Resources of Michigan State University, both within and
without the university.
To Mr. K. Wilson, Director, Waterways Division,
Michigan Department of Natural R e s o u r c e s , for financial
assistance which enabled me to do this research.
To Mr. R. Lanier, Field party Leader, Southwest
Resources Group, Economic Research Service, through his
generosity, has allowed me to work full-time towards the
completion of my degree.
To my wife, Theresa Anne, I pay tribute.

Through

crisis after crisis she remained steadfast, understanding,
and sympathetic.

T A B L E O F CONT E N T S
Page
LIST OF

T A B L E S .......................................

xi

LIST O F

F I G U R E S .......................................

xii

LIST OF

A P P E N D I C E S ...................................

xiv

Chapter
I.

INTRODUCTION

................................

1

The P r o b l e m ...........................

2

S emantics of C a r r y i n g C a p a c i t y . . .
The I m p o r t a n c e o f C a r r y i n g C a p a c i t y
to M a n a g e m e n t ....................

II.

3
4

Objectives of the S t u d y .............

6

REVIEW OF L I T E R A T U R E ....................

7

Previous R e s e a r c h .........................
E x i s t i n g C a r r y i n g C a p a c i t y Standards
and C u r r e n t S u r v e y s ................
C o n c lusions from R e v i e w of the L i t e r ­
ature on C a r r y i n g C a p a c i t y Standards
.
III.

8
10
18

RESEARCH D E S I G N F O R M U L A T I O N .........

20

The P r o b l e m S t a t e m e n t ................

20

S u m m a r y ..............................
. . . . . . . .
Objectives.
H y p o t h e s e s ...........................

20
.

20
21

The Study A r e a .......................
Selection . . . . .
Geographical and Geological Features
C h e m i c a l and P h y s i c a l Features . . .
v

21
.

21
23
30

Chapter

Page
B i o l o g i c a l C h a r a c t e r i s t i c s ...............
Climate
* • • ■ • • • • * • •
L a k e D e v e l o p m e n t .................
31

IV.

M E T H O D S A N D PR O C E D U R E S .
The I n t e r v i e w

.

..............

.............................

The Interview Schedule

..................

33
33
38

T h e Q u e s t i o n n a i r e .....................
41
.........................
Aerial Photography
I n t e r p r e t a t i o n of the P h o t o g r a p h s
. . .

42
45

G r i d C o n s t r u c t i o n .................
45
A c t i v i t y I n t e r p r e t a t i o n ..................

53

B o a t i n g S p a c e C o n s u m p t i o n ......
58
B o a t i n g D i s p e r s i o n ......................

63

U s e r A t t i t u d e ........................

V.

30
31

65

P u b l i c A c c e s s U s e r .................
R i p a r i a n U s e r .....................

65
68

A N A L Y S I S ................................

69

P h a s e I— M e a s u r e s of L e v e l of B o a t i n g
A c t i v i t y I n t e n s i t y .................

69

Least Squares Deletion Analysis
. . .
T h e B e s t P i t C u r v e .................
71
P r o c e d u r e s for D e t e r m i n i n g Le v e l s of
Boating Activity Intensity. . . .
Procedure 1
Procedure 2
Procedure 3
Procedure 4

......................... .
.....................
.
.
.
..........
.....................

I l l u s t r a t i o n b y the P l o t XY C o m p u t e r
R o u t i n e ............................

73
73

73
73
74
74

P h a s e I I — U s e r A t t i t u d e and L e v e l of
B o a t i n g A c t i v i t y I n t e n s i t y R e l a tionship.
P r o c e d u r e s for C o m p a r i n g User A t t i t u d e s
w i t h L e v e l s of B o a t i n g A c t i v i t y
I n t e n s i t y ........................
75

vi

69

74

Chapter

Page
Procedure
Procedure
Procedure
Procedure

VI.

1
2
3
4

...........................
...........................
...........................
.................

75
75
75
76

Plot XY Computer R o u t i n e ..............

76

Phase III— The Relation of User Attitudes
to Boating Conditions by Socio-economic
Characteristics
........................

76

Frequency Dist r i b u t i o n s.................
Chi-Square T e s t ........................

77
77

R E S U L T S ......................................

78

Phase I— Measures of Level of Boating
Activity Intensity
.....................

78

Procedures for Determining the Best
Method of Expressing the Intensity
of Boating Activity
.................

82

Procedure 1 ...........................
Procedure 2 ...........................
Procedure 3 ...........................

82
83
84

Phase II— Relationship of User Attitudes
to the Level of Boating Activity
I n t e n s i t y ...............................

85

Procedures for Comparing User Attitudes
with Levels of Boating Activity
Intensity ..............................

87

Procedure
Procedure
Procedure
Procedure

1
2
3
4

...........................
...........................
...........................
...........................

87
90
92
93

Phase III— The Relation of User Attitudes
to Boating Conditions by Socio-economic
Characteristics
........................

94

Frequency D i s t r ibutions .................
Chi-Square T e s t ........................

95
95

Chapter
VII.

Page
SUMMARY A N D D I S C U S S I O N .........................
Levels of B o a t i n g Acti v i t y Intensity.

.

97

C o n s u m p t i o n ...............................
D i s p e r s i o n ...................................
C o n s u m p t i o n - D i s p e r s i o n Relationship
. .

97
100
102

User A t t i t u d e

.

.

.

Public Access Boater
R iparian O w n e r Boater

.

.

.

.

.

.

.

104

.....................
.....................

Rel a t i o n s h i p of User Attitudes to the
Level of B o a t i n g A c t i v i t y Intensity

.

104
105
.

106

Public A c c e s s ................................
Riparian O w n e r
............................

106
109

Inverse R e l a t i o n s h i p of the N u m b e r of
Acres Per B o a t to the Level of Boa t i n g
A c t i v i t y Intensity .........................

110

Nu m b e r of A c r e s Per B o a t ..................

110

A M e t h o d for D e t e r m i n i n g Recreational
B o a t i n g C a r r y i n g C a p a c i t y ..................

Ill

A p p l i c a t i o n ................................

112

Step 1
Step 2
Step 3

VIII.

.

96

...................................
...................................
...................................

113
114
114

C o m p a r i s o n Of A t t i t u d e s Toward B o a t i n g
C o n d i t i o n s by Respondents w i t h D i f f e r e n t
S o c i o - e c o n o m i c C h a r a cteristics . . . .

115

General C h a r acteristics of the Public
Acc e s s U s e r ................................

115

I n c o m e ...................................
E d u c a t i o n ................................
O c c u p a t i o n ................................

118
118
119

CO N C L U S I O N S A N D R E C O M M E N D A T I O N S ..............

120

C o n c l u s i o n s ...................................
R e c o m m e n d a t i o n s ................................

120
122

viii

Chapter

Page
........................
........................
........................
........................

123
124
125
126

LIST OF R E F E R E N C E S ...................................

127

Recommendation
Recommendation
Recommendation
Recommendation

1
2
3
4

APPENDICES
Appendix
A.
B.
C.

D.

E.

F.

Letter, Interview Schedule, and Question­
naire
.....................................

131

Values Used for Constructing Perspective
G r i d s .....................................

141

Tables Showing Sample Dispersion C o e f ­
ficients, Total Dispersion Coefficients,
Space Consumption Sample Coefficients
and Space Consumption Tracing Paper
Coefficients . . . . . . . . . .

143

Tables Showing User Attitude Responses,
Intensity Coefficients, Space Consumption
Safety Coefficients, and Number of Boats.

150

Tables Showing Frequency Distribution for
I ncome, E d u c a t i o n , and Occupation
Classes by Response, Chi-Square on
Income, Education, and Occupation . . .

158

Tables and Plots Showing Least Squares
Deletion Analysis for Sample Dispersion
Coefficients and Total Dispersion C o e f ­
ficients , Space Consumption Safety Coef­
ficients and Space Consumption Tracing
Paper Coefficients and Sample Dispersion
Coefficients, Space Consumption Safety
Coefficients and Sample Dispersion
Coefficients ...............................

160

Page

Ch a p t e r
G.

Tables and Plots Showing L e a s t Squares
D e l e t i o n A n a l y s i s for User A t t i t u d e
Indices and Intensity Coefficients, User
A t t i t u d e Indices and Space C o n s u m p t i o n
S a f e t y Coeffi cients, User A t t i t u d e In­
dices for R i p a r i a n Owners and Space C o n ­
sump t i o n Safety Coefficients, N u m b e r of
Ac r e s per B o a t and Space C o n s u m p t i o n
Safety C o e f f i c i e n t s .....................

x

171

LIST OF TABLES
Table
1.

2.

3.

4.

Page
T o t a l B o a t s C o u n t e d and P e r C e n t B o a t e r s
I n t e r v i e w e d at A c c e s s Sites, J u l y 4
Through September
1,19 69 ..................

39

V a r i a t i o n in T o t a l B o a t Number, S p a c e C o n ­
sumption, a n d D i s p e r s i o n for F i v e P h o t o
F l i g h t s on Union, Cass, a n d O r c h a r d L a k e s
(June 29, 1 9 6 9 ) .............................

44

M e a n D i s t a n c e (Feet) B e t w e e n B o a t s b y
A c t i v i t y (Tracing P a p e r Technique)
A u g u s t 24 a n d 30, 1969 ......................

61

Range and M e a n V a l u e s for U s e r A t t i t u d e
Indices, S p a c e C o n s u m p t i o n C o e f f i c i e n t s ,
and A c r e s p e r B o a t (July 4 T h r o u g h
S e p t e m b e r 1, 1 9 6 9 ) .........................

91

LIST OF FIGURES
Figure
1.

Page
Relationship Between Acres and Boat Number
Observed and Circumference of an
Ellipsoid Lake.
Source:
[Threinen,
An Analysis of Space D e m a n d s , p. 8].

15

U nion Lake, Pontiac, Michigan. T.2N, R.8-9E.,
Sections 1, 5, 8.
(460.6 A c r e s ) . . . .

25

Cass Lake, Pontiac, Michigan.
T.2-3N,
R.9E., Sections 2, 3, 4, 9, 10, 11, 33,
34, 35.
(1209.9 A c r e s ) .....................

27

O rchard Lake, Orchard Lake Village, Michigan.
T.2N, R.9E., Sections 9, 10, 11, 14, 15.
(778.9 Acres) ...............................

29

Lake Maps Shown to Respondents During Inter­
v i e w s ..........................................

37

A ngular Relations of an Oblique Photograph.
Source:
[Manual of P h o t o g r a m m e t r y ,
p. 8 8 7 ] ......................................

47

Perspective Grid.
Source:
[Manual of
P h o t o g r a m m e t r y , p. 8 8 7 ] .....................

49

High Oblique Photograph Projected on a
Perspective G r i d ............................

52

Procedure for Transferring Boating Activity
Locations from a Photograph to 1" =
400' M a p ......................................

52

10.

Photo of Map of Cass Lake Divided Into Zones.

55

11.

Photo of M a p of Union Lake Divided Into
Z o n e s ..........................................

55

2.
3.

4.

5.
6.

7.
8.
9.

xii

Figure

Page

12.

P h o t o of M a p of O r c h a r d Lake D i v i d e d Into
Z o n e s .............................
55

13.

Techn i q u e Used for M e a s u r i n g Boa t i n g
Trails by M a p M e a s u r e ...........

14.
15.
16.

T r a c i n g Paper T e c h n i q u e for D e t e r m i n i n g
Co n s u m p t i o n b y A c t i v i t i e s
. . . .

57
.

57

Exa m p l e of Chart U s e d to Rec o r d F a v o r a b l e
and Unfavorab le Responses
..............
V a r i a t i o n of Tot al Surface W a t e r C o n s u m e d
by A c t i v i t y on Union, Cass, and
Orch a r d Lakes D u r i n g A u g u s t 24, 1969.

xiii

67

.

98

LIST OF APPENDICES
Appendix
A.

Page

Letter, Interview Schedule, and
Questionnaire

Al.

Copy of Letter Requesting Agencies and
Universities for Information on Carrying
C a p a c i t y ..........................................131

A2.

Copy of Interview Schedule Used at Public
Access S i t e s ...................................... 133

A3.

Copy of Questionnaire Used by Riparian
O w n e r s ............................................. 137

B.

Values Used for Constructing Perspective
Grids

Bl.

Grid for

400-Foot E l e v a t i o n ..................... 141

B2.

Grid for

4 50-Foot E l e v a t i o n ..................... 141

B3.

Grid for

500-Foot E l e v a t i o n ..................... 142

C.

Cl.

C2.

Tables Showing Sample Dispersion C o e f ­
ficients, Total Dispersion Coefficients,
Space Consumption Sample Coefficients, and
Space Consumption Tracing Paper Coefficients
Sample Dispersion Coefficients and Total
Dispersion Coefficients for Union, Cass,
and Orchard Lakes {July 17,1969) . . . .
Space Consumption Safety Coefficients and
Space Consumption Tracing Paper C o e f ­
ficients for Union, Cass, and Orchard
Lakes (August 23 and 24, 19 6 9 ) ...............

xiv

143

144

Appendix
C3.

C4.

D.

Dl.

D2.

D3.

D4.

E.

El.

E2.

Page

Space Consumptio n T r a c i n g Paper Coefficients
and Sample Dispersion Coefficients for
Union, Cass, and Orchard Lakes (August 23
and 24, 1 9 6 9 ) ...............................

146

Space Consumption Safety Coefficients and
Sample Dispersion Coefficients for Union,
Cass, and Orchard Lakes (August 23 and 24,
1 9 6 9 ) ..........................................

148

Tables Showing User Attitude Responses,
Intensity Coefficients, Space Consumption
Safety Coefficients, and Number of Boats
User Attitude Responses and Intensity C o e f ­
ficients for Union, Cass, and Orchard
Lakes (August 23 and 24, 1969)
. . . .

150

User Attitude Responses and Space C o n ­
sumption Safety Coefficients for Union,
Cass, and Orchard Lakes (August 23 and
24, 1 9 6 9 ) ...................................

153

Space Consumption Safety (Sq.Ft.), Number
of B o a t s , User Attitude Responses for
Union, Cass, and Orchard Lakes (August 23
and 24, 1 9 6 9 ) .
... .........................

155

User Attitude Indices and Space Consumption
Safety Coefficients for Riparian Owners
on Union, Cass, and Orchard Lakes
(August 23, 24, 30, 31, and September 1,
1 9 6 9 ) ..........................................

157

Tables Showing Frequency Distribution for
Income, Education, and Occupation Classes
by Response, Chi-Square Test on Income,
Education, and Occupation
Frequency Distribution for Income, E d u ­
cation, and Occupation Classes by
Response (Union, Cass, and Orchard
Lakes, July 4 through September 1, 1969) .

158

Chi-Square Test on Income, Education, and
Occupation Classes by Response for
Union, Cass, and Orchard Lakes
. . . .

159

xv

Page

Appendix
F.

Fl.

F2.

F3.

F4.

F5.

F6.

F7.

T a b l e s a n d Plots S h o w i n g L e a s t S q u a r e s
D e l e t i o n A n a l y s i s for S a m p l e D i s p e r s i o n
C o e f f i c i e n t s and T o t a l D i s p e r s i o n C o e f ­
ficients, Space C o n s u m p t i o n S a f e t y C o e f ­
ficients and Space C o n s u m p t i o n T r a c i n g
P a p e r C o e f f i c i e n t s and S a m p l e D i s p e r s i o n
C o e f f i c i e n t s , S pace C o n s u m p t i o n S a f e t y
C o e f f i c i e n t s and S a m p l e D i s p e r s i o n C o e f ­
ficients .
Least Squares Deletion Analysis
Sample Dispersion Coefficients
Total Dispersion Coefficients
Cass, and O r c h a r d L a k e s (July

for
and
for Union,
17, 1969)

160

P l o t s of Sample D i s p e r s i o n C o e f f i c i e n t and
T o t a l D i s p e r s i o n C o e f f i c i e n t for Union,
Cass, O r c h a r d L a k e s (July 17, 1969) .

161

L e a s t S q u a r e s D e l e t i o n A n a l y s i s for S p a c e
C o n s u m p t i o n S a f e t y C o e f f i c i e n t s and S p a c e
Consumption Tracing Paper Coefficients
for Union, Cass, and O r c h a r d La k e s
(August 23 and 24, 1969 combined)
.
.

162

Plots of Space C o n s u m p t i o n S a f e t y C o e f ­
f i c i e n t a n d Space C o n s u m p t i o n T r a c i n g
P a p e r C o e f f i c i e n t for Union, Cass, and
O r c h a r d Lakes (August 23 and 24, 1969
.........................
.
combined)

163

L e a s t S q u a r e s D e l e t i o n A n a l y s i s for S p a c e
Consumption Tracing Paper Coefficients
and S a m p l e D i s p e r s i o n C o e f f i c i e n t s for
Union, Cass, and O r c h a r d Lakes (August
23 a n d 24, 1969) .........................

164

Plots of Space C o n s u m p t i o n T r a c i n g P a p e r
C o e f f i c i e n t and S a m p l e D i s p e r s i o n
C o e f f i c i e n t for Union, Cass, a n d O r c h a r d
Lakes (August 23 a n d 24, 1969)

165

L e a s t Squ a r e s D e l e t i o n A n a l y s i s for S p a c e
C o n s u m p t i o n S a f e t y C o e f f i c i e n t s and
Sa m p l e D i s p e r s i o n C o e f f i c i e n t s for Union,
Cass, and O r c h a r d L a k e s (August 23 a n d
24, 1969)
................................

167

xvi

Page

Appendix
F8.

G.

Gl.

G2.

G3.

G4.

G5.

G6.

G7.

Plots of Space Consumption Safety C o e f ­
ficient and Sample Dispersion C o e f ­
ficient for Union, Cass, and Orchard
Lakes (August 23 and 24, 1969) . . .

•

169

Tables and Plots Showing Least Squares
Deletion Analysis for User Attitude Indices
and Intensity Coefficients, User Attitude
Indices and Space Consumption Safety C o e f ­
ficients, User Attitude Indices and Space
Consumption Safety Coefficients for
Riparian O w n e r s , Number of Acres per Boat
and Space Consumption Safety Coefficients
Least Square Deletion Analysis for User
Attitude Indices and Intensity C o e f ­
ficients for Union, Cass, and Orchard
Lakes (August 23 and 24, 1969)
.

171

Plots of User Attitude Index and Intensity
Coefficient for Union, Cass, and Orchard
Lakes (August 23 and 24 combined) .
.
.

172

Least Squares Deletion Analysis for User
Attitude Indices and Space Consumption
Safety Coefficients for Union, Cass, and
Orchard Lakes (August 23 and 24, 1969)

173

Plots of User Attitude Index and Space
Consumption Safety Coefficient for Union,
Cass, and Orchard Lakes (August 23 and
24, 1969 combined) . . " .................

174

Least Squares Deletion Analysis for User
A ttitude Indices and Space Consumption
Safety Coefficients for Union, Cass, and
Orchard Lakes (July 4 Through September
1, 1969)
...................................

175

Plot of User Attitude Index and Space
Consumption Safety Coefficient for Union
Lake (July 4 Through September 1, 1969) .

176

Plot of User Attitude Index and Space
C onsumption Safety Coefficient for Cass
Lake (July 4 Through September 1, 1969)

177

xvii

.

Ap p e n d i x
G8.

G9.

G10.

Gil.

G12.

G13.

G14.

Page

Plot, of User Attitude Index a n d Space
Con s u m p t i o n Safety C o e f f i c i e n t for
O rchard Lake (July 4 T h r o u g h S e p t e m b e r
1, 1 9 6 9 ) ....................................

178

Least Squares Deletion A n a l y s i s for User
Attitude Index and Space C o n s u m p t i o n
Safety Coefficients for R i p a r i a n Own e r s
on Union, Cass, and O r c h a r d Lakes
(August 23, 24, 30, 31, and Septe m b e r 1,
1 9 6 9 ) .......................................

179

Plots of User A t t i t u d e Index and Space
Consumption Safety C o e f f i c i e n t for
Riparian Owners on Union, Cass, and
Orchard Lakes (August 23, 24, 30, 31,
and September 1, 1 9 6 9 ) .................

180

Least Squares D eletion A n a l y s i s for the
N umber of Acres per B o a t and Space C o n ­
sumption Safety Coef f i c i e n t s for Union,
Cass, and Orc hard Lakes (July 4 T h r o u g h
September 1, 1 9 6 9 ) .........................

181

Plot of the Number of Acres per B o a t and
Space Con s u m p t i o n Sa f e t y C o e f f i c i e n t
for Union Lake (July 4 T h r o u g h
September 1, 1 9 6 9 ) ..........................

182

Plot of the Number of Acres per B o a t and
Space Consump tion Safety C o e f f i c i e n t for
Cass Lake (July 4 T h r o u g h S e p t e m b e r 1,
1 9 6 9 ) .......................................

183

Plot of the Number of Ac r e s per B o a t and
Space C o n s u mption Safety C o e f f i c i e n t
for Orchard Lake (July 4 T h r o u g h
September 1, 1 9 6 9 ) ..........................

184

xviii

CHAPTER I
INTRODUCTION

Participation in outdoor recreation is increasing
at a startling rate.

In 1967, the Bureau of Outdoor

Recreation found that "present and anticipated increases
in major summertime outdoor activities surpass predictions
made by the Outdoor Recreation Resources Review Commission
in I960."1

The actual increase was four times greater than

that originally forecast.
The survey by the ORRRC showed that water was the
key element in the increase in demand for outdoor recre­
ation.

It reported that "44 per cent of the population
2
prefer water-based activities over any o t h e r ."
Resource
managers generally agree that improvement of access to
surface waters is an important stimulus to water-based
recreation activity.

^Bureau of Outdoor Recreation, Outdoor Recreation
Trends (Washington, D.C.:
Government Printing Office,
April, 1967), p. 12.
2

Outdoor Recreation Resources Review Commission,
Outdoor Recreation for America (Washington, D.C.:
Government Printing Office, 1962), p. 25.

1

2
The continuous expansion in population together
w i t h a shorter average work w e e k mean that more people
will w a nt to act on their preference for water-based
recreation and will have the time to do so.
cies are, therefore,

State a g e n ­

faced w i t h the need to make effective

plans for development of lakes and streams.
to do this successfully,

If they are

they must be able to evaluate

the ability of a given body of w a t e r to accommodate
recreation.
The P r o b l e m
The tremendous growth in recreational boating has
focused attention on the question of the ability of su r ­
face waters to support the different types of recreational
activities.

A limited number of acres of water available

for boating are being used more and more intensively, and
the potential for accidents is similarly increasing.

In

1961, O akland County, Michigan had thirteen boating ac c i ­
dents serious enough to be reported, with eleven cases of
death or injury.1

By 1969, there were fifty reported

accidents, with thirty-eight cases of death or injury.
It seems to be a valid assumption that the use of surface
water areas will continue to increase, and a concomitant
increase in boating accidents will occur.

Moreover, many

1Letter from S. K. Swenerton, Lieutenant (j g ) ,
Investigating Officer, United States Coast Guard, Detroit,
Michigan, May 4, 1970.

3
o u t d o o r r e c r e a t i o n m a n a g e r s b e l i e v e t h a t an i n c r e a s e in
the i n t e n s i t y of use of w a t e r r e s u l t s in d e t e r i o r a t i o n o f
b o t h the e n v i r o n m e n t a n d the r e c r e a t i o n a l e x p e r i e n c e .
If a g e n c i e s c o n c e r n e d w i t h w a t e r m a n a g e m e n t a r e to
f ollow a p o l i c y of m a i n t a i n i n g h i g h q u a l i t y w a t e r r e c r e ­
a t i o n , a l t e r n a t i v e m e t h o d s suit a b l e for d o i n g so m u s t be
adopted.
natives,

Fur t h e r m o r e ,

in o r d e r to p r o v i d e s u i t a b l e a l t e r ­

it is n e c e s s a r y to have v a l i d m e t h o d s of a n a l y s i s .

L a c k of these m a y re s u l t in a m i s a l l o c a t i o n of w a t e r r e ­
sources and p u b l i c funds.
S e m a n t i c s of C a r r y i n g
Capacxty
P r e s e n t m e t h o d s u s e d for e v a l u a t i n g the c a r r y i n g
c a p a c i t y of w a t e r d i f f e r and g e n e r a l l y h a v e n o e m p i r i c a l
j u s t i fication.*fusing.

T o b e g i n with,

the n o m e n c l a t u r e is c o n ­

Webster's New World Dictionary defines capacity

as "a m a x i m u m a m o u n t of h o l d i n g space," w h i l e c a r r y i n g
means

"supp o r t i n g . "

a m a x i m u m quantity.

T o g e t h e r the terms i m p l y s u p p o r t of
This is an a c c u r a t e d e f i n i t i o n ,

but

it is h a r d l y w h a t r e c r e a t i o n m a n a g e r s w a n t in o p e r a t i o n a l
d efinition.

Furt h e r m o r e ,

for e v e r y s c i e n c e d i s c i p l i n e ,

*"M. C h u b b and P. Ashton, Parks and R e c r e a t i o n
S t a n d a rds R e s e a r c h , a r e p o r t to the N a t i o n a l R e c r e a t i o n
and P a r k A s s o c i a t i o n at the N a t i o n a l F o r u m o n P a r k a n d
R e c r e a t i o n S t a n d a r d s in Kansas City, M i s s o u r i , J a n u a r y
12-14, 1969, R e c r e a t i o n R e s e a r c h P l a n n i n g Unit, D e p a r t m e n t
of P a r k and R e c r e a t i o n Resources, C o l l e g e o f A g r i c u l t u r e
and N a t u r a l Resources, M i c h i g a n State U n i v e r s i t y , T e c h n i c a l
R e p o r t N u m b e r 5 (East Lansing, Michigan:
J a n u a r y , 1969) ,
pp. 2-4.

4
carrying capacity has separate meaning and subsequent
shortcomings.
Chubb has defined the carrying capacity of a
recreation resource in two different ways:
capacity "is the capability of an area
recreation opportunities,

first, spatial

. . .

to provide

judged solely on the space avail­

able and the space required to make the activity concerned
a satisfactory experience";

second, carrying capacity has

a "distinguishing feature being based on consideration of
the amount of use that can take place without significant
deterioration of the site over time."^
Carrying capacity for this study will not be con­
sidered in terms of the traditional "standard" expressed
as an arbitrary number of acres per boat.

Instead, a range

of values will be presented for management to interpret.
This concept is based on the principle that for a given
area there is no single level of capacity over time, since
capacity is linked to levels of satisfaction by its users.
The Importance of Carrying
Capacity to Management
In any attempt to control an area for a quality
experience and to maintain a recreation resource, managers
must consider the attitudes of participants.

Constant

complaints by boaters and riparian owners make state
1
M. Chubb, "Outdoor Recreation Land Capacity:
ConceptB, Usage, and Definitions" (unpublished Master's
thesis, Michigan State University, 1964), p. 133.

5
agencies aware of u n f a v o r a b l e conditions.

A s a result,

r e s t r i c tive regulations are p u t into e f f e c t by r e c r e a t i o n
a d m i nistrators in order to reduce the d i s s a t i s f a c t i o n in
some cases.

T o determine w h e t h e r or not it is a p p r o p r i a t e

to r e s t rict an activity on a w a t e r body, a m a n a g e r m u s t
k n o w b o t h the basic r e l a t i o n s h i p of users to the p h y s i c a l
resource and the ways in w h i c h s a t i s f a c t i o n w i l l change
w i t h d i f f e r e n t amounts of use.

O n e factor alone is not

an adequate indicator of capacity.

W a t e r c a r r y i n g ca p a c i t y

is a c o m b i n a t i o n of b o t h factors, a r e l a t i v e c o n c e p t w h i c h
becomes a m a t t e r of a d m i n i s t r a t i v e choice.
M anagers are often c o n c e r n e d w i t h the p r o b l e m of
deciding w h a t policies to follow in the future w i t h r e s p e c t
to overcrowding.

Equ a l l y important is the p r o b l e m of how

control of lakes for s u s t a i n e d periods of time affects
user satisfaction.

N u m e r o u s techniques,

such as limiting

the n u m ber of b o a t s , re g u l a t i n g b o a t s p e e d s , zoning areas
for specific use,

and formulating traffic patterns,

are

used to control w a t e r activities.
If one aspect of w a t e i - b a s e d a c t i v i t i e s is c o n ­
trolled, however,
For example,
on a lake.

a change may occur in some other aspect.

suppose a c e r t a i n nu m b e r of boats is allowed
The d e n s i t y of b o a t i n g m i g h t decrease, b u t the

average v e l o c i t y of the boats m i g h t increase,
additional wave action and more shore erosion.

cau s i n g
Another

example is the diffic u l t y in a n t i c i p a t i n g the increase in

6

use of p u b l i c
when better

lake

facilities

(beaches a n d p i c n i c areas)

launching ramps and more trailer parking space

are provided.

There are man y interrelations b e tween user

behavior and recreation management.
vide

study of th e m can p r o ­

i n s i g h t i n t o the b e h a v i o r a l p a t t e r n s a n d p h y s i c a l r e ­

lationships

resulting from management control m e a s u r e s .
O b j e c t i v e s o f the S t u d y

T h e W a t e r w a y s D i v i s i o n of the M i c h i g a n D e p a r t m e n t
of N a t u r a l R e s o u r c e s h a s t h e r e s p o n s i b i l i t y of p r o c u r i n g
a n d o p e r a t i n g p u b l i c b o a t i n g a c c e s s sites.
justify acquiring new access
sites

In o r d e r to

sites and manag i n g p r esent

to a c c o m m o d a t e t h e i n c r e a s i n g r e c r e a t i o n a l d e m a n d

for w a t e r - b a s e d r e c r e a t i o n ,

the d i v i s i o n n e e d s a m e t h o d o f

a s s e s s i n g the c a r r y i n g c a p a c i t y of s u r f a c e w a t e r s .

It is

a l s o i n t e r e s t e d in a m e t h o d of d e t e r m i n i n g b o a t e r ' s b e ­
h a v i o r o n i n t e n s e l y u s e d lakes c l o s e to l a r g e m e t r o p o l i t a n
areas.

A t t h e r e q u e s t of the d i v i s i o n ,

a proposal was

s u b m i t t e d b y the R e c r e a t i o n R e s e a r c h a n d P l a n n i n g U n i t a t
Michigan State University,

to s t u d y a n d q u a n t i f y r e l a t i o n ­

sh i p s b e t w e e n a t t i t u d e s of b o a t u s e r s a n d v a r y i n g l e v e l s
of u s e o n d i f f e r e n t s u r f a c e wat e r s .
cedure developed

from this

U l t i m a t e l y the p r o ­

s t u d y m i g h t be u s e d as a b a s i s

for a l l o c a t i n g w a t e r r e s o u r c e s a m o n g a g r o w i n g n u m b e r o f
u s e r s w i t h a m i n i m a l d e c l i n e in u s e r s a t i s f a c t i o n o r e m ­
p l o y e d to j u s t i f y the r e s t r i c t i o n of u s e t o a d e s i r a b l e
maximum where areas are already over-used.

CHA P T E R II
REVIEW OF LITERATURE

The main purpose of this review of literature is
to organize and present relevant material about the study
subject.

For purposes of classification and organization,

it has been divided into three major sections:
vious research,

(1) p r e ­

(2) existing carrying capacity standards

and current surveys, and

(3) conclusions from review of

the literature of carrying capacity standards.
In the initial phase of the literature review,
letters were written to authorities that use or have
formulated capacity terms for planning.
thirty-two federal,

One hundred and

state, and private agencies including

several universities responsible for water-recreation
planning were asked to explain their recreation standards.^
The response indicated that the recreation space requ i r e ­
ments and water carrying capacities used were generally
2
developed in an arbitrary manner.

^See Appendix A1 for letter requesting agencies
and universities for information pertaining to carrying
capacity.
2
Chubb and Ashton, Standards Research, pp. 63-76.
7

8

Previ o u s Research
T h e c a r r y i n g c a p a c i t y of w a t e r has b e e n the s u b j e c t
of c o n s i d e r a b l e study and has b e e n i n t e r p r e t e d in differ e n t ,
ev e n c o n f l i c t i n g w a y s .^

W i t h o u t a v a l i d basis

for i n t e r ­

p r e t i n g carr y i n g capacity, m a n y bodies of w a t e r m a y be u s e d
far in excess of their d e s i r a b l e capabilities.
C l a w s o n and K n e t s c h suggest that p e o p l e g e n e r a l l y
a n t i c i p ate e n j o y m e n t and solitude w h i l e p a r t i c i p a t i n g in
a r e c r e ational experience and place a high value on o b t a i n ­
ing them.

But for everyone sharing in a r e s o u r c e - b a s e d

activity,

a c o n d i t i o n of use will e x i s t w h e n it becom e s

u n d e s i r ably cro w d e d for that person.
from an activity w i l l diminish,

T h e sati s f a c t i o n

and after some p o i n t it

may no longer be w o r t h experiencing.

Levels of s a t i s ­

faction w i l l not be the same for all areas and types of
recre a t ional use.

O v e r c r o w d i n g of outdoor r e c r e a t i o n

areas starts to occur w h e n the intensity of r e c r e a t i o n use
rises above an o p t i m u m level of sati s f a c t i o n of the u s e r s .
The authors conclude that:
. . . our k n o w l e d g e of the relation b e t w e e n i n t e n s i t y
of use and satisfaction per u s e r is m o s t incomplete.
It is entirely p o s s i b l e that i n t e n s i t y of use co u l d
vary cons i d e r a b l y w i t h o u t much, if any, loss in
satisfaction, b u t that extremes of intensity w o u l d
me a n losses in satisfactions to the users at such
t i m e s .2

^I b i d ., pp.
2

45-46.

M. C l a w s o n and J. I». Knetsch, E c o n o m i c s of O u t d o o r
Recreationf Resources for the Fu t u r e ( B a l t i m o r e , Maryland:
Johns Hopkins P r e s s ) , p. 170.

9
LaPage suggests that there are two main objectives
of recreation management:

quantity and quality.^- An in­

crease in the number of people using a resource may not
necessarily result in a decrease in the quality of an
individual experience.

Management must find the methods

of insuring a compromise between the two objectives.

A

reduction in either direction can only be determined by
methods of social research directed toward an understanding
of the relative values involved.

Both quantity and quality

are dependent mainly upon individual preferences.

Many

people would not indulge in outdoor recreation if it were
not for the comfort of knowing there are others nearby;
many are relatively immune to high levels of crowding,
provided there are compensating facilities and alter­
natives .

F u r t h e r m o r e , the overcrowding of recreation

areas may result in hazards to public health and safety
as well as danger to the resource itself.
LaPage observed that satisfaction is a qualitative
value and is a function of the effect of the recreation
resource on people, the effect of people on the resource,
and the effect of people on each other.

"The utility of

observations such as this, not only for determinations of
carrying capacity and recreational productivity, but in
the realm of recreational land values as well, creates

^W. F. LaPage, Some Observations on Campground
Trampling and Ground Cover R e s p o n s e , Note NC-68 (St. P a u l ,
Minnesota:
U.S. Forest Service, North Central Forest
Experiment Station, 1967).

10

cogent: argument: for further investigative w o r k along
these same l i n e s . " 1
Sirles has related reservoir recreation c o s t to
capacity.

He ca l c u l a t e d a capacity coefficient to d e ­

scribe the m a x i m u m n u m b e r of people w h o can be a c c o m m o ­
d a t e d s i m u ltaneously per unit of area for a p a r t i c u l a r
activity.

The d e t e r m i n a t i o n of an appropriate v a l u e of

the c o e f f i c i e n t for camping,

swimming, picnicking,

and

b o a t i n g is b a s e d on psyc h o l o g i c a l rather than p h y s i c a l
crowding.

But individuals have different p s y c h o l o g i c a l

p e r c e p t ion of crowding.

Some prefer crowds, w h i l e others

p r e f e r to be completely d i s s o c i a t e d from o t h e r people.
T h e s e d i f f e r e n t attitudes cause the capacity of r e c r e a t i o n
areas to vary daily according to the type of p e o p l e u s i n g
them at a given time.

Sirles concludes that a useful

refinement of b e n e f i t - c o s t analysis w o u l d be one show i n g
that use of recreation areas is influenced b y limited and
o v e r c r o wded facilities.
E x i s t i n g C a r r y i n g C a p a c i t y Standards
and C u r r e n t Surveys
The United States Forest Service m a d e the first
significant attemp t to measure recreation capacity.

The

1l b i d .
2

S.
E. Sirles, III, A p p l i c a t i o n of M a r g i n a l E c o ­
nomic A nalysis of Reser v o i r Recrea t i o n P l a n n i n g , W a t e r Resources Institute (Lexington:
Univer s i t y of K e n t u c k y ) ,
1968.

11

derived berm was called
as

"Safe C a p a c i t y "

and was defined

"the n u m b e r of v i s i t o r s w h i c h c a n p r o p e r l y a n d s a f e l y

b e a c c o m m o d a t e d w i t h o u t d a m a g e to a n a r e a or s i t e b e y o n d
t h a t w h i c h c o u l d b e c o n s i d e r e d n o r m a l w e a r a n d tear."***
A n u m b e r r e p r e s e n t i n g t h e a c r e a g e of a r e c r e a t i o n r e s o u r c e
n e e d e d to s a t i s f a c t o r i l y a c c o m m o d a t e o n e v i s i t o r - d a y o f
u s e of t h e r e s o u r c e w a s u s e d as a m u l t i p l e t o " d e t e r m i n e
the n u m b e r o f a c r e s

r e q uired to accommodate the de m a n d
2
p r e d i c t e d for a p a r t i c u l a r a c t i v i t y . "
T h e B u r e a u of L a n d M a n a g e m e n t r a t e d c a p a c i t y as
t he p o t e n t i a l u s e o f an a r e a t o the y e a r 1976.
Areas were
3
j u d g e d "light," " m o d e r a t e , " a n d "heavy."
The agency used
the term,

"total i n s t a l l e d c a p a c i t y , "

d e f i n e d as

"the

t o t a l n u m b e r of p e o p l e w h o c a n b e a c c o m m o d a t e d w i t h o u t
c r o w d i n g a t one t i m e b y t h e f a c i l i t i e s w h i c h h a v e b e e n
4
i n s t a l l e d in the r e c r e a t i o n site."
T h e B u r e a u of O u t d o o r R e c r e a t i o n s u g g e s t s t h e
u se of t w o c r i t e r i a t o r a t e the c a p a c i t y of an area:

^U.S., D e p a r t m e n t of A g r i c u l t u r e , F o r e s t S e r v i c e ,
W o r k P l a n for t h e N a t i o n a l F o r e s t R e c r e a t i o n S u r v e y
( W a s h i n g t o n , D . C .:
G o v e r n m e n t P r i n t i n g o f f i c e , 1959),
p. 8.
2Ibid.
3

U.S., D e p a r t m e n t o f I n t e r i o r , B u r e a u o f L a n d
M a n a g e m e n t , B u r e a u of L a n d M a n a g e m e n t M a n u a l , R e c r e a t i o n
M a n u a l ( W a s h i n g t o n , D . C .:
Government Printing Office,
1 & 6 3 ) , s e c t i o n 11-B, .01.
4 Ibid.

12

(1) h o w well could its resources and facilities accommodate
increased activity, and

(2) was it overcrowded.

The r a t ­

ings were made by estimating the increase possible, or
state of over-use, to the nearest 10 per cent.**Porter used two methods to measure the optimum
capacity of r e s e r v o i r s .

The first method was the a p p l i ­

cation of existing standards as the basis of an "area of
use system."

The second method was a "multiple point

value system" of placing w e i g h t e d values on different
conditions of each factor.

Porter concluded that:

A factor in need of further investigation is that of
the tolerance to crowding by the recreationist.
The
social tolerance to crowding is a factor that has
been neglected and yet is one that could have far
reaching effects in the development of park a r e a s . 2
Lucas studies the capacity of a recreational area
to provide satisfaction.

The study was conducted on the

Quetico-Superior Area for a wilderness experience by
canoe.

He i n d i c a t e d :

The capacity of a recreational area is its ability
to provide satisfaction— that is the service being
produced, and this service m u s t be described both
in quantity and quality terms.
T w o types of factors
set limits to numbers of people and their satisfaction:

U.S., Department of Interior, Bureau of Outdoor
Recreation, Nationwide Plan (Manual— Planning and Surveys
Series) (Washington, D.C.:
Government Printing Office,
1964), p. 241.
2

K. R. Porter, "The Criteria and Techniques for
Estimating Optimum Recreational C a p a c i t y at Water Resource
Projects" (unpublished Master's thesis, Texas Technological
College, 1969), p. 54.

13
(1) p h y s i c a l factors, and (2) the a t t i t u d e s of people.
B o t h t y p e s of factors are r e l a t e d to the r e s o u r c e b a s e
a n d Its use and m a n a g e m e n t . 1
H a u g e n and S o h n s t u d i e d cy c l e s a n d f l u c t u a t i o n s In
r e c r e a t i o n a c t i v i t i e s on s e l e c t e d Iowa lakes b y m e a n s of
i n t e r v i e w s a n d p h o t o g r a p h s of c o n f l i c t s b e t w e e n users.
T h e y e s t a b l i s h e d c a p a c i t y s t a n d a r d s for e n t i r e b o d i e s of
water together with

zo n i n g p r o c e d u r e s
2
flicts b e t w e e n u s e r groups.

to m i n i m i z e con-

B e u l i n g s u r v e y e d 836 lakes in W i s c o n s i n b y a e r i a l
observation.

T h e n u m b e r of boats

fishing,

cruising ,

and

w a t e r skiing, was r e c o r d e d w i t h time and w e a t h e r c o n ­
ditions .
I n t e r p r e t a t i o n of the d a t a s u g g e s t e d t h a t h i g h e s t
d e n s i t y of use o c c u r r e d on small lakes in the n o r t h and
c e n t r a l p a r t s of the state, w h e r e a s in the south, m e d i u m ­
sized lakes h a d a d e n s i t y g r e a t e r t h a n one b o a t per t wenty
acres.

W h e r e a d e n s i t y of one b o a t per ten acres w a s

a r b i t r a r i l y set,

s m a l l lakes h a d the h i g h e s t de n s i t i e s ,

1

R. C. Lucas, T h e R e c r e a t i o n a l C a p a c i t y of the
Q u e t i c o - S u p e r i o r A r e a ( S t . Paul, Mi n n e s o t a :
U . S . Forest
S e r v i c e , L a k e S t a t e F o r e s t E x p e r i m e n t Station, 1964), p.
2
A. O. H a u g e n and A. J. Sohn, C o m p e t i t i v e R e c r e ­
a t i o n a l Uses of S e l e c t e d Iowa L a k e s , C o m p l e t i o n R e p o r t o f
P r o j e c t No. A - 0 0 5 - 1 A (Ames, Iowa:
Iowa State W a t e r R e ­
sources R e s e a r c h Institute, 1968).
3

A. Beuling, A S u m m a r y and A n a l y s i s of O b s e r ­
vations on B o a t i n g 1 9 5 T (Madison, W i s c o n s i n :
Wisconsin
C o n s e r v a t i o n D e p a r t m e n t , 1963).

5.

14
medium-sized lakes had the next highest, and large lakes
had the lowest values.
Beuling postulated a possible relationship between
numbers of boats on lakes and lake size.

The square root

of the areas was plotted horizontally, and the square root
of the number of boats vertically.

The lakes selected for

study had the same population pressures.

A curvilinear

relationship indicated that as the size of the lake in­
creases the rate of increase of boat density begins to
decline after a certain size lake is reached.1
Threinen surveyed the water resources of three
southeastern counties in Wisconsin.

He made the following

observations about b o a t i n g :
Boating demand is consumptive of shore and water
space and that space consumption on water is directly
proportional to speed.
Therefore consumption of the
water space is much higher for fast boats and for
indiscriminate travel such as with water skiing.
A
water ski rig has 75 feet of rope for towing plus the
length of boat to make a total of 90 feet.
Speeds of
12 miles per hour are required to achieve necessary
dynamic lift for planning of a skier with his skies.
Water skiing is the activity of fast boats and it is
an activity which keeps them occupied for extended
periods.
Without water skiing, fast boating would
find less employment on the small inland waters.
Speed is not a very significant element for the
transportation of fishermen or for sightseeing be­
cause sightseeing is most enjoyed at lower speeds.
The intensity of motorboating reaches a peak in early
summer and declines as the summer ends.
Aerial surveys and counts of boats have shown that
the number of boats on a lake is related to the amount
of shore and that a high shore-area ratio results in
high concentration.
Figure [reproduced on p. 15 as
Figure 1] illustrates that smaller lakes are charac­
teristic of high densities.
The number of boats in

1Ibid.

15

100

-

10-

10

-10

AREA CIRCUMFERENCE

(1x4 ellipse

too

1000

10,000

LAKE SIZE (acres)
Figure 1.— Relationship between acres and boat
number observed and circumference of an ellipsoid l a k e .
The slope of boat numbers-area nearly corresponds to an
area-circumference slope.
Source:
[Threinen, A n An a l y s i s
of Space D e m a n d s , p. 8]

MILES OF SHORE

NUMBER OF BOATS

BOAT NUMBERS

16
u s e for f i s h i n g or a n y k i n d o f b o a t i n g is m u c h l o w e r
t h a n t h e n u m b e r p r e s e n t on t h e l a k e . T h e c o m m o n l e v e l
of u s e a t a p e a k a c t i v i t y p e r i o d is 10 p e r c e n t o f t h e
boats present.
T h e s p a t i a l d e m a n d o n w a t e r for b o a t i n g a t low
s p e e d s c a u s e s a n e g l i g i b l e a m o u n t of i n t r a - a c t i v i t y
and inter-activity interference arises.
Waves from
s p e e d i n g b o a t s d r i v e s o u t t h e f i s h i n g bo a t s , l i k e w i s e
w i t h rowing, p a d d l i n g , a n d s a i l b o a t i n g .
Water skiing
is d e n s i t y d e p e n d e n t a n d w h e n p u r s u e d t o e x c e s s , it
l i m i t s the n u m b e r o f p a r t i c i p a n t s .
Aerial counts
frequently illustrate tha t the de n s i t y of w a t e r skiing
s e l d o m b u i l d s u p to m o r e t h a n a b o u t o n e b o a t p e r 20
a c r e s of w a t e r .
As the n u m b e r builds up an element
o f f e a r i n f l u e n c e s the d o w n e d w a t e r skier, t h e r e f o r e
20 a c r e s is the m i n i m u m s p a t i a l r e q u i r e m e n t for w a t e r
skiing. *■
Peterson polled several
recreation agencies
s t a n d a rds.
lation and

He

federal,

st a t e ,

and county

for the o r i g i n of t h e i r r e c r e a t i o n

found basic research lacking

j u s t i f i c a t i o n of s t a n d a r d s .

in the f o r m u ­

Most standards

were based on personal e x p e r i e n c e .
He believes,
of e x i s t i n g s t a n d a r d s

furthermore,

t h a t the a r b i t r a r y n a t u r e

for w a t e r —b a s e d r e c r e a t i o n m a k e s

it

d i f f i c u l t to i d e n t i f y t h e u n d e r l y i n g c o n c e p t s

for d e t e r ­

mining carrying capacity.

adminis­

trators,

and managers

Resource planners,

indicated a need

resource and user s a t i s faction studies
2
v a l i d standa r d s .

for b a s i c n a t u r a l
to o b t a i n m o r e

W. W. T h r e i n e n , A n A n a l y s i s o f S p a c e D e m a n d s for
W a t e r a n d S h o r e , T r a n s a c t i o n s o f the T w e n t y —N i n t h N o r t h
American Wildlife and Natural Resources Conference
(Washington, D.C.:
W i l d l i f e M a n a g e m e n t Institute, March,
1964), pp. 358-59.
2

G. A. P e t e r s o n , "An A p p l i c a t i o n of W a t e r R e c r e ­
ation Capacity to R e s e r v o i r D e v e l o p m e n t Planning" (unpub­
lished M a s t e r ' s thesis, T e x a s A & M U n i v e r s i t y , 1968), p. 12.

17
Wilcox and Held recently proposed for the National
Park System:
. . . a t e c h n i q u e , or t e c h n i q u e s , for determining in
as exact and objective manner as possible the capacity
of recreation lands to absorb use for a sustained
period of time without destroying definable and m e a ­
surable park and recreation values.
The authors state that recreational carrying capacity is
not an absolute numerical value but a dynamic measure
changing with design, user perception,
controls.

and management

They conclude:

The major consideration in determining the level of
use of an area is the trade-off between benefits
w hich result from admitting additional users to the
area or permitting more intensive use of the area and
the losses, if any, associated with the increase or
intensification of use. 3Crysdale is currently engaged in an analysis of
spatial relationships and resource requirements for water
2
skiing.
He proposes to study both the attitude of people
using a body of water and its physical characteristics
necessary to support water skiing.

He proposes to divide

the number of water skiers of a body of water of known
size, depth, and physical attributes into the acreage
believed to be capable of accommodating that activity.

A. T. Wil c o x and R. B. Held, "A Study to Develop
Practical Techniques for Determining the Carrying Capacity
of Natural Areas in the National Park System" (unpublished
study proposal on file at the Center for Research and
Education, Estes Park, Colorado, 1967).
2

D. Crysdale, "An Analysis of Spatial Relationships
and Resource Requirements for Waterskiing" (unpublished
study proposal on file at Department of Park and R e c r e ­
ation Administration, North Carolina State University,
1969) .

18
T h e d e l i n e a t i o n of a c r e a g e to a c c o m m o d a t e w a t e r sk i i n g
w i l l b e b a s e d u p o n four c o n c e n t r i c zones of sensitivity;
ph y s ical,

o b j e c t i v e safety,

s u b j e c t i v e safety,

and social.

A s a b o a t a n d w a t e r s k i e r i n c r e a s e t h e i r speed,

the c o n ­

c e n t r i c zones m a y b e c o m e h o u r - g l a s s s h a p e d w i t h the c o n ­
s t r i c t i o n o c c u r r i n g at the boat.

T h e zones w i l l i n c r e a s e

and d e c r e a s e in size d e p e n d i n g on the speed of the boat.
W h e n the so c i a l zones of the w a t e r skiers overlap,

they

be c o m e a w a r e of c r o w d i n g a n d the s a t i s f a c t i o n of th e i r
e x p e r i e n c e m a y decrease.
Q u e s t i o n n a i r e s w i l l be d i s t r i b u t e d to lake u s e r s
on a r a n d o m s e l e c t i o n b a s i s

to h e l p p r o v i d e a c c u r a t e

i n t e r p r e t a t i o n s of the a e r i a l p h o t o g r a p h s a n d o b t a i n the
users*

s e n s i t i v i t y to a n d a t t i t u d e c o n c e r n i n g crowding.

F o l l o w - u p q u e s t i o n n a i r e s w i l l be m a i l e d to all b o a t e r s
i n t e r v i e w e d at the lake to a t t e m p t to p r o b e w a t e r s k i e r s '
c o n s c i o u s n e s s of d i s t a n c e r e l a t i o n s h i p s to o t h e r b o a t e r s
using the w a t e r surface.
C o n c l u s i o n s f r o m R e v i e w of the L i t e r a t u r e
o h C a r r y i n g C a p a c i t y Standards'
T h e r e v i e w of r e l e v a n t l i t e r a t u r e has r e v e a l e d a
n u m b e r o f d i v e r g e n t a p p r o a c h e s to the p r o b l e m of d e t e r ­
mining carrying capacity,

a l t h o u g h there app e a r s

a g r e e m e n t on a n u m b e r of issues.
be d e f i n e d in a b s o l u t e terms.

First,

to be

capacity cannot

A si n g l e figure c a n n o t

represent areas characterized by different environmental

19
and social variables.

S e c o n d , bo a large extent the

recreational carrying capacity of an area is set by
management goals; as a result use has been restricted in
certain cases.

Third, capacity is largely influenced by

the user's attitude of different levels of use and of
various types of use.

Fourth, capacity can be changed by

different management practices, control measures, and by
the use of all available resources.

Finally,

the research

to date on attitudes concerning recreational experiences
has been mainly conducted in wilderness areas.
The consensus of the studies reviewed in this
chapter is that user satisfaction with a recreation
experience may decline with an increase in the density
of use of the recreational facility.

A majority of

workers in the field seem to have a preconceived c o n ­
viction that this is true.

It is significant that no

study came to an opposite conclusion.

C H A P T E R III
R E S E A R C H DESIGN F O R M U LATION
T h e P r o b l e m Statement:
Summary
Re c r e a t i o n resources should be e v a l u a t e d for two
different d e t e r m i n a n t s of use in p l a n n i n g for h e a v i l y u s e d
surface waters.

T h e s e are:

recreation experience,

and

(1) the p s y c h o l o g y of the
(2) the ability of the p h y s i ­

cal resource to a c c o m m o d a t e vary i n g levels of u s e .
Objectives
This r e s e a r c h p r o b l e m attempts to investigat e
recreational e x p e r i e n c e s of w a t e r - o r i e n t e d user groups on
three intensively used lakes.

B a s e d upon these i n v e s t i ­

gations an a t t e m p t w i l l be made to quan t i f y c a r r y i n g
capacity taking a c c o u n t of b o a t e r attitudes to w a r d v a r y ­
ing levels of use.

A n a t t e m p t w i l l also be made to relate

the socio-economic c h a r a c t e r i s t i c s of boaters to their
attitude toward b o a t i n g conditions at the same p o i n t in
time and at the same location.

20

21

Hypotheses
It Is assumed in this study that the opinions of
boaters using surface waters can be used effectively in
the development of carrying capacity v a l u e s .
The first hypothesis to be tested is that the
level of user dissatisfaction is directly related to in­
tensity of use.

The level of dissatisfaction is defined

as the number of users in relation to the total number of
users interviewed indicating that unfavorable boating
conditions existed at a particular period in time.
The second hypothesis is that the space available
for boating is inversely related to the intensity of use.
The space available for boating is defined as the number
of acres of water surface used per boat in a particular
lake zone over time.
The third hypothesis is that selected socio­
economic characteristics of boaters indicating unfavorable
attitudes toward conditions of use differ significantly
from those indicating favorable attitudes toward conditions
of use.
The Study Area
Selection
At present the limited research on attitudes con­
cerning recreational experiences has been directed toward
wilderness use.

Equally important is the need for similar

22

research on intensively used water surfaces.

The attitudes

concerning wilderness perception involve fewer people than
do those in highly used areas close to large population
centers.

The question whether the quantified insights of

wilderness attitude and subsequent management practices
are applicable to high-use water recreation areas can be
answered only by intensive attitude studies of high-use
recreation l a k e s .
Three Oak l a n d County lakes were selected as the
study area for this investigation.

Several factors were

involved in this choice:
1.

The Waterways Division, Michigan Department of
Natural Resources asked that highly used lakes
near a large metropolitan area be studied.

2.

Oakland and Wayne counties together account for
one-fourth of all registered boats in Michigan.
Approximately 1,000 lakes in Oakland County are
within one-half hour's driving time from the
Detroit Metropolitan area.

Several hundred of

these lakes are large enough to support w a t e r
skiing.
3.

The Marine Division of the Oakland County
Sheriff's Department
bility)

(water safety respon s i ­

and the Waterways Division of the

Department of Natural Resources suggested five

23

large lakes r e p o r t i n g a h i g h n u m b e r o f b o a t i n g
a c c i d e n t s , v i o l a t i o n s , a n d u s e r c o n f l i c t s in
southeast Michigan.
4.

A v a i l a b l e r e s e a r c h funds
interviewers.

l i m i t e d the n u m b e r o f

A m i n i m u m number was needed at

e a c h lake to o b t a i n m a x i m u m r e s p o n s e s .
5.

Scheduled aerial photography at hourly inter­
vals r e s t r i c t e d the s t u d y to a t o t a l of t h r e e
lakes.

6.

E a c h lake h a d o n e p u b l i c a c c e s s site, a n d the
r e m a i n i n g r i p a r i a n l a n d w a s p r i v a t e l y owned.

G e o g r a p h i c a l and G e o l o g i c a l
F e a t u res
Union, Cass,
4 respectively)

and O r c h a r d lakes

are s i t u a t e d a b o u t

Pontiac, M i c h i g a n .

(Figures 2, 3, and

five m i l e s s o u t h w e s t of

C a s s and O r c h a r d lakes are w i t h i n the

C l i n t o n R i v e r Waters h e d .

Union Lake drains

into the Huron

River W a t e r s h e d .

The d r a i n a g e a r e a is r e l a t i v e l y s m a l l on

all t hree lakes.

Average

lake e l e v a t i o n is 928

feet above

sea level.
O a k l a n d C o u n t y has o v e r 1,000 n a t u r a l lake s a n d
v i r t u a l l y all of these,

i n c l u d i n g Union, Cass,

are of g l a c i a l origin.

S a n d and g r a v e l soils p r e d o m i n a t e

in the s h a l l o w waters,

e x c e p t for some d e p o s i t s at the ten

to t h i r t y foot c o n t o u r depths.
feet.

Average

and Orchard,

lake d e p t h is 100

1,5,8.

Figure 2.— Union Lake, Pontiac, Michigan.
(460.6 Acres).

T.2N, 4.8-9E., Sections
ro

Figure 3.— Cass Lake, Pontiac, Michigan.
2,3,4,9,10,11,33,34,35. (1209.9 Acres).

T.2-3N, R.9E., Sections

Figure 4.— Orchard Lake, Orchard Lake Village, Michigan.
R.9E., Sections 9,10,11,14,15. (778.9 Acres).

T.2N,
NJ
00

29

I
\ ;
,<
i

t>
\

(«»k\

‘
i-

»

■i

30
C h e m i c a l and Phys i c a l Features
T h e w a t e r of Union, Cass,

a n d O r c h a r d lakes is

fairly c l e a r and m o d e r a t e l y hard.

T h e d e p t h limit of

v i s i b ility is about fifteen feet.

T h e pH values are 7.2

to 8.5, and m e t h y l orange a l k a l i n i t y tests r a n g e from 83
to 115 parts p e r m i l l i o n of c a l c i u m c a r b onate
i n d i c ating alkalinity.

In summer months,

further

the d i s s o l v e d

oxygen is su f f i c i e n t to support fish life at forty foot
depths.

Surface w a t e r temperatures range from 60° to

75°F. to 40° and 4 5 ° F. at lower depths.
season,

D u r i n g the summer

temperatures of the e p i l i m n i o n m a y vary gre a t l y

from day to day d e p e n d i n g upon air t e m p e r a t u r e .

Tempera­

tures in the h y p o l i m n i o n remain u n i f o r m w h i l e the t h e rmocline show sharp drops at successive d o w n w a r d depths.
Biological C h a r a c t e r i s t i c s
B i o l o g i c a l l y all three lakes are productive.

Sub-

m e rgent v e g e t a t i o n grows in d e e p e r pa r t s of shoal areas
moderate abundance.

The p r i n c i p l e s u b m e r g e n t species are

musk grass, coontail, and p o n d weed.
(chiefly bullrushes)

E m e r g e n t plan t s

are common in sha l l o w areas.

A wide vari e t y of forage fish is found in all
three lakes.
abundant.

B l u n t nose min n o w s and silversides are

Game fish include y e l l o w perch,

largemouth bass,

rock bass,

smallmouth bass, bluegill, p u n k e n s e e d

sunfish, n o r t h e r n pike, cisco,
yellow bullheads,

in

lake trout, walleye,

and longnose gar.

31
Climate
O a k l a n d C o u n t y is in s o u t h e a s t e r n M i c h i g a n a n d t h u s
is b u f f e r e d on t h r e e s i d e s b y the G r e a t L a k e s w h i c h e x e r t
a m o d e r a t i n g i n f l u e n c e o n the c l i m a t e .
c o l d a n d h e a t a r e t h e r e f o r e n e i t h e r as
as w o u l d b e the c a s e a t t h i s
L a kes.

The county's

i n c h e s of w h i c h
months.

l o n g n o r as

a v e r a g e a n n u a l p r e c i p i t a t i o n is 3 0 . 6 0

29 p e r c e n t o c c u r s

in the t h r e e s u m m e r
from about May

7,

11, o r a p e r i o d o f 157 days.

S u m m e r s are c h a r a c t e r i z e d b y w a r m m o d e r a t e
at u r e s w i t h
Airmass

intense

latitude w i t h o u t the Great

The growing season extends

to O c t o b e r

Periods of extreme

light surface winds

temper­

f r o m the w e s t a n d s o u t h w e s t .

type thunderstorms may occur in the afternoon,

w i n d s g u s t i n g f r o m n o r t h w e s t to s o u t h e a s t .

The

with

thunder­

s t o r m s u s u a l l y y i e l d h e a v y a m o u n t s o f p r e c i p i t a t i o n in
r e l a t i v e l y s h o r t p e r i o d s of t i m e .
o v e r e x t e n s i v e u r b a n ar e a s ,

When heavy showers move

existing drainage

overflow and subsequently raise

lake

levels

systems often

in a s h o r t

p e r i o d of t i m e .
La k e D e v e l o p m e n t
Union and Cass
development.
2 a n d 3.

lakes h a v e u n d e r g o n e

intensive

T h i s is e v i d e n t f r o m e x a m i n a t i o n o f F i g u r e s

M o s t residences are p e r m a n e n t y e a r a r o u n d homes

varying from small run-down cottages
level h o u s e s w i t h

large

to e x p e n s i v e m u l t i ­

lake f r o n t a g e .

Most homes have

32
septic tank systems.

'Jo facilities are mainta i n e d for

providing storm water drainage other than roadside ditches.
Most runoff water empties into nearby marshlands or inlet
and outlet streams.
mostly oiled.

Roads in and around the lakes are

Both lakes have a public access site.

The

Dodge Brothers 4 State Park is located on Cass Lake.
O rchard Lake is entirely surrounded by expensive
estates and a large country club.

Orchard Lake Village

maintains a full-time police force,

roads are p a v e d and

have extensive storm wa t e r drainage systems.

Residents

either have septic tanks or are connected to city s e w e r s .
The lake has one public access site.

C H A P T E R IV
METHODS AND PROCEDURES

T h e c a r r y i n g c a p a c i t y of w a t e r for r e c r e a t i o n a l
b o a t i n g is d e p e n d e n t u p o n the attit u d e s of p a r t i c i p a n t s
as t h ese m a y be m o d i f i e d b y levels of use
pp.

8, 10,

and 12).

(see C h a p t e r I I ,

T h e a t t i t u d e of the b o a t e r s

cated by their responses

is i n d i ­

to v a r y i n g levels of use.

Two

v a r i a b l e s w e r e c h o s e n to d e s c r i b e the level o f b o a t i n g
a c t i v ity on a b o d y of water.
s u m p t ion of w a t e r surface,

T h e s e were:

and

(1) c o n ­

(2) d i s p e r s i o n of boats.

T h e o b s e r v a t i o n p e r i o d s on Union, Cass,
O r c h a r d lakes w e r e s c h e d u l e d e v e r y w e e k e n d ,
day d u r i n g the summer, w e a t h e r pe r m i t t i n g ,
t h rough S e p t e m b e r 1,

1969.

and

a n d on e w e e k ­
from July 4

R e s p o n s e s to h i g h d e n s i t y u s e

c onditions w e r e c o n t i n u o u s l y o b t a i n e d b y m e a n s of i n t e r ­
views of b o a t e r s as t h e y left the lakes;

the areas w e r e

p h o t o g r a p h e d at o n e - h o u r i n t e r v a l s .
The Interview
E a r l y in the f o r m u l a t i o n of this study,

it was

d e c i d e d to focus on the a t t i t u d e s a n d b e h a v i o r o f w a t e r o r i ented users u s i n g p u b l i c ac c e s s sites on i n t e n s e l y u s e d
33

34
lakes.

The interview schedule employed in this investi­

gation was divided into three p a r t s :

(1) the first section

dealt with the composition of the boating party and the
type of boat,

(2) the second section asked for information

on boating activity by designated areas,

(3) the third

section sought data on the socio-economic characteristics
of b o a t e r s .
Several steps were involved in the preparation of
the interview used in this study:
1.

The author prepared a series of rough drafts
under the direction of his major professor.

2.

After an acceptable draft of the interview
schedule had been prepared,

the author inter­

viewed the Park Superintendent of Dodge
Brothers 4 State Park on Cass Lake, the
deputy sheriff in charge of water safety, of
the Marine Division, Oakland County Sheriff's
Department, and the Chief of the Waterways
Division, Michigan Department of Natural
Resources•

The questions asked in the inter­

view schedule were discussed with each of
these persons to obtain their views on inter­
preting attitudes of boaters and use patterns.
3.

Another revision in the content and arrangement
of the interview schedule was made after these

35
critiques.

A t the req u e s t of the W a t e r w a y s

C o m m i s s i o n , several additional q u e s t i o n s w e r e
included.
4.

The interview was then t e s t e d b y a d m i n i s t e r i n g
it to a sample of boaters d u r i n g a h i g h - u s e
period.

5.

A n o t h e r revision of the q u e s t i o n s and format
was then

6.

undertaken by the author.

Finally, the interview was a g a i n te s t e d by
administering it to boaters d u r i n g a h i g h - u s e
period before July 4.

The interview schedule was s u p p l e m e n t e d b y a m a p
of the lake involved.

On this map,

the lake w a s d i v i d e d

into n umbered geographically distinct z o n e s .1
final

In its

form, the interview was desi g n e d to o b t a i n as m u c h

relevant information

as possible about the b e h a v i o r o f

individual b o a t e r s .

The following is a sum m a r y of the

information w h i c h the interview was d e s i g n e d to obtain:
1.

the

2

Information p e r t a i n i n g to time spent on
boating
a.

arrival and departure times of b o a t e r

b.

total days respondent u s e d the lake for
boa t i n g to date

^See Figure 5 for lake maps shown to r e s p o n d e n t s
during i n t e r v i e w s .
2
See A p p e n d i x A2 for interview s c h e d u l e u s e d at
public access sites.

36

Figure 5.— Lake maps
during i n t e r v i e w s .

sh o w n to r e s p o n d e n t s

37

■in m m ■"i" i. r i'iw i ■11 ii ■ i uip i

0*C«M*D

LMMt

38
c.

total days r e s p o n d e n t b o a t e d anywhere to
date

d.

time spent on various recreational and
r e l a t e d activities at the lake conce r n e d

2.

L o c a t i o n of b o a t i n g activities and use patterns

3.

C o m p o s i t i o n of the b o a t i n g party
a.

n u m b e r of people in the party by age and
sex

b.

n u m b e r of boats in the party

4.

T y p e of b o a t and h o r s e p o w e r

5.

In f o r m a t i o n a b o u t the reason the lake was
selected for b o a t i n g

6.

I n f o rmati on c o n c e r n i n g the boater's attitudes
c o n c e r n i n g amount of use and quality of the
ex p e r i e n c e

7.

In f o r m a t i o n about occupation,

income,

and

education.
O n l y c e r t a i n port i o n s of the data obtained from
the i nterviews were used in this study.

The remaining

information w i l l be inc o r p o r a t e d into the final report
submitted to the W a t e r w a y s D i v i s i o n of the M i c h i g a n
D e p a r t m e n t of N a t u r a l R e s o u r c e s .
The I n t e r v i e w Schedule
T h e i n t e r v i e w i n g was c o n d u c t e d between 1000 hours
and 19 30 hours on w e e k e n d s

(and the one weekday)

three lakes as shown in Table 1.

at all

Each interview team

39
TABLE 1
TOTAL BOATS COUNTED AND PER CENT BOATERS INTERVIEWED
AT ACCESS SITES JULY 4 THROUGH SEPTEMBER 1, 1969
Number
of Boats
Interviewed

Number
of Boats
Counted

_
.
interviewed
interviewed

Lake

Date

Union
Cass
Orchard

July 4
July 4
July 4

4
3
12

4
3
12

100
100
100

Union
Cass
Orchard

July 5
July 5
July 5

32
69
83

34
72
89

94
95
93

Union
Cass
Orchard

July 6
July 6
July 6

34
54
54

92
93
92

Union
Cass
Orchard

July 20
July 20
July 20

28
51
59

Union
Cass
Orchard

July 26
July 26
July 26

29
66
75

37
58
59
31
57
65
33
72
80

Union
Cass
Orchard
Union
Cass
Orchard

Aug. 2
Aug. 2
Aug. 2

28
65
63

32
71
72

88
92
88

Aug. 3
Aug. 3
Aug. 3

41
59
74

47
69
89

87
86
83

Union
Cass
Orchard

Aug. 9
Aug. 9
Aug. 9

30
42
26

87
81
88

Union
Cass
Orchard
Union
Cass
Orchard

Aug. 10
Aug. 10
Aug. 10

26
34
23
41
59
71

45
69
82

91
86
87

A u g . 17
Aug. 17
Aug. 17

20
43
34

22
49
38

91
88
89

Union
Cass
Orchard

Aug. 21
Aug. 21
Aug. 21

3
9
5

3
9
5

100
100
100

90
89
91
88
92
94

40
TABLE 1— Continued

Lake

N umber
of Boats
Interviewed

Date

Number
of Boats
Counted

Per Cent
Interviewed

Union
Cass
Orchard

A u g . 23
A u g . 23
A u g . 23

28
56
57

33
66
69

84
85
83

Union
Cass
Orchard

Aug.
Aug.
Aug.

24
24
24

39
46
58

43
57
68

91
81
85

Union
Cass
Orchard

A u g . 30
Aug. 30
Aug. 30

22
38
52

26
43
61

85
88
85

Union
Cass
Orchard

Aug. 31
A u g . 31
A u g . 31

35
49
67

91
83
84

Union
Cass
Orchard

Sept. 1
Sept. 1
Sept. 1

32
41
56
33
28
50

37
33
60

89
85
83

41
consisted of two or three students.

Frequently,

a deputy

from the Marine D i v i s i o n of the O a k l a n d C o u n t y Sher i f f ' s
Department assisted at the lake's p u b l i c access site by
d i r e cting depar t i n g b o a t e r s to the i n t e r v i e w team.

Almost

every boater was in t e r v i e w e d be f o r e 1500 and after 1700
hours.

F r o m 1500 to 1700 hours

(the m o s t c r o w d e d t i m e ) ,

approximately 80 per c e n t of the boa t e r s w e r e inter v i e w e d . ^
It took approximately six m i n u t e s to a d m i n i s t e r the i n t e r ­
view schedule.

A n analysis of the responses o b t a i n e d in

the i nterviews will be u n d e r t a k e n in C h a p t e r V.
The Questionnaire
Early in the study,

it was d e c i d e d to also i n v e s t i ­

gate the attitudes and p a t t e r n s of b o a t i n g use of r i p a r i a n
owners on each lake.

A self-administered questionnaire

was d esigned for this purpose.

2

Each questionnaire with

a self-addressed stamped e n v e l o p e w a s i n d i v i d u a l l y d i s t r i ­
buted to all riparian owners or o c c u p a n t s of the property.
The potential respondents w e r e a s k e d to desc r i b e their
feelings about the l a k e 's use for a previ o u s w e e k

(August

"^The interview teams u s e d h a n d counters to c o u n t
all boats leaving the access site.
In addition, the
boater registration n u m b e r w a s o b t a i n e d for all boaters
not interviewed.
See T a b l e 1 for the total boats c o u n t e d
and per cent boaters interviewed.
2

T h e q u e s t i o n n a i r e was p r e p a r e d by Mr. Robe r t
Dittrick, graduate assistant, D e p a r t m e n t of Park and
Recreation Resources, M i c h i g a n State University, as p a r t
of the contract w i t h the W a t e r w a y s Commission.
See
Ap p endix A3 for questionnaire.

42
18 through 24).

The questionnaire was distributed again

in a similar manner the following week
September 1).

(August 25 through

The average response to the questionnaire

amounted to 63 per cent.
Information relating to specific times of unfavor­
able activity conditions was extracted from these question­
naires for this study.

An analysis of the responses is

given in Chapter V .
Aerial Photography
The use-patterns of boaters were recorded by
aerial photography.
vertical photographs.

Initially,

it was intended to use

A 35mm 250 frameback motorized

camera with intervolometer was ordered.

Shortly before

the study started, the Recreation Research and Planning
Unit was notified that the equipment would not be avail­
able until after completion of the study.

A Nikkormat

35mm single lens reflex camera equipped with a 50mm fl.4
Nikkor lens was borrowed and used for the entire summer.
Black and white panchromatic film of various film
speeds

(ASA 25, 32, 64, 120, and 600) and several color

films, Kodacrome
Ektacrome

(ASA 25), Ektacrome

(ASA 64), High Speed

(ASA 160), were tested at different elevations.

The purpose was to select the film which would permit
enumeration of the boating activities underway and
measurement of other phenomena such as boat speeds.
After an analysis of these tests, High Speed Ektacrome

43
(ASA 160)

at an altitude of 500 feet above the lake levels

was selected.

The camera was hand held and the exposures

were high oblique.

Several trial flights followed to

determine sequential exposure stations for all three
lakes.

Total flight time needed to cover all three lakes

was thirty-five minutes.
The purpose of the photography was to record levels
of boating use over t i m e .

Continuous photography of the

water surface was not possible because of the high cost of
aircraft rental and the two-hour flight time limit of the
aircraft.

In order to obtain a representation of the

water surface usage for a given hour with minimal p h o t o ­
graphy, a test was conducted in w h i c h all three lakes were
continuously photographed for one hour during a high-use
weekend.

This resulted in five complete "flights" per

lake using the predetermined photography p r o c e d u r e s .
Examination of the photographs showed that the total
number of boats in each lake zone varied only slightly
over a given one-hour time span
was, therefore,

(see Table 2).

The author

able to assume that photographing the

water surface once during an hour w o u l d adequately r e p r e ­
sent the level of use for that hour.
Aerial photography flights were generally u n d e r ­
taken on the following schedule:
1800,

0800,

1000,

1400, 1500, 1600,

1700,

flight at sundown

(approximately 1930 h o u r s ) .

1200,

1300,

1900 hours, and one final

TABLE 2

VARIATION OF TOTAL BOAT NUMBER, SPACE CONSUMPTION, AND DISPERSION FOR FIVE PHOTO
FLIGHTS ON UNION, CASS, AND ORCHARD LAKES (JUNE 29, 1969)a

TIm
1*00

-------- 1taion
Space Con*.
Total
Safety
Boat
Laka
(Acraa)
Count
Zona

i
]
4
5

11
12
10
ft
S
1
IS
_ .11
Jl
12
10
10
6

25.11
3».7)
12.72
K.U
3.02
11.92
21.7*
19.77
23.33
39.10
21.22
27.33
0.13

7
|
1
}
3
4

is
ii
u
11
11
10

23.99
20 .ta
23.29
39.37
22.13
27.90

ft

I
u
11
u
1)
11

1
2
3
4
5

ft
f

1423

1433

144?

7
1
1
2
3
3
ft
7
I
1
2
1

....

2.06
1.10
1.71
1.03
1.16
1.(2
2.35
1.71

2.32
3.67
3.39
2.(1
3.12
3.23
1.21
J.IJ
1.16
2.21
3.22
1.99
3.23
2.H
3.11
2.02
2.13
3.11
2.35
1.66
2.07
3.22
. ?,Pii.ii
3.01
1.22
1.99
3.21
2.01
6.07
3.27

Tie*
1300

Total
Boat
Count

Lake
Zona

1
2
3
4
5
ft
7

ft
1525

1337

u u

9
1
2
3
4
5
ft
7
1
9
1
2
3
4
3
6
7
8
ft
1
2
3

70.37
120.93
50.72
32.36
25.51
26.63
73.92
26.(3
37*99
60. U
122.00
51.23
33.12
27.31
29.72
33.31
2(.91
*0.11
71.22
130.1*
60.73
*0.23
27.11
29.(6
10.12
30.19
*3.»L_
75.37
133.11
70.U
11.37
26.33
30.11
13.19
37.33
13.97

34
23
19
23
13
IS
4ft
13
11
34
23
19
24
14
IS
47
13
1ft
35
23
1ft
25
14
15
49
14

1
2
9
4
5
ft
7
B

ft

1511

Can
Space Cana.
Safety
(Acret)

- 1*33
24
20
25
14
IS
52
1ft
20

R S R 5 S S R 3 3
KSEfSiS
J S S

>
ft
7
•

6
*
1*
__ u
11
11
11
11
7
1
It
11

H.I9
2t.U
20.40
27.01
10.37
23.71
27.33
7.03
16.20
21.35
... » . n ..
17.32
10.92
23.19
21.31
7.90
16.31
23.01
20.62

Ottpereiea
Scpli
Coafflcfaat

4

Tba aqilanatlen of ip K l a re n a ,t too *od dlipenlire a n preeented In

1

i

5
6
7
•
9

ffk

nW

(3 .

D1apart!on
5«pl«
Coafflelant

—

3,55
4,39
3,5ft
2,io
2*55
2*77
1,59
l.ftO
9*09
i,oi
3.Z7
2*46
3*44
3,04
4.09
2.23
3.10
4.5ft
i.ur2.26
3.33
1.00
l.0(
2.11
1.01
2.0(
2.76
1 .0
0.(9
1.21
3.22
1.11
2.01
1.01
%99
1.03
0.(9
2.12
2.03
1.90
2.09
0.(6
1.91
2.02
2.H

TIm
1600

1610

lake
lane
1
2
3
1
3
6
7
1
3
4
5

ft
1620

1631

I6li

7
1
2
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4

ft
7

0i
Total ' Sptft Gona*
Boat
Cotint
a
22
13
13
15
2ft
11
i
22
13
17
17
27
13
B
23

6.52
51.56
16.26
20.(6
11.76
16.26
15.76
Ml
53.63
15.23
20,62
13.71
17.U
15.70
(.33
31.61

13
15
2B
13
B
24
IS
17
17
2ft
15
9
27
1ft
16
13
32

11.11
11.23
K.37
_ 11.01
1.11
55.31
16.13
11.21
17.23
19.(3
16,93
7.01
56.33
19.11
16.19
K.61
16.11
19.21

«

la*U
Caaf fldent
1.(3
2.76
2.20
2.36
3.37
2.39
3.27
(.a
1.12
3.11
1.36
2.03
1.57
2.22
T.'« ’
3.21
3.37
1.90
3.02
2.96
3.U
1.99
2.(7
3.U
2.91
l .d
3.01
1.19
1.69'
3.22
1,11
3.03
3.07
1.99
2.11

45
Interpretation of the Photographs
Grid Construction
The location of boats on the aerial photographs
was interpreted by means of one p o i n t perspective q u a d r i ­
lateral gri d s . 3-

These grids are a representation in

perspective of imaginary squares laid out on the ground.
The size of these squares is dependent on the camera
depression angle and height of the camera at the time of
exposure.
The 35mm color slides were proje c t e d a distance
of 90 inches onto a viewing screen.
24-x36-inch image.

This prod u c e d a

The first step in p r e p a r i n g a grid

was to locate the principal point on the projected image
and draw the apparent horizon.

A principal line was

drawn through the principal point at right angles to the
apparent horizon.

The depression angle

(6') of the

optical axis from the apparent horizon was calculated as:

9 ' = arc tan

ph '
£ ■■■

where
P is the principal point in the p h o t o g r a p h ,
h* is the apparent horizon, and
f is the focal length of the camera.

^American Society of P h o t o g r a m m e t r y , Manual of
Photogramme try (Menasha, W i s .: Banata Publishing Co.),

46
The vertical angle a

(see F i g u r e 6)

(subte n d e d a t

the e x p o s u r e s t a t i o n b y rays to the a p p a r e n t and t r u e h o r i
zon) w a s c o m p u t e d b y the f o l l o w i n g equation:

a = arc tan 0.9216

✓

R

R <!

where
H is the f l i g h t a l t i t u d e a b o v e m e a n t e r r a i n
elevation,
R is the ra d i u s of the earth,

and

0.9216 is a c o n s t a n t for c o r r e l a t i n g a t m o s p h e r i c
refraction.
W h e n H is small in c o m p a r i s o n to R,

2

the e x p r e s s i o n H / R

2

may be d r o p p e d w i t h o u t s i g n i f i c a n t e f f e c t o n the v a l u e of
a and the e q u a t i o n b e c o m e s :
a

(in minutes)

= 0.98

/H

(in f e e t ) .

The d e p r e s s i o n a n g l e 6 of the o p t i c a l axis

from the true

h o r i zon i s :
0

=

0

'

+

a

The d i s t a n c e b e t w e e n the t r u e and a p p a r e n t h o r i z o n
on the p h o t o g r a p h is:
h h ' = f tan 0 - Ph *.

1l b i d . , p.

889.

(hh')

/

TRUE HORIZON

-H

PHOTO PLANE

Figure 6.— Angular relations of an oblique photograph.
[Manual of Photograimnetry, p. 887]

Source:

48
The next step was to const r u c t the true h o r i z o n
through h, p e r p e n d i c u l a r to the principal line
Figure 7).

(see

F o r t y - f o o t grid intervals w e r e selected.

Maps of o n e - i n c h per 400 feet scale w e r e c o n s t r u c t e d for
recording the a c t i v i t i e s .

P o i n t D was es t a b l i s h e d b y the

following formula:
._
hD

/•
, .
H sec 0
(in inches) = --- —-m

where
m is the distance apart from D

(one-inch).

T h r o u g h p o i n t D a line was drawn parallel to the
true horizon.
point D.

O n e - i n c h segments

(m) were m a r k e d off from

T h e s e marks w e r e joined w i t h h.

The resu l t was

a fan p r o j e c t i o n of a series of lines 40 feet apart on
the ground.

A l l lines at 45 degrees to the princip a l

line vanish at the same point.

W h e n the v a n i s h i n g p o i n t

was established, diagonals w e r e drawn to estab l i s h a p r o ­
jection of 40-foot squares.

The two vanishing points,

left and right of h, are located on the true horizon,

a

distance h v from h and derived by the following formula:
h v 1 = h v 2 = f sec 6.

The last step was to d r a w a line from p o i n t v,
through P

(see Figure 7).

A series of lines at right

vr

49

F i g u r e 7.— P e r s p e c t i v e grid.
of P h o t o g r a m m e t r y , p. 8891

Source:

[M a n u a l

50
angles to the principal line through the points inte r ­
sected by the line Pv^ gives a 40-foot grid.
Preliminary examination of the photographs r e ­
vealed considerable variation in the principal line d i s ­
tances between the apparent horizon and the principal
points, due to differences in camera angle and aircraft
elevation.

Forty different perspective grids were c o n ­

structed for two- through twelve-inch principal line
distances at one-quarter-inch intervals.

The procedure

was repeated three times for each interval at 400-,

450-,

and 500-foot flight elevations producing a total of 120
g r i d s .^
The appropriate grids were selected for each
photograph by measuring the distance from the apparent
horizon to the principal point on the projected image.
The image was then projected onto each of the three
selected grids

(400, 450, and 500 elevation)

until a

known distance on the photograph was accurately re p r e ­
sented by the grid.

Figure 8 illustrates a high oblique

photograph projected on a perspective grid.

The grid

with the closest measurement of the distance was selected
for interpreting the location of activities.

See Appendices B 1 , B 2 , and B.'.* or perspective
grid construction calculations on 400-, 450-, and 500-foot
flight elevations.

51

Figure 8.— High oblique photograph projected
on a p e r s p e c t i v e grid.

F i g u r e 9 . — P r o c e d u r e for t r a n s f e r r i n g b o a t i n g
a c t i v i t y l o c a t i o n s f r o m a p h o t o g r a p h to 1" = 400*
map.

53
A c t i v i t y Inter p r e t a t i o n
T he five rec r e a t i o n a l activities selected for
study w e r e fishing,

sailing,

cruising, and w a t e r skiing.

swimming from a n c h o r e d boats,
T h e location of every b o a t

pa r t i c i p a t i n g in an activity was transferred from the high
oblique p h o t o g r a p h image to a m a p w i t h a scale 1" — 400*.
Figure 9 illustrates the p r o c e d u r e for transferring b o a t ­
ing activity locations from a p h o t o g r a p h to a 1" = 400'
map.
E a c h lake map was d i v i d e d into seven to nine zones
identical to those used on the inte r v i e w i n g m a p s .

Figures

10, 11, and 12 illustrate e a c h lake m a p d i v i d e d into zones.
Fishing,

sailing,

and swimm i n g activities g e n e r a l l y did

not have m o v e m e n t d i s t i n g u i s h a b l e on successive p h o t o ­
graphs and thus w e r e p l o t t e d in static p o s i t i o n s .

Cruis­

ing and w a t e r skiing dis r u p t the w a t e r surface and p r o ­
duce r e c o g nizable trails on the photographs.

For each

zone a series of o v e r l a p p i n g ph o t o g r a p h s was interpreted.
The m ov i n g boats and trails w e r e plo t t e d for two or m o r e
sequential exposures.

The lengths of the trails w e r e

dependent upon b o a t i n g speed;

faster boats covered more

water and left longer trails than slower boats.

Ea c h

trail length was m e a s u r e d from its b e g i n n i n g to the first
boat p o s i t i o n or zone b o u n d a r y by means of a m a p measure.
Figure 13 illustrates the technique for m e a s u r i n g b o a t i n g

54

F i g u r e 1 0 . — P h o t o o f m a p of C a s s L a k e
d i v i d e d into z o n e s .

F i g u r e 1 1 . — P h o t o of m a p o f U n i o n L a k e
d i v i d e d into z o n e s .

F i g u r e 1 2 . — P h o t o of m a p o f O r c h a r d L a k e
d i v i d e d into z o n e s .

56

Figure 1 3 . — T e c h n i q u e used for m e a s u r i n g
b oa t i n g trails by m a p measure.

Figure 14.
T r a c i n g paper technique for
d e t e r mining co n s u m p t i o n of space by various b o a t i n g
activities.

58
trails.

The trail length for each activity was recorded
t

for each flight for all z o n e s .
The total number of boats involved in each activity
was determined for every z o n e .

A computer p r o g r a m was

developed to divide each z o n e 's area by this total number
of b o a t s . T h e

quotient values gave the number of acres

per boat for every zone on the three lakes for each
flight.
Boating space c o n s u m p t i o n .— M o v i n g or stationary
boats "consume" measurable water surface areas.
of space used is dependent upon the activity.

The amount
As observed

fishing, swimming, and sailing use small amounts
p. 57) .

(see

Cruising and water skiing consume large amounts

of space as the boats involved constantly change direction
and s p e e d .
Two procedures were used to obtain a value for the
consumption of water surface by boa t i n g activities.
value was named "the space consumption coefficient."

This
In

order to distinguish the coefficients produ c e d by the
first procedure from those produced b y the second, they
will be referred to as "the space consumption tracing
paper coefficient," abbreviated to SCTPC and "the space
consumption safety coefficient" abbreviated to S C S C .

^This program was developed by W. B. Allard,
Statistician, Applications Programming, Comp u t e r Center,
Michigan State University, East Lansing, Michigan.

59
T h e first: p r o c e d u r e u s e d t r a c i n g p a p e r to r e c o r d
the d i s t a n c e

f r o m b o a t s e n g a g e d in a s e l e c t e d s t a t i c

ac t i v i t y to the c l o s e s t b o a t s i n v o l v e d in any activity.
F i g u r e 14 i l l u s t r a t e s

the t r a c i n g p a p e r t e c h n i q u e for

determining boat consumption by stationary and moving
a c t i v i t y on m a p s

(by fl i g h t and lake)

photo interpretation.
ties

(fishing,

t h a t w e r e u s e d in

For interpreting stationary activi­

swimming,

a n d s a i l i n g ) , the p r o c e d u r e w a s

to p l a c e a p i e c e of t r a c i n g p a p e r on top of the b o a t c o n ­
cerned a n d the p o s i t i o n s of the three c l o s e s t b o a t s w e r e
m a r k e d o n the t r a c i n g p a p e r .

T h i s w a s m o v e d to a n o t h e r

boat i n v o l v e d in the same a c t i v i t y a n d the p o s i t i o n s of
the three c l o s e s t b o a t s w e r e s i m i l a r l y recorded.
pr o c e d u r e w a s

r e p e a t e d for all b o a t s a c c o r d i n g to a c t i vity.

The space c o n s u m p t i o n
water skiing)

The

for m o v i n g a c t i v i t i e s

(cruising a n d

w a s r e c o r d e d in a d i f f e r e n t manner.

The

center of a p i e c e of t r a c i n g p a p e r w a s p l a c e d o n top of
the b o a t trail.

T h e t r a c i n g p a p e r w a s m o v e d a l o n g the

b o a t trail and e v e r y b o a t p e r p e n d i c u l a r
1000

feet away)

to the trail was

The d i s t a n c e

(not m o r e t h a n

recorded.

f r o m e a c h m a r k on the t r a c i n g p a p e r

for every f l i g h t a n d lake on two s e l e c t e d days'*' was m e a ­
sured f r o m the center,

c o n v e r t e d to feet;

the m e a n d i s t a n c e s

i
A u g u s t 24 a n d 30 w e r e s e l e c t e d to test this p r o ­
cedure b e c a u s e the b o a t i n g p a t t e r n s w e r e m o r e c o m p l e x a n d
the n u m b e r of b o a t s u s i n g the lakes w a s g r e a t e r t h a n o n
any o t h e r day w h e n o b s e r v a t i o n s w e r e made.

60
were then derived.

Table 3 lists the mean distances b e ­

tween boats by activity

(in feet), each flight, for the

two d a y s .
The mean distance between boats for stationary
activities was used in the following formula in computing
acres consumed for each flight:

mean distance
between boats
by stationary
activity from
Table 3 (in feet)

1

43566

acres consumed,

The acres consumed by each activity varied according to
flight time and over the two d a y s .

The range of acres

computed for fishing was from 9.38 to 26.73 acres;

for

swimming from 11.53 to 26.21 acres; and sailing from 11.34
to 18.02 acres.

During the most congested hours of use

(observed to be 1300 to 1600 h o u r s ) , the number of acres
consumed by these activities was relatively constant.
average space consumed per activity was computed.

The

The

resultant average consumption of space for fishing was
5.25 acres; swimming 13.95 acres; and sailing 16.61 acres.
The mean distance between a moving boat and all
boats for each flight was used in the following formula
to compute acres consumed by moving activities:

61
TABLE 3
M E A N DISTANCE (FEET) BETWEEN BOATS BY A C T I V I T Y
(TRACING P A P E R TECHNIQUE)
F light
(hours)

Fishing

Swimming

Sailing

Cruising

Water
Skiing

A u g u s t 2 4 f 1969
390

600

360

430

440

390

440

420

450

390

430

510

600

410

500

500

530

0800

630

610

1000

580

440

1200

400

1300

300
_ a

1400
1500

-

410

480

490

450

1600

220

520

520

390

470

1900

300

500

490

570

520

A u g u s t 30, 1969
0900

610

520

540

500

450

1200

430

460

460

440

430

1300

490

400

360

320

360

1400

270

370

370

330

420

1500

-

390

350

360

370

1600

-

340

340

370

350

1700

-

520

340

320

360

320

350

430

360

1900

540
a

Blank spaces in this table indi c a t e that no
boats involved in the activity w e r e observed.

62
mean distance
between a moving
b o a t to all b o a t s —
from Table 3
(in feet)

x
H

x

l e n g t h of
boating trail
f r o m lake
m a p s (in
feet)

x

[«65o]

a c r e s consumed.
The range of the m e a n d i s t a n c e b e t w e e n a m o v i n g b o a t a n d
all boats u s e d for c o m p u t i n g acres c o n s u m e d b y c r u i s i n g
ranged from 640 to 1000
880 feet.

feet and for w a t e r s k i i n g 7 20 to

D u r i n g the h o u r s of 1300 to 1600 the total

number of acres c o n s u m e d b y c r u i s i n g a n d w a t e r s k i i n g w e r e
also o b s e r v e d to b e r e l a t i v e l y constant.
values for the h o u r s w e r e averaged.

The diameter

The diameter used

for c o m p u t i n g a c r e s c o n s u m e d b y c r u i s i n g w a s
for w a t e r skiing/

720 feet and

760 feet.

The space c o n s u m p t i o n t r a c i n g p a p e r c o e f f i c i e n t
procedure S C T P C - P

s u m m e d all b o a t s c o n s u m i n g w a t e r s u r f a c e

by a cti v i t y in a p a r t i c u l a r lake zone for e a c h f l i g h t a n d
divided this total b y the acres in the lake z o n e .

The

quotient was e x p r e s s e d as a p e r c e n t a n d is c a l l e d "the
space c o n s u m p t i o n t r a c i n g p a p e r c o e f f i c i e n t " SCTPC.

A

computer p r o g r a m w a s d e v e l o p e d to d e t e r m i n e the p e r c e n t
area consumed,

for e a c h flight,

b y all a c t i v i t i e s on all

lake z o n e s .^

1 W. B. A l l a r d , M i c h i g a n S t a t e U n i v e r s i t y ,
Center, d e s i g n e d this program.

Computer

63
The second procedure used to obtain a value for
the consumption of water surface by boats,

"the space c o n ­

sumption safety coefficient" SCSC, used the m i n i m u m legal
distance of 100 feet between anchored and traveling boats
prescribed by the State of M i c h i g a n Marine L a w Enforcement
Manual.^

The 100-foot distance was substituted in the

formulas on pages 60 and 62 for converting m e a n distances
between boats to acres consumed by stationary and moving
activities.

The acres consumed by fishing,

sailing were 0.72 acres.

swimming, and

The mean diameter distance used

for calculating cruising and water skiing was 1 00 feet.
The space consumption safety coefficient procedure
SCSC-P totaled the water surface consumed by activities in
a particular lake zone by flight and divided by the acres
in the lake zone.

The quotient was expressed in per cent

and called "the space consumption safety coefficient" SCSC.
A computer program was also developed to determine the
per cent area consumed for each flight by all activities
2
on all lake z o n e s .
Boating d i s p e r s i o n .— Boaters position themselves
about a water surface while p a r t i cipating in an activity.
The spatial relationship between boats varies w i t h the

^State of Mi ch i g a n Law E n f o r cement Manual (Lansing,
Michigan: Department of C o n s e r v a t i o n , Boat and Water
Safety Section, 1967).
2
W. B. Allard, Mich i g a n State University, Computer
Center, also designed this program.

64
number o£ boats and the type of activity.

Disper s i o n was

d e f i ned for p u r p o s e s of this p r o j e c t in terms of distances
b e t w e e n boats ab o u t a center of gra v i t y mean.

The f o llow­

ing formula w a s used:

D = iy/

I ^ [ ( x ± - 5c) 2 +

(y± - y ) 1 2

where
D

(dispersion) is the square root of the
average s q u a r e d distance,

x

is the ordinate measurement,

y

is the a b s c i s s a m e a s u r e m e n t . ^

and

This formula y i e l d e d a value for the dis t r i b u t i o n
of boats a b o u t the w a t e r surface w h i c h w i l l be termed "the
dispersion coefficient."

Two p r o c e d u r e s for calc u l a t i n g

this value w e r e developed.
T h e first procedure,

"the total disper s i o n c o e f ­

ficient procedure" T D C - P , r e c o r d e d all boats and their
trails for e v e r y 40— foot interval on the lake maps by X
and Y coo r d i n a t e s

for one day of h i g h usage

(July 17).

The d i s p e r s i o n c o e f f i c i e n t w h i c h r e s u l t e d from this p r o ­
cedure was c a l l e d the "total d i s p e r s i o n coefficient" T D C .

■'"This formula was o b t a i n e d from D. Gilliland,
Associate P r o f e s s o r of Statistics, D e p a r t m e n t of S t a ­
tistics and Probability, M i c h i g a n State University, E a s t
Lansing, Michigan.

65
Analysis of this procedure was found to be excessively
time-consuming, and therefore it was shortened.
The second procedure,

"the sample dispersion

coefficient procedure" S D C - P , modified the TDC-P to record
all boats and trails for every 400-foot interval on the
lake maps for the same date

(July 17).

The dispersion

coefficient which resulted from this procedure was called
"the sample dispersion coefficient" SDC.
The two procedures will be compared in Chapter V.
Four additional days

(August 21, 23, 24, and 31), which

were considered to have the highest use, were studied by
"the sample dispersion coefficient procedure" and will be
compared with "the space consumption coefficient procedure"
in Chapter V.
User Attitude
Public Access User
The perception of a boater about the use of a body
of water is influenced by numerous factors.

Some examples

of the conditions that might affect this mental state are
number of boats present, types of activity, conflicts of
use, space availability for activity,

the boater's p r e f e r ­

ence in recreational activities, and his regard for b o a t ­
ing safety.

The attitude of the boater is the result of

his perception of conditions of use.

The author was p r i ­

marily interested in obtaining responses of boat users
indicating if their attitudes toward boating conditions

66
were favorable or u n f a v o r a b l e over a given p e r i o d o f -time.
Data on attitude was deri v e d from the inter v i e w sch e d u l e
for e i t h e r response by day,
6 ), reason c r o w d e d

18), acti v i t y

lake, reason in area

(Question 18), time crowded,

(Question
(Question

(Question 12), acti v i t y experience

14), and socio-econo mic characteristics

(Question

(Questions 15-17).

User a t t i t u d e was inferred from the boater' s r e ­
sponse to Q u e s t i o n 13 in the interview.

The respon d e n t s

indicated w h e r e their activity took place by lake zones
and whet h e r or not hours of unfavorable or favorable levels
of b oa t i n g occurred.

A technique for recording favorable

and unfavorable responses was d e v i s e d for each lake by
zone and time

2
(that is, each f l i g h t ) .

The units in e a c h

element w e r e tot a l e d on the three lakes by flight a n d day
for each chart.

A comp u t e r p r o g r a m was devel o p e d to

calculate "a user attitude index" U A I .^

The p r o g r a m

summed the u n f a v orable responses by e l e m e n t and d i v i d e d
this total by the c o r r e s p o n d i n g elements for the total
responses

(unfavorable and favorable r e s p o n s e s ) .

expressed in per cent was obtained.

A value

The procedure u s e d to

^See i n t e r v i e w schedule in A p p e n d i x A 2 .
2

Figure 15 illustrates the technique for r e c o r d i n g
either favorable or unfavorable levels of boating.
3
P r o g r a m m e d by J. N. Teeter, Programmer, C o m p u t e r
Center, Mich i g a n State University, E a s t Lansing, Michigan.

67

Favorable

Unfavorable

Zone 0 8 0 0 1 0 0 0 1 2 0 0

1300

Date
Lake

1400

1500

1600

1700

1800

1

1

1

1

1900

2000

1
2
3
4
5
6

f

1

1

7
8
9

Figure 15.--Example of chart used to record
favorable and unfavorable responses.a

aThe chart was used for recording hourly time
units of favorable or unfavorable responses to levels of
boating.
An example is illustrated above.
The time units
from the list of unfavorable boating responses are recorded
in the elements.
The respondent stated an unfavorable
boating condition occurred in zone 6 between 1 2 0 0 to 1800
h ours. A mark is placed in each hour indicating the con­
dition corresponding to that area.
The procedure is re­
peated for the responses by lake, lake zones, and day.
Similarily the procedure is applied to another chart for
the favorable boating responses on the same lake, and day.

68
determine this value was ca l l e d "the user attitude index
procedure" U A I - P .
Riparian User
The attitude o f the riparian o w n e r toward lake
usage was i n v e s tigated on the last two weeke n d s of the
project

(August 23, 24,

30,

31, and September 1, 1969).

The q u e s t i o n n a i r e sent to riparian owners p r o v i d e d r e ­
sponses c o n c e r n i n g total lake conditions only.

The

respondents w e r e not asked to relate activities and atti
tudes to p a r t i c u l a r lake zones as were the public access
users.
The user attitude index procedure UAI-P was modi
fied for interpreting responses
Similarly,

to total lake conditions

the space c o n s u m p t i o n safety c o e f f i c i e n t p r o ­

cedure was adjusted for total lake usage.

The values

derived by b o t h procedures are compared by flights on
each lake in C h a p t e r V.

CHAPTER V
ANALYSIS

T he

a n a l y s i s was d i v i d e d i n t o -three s u c c e s s i v e

phases. The first p h a s e

c o n s i s t e d of e x a m i n i n g the r e ­

lationships a m o n g the v a r i o u s m e a s u r e s of level of b o a t i n g
activity intensity.

T h e s e c o n d p h a s e c o m p a r e d the a t t i ­

tudes c o n c e r n i n g b o a t i n g e x p e r i e n c e s w i t h the level of
boating in or der to h e l p d e v e l o p a m e t h o d for e v a l u a t i n g
boating c a r r y i n g c a p a c i t y w h i c h takes into a c c o u n t u s e r
attitude as w e l l as b o a t i n g activity.
correlated r e s p o n s e s

The third phase,

to e i t h e r u n f a v o r a b l e o r fav o r a b l e

boating c o n d i t i o n s w i t h s o c i o - e c o n o m i c data.
P h a s e I— M e a s u r e s of L e v e l of B o a t i n g
Activity Intensity
Least Squares D e l e t i o n
A nalysis
T he
measures of

o b j e c t i v e of P h a s e I was

to e x a m i n e v a r i o u s

the level of b o a t i n g a c t i v i t y for p o s s i b l e

relationships.

A le a s t squares s t e p w i s e d e l e t i o n a n a l y s i s

was used for this purpose.

A l l c o m p u t a t i o n s w e r e m a d e on

the CDC 3 600 and 6500 c o m p u t e r s

69

loc a t e d at the M i c h i g a n

70
State University Computer Laboratory.

The results of the

computer analysis were checked by comparison with prior
calculations on a desk calculator.
The least squares deletion procedure'*' is helpful
in estimating relationships between dependent and inde­
pendent variables.

In the first step, an initial least

squares equation is obtained by using all of the inde­
pendent variables.

One variable

(X^)

is then deleted from

the equation and another least squares equation calculated.
The procedure of deleting variables is repeated until a
particular significant probability
.05 per cent)

(for e x a m p l e , Sig. =

of the partial regression coefficient of

the variable being considered for deletion is obtained.

2

M. Rafter and W. L. Ruble, STAT. Series De ­
scription No. 8 (East Lansing, Mich.7 Agricultural
Experiment Station, Michigan State University, 1969) .
2

The deletion takes place on the basis that for
each partial regression coefficient (bj_) a Fb^ is c a l c u ­
lated and tested for significance.
The Fbi statistic
calculated at a given step may be used to test the null
hypothesis, H0 , that the independent variable
can
account for none of the variation in the dependent v a r i ­
able (above that accounted for by the remainder of the
independent variable and the overall mean of the dependent
variable) against the alternative. H i , that
can account
for variation in the dependent variable (above that a c ­
counted for by the remainder of the independent variables
and the overall mean of the dependent variables) . The
denominator of the Ffc,^ statistic (standard error of b^ =
Sfc.) is based on all of the independent variables p r e ­
sently in the least squares equation at that point.
It
does not include the effect of variables which may have
been dropped out of the equation during preceding steps.
For further information see Rafter and Ruble, S T A T .
Series No. 8 .

71
The p r o c e d u r e c o n t i n u e s to delete varia b l e s one at a time,
recalculating an e q u a t i o n each time a vari a b l e is deleted.
In each case,

the p a r t i a l r e g r e s s i o n c o e f f i c i e n t p r o vides

an estimate of the rate of change in the d e p e n d e n t variable,
associated w i t h one u n i t change in the i n d e p e n d e n t v a r i a b l e
T-values are d e r i v e d for each v a r i a b l e c o e f f i c i e n t by
dividing the c o e f f i c i e n t b y the stan d a r d error of the
coefficient w i t h n-1 deg r e e s of freedom.
t test is u s e d to t e s t the hypoth e s i s
regression coefficient:
H

o

:

for the par t i a l

that is

b = 0.

As the varia b l e s are deleted,
multiple c o r r e l a t i o n c o e f f i c i e n t
the regression
decreased

A two-ta i l e d

(about the mean)

1

the square of the

2

(R ) decre a s e s w h i l e

deg r e e s of freedom are

(while e r r o r degrees of fre e d o m increase)

and

the significance of the overall analy s i s of vari a n c e as
indicated by the F ratio is increased.
The Best Fit Cu r v e
T he o b j e c t i v e of Phase I was to examine wa y s of
measuring the b o a t i n g activity intensity.

Preliminary

plotting of e a c h i n d e p e n d e n t variable aga i n s t a d e p e n d e n t
variable s u g g e s t e d gen e r a l linear relationships.

^The square of the m u l t i p l e c o r r e l a t i o n co e f f i c i e n t
is obtained by d i v i d i n g the sums of squares of the d e v i ­
ations due to r e g r e s s i o n in the analysis of vari a n c e of the
least squares r e g r e s s i o n p r o b l e m by the total sums of
squares.

72
The 4th degree polynominal equation was written
for expressing variables on each procedure a s :

y = b0 +

+ b2xx2 + b3Xl3 + b ^ j 4

where:
y = estimate of the dependent variable
x = independent variable
b
°

= a constant term on the y axis intercept
found by the equations
b o = Y - (bjX-L + b 2x 2 ... b nSn )

where:
n = the number of independent variables,
b. = the least squares regression coefficient
1
corresponding to variable Xi found by the
equation:
k
n
k
n
b = E C..
£ x . + Y. +
£ C..
£ (x..
j-o 13 t - 1
3
3=1
13 t=l
for i = 1, 2,

_
- x.) (Y

_
- Y)

3

n

w h e r e:
C. .

is the element of the i^h row and the
column of the row sums of squares and cross
products matrix.

73
Procedures for Determining
Levels of Boating Activity
Intensity
Procedure 1 .— The first procedure was condu c t e d to
justify sampling the dispersion data.

Values obtai n e d by

the sample dispersion coefficient procedure
designated as the dependent variable)

(the SDC was

were compared w i t h

those obtained by the total dispersion coefficient
procedure

(TDC was designated as the independent variable)

for one day

(July 17) by hour, lake, and lake zone.

Procedure 2 .— The second procedure compared values
obtained by the space consumption safety coefficient p r o ­
cedure

(SCSC was designated as the dependent variable)

with

those derived by the space consumption tracing pape r t e c h ­
nique procedure
variable)

(SCTPC was designated as the independent

for similarities in order to determine the

method to be used for future computations.

Two days

(August 23 and 24) were used to compare the values p r o ­
duced by the two procedures by h o u r , l a k e , and lake z o n e .
Procedure 3 .— The third procedure investigated
the relationship between values derived by the space c o n ­
sumption safety coefficient procedure SCSC-P
as the dependent variable)
ficir-:t procedure SDC-P

(designated

and the sample dispersion coef-

(designated as the independent

variabj >) for the same flights.

The levels of boat i n g

74
a c t ivity w e r e c a l c u l a t e d in this m a n n e r b y zone,
and h o u r for two d a y s

(August 23 a n d 24).

P r o c e d u r e 4 .— In the f o u r t h p r o c e d u r e ,
values

(designated as the d e p e n d e n t variable)

by the S C T P C - P values
able)

lake,

the S C S C - P
were replaced

(designated as the i n d e p e n d e n t v a r i ­

and c o m p a r e d in a m a n n e r s i m i l a r to P r o c e d u r e

3 for

the same flights.
I l l u s t r a t i o n by the P l o t XY
C o m p u t e r Rou t i n e
The final least squ a r e s e q u a t i o n s

for P h a s e

I

procedures w e r e g r a p h i c a l l y i l l u s t r a t e d b y m e a n s o f the
plot XY c o m p u t e r r o u t i n e .^
series rou t i n e

P l o t XY is a s t a t i s t i c a l

for g e n e r a t i n g co d e s

f r o m the C D C
2
co m puter to d i r e c t a m e c h a n i c a l p l o t t e r .

3600

P h a s e I I — U s e r A t t i t u d e a n d L e v e l of
Boating Activity Intensity
Relationship
T he o b j e c t i v e of P h a s e II w a s

to e x a m i n e the

re l a tionships b e t w e e n u s e r a t t i t u d e s a n d m e a s u r e s of b o a t ­
ing activity.

T h e least s q u a r e s s t e p w i s e d e l e t i o n a n a l y s i s

was used for this purpose.

1P l o t XY w a s p r o g r a m m e d b y P. M. S c h w i s i n , S T A T .
Series D e s c r i p t i o n No. 16 P l o t XY (East L a n s i n g , M i c h .:
Agriculture Experiment S t a t i o n , Michigan State University,
1969) .
2T h e C a l c o m p m e c h a n i c a l x - y p l o t t e r is a m e c h a n i c a l
device w h i c h c o n s i s t s of a p e n m o u n t e d in an a r m t h a t
slides b a c k and f o r t h h o r i z o n t a l l y w h i l e drawing.
The
p l otter p a p e r is fed a r o u n d a d r u m w h i c h m o v e s b a c k a n d
forth v e r t i c a l l y w h i l e drawing.

75
Procedures for Comparing User
Attitudes with Levels of
Boating Activity
Intensity
Procedure 1 .— The first procedure made two com­
parisons between user attitudes and levels of boating.
First, the user attitude index procedure (UAI designated
as the dependent variable) was compared with the space
consumption safety coefficient procedure
as the independent variable)
24) by flight.

Second,

for two days

(SCSC designated
(August 23 and

the UAI values were compared with

a new procedure for assessing the level of boating.

The

new procedure, called "the intensity coefficient procedure"
IC-P, divided the SCSC by the SDC.^

Both comparisons were

made for all flights on each lake for August 23 and 24.
Procedure 2 .— The second procedure compared the
UAI values

(designated as the dependent variable) with the

SCSC-P values

(designated as the independent v a r i a b l e ) .

Each lake was analyzed for all observations and flight
intervals made during the summer.

This was an extension

of the first part of the analysis of Procedure 1.
Procedure 3 .— The third procedure investigated the
relationships of riparian owner attitudes to levels of

^The SCSC was in square feet and the SDC was in
feet. The SDC was squared to obtain a dimensionless
quotient.
The purpose of combining the two coefficients
was a final attempt to incorporate dispersion in the m e a ­
sure of boating activity.

76
boating.

The UAI values

(designated as the dependent

variable) were modi f i e d to represent the total lake usage
on two weekends.

The SCSC values

(designated as the inde­

pendent variable)

were also modified to evaluate levels of

boating for the entire lake.
Procedure 4 .— The fourth procedure compared the
number of acres per boat
variable)

(designated as the dependent

with the SCSC values

pendent v a r i a b l e ) .

(designated as the inde­

Data from the three lakes and all

flights and interviews made during the summer were a n a l y ­
zed in this manner.
Plot XY Comp u t e r Routine
The plot XY computer routine was again used to
illustrate the relationships in the procedures of Phase II.
Phase III— The Relation of User Attitudes to
Boating Conditions by Socio-economic
Characteristics
The objective of Phase III was to compare selected
socio-economic characteristics obtained from the interviews
at the public access sites of boaters who indicated u n ­
favorable conditions of use with those of boaters indicat­
ing favorable conditions at the same point in time and at
the same location.

The purpose of comparison was to d i s ­

cover if there is a significant relationship between socio­
economic characteristics and the attitude of boaters.

77
Examination of frequency distributions and chi-square
analysis were used to accomplish the objectives in Phase
III.
Frequency Distributions
The socio-economic variables analyzed were income,
education, and occupation.

Each variable was divided into

classes and frequency distributions were computed for the
three lakes at all observation p e r i o d s .
Chi-Square Test
The chi-square analysis is useful for examining
relationships between populations under similar circu m ­
stances.

It is used for determining whether actual d iffer­

ences are greater than could be expected on the basis of
chance variations.

The test was conducted between the two

types of responses for each socio-economic v a r i a b l e .

C H A P T E R VI
RESULTS

The complete data for the various measures of
level of boating activity intensity used in Phase I of
the analysis are presented in Appe n d i x C.
The Phase II data, presented in Appendix D are
the comparisons of attitude with the level of boati n g
activity intensity during July 4 through September 1.
The frequency distributions for responses to boating
conditions in Phase III are presented in Appendix E.
Phase I — Measures of Level of Boating
Activ i t y Intensity
The relationships between the various measures of
the intensity of boating activity were tested in Phase I
procedures by the least squares stepwise deletion routine.
The results are tabulated in Appe n d i x FI as shown in the
excerpt on the following page.

The entire tabulation of

this data and the remaining Phase I procedures are i n ­
cluded in Appendix F.
An analysis of variance was performed in each
procedure to determine the significance of the overall

78

APPENDIX FI

July 17

54

Union
|
|

0.2476

269.4374

0.0005

0

-0.0062

0.0000

0.998

3

1.2163

526.6913

<0.005

6

-0.0099

160.7748

<0.0005

•H
h

1

S i g n i ficance
(Sig.) Fb

P artial
Regres s i o n
Coefficients

.91

r

V ariables
Introduced

3

PS

Ho
S ignificance

<N

13 <W Q)
U 0 -P
id as
13 u g
C O-H
(0 w +>
+1 1-1 «
tflUH

F Test

Number
Step

Number of
Observations

0)
V
<0
Q

Lake

j

j

LEAST SQUARES DELETION ANALYSIS FOR SAMPLE DISPERSION COEFFICIENTS AND
TOTAL DISPERSION COEFFICIENTS FOR UNION, CASS, AND ORCHARD LAKES
(July 17, 1969)

80
reduction in sums of squares due to regression on deleting
equations.

Analysis of variance showed the final equations

as significant at the 5 per cent level
through F 8 ) .

(see Appendix FI

The partial regression coefficients, the

square of the multiple correlation coefficient,
error of estimate, F Test

standard

(performed on the overall analysis

of v a r iance), the F^

and the significance probability for
i
on every equation for all procedures in the analysis

are presented in Appendix Fl through F 8 .
gression coefficients

The partial re­

(b^) provide an estimate of the rate

of change of the dependent variable associated with one
unit change in each independent variable as listed in
Appendix Fl through F 8 .

The partial regression coef­

ficients cannot be ranked according to their values b e ­
cause they are not in standard units of measure.
the computed t-values

(t^

~ Fb .

However,

^ degree of freedom)

of the partial regression coefficients can be ranked b e ­
cause they represent the value of the partial regression
coefficient in terms of its standard error.

The ranking

of the partial regression coefficients is based on their
respective t-values.

The coefficients ranked in order of

their contribution to the regression are b
b

> b
>
i
i -1
The standard deviations of the partial

> b
.
i -2
x i-n
regression coefficients were found by the following
formula:

where:
S
C .3

is the standard error of estimate, and

t.h

is the element of the i
row and j
column
0 f the inverse of squares and cross products
matrix.

The standard error of estimate
the mean square for error)

{square root of

was computed for the overall

analysis of variance for each deleted equation.

The

standard error of estimate is in the same units of measure
as the original data.

Therefore, approximately 95 per cent

of the dependent variable in each procedure can be expected
to vary from the mean + units

(S^ ) of the original data.
i
The principal objective of Phase I was to examine

quantitative expressions of the intensity of boating a c t i v ­
ity and determine if relationships exist between these e x ­
pressions.

The least squares deletion routine was used for

each procedure in Phase I .

The various measures of the

level of boating activity intensity were compared for the
2
square of the multiple correlation coefficients (R ).
The
2
R value shows the percentage of the variability around
the mean of the dependent variable which was associated
with variation in the independent v a r i a b l e s .
that produce the highest R
procedures.

The variables

values were used in Phase I

82
P r o c e d u r e s for D e t e r m i n i n g the
Best M e t h o d of E x p r e s s i n g the
Intensity of B o a t i n g A c t i v i t y
P r o c e d u r e 1 .— T h e first p r o c e d u r e c o m p a r e d the
sample d i s p e r s i o n c o e f f i c i e n t SDC v a l u e s w i t h the total
d i s p e r s i o n c o e f f i c i e n t T D C v a l u e s on J u l y 17 for the three
lakes

(see A p p e n d i x F l ) .

had R 2 's of

.91,

.8 8 , and

Union, Cass,

.75 respectively.

ships b e t w e e n the two p r o c e d u r e s
sented in A p p e n d i x F2.

and O r c h a r d lakes
The relation­

for e a c h lake are p r e ­

The regression equation illus­

t r a ting the e f f e c t s of the s e l e c t e d i n d e p e n d e n t v a r i a b l e s
on SDC a r e :
U n i o n Lake,

Cass Lake,

Y = -0.0002 + 1.2163

Y = 0.0488 + 1.1263

O r c h a r d Lake,

(X3 ) - 0. 0 1 0 1

Y = 0.1828 + 1.4120

+ 0.0506

(X3 > - 0.0099

(X4 )

(X5 )

(X4 ) - 0.5204

(X5 )

(Xg ) m1

The h i g h c o r r e l a t i o n b e t w e e n the two c o e f f i c i e n t s

indi­

cated either p r o c e d u r e c o u l d be u s e d to d e s c r i b e d i s p e r s i o n .
The SDC-P was s e l e c t e d b e c a u s e it e n a b l e d the a u t h o r to
extend the e x a m i n a t i o n of the n u m b e r of b o a t i n g p o s i t i o n s
and to record fewer c o o r d i n a t e s .

‘'"Variables are:
T D C as (X3 ) , TDC squa r e d as
TDC cubed as (X^) , a n d T D C fourth d e g r e e as ( X g ) .

(X 4 ) ,

83
Procedure

2 .— T h e

second procedure

space c o n s u m p t i o n s a f e t y c o e f f i c i e n t s
consumption
lakes

SCSC

tracing paper coefficients

for A u g u s t

23 a n d

24

compared
and the

(see A p p e n d i x F3) .

three
2
T h e R *s

for Union,

Orchard lakes were

.84 r e s p e c t i v e l y .

relationships between

.79,

and

the two p r o c e d u r e s

presented in A p p e n d i x F 4 .

Cass,

for each

The regression equation

trating the e ffects of the s e l e c t e d

space

S C T P C on the

derived between the coefficients
.77,

the

and
The
lake are
illus­

independent variables

on S C S C a r e :
U n io n Lake,

Y = -0.0134

+

+ 0.0033
Cass Lake,

Y =

-0.0367

+ 0.0008
Orch a r d Lake,

+

0.2128

(X4 > - 0 . 0 3 5 6

<X1 2 )
0.2026

(X4 ) - 0 . 0 2 2 3

Y = 0.0156 + 0.1062

(X4 )

(X1 3 ) , 2

The h i g h c o r r e l a t i o n b e t w e e n t h e t w o c o e f f i c i e n t s

sumption.

could be used

The SCSC-P was

in P h a s e II.

selected

The procedure

allowed

indi­

to des c r i b e c o n ­

for

further analysis

for the easi e r data

conversion techniques p r e v i o u s l y d i s c u s s e d in C h a p t e r
2

(X^)

(X1 2 )

+ 0.0002

cated either p r o c e d u r e

(Xi;Lj

IV.

V a r i a b l e s are:
S C T P C a s (X 4 ) , S C T P C s q u a r e d a s
( X u ) , S C T P C c u b e d as (X1 2 ) , a n d S C T P C f o u r t h d e g r e e as (X^2 )

84
P r o c e d u r e 3 .— T h e t h i r d p r o c e d u r e m a d e two c o m ­
p a r i s o n s b e t w e e n c o n s u m p t i o n and d i s p e rsion.

First,

S C S C 1s a n d S D C 's w e r e c o m p a r e d for the three

lakes on

A u g u s t 23 a n d 24.

Second,

S C T P C *s and S D C 's w e r e com2
pared for the t h r e e lakes on the s a m e d a y s . The R 's

d e r i v e d f r o m b o t h of t h e s e c o m p a r i s o n s b y lake e x h i b i t e d
2
low v a l u e s (see A p p e n d i x F5 and F 7 ) . A l l R 's w e r e less
than

.35.

T h e o v e r a l l a n a l y s i s of v a r i a n c e on U n i o n a n d

Cass lakes p r o d u c e d s i g n i f i c a n t r e s u l t s

(thereby r e j e c t ­

ing the H q t h a t n o n e of the sums of s q u a r e d d e v i a t i o n s
from the m e a n of the d e p e n d e n t v a r i a b l e is a c c o u n t e d for
by the i n d e p e n d e n t v a r i a b l e ) .

Orchard Lake did not p r o ­

duce s i g n i f i c a n t r e s u l t s b e t w e e n the m e a s u r e s of the level
of b o a t i n g a c t i v i t y i n t e n s i t y

(thereby a c c e p t i n g the H q

that none o f the sums of s q u a r e d d e v i a t i o n f r o m the m e a n
of the d e p e n d e n t v a r i a b l e
pendent v a r i a b l e

is a c c o u n t e d for by the i n d e ­

for al l its e q u a t i o n s ) .

It s h o u l d be

noted t h at the p l o t s i n d i c a t e t h a t e v e n t h o u g h a s t r o n g
r e l a t i o n ship w a s n o t e x h i b i t e d in any case,

the i n d i v i d u a l

lakes t e n d e d to y i e l d the same type of c u r v e ac r o s s the
two days e x a m i n e d
sion e q u a t i o n s

(see A p p e n d i x F 6 and F 8 ) .

The regres­

i l l u s t r a t i n g the e f f e c t s of the sele c t e d

i ndependent v a r i a b l e s on S C T P C are:
U n i o n Lake, Y = 0.2456 + 0.7728

(X1 5 > - 0.2267

(Xl g )

85
Cass Lake,

Y = -0.0604

+ 32.0892

+ 7.8632
O r c h a r d Lake,

Y =

The regression equation

Cass Lake,

illustrating

Y =

(X1 6 ) .

the effects

of the

on SCSC a r e :

0.0379

+

Y = -0.0097

0.0957

(X1 5 ) - 0 . 0 2 7 1

+ 1.8695

+ 0.4349
Orchard Lake,

(X1 5 ) - 0 . 7 5 0 1

<X1 4 )

1.9575.

selected independent variables
U n i o n Lake,

(X5 ) - 2 7 . 2 3 8 5

(X5 ) - 1 . 5 0 9 3

<X1 5 ) - 0 . 0 4 1 9

(X1 6 )
(X1 4 )

(X1 6 >

Y = 0.2387.^

P h a s e I I — R e l a t i o n s h i p o f U s e r A t t i t u d e s to
the L e v e l of B o a t i n g A c t i v i t y I n t e n s i t y
The relationships
and v a r i o u s m e a s u r e s

of the

were tested in the P h a s e
stepwise de l e t io n
A p p e n d i x G3

between

II p r o c e d u r e s

routine.

The

second phase

user attitude
ing levels

included

the

are

on the

least squares

t a b u l a t e d in
following page.

data and the remaining Phase

in A p p e n d i x G.

of t h e a n a l y s i s

indices UAI w i t h

of b o a t i n g o n

by

results

as s h o w n i n t h e e x a m p l e

II p r o c e d u r e s a r e

index

intensity of b oating activity

The e n t i r e t a b u l a t i o n of t h i s

The

the u s e r a t t i t u d e

first compared

two procedures

two days.

Second,

^ V a r i a b l e s are:
S D C a s (X5 ) , S D C
SDC c u b e d as ( X ^ ) , a n d S D C f o u r t h d e g r e e

for d e s c r i b ­

user attitude

s q u a r e d as
as (X^g) .

(X^4 ) ,

APPENDIX G3

Partial
Regression
Coe f f i c i e n t s

0.1865

9.0537

0.004.

0

0.2226

■H
A
h

Significance
(Sig.) F.
i

Variables
In t r o d u c e d

.11

Si g n i ficance

4

Ho

72

F Test

Union

Standard
Error of
Estimate

|
Step

August
23

<D

*
(d

Number

1

OJ
oi

|
A

Number of
Observations

0)
■p
(0
Q

1

LEAST SQUARES DELETION ANALYSIS FOR USER ATTITUDE INDICES AND SPACE CONSUMPTION
SAFETY COEFFICIENTS FOR UNION, CASS, AND ORCHARD LAKES
(AUGUST 23 and 24, 1969)

48.9562

<0.0005

14

0.6211

9.0537

0.004

87
indices UAI a n d space c o n s u m p t i o n s a f e t y c o e f f i c i e n t s S C S C
were a n a l y z e d b y flights and lake for the e n t i r e s u m m e r
observations.

Third,

U A I 's for r i p a r i a n o w n e r a t t i t u d e s

w e r e c o m p a r e d to S C S C *s for the last two w e e k e n d s o f the
summer.

Finally,

the n u m b e r of acres per b o a t w e r e c o m ­

pared to S C S C 1s by flights and lake for the e n t i r e
observations.

summer

The procedures were evaluated both by means

of m a t h e m a t i c a l e q u a t i o n s and b y p l o t t i n g g r a p h s .

The

least s q uares d e l e t i o n rou t i n e and p l o t X Y r o u t i n e w e r e
used in e a c h procedure.
Procedures for C o m p a r i n g
At t i tudes w i t h Le v e l s of
ing A c t i v i t y I n t e n s i t y

User
Boat­

P r o c e d u r e 1 .— T h e first p r o c e d u r e e x a m i n e d two
comparisons b e t w e e n a t t i t u d e s and m e a s u r e s of level of
boating a c t i v i t y intensity.

T h e p r o c e d u r e u s e d the

squares d e l e t i o n r o u t i n e on the three lakes

least

for A u g u s t 23

and 24.
In the first case,

user a t t i t u d e i n d i c e s UAI w e r e
2
compared w i t h i n t e n s i t y c o e f f i c i e n t s I C . T h e R 's d e ­
rived and p l o t t e d indices and c o e f f i c i e n t s

for b e s t fit

curves on e a c h lake are p r e s e n t e d in A p p e n d i x Gl a n d

G2.

The r e g r e s s i o n e q u a t i o n s

the

i l l u s t r a t i n g the e f f e c t s o f

selected i n d e p e n d e n t v a r i a b l e s on UAI are:
U n i o n Lake,

Y = 0.1827 + 0.0209
+ 0.0001

<X1 4 ) - 0. 0 0 2 6

<X1 5 )

88
Cass Lake,

Y - 0.0895 + 0.0595
+ 0.0003

O r c h a r d Lake,

<X5 ) - 0 . 0 0 8 1

<X1 4 )

<X1 5 ) - 0 . 0 0 0 1

Y = 0.2083 + 0.0102

(Xg ) . 1

In t h e s e c o n d c a s e , U A I *s w e r e c o m p a r e d w i t h S C S C 1 s . T h e
2
R *s a n d b e s t f i t c u r v e s o n e a c h l a k e a r e p r e s e n t e d I n
A p p e n d i x G3 a n d G 4 .
the e f f e c t s

of t h e

The regression equation

Illustrating

selected Independent variables

on UAI

are:
Union Lake,
Cass Lake,

Y = 0.2189

Y - 0.1642 + 0.0936

O r c h a r d Lake,
The results
the s e c o n d c a s e

+ 0.5422

Y = 0.2180

of the

revealed

(X5 >

0.1826

first case

(Xg ) . 2

and the results

little difference.

on the Y X p l a n e b e t w e e n U A I

and the

the S C S C d e p a r t e d c o n s i d e r a b l y
Numerous points w e r e

+

(X5 )

The points

IC a n d b e t w e e n U A I

from the best

and

fit curve.

found at approximate coordinates

"'’V a r i a b l e s are:
IC as (X 5 ) , IC s q u a r e d as
IC c u b e d as ( X ^ ) , a n d IC f o u r t h d e g r e e as (X^g) .
2

of

of

(X 1 4 ) ,

V a r i a b l e s are:
S C S C as ( X c ) , S C S C s q u a r e d as
(X1 4 ) , S C S C c u b e d as ( X . c )t a n d S C S C f o u r t h d e g r e e as
<X 1 6 > •

89
5,100 and 100,5.^

E x a m i n a t i o n of the points c l u s t e r e d

about the 5,100 coordinates r e v e a l e d they w e r e compu t e d
2
from a small number of r e s p o n s e s .
The points c l u s t e r e d
about the 100,5 coordinates w e r e found to have b e e n de3
rived under similar circumstances.
U n i o n Lake e x h i b i t e d
2
the h i g h est R 's.
The points on the Y X p l a n e i n v o l v i n g
the UAI and the IC and i n v o l v i n g the UAI and SCSC followed
a general linear fit

(see A p p e n d i x G2 and G 4 ) .

A comp u t e r

program was dev i s e d to e l i m i n a t e poi n t s at the app r o x i m a t e
4
coordinates of 5,100 and 100,5.
Both p r o c e d u r e s , SCSC-P and I C - P , for d e s c r i b i n g
the level of boa t i n g act iv i t y i n t e n s i t y w h e n c o m p a r e d to
2
the UAI-P had similar R *s (see A p p e n d i x Gl and G 3 ) . The

The 5,100 coordinates i l l u s t r a t e hi g h e r user
attitude indices for low c o n s u m p t i o n values.
The 100,5
coordinates illustrate low user atti t u d e indices for h i g h
consumption v a l u e s .
2

For example, one b o a t e r i n d i c a t e d an un f a v o r a b l e
boating condition occu r r e d at 0800 hours in lake zone 3.
If the total number of responses to the lake zone for 08 00
was one, and had he been the only b o a t e r p r e s e n t d u r i n g
aerial photography, the UAI w o u l d be 100 for a low level
of boating.
3

For example, five boat e r s i n d i c a t e d u n f a v o r a b l e
boating conditions compared w i t h a total of s e v e n t y - f i v e
responses for 1600 hours in lake zone 3.
If the seventyfive boaters were photographed, the UAI w o u l d be .06 for
a high level of boating.
4

Pro g r a m by W. B. Allard, M i c h i g a n State U n i ­
versity, Comp u t e r Center.
A l l h o u r l y a t t i t u d e responses
of 5 or less (including 0) w e r e eliminated.

90
SC S C - P a l l o w e d e a r l i e r

interpretation of data and was

s e l e c t e d to r e p r e s e n t the m e a s u r e of t h e l e v e l o f b o a t i n g
activity intensity
Procedure

for f u r t h e r a n a l y s i s .
2 .— T h e s e c o n d p r o c e d u r e b r o u g h t t o g e t h e r

all d a t a to b e i n t e r p r e t e d b y t h e U A X - P a n d the SCSC - P .
C o m p a r i s o n s w e r e m a d e b e t w e e n U A I *s a n d S C S C 's b y th e l e a s t
squares d e l e t i o n r o u t i n e o n e a c h l a k e
The R
.35,

's d e r i v e d for U n i o n ,
.34,

and

Cass,

.21 r e s p e c t i v e l y .

(see A p p e n d i x G 5 ).

and O r c h a r d lakes were
Overall analysis of vari­

ance for t h e r e g r e s s i o n e q u a t i o n s p r o v i d e d
F - t e s t s a t the 5 p e r c e n t l e v e l

for e a c h

significant

lake.

The plot

XY r o u t i n e

i l l u s t r a t e d the r e s u l t s b y g r a p h i c a l l y p l o t t i n g

all data.

C u r v e s o f b e s t fit for the p l o t s w e r e d r a w n

for e a c h e q u a t i o n

(see A p p e n d i x G 6 , G 7 , a n d G 8 ) .

The regression equations

i l l u s t r a t i n g the e f f e c t s

of the s e l e c t e d i n d e p e n d e n t v a r i a b l e s on the UAI are:
Union Lake,

Y = 0.0306 + 3.5665
+ 3.3932

Cass Lake,

- 6.4558

(X1 4 )

(X1 5 )

Y = 0.0656 + 0.1745

O r c h a r d Lake,

(Xg)

(Xg)

Y = 0.0995 + 4.7952
+ 44.9732

- 0.0079

(X1 4 )

(Xg)- 2 3 . 1 9 7 2

(X1 5 ) - 3 2 . 7 1 8 1

(X1 4 )

(X ^ ) . 1

^ V a r i a b l e s are:
S C S C as (X 5 ) , S C S C s q u a r e d as
(X1 4 ) , S C S C c u b e d as (X-^g) , a n d S C S C f o u r t h d e g r e e as (X^g) .

91
The R 2,s

of

.35,

.34,

and

.21 s h o w t h a t a b o u t

21 p e r c e n t o f t h e v a r i a b i l i t y
with variation
and O r c h a r d

the S C S C m e a n s

in the UAI w a s

in t h e i n d e p e n d e n t v a r i a b l e s

lakes

respectively.

Table

and range of values

variable on Union,

Cass,

35,

TABLE

on Union,

4 lists

lakes.

and

associated

encountered

and Orchard

34,

Cass,

the UAI

and

for each

The

standard

4

RANGE A N D ME A N VALUES F O R U S E R A T T I T U D E INDEX, SPACE
CONSUMPTION SAFETY COEFFICIENT, AND ACRES PER
BOA T F O R UNION, CASS, A N D O R C H A R D LAK E S
(JULY 4 T H R O U G H S E P T E M B E R 1, 1969)
Maximum
Value

Variable

Lake

Union

Cass

Orchard

UAI
SCSC
Ac res/Boat

0 .000
0 .008

UAI
SCSC
Acres/Boat

0 .000
0 .002

0.801

1.355
298 .490

UAI
SCSC
Acres/Boat

0 .0 0 0
0.005
3.166

0.723
141.320

1.820

error of e s t i m a t e s w e r e
0.1913

c o m p u t e d as

(see A p p e n d i x G 5 ) .

is in u n i t s
Therefore,

of m e a s u r e

The

approximately

Mean
Value

0 .294
0.248
13.457

1.000

1.129
81.470

0.287
0 .253
18.636

1.000

0 .136
0 .147
18.049

1.000

0.2652,

0.2548,

and

standard error of estimate

identical

to t h e o r i g i n a l d a t a .

9 5 per cent of

Lake c a n be e x p e c t e d to v a r y +
.29.

Minimum
Value

.26 u n i t s

Similarily Cass Lake would vary +

the UAI

on Union

from the m e a n of
.25 u n i t s

from the

92
m e a n of

.28 and O r c h a r d L a k e w o u l d v a r y ±

the m e a n of

.19 u n i t s f r o m

.13.

P r o c e d u r e 3 .— T h e third p r o c e d u r e c o m p a r e d the
r i p arian owners'
(SCSC)

attitudes

(UAI)

to t h e level of b o a t i n g

for two w e e k e n d s on e a c h lake.

for Union,

Cass,

respectively.

The derived R

and O r c h a r d lakes w e r e

.49,

2

's

.47, a n d

.10

T h e o v e r a l l a n a l y s i s of v a r i a n c e for the

r e g r e s s i o n e q u a t i o n s was s i g n i f i c a n t at the 5 per c e n t
level

(see A p p e n d i x G 9 ) .

The regression equations

illus­

t r a ting the e f f e c t s of the s e l e c t e d i n d e p e n d e n t v a r i a b l e s
on UAI for r i p a r i a n o w n e r s are:
U n i o n Lake,

Y = 7.8603 + 130.4458
- 189.0972

C a s s Lake,

(X5 )

Y = 6.3436 + 323.9609
- 44 7.8 4 6 1

O r c h a r d Lake,

(X4 )

(X5 )

(Xg)

Y = 2.4128 + 112.8 6 8 2

(Xg ) . 1

Each lake was p l o t t e d for the b e s t fit curve f r o m the
equations

(see A p p e n d i x G 1 0 ) .

V a r i a b l e s are:
SCSC as (X3 ) , S C S C s q u a r e d as
SCSC c ubed as ( X g ) , and SCSC fo u r t h d e g r e e as ( X g ) .

(X4 ) ,

I

93
Procedure

4 .— T h e

f o u r t h p r o c e d u r e c o m p a r e d the

n u m b e r of a c r e s p e r b o a t w i t h S C S C ' s o n a l l o b s e r v a t i o n
data for t h e t h r e e
squares e q u a t i o n s
and

lakes

(see A p p e n d i x G i l ) . T h e l e a s t
2
for e a c h l a k e p r o d u c e d R *s o f .72, .65,

.79 for Union, C a s s ,

The o v e r a l l a n a l y s i s

and O r chard Lakes

of v a r i a n c e

s i g n i f i c a n t at the 5 p e r c e n t
for e a c h lake w e r e p l o t t e d .
e q u a t i o n s are i l l u s t r a t e d

respectively.

for the e q u a t i o n s w a s

level.
The best

The relationships
fit curves

in A p p e n d i x G 1 2 , G13,

The regression equations

from the
and G 1 4 .

i l l u s t r a t i n g the e f f e c t s

of the s e l e c t e d i n d e p e n d e n t v a r i a b l e s o n t h e n u m b e r of
acres p e r b o a t a r e :
U n i o n Lake,

C a s s La ke,

Y = 4.7387 + 64.3988
- 296.4646

(X? ) + 4 2 4 . 9 1 2 9

- 192.4412

(X9 ) + 0 . 6 3 9 3

Y = 27.5915
+

(X3 )

- 102.4274

136.8646

+ 0.5937

(X1 Q )

(X3 )

(X? ) - 5 8 . 3 1 0 0

(X1 Q )

(Xg )

(Xg)

94
O r c h a r d Lake,

The R

2

's of

.72,

Y = 2.6954 + 101.1552

(Xg )

+ 616.5863

<X7 ) + 1306.9504

- 905.1159

(Xg ) + 0.6923

.65, and

(X0 )

(X^ ) . 1

.79 show that about 72, 65, and

79 per c e n t of the v a r i a b i l i t y in the number of acres per
boat was a s s o c i a t e d w i t h v a r i a t i o n in the independent v a r i ­
ables on Union, Cass,

and Orc h a r d lakes respectively.

Table 4 lists the number of acres per b o a t and the safety
consumption means and range of means en c o u n t e r e d for each
variable on Union, Cass,

and O r c h a r d lakes.

error of e s t i mates were computed as 6.640,
8.5561

(see A p p e n d i x G i l ) .

T h e standard
16.0940,

and

A p p r o x i m a t e l y 95 per cent of

the number of acres per boat on U n i o n Lake can be e x p e c t e d
to vary + 6.64 units from the m e a n of 13.45.

S i m i lari l y

Cass Lake w o u l d e x p e c t to vary +

16.09 units from the

of 18.63,

v a r y + 8.55 units

and O r c h a r d Lake w o u l d

mean

from

the mean of 18.04.
Phase I I I — The Rela t i o n of User A t t i t u d e s
to B o a t i n g Co n d i t i o n s by S o c i o -economic
Charac t e r i s t i c s
The third p h a s e of the analysis compared the s o c i o ­
economic c h a r a c t e r i s t i c s of boaters indicating un f a v o r a b l e

^Variables are:
SCSC as (X3 ) , SCSC squared as
(X7) , SCSC cubed as (Xg ) , SCSC fourth degree as (X<j) , and
the SCSC inverse as (X^ q ) .

95
conditions w i t h those i n d i c a t i n g f a v o r a b l e c o n d i tions.
The r e s p o n s e s w e r e t a b u l a t e d in the f o r m of f r e q u e n c y
d i s t r i b u t i o n s and e v a l u a t e d by c h i - s q u a r e analysis.
Frequ e n c y D i s t r i b u t i o n s
A f r e q u e n c y a n a l y s i s was p e r f o r m e d on e a c h s o c i o ­
economic v a r i a b l e by r e s p o n s e to b o a t i n g c o n d i t i o n s on
Union, Cass,

and O r c h a r d lakes.

T h e a n a l y s i s is p r e s e n t e d

in A p p e n d i x El.
Chi-Square T e s t
A chi-square test was performed between responses
for income,

education,

and o c c u p a t i o n va r i a b l e s .

examined the v a r i a b l e c l a s s e s as a whole,

T h e test

n o t separately.

All c h i - square v a l u e s d e r i v e d b e t w e e n r e s p o n s e s w e r e f ound
significantly d i f f e r e n t at the 5 p e r c e n t level
A p p endix E2) .

(see

CHAPTER VII
SUMMARY AND DISCUSSION

This
of:

chapter will be devoted to the p r e s e n t a t i o n

(1 ) a s u m m a r y o f

study

between user attitudes
activity intensity,

and

and

findings

on the r e lationships

levels of recreational b o a t i n g

(2 ) v a r i o u s

implications

of

the

information and data collected.
The

s u m m a r y of r e s e a r c h

findings will be

1.

Levels

2.

User attitudes.

3.

T h e r e l a t i o n s h i p of user attitudes

in six

parts
of b o a t i n g a c t i v i t y

level of b o a t i n g a c t i v i t y
4.

The

intensity.

to t h e

intensity.

inverse r e lationship of the number

acres p e r b o a t to the

of

l e v e l of b o a t i n g a c t i v i t y

intensity•
5.

The development of a method

for d e t e r m i n i n g

recreational boating carrying capacity.
6.

The

comparison of attitudes

conditions

toward boating

by respondents w i t h different

socio-economic

characteristics.

96

97
Levels of B o a t i n g A c t i v i t y Inten s i t y
T h e Intensity of r e c r e a t i o n a l b o a t i n g acti v i t y on
a water surface over time is d e p e n d e n t u p o n the nu m b e r and
types of boats and the m i x t u r e of a c t i v i t i e s involved.

The

assessment of this dyn a m i c c o n d i t i o n of w a t e r use was d e ­
scribed in terms of space c o n s u m e d by b o a t i n g activi t i e s
and the d i s p e r s i o n of boats on the w a t e r surface.

Var i o u s

comparisons between the space c o n s u m e d and the d i s p e r s i o n
of the boats were made on the three lakes.

O n c e a simple

measure of the level of b o a t i n g a c t i v i t y i n t e n s i t y was
formulated,

the mea s u r e der i v e d c o u l d be c o m p a r e d m a t h e ­

matically for possible rela t i o n s h i p s w i t h user attitudes.
Consumption
The consumption of space by r e c r e a t i o n a l boa t i n g
is related to the type of activity,
time of day.

speed of boats,

and

I n t e rpretation of the aerial p h o t o g r a p h s

confirmed that in a given p e r i o d of t i m e , boats involved
in fishing,

swimming,

and sailing used r e l a t i v e l y small

areas whereas c r u i s i n g and w a t e r sk i i n g u s e d e x t e nsive
areas.

Figure 16 illustrates the v a r i a t i o n of total s u r ­

face water consumed by a c t i v i t y on Union,
Orchard lakes for A u g u s t 24,

Cass, and

1969.

The space con s u m p t i o n tra c i n g p a p e r c o e f f i c i e n t
procedure was used to investigate the spatial co n s u m p t i o n
of different boa t i n g activities.

The acreage c o n s u m e d by

the different activities w e r e found to v a r y over time on

M

10
Acr«» C«<

00

I

.Li

H
ato
^c*oo1Leap LicS' 'isolcT‘ ’litoc 11eoo i rio c I1
(ijib

tain

Tltt

Cau

Orck«H

Figure 16.— Variation of total surface water consumed by activity on Union,
Cass, and Orchard lakes during August 24, 1969.

99
each lake.

T h e areas c o m p u t e d by the space c o n s u m p t i o n

tracing p a p e r p r o c e d u r e SCTPC-P for all flights on A u g u s t
24 and 30 ranged f r o m 9.38 to 26.73 acres for fishing,
11.53 to 26.21 acres for swimming,
for sailing.

and 11.34 to 18.02 acres

The d i a m e t e r s used in c o m p u t i n g acres c o n ­

sumed for the m o v i n g a c t i v i t i e s r a n g e d from 640 to 1000
feet for c r u i s i n g and 720 to 880 feet for w a t e r skiing.
During the m o s t c o n g e s t e d hours of use

(generally o b ­

served to be 1300 to 1600 h o u r s ) , the range of acres c o n ­
sumed by the ac t i v i t i e s was r e l a t i v e l y consistent.

This

period was selec t e d for analysis and the average space
consumed per a c t i v i t y was computed.

T h e r e s u l t a n t space

consumption va l u e s for fishing were 5.25 acres;
13.95 acres;

and sailing,

for c o m p uting c r u i s i n g was

16.64 acres.

swimming,

The d i a m e t e r used

7 20 feet and for w a t e r skiing,

760 feet.
W h e n the a p p r o p r i a t e average acreage consumpti o n
value is a p p l i e d to the nu m b e r of boats in each activity,
the total area c o n s u m e d d u r i n g high use periods often
exceeds the lake a c r e a g e .

A t these t i m e s , the calcula t e d

areas for each b o a t o v e r l a p one another.

These over­

lapping areas are sha r e d by two or m o r e boaters.
The space c o n s u m p t i o n safety c o e f f i c i e n t p r o ­
cedure SCSC-P empl o y e d the minimal

legal distance of

100 feet b e t w e e n s t a t i o n a r y and m o v i n g boats.

F e w in­

stances were o b s e r v e d w h e n total acres consumed exceeded
the lake a c r e a g e .

100
T h e S C S C —P and S C T P C - P w e r e c o m p a r e d for s i m i l a r i ­
ties on e a c h lake zone by time and lake, and for t w o days.
A h i g h c o r r e l a t i o n e x i s t e d b e t w e e n the two a p p r o a c h e s
the t h r e e lakes

(see A p p e n d i x f3 and F 4 ) .

was u s e d to a s s e s s

for

Each approach

total c o n s u m p t i o n for all a c t i v i t i e s on

a w a t e r sur f a c e and p r o d u c e d s i m i l a r results.
was s e l e c t e d for e a s e of d a t a computation.

The SCSC-P

The a u t h o r

felt that the 10 0 - foot m i n i m a l d i s t a n c e b e t w e e n b o a t s
p o r t r a y e d a b e t t e r p h y s i c a l c o n s u m p t i o n of s u r f a c e w a t e r
space t h a n d i d the t r a c i n g p a p e r approach.
of maps

(interpreted f r o m the photographs)

The m a j o r i t y
showed that

boaters d i d in m o s t cases m a i n t a i n a 1 0 0 - f o o t or g r e a t e r
distance.

M o v i n g b o a t e r s w e r e o b s e r v e d to stay o u t s i d e

the 1 0 0 - f o o t m i n i m a l d i s t a n c e w h e n p a s s i n g s t a t i o n a r y a n d
other m o v i n g b o a t s .
D i s p e r s i on
T he d i s p e r s i o n of b o a t s a b o u t a w a t e r s u r f a c e is
d e p e n d e n t u p o n the type of activity.
of p h o t o g r a p h s

The interpretation

i n d i c a t e d s w i m m i n g and f i s h i n g w e r e st a t i c

and g e n e r a l l y o c c u r r e d n e a r s p e c i f i c p h y s i c a l f e a t u r e s o f
the lake.^

W a t e r skiing,

cruising,

and sailing were

found

d i s t r i b u ted w i t h c o n t i n u o u s l y c h a n g i n g p a t t e r n s t h r o u g h o u t
the lake

(see T a b l e

2).

^ S w i m m i n g f r o m b o a t s t o o k p l a c e near s h a l l o w a n d
sandy shoals, w h e r e a s fis h i n g w a s d o n e c l o s e to w e e d b e d s
and h o l e s .

101
Two methods were proposed
in b o a t i n g p o s i t i o n s .
the d i s t a n c e s
each lake

The

to investigate changes

first method w o ul d have measured

from a p r o j e c t e d line or p o i n t

zone)

to t h e b o a t s .

The mean distance would be

computed for each activity by hour and
the m e a s u r e

is r e l a t i v e

on t h a t o r i g i n ,

lake

zone.

a second method was proposed which depends

selected

the b o a t p o s i ­

The

second m ethod was

The

t o t a l d i s p e r s i o n c o e f f i c i e n t p r o c e d u r e T D C —P

r e c o r d e d d a t a in t e r m s o f

forty-foot

for

f u r t h e r use.

intervals.

preting and reco r d i n g the data was e x t r e m e l y
ing a n d

therefore the

The SDC

TDC m i n u s m o s t of t h e p o i n t s
that

n u m b e r s of b o a t s ,
effect upon
of b oats.
larities.

related

used

to c o m p u t e

fro m the b o a t i n g t r a i l s .

the d e l e t i o n of po i n t s w o u l d

lead to a l a r g e r c o m p u t e d d i s p e r s i o n .
w o u l d be c l o s e l y

time c o n s u m ­

is c o m p u t e d o n t h e

b a s i s of t h e s a m e b o a t i n g c o o r d i n a t e s

One w o u l d a n t i c i p a t e

Inter­

sample dispersion coefficient p r o ­

c e d u r e S D C —P w a s d e v i s e d .

Sample dispersion

to total dispersion.

For

large

the d e l e t i o n of p o i n t s w o u l d ha v e

the c o m p u t e d d i s p e r s i o n

less

than for small numbers

The SDC's

a n d T D C 1s w e r e c o m p a r e d for s i m i 2
T h e r e s u l t a n t R 's w e r e h i g h , i n d i c a t i n g t h a t

either proce d u r e
sion o f b o a t s
and F 2 ).

Since

to an arbitrary origin and depends

only u p o n the g e o m e t r i c c o n f i g u r a t i o n of
tions.

(placed in

could be used to represent the d i s p e r ­

about a water

surface

(see A p p e n d i x Fl

102
Consumption-Dispersion
R e l a t i o n ship
T h e c o n s u m p t i o n of w a t e r s p a c e and the d i s p e r s i o n
of boats a b o u t a w a t e r s u r f a c e w e r e i n v e s t i g a t e d for a
possible r e l a t i o n s h i p w h i c h w o u l d d e s c r i b e the level of
boating a c t i v i t y intensity.

T h e S C T P C —P and S C S C —P w e r e

compared w i t h the S D C - P on e a c h lake for two days.

Intui­

tively one w o u l d e x p e c t t h a t the r e l a t i o n s h i p b e t w e e n c o n ­
sumption and d i s p e r s i o n w o u l d s h o w t h a t as the c o n s u m p t i o n
of the w a t e r surface increa s e s ,
boaters decreases.

the d i s t a n c e b e t w e e n

T h e d i s p e r s i o n w o u l d d e c r e a s e to the

point w h e r e a c t i v i t y c o u l d n o l o n g e r take place.
2
The R 's d e r i v e d f r o m the c o m p a r i s o n of the S C S C
and the SCTPC w i t h the SDC w e r e u s e d in d e t e r m i n i n g the
significance of the r e l a t i o n s h i p b e t w e e n c o n s u m p t i o n and
dispersion.

The o v e r a l l a n a l y s i s of v a r i a n c e

for the two

comparisons on U n i o n and Cass

lakes w a s found s i g n i f i 2
cant at the 5 p e r c e n t l e v e l . T h e R 's w e r e r e l a t i v e l y
low (less than

.34) w i t h the m a j o r i t y at

Orchard Lake e x h i b i t e d n o r e l a t i o n s h i p
and F7) .

T h e final r e g r e s s i o n e q u a t i o n

.18 o r less.

(see A p p e n d i x F5
for e a c h lake

relationship was p l o t t e d and is p r e s e n t e d in A p p e n d i x F 6
and F 8 .
The points on the YX p l a n e of the r e l a t i o n s h i p
between SCSC and SDC a n d b e t w e e n S C T P C and SDC i n c r e a s e d
at an i n c r e a s i n g rate for low c o n s u m p t i o n and d i s p e r s i o n
coefficients on U n i o n a n d C a s s

lakes.

A s the two

103
coefficients
points

for c o n s u m p t i o n a n d d i s p e r s i o n

points w e r e

2

for extreme values.

Th e m a j o r i t y of

scattered and held no continuity

lationship.

values.
observed

positions on a water
photograph per hour

surface

to b e c o n s t a n t l y
o v e r time.

increase

2).

estimate

But additional

the cost of obt a i n i n g

would not provide

single aerial

Additional

per hour c o u l d have p r o v i d e d a b e tter
(see T a b l e

A

changing

does not accurately present moving

activities by dispersion analysis.

persion

for a r e ­

Orchard Lake portrayed a constant term and

Boats were

would

the

I n c r e a s e d at a d e c r e a s i n g rate a n d then d e c r e a s e d at

a decreasing rate

zero R

Increased,

flights
of d i s ­

aerial photography

i n f o r m a t i o n and

an e a s y m e t h o d of a s s e s s i n g the

level

of b o a t i n g .
In c o n t r a s t w i t h
water surface,
assessing the

the d i s p e r s i o n of boats

the SCSC-P provides
level

of boating.

an e a si e r m e t h o d

The

examination of

boating activities,

by

hour,

the n u m b e r of b o a t s

revealed that

surface does
S D C —P

the SCSC-P

not drastically

(see T a b l e

2).

activity on the three

on a

continuously

change as

for
the

for one

using the water
indicated by

the

The consumption of space by each
lakes m a i n t a i n e d r e l a t i v e l y the

same val u e o v e r one h o u r .
The
used for

SCSC

for de s c r i b i n g the

l e v e l of b o a t i n g w a s

further comparisons with the user attitude

procedure.

index

104
User Attitude
Boaters p a r t i c i p a t i n g in an activity p e r c e i v e
varying condit i o n s of use on a w a t e r surface o v e r time.
The user's attitude toward v a r y i n g levels of use was i n d i ­
cated by hours of favorable or u n f a v orable use indicated
during interviewing.

The user's attitude was q u a n t i f i e d

in percentage t e r m s .

The number of un f a v o r a b l e responses

was d i v i ded by the total number of responses
and favorable)

for each lake zone,

(unfavorable

lake, hour, and day.

The user attitude index procedure was used to
demonstrate that, as the level of use intensified,

the

ratio of the number of u n f a v orable responses to all r e ­
sponses r e p o r t e d du r i n g i n t e r v i e w i n g likewise increased.
As expected,

as use increased,

the unfavorable responses

increased and came to ex c e e d the favorable r e s p o n s e s .

The

resultant user attitude index U A I , increased from a low
index to a m a x i m u m possible index of 1 0 0 .
Public A c c e s s Boater
Several problems arise in q u a n t i f y i n g the UAI for
hour intervals.

First of all,

lake zones bec o m e equal l y

weighted w h e n interpreted by a per cent scale.
stance, a UAI of

For i n ­

.75 der i v e d from 100 total o b s e r vatio n s

in a p a r ticular lake zone is not e q u i v a l e n t to a UAI of
.75 derived from twenty-five total observations in another
lake zone.

This p r o b l e m is e v i d e n t w h e n boa t e r s

105
inaccurately identify where participation took place or
w h e n c e r t a i n lake zones r e c e i v e d m o r e use t h a n o t h e r zones.
A n o t h e r p r o b l e m is a l s o p r e s e n t w h e n a few r e ­
sponses

for e a r l y h o u r use o c c u r o u t of a low total n u m b e r

of r e s p o n s e s t h a t i n d i c a t e u n f a v o r a b l e b o a t i n g c o n d i t i o n s .
The r e s u l t is a h i g h U A I .1
d e v i a t i o n of o b s e r v a t i o n s

T h e p r o b l e m r e v o l v e s a r o u n d the
(high U A I — low SCSC)

e s t i m a t e d v a l u e s of the d e p e n d e n t v a r i a b l e
values of the i n d e p e n d e n t variable.
duces a large s u m o f squares
analysis.

a b o u t the

for e a c h o f the

The s i t u a t i o n p r o ­

for e r r o r in r e g r e s s i o n

A low sq u a r e of the m u l t i p l e c o r r e l a t i o n c o e f ­

ficient results.
Similarily,
few r e s p o n s e s

the same p r o b l e m is p r o d u c e d w h e n a

for p e a k p e r i o d s of use o u t of a large

number of to t a l r e s p o n s e s
conditions.

indicate unfavorable boating

T h e r e s u l t is a low UAI.

Ripar i a n O w n e r B o a t e r
The r i p a r i a n o w n e r p a r t i c i p a t i n g in a b o a t i n g
activity a l s o p e r c e i v e s a c o n d i t i o n of use o n a w a t e r
surface.

T h e a t t i t u d e r e s u l t i n g from v a r i o u s

use was s i m i l a r l y e x p r e s s e d as a UAI.

levels of

I n t e r p r e t a t i o n of

this UAI e n c o u n t e r e d the same p r o b l e m s as d i s c u s s e d w i t h
the p u b l ic a c c e s s boater.

R i p a r i a n r e s p o n s e s to u n f a v o r ­

able c o n d i t i o n s on the l a s t two w e e k e n d s of the s u m m e r
^ h e s i t u a t i o n o c c u r r e d in the e a r l y m o r n i n g w h e n
fishermen r e p o r t e d u n f a v o r a b l e c o n d i t i o n s c r e a t e d b y w a t e r
skiers.

106
p r o d u c e d h i g h U A I *s
conjecture

(see A p p e n d i x 6 9 a n d G l O ) .

that riparian owners

to b o a t i n g c o n d i t i o n s
rights

s e e m to b e m o r e

and believe

to t h e w a t e r b o d y

One

can

sensitive

they have more vested

than public

access boaters.

R e l a t i o n s h i p o f U s e r A t t i t u d e s to t h e L e v e l
of B o a t i n g A c t i v i t y I n t e n s i t y
The

first hypoth e s i s

tested

in this

study was

that

a relationship exists between user

attitude

and the

of b o a t i n g a c t i v i t y

that

level of d i s ­

intensity,

and

satisfaction increases w i t h the

level

establishment of the relati o n s h i p was
steps

in d e v e l o p i n g a m e t h o d

of

boating carrying capac i t y on
waters.

The

least

squares

the

of b o a t i n g .

The

the

two

assessing

first of

recreational

intensively used

deletion

level

surface

routine was

u s e d to

t e s t the h y p o t h e s i s .
Public Access
The user attitude

index and

level o f b o a t i n g a c t i v i t y

responses

access

sites.

describing the

level of b o a t i n g

and IC-P)

separately

were

possible

relationships

IC-p w a s

the

final a t t e m p t

of use

Two procedures

activity

lake

used

to c o n d i t i o n s

compared with

on each

s u m p t i o n as a m e a s u r e o f

of the

intensity procedures were

to i n v e s t i g a t e t h e b o a t e r ' s
o b t a i n e d a t the p u b l i c

two m e a s u r e s

intensity
the U A I-P

for t w o d a y s .

for

(SCSC-P
for
The

to c o m b i n e d i s p e r s i o n and c o n ­

the

level of b o a t i n g activity

107
intensity.

T h e IC-P d e f i n e s the r e l a t i o n s h i p t h a t as the

c o n s u m p t i o n of w a t e r sur f a c e i n c r e a s e s f the d i s p e r s i o n
d e c r e a s e s a n d the q u o t i e n t i n c r e a s e s .
T h e c o m p a r i s o n b e t w e e n U A I 1s s e p a r a t e l y w i t h two
c o e f f i c i e n t s of levels of b o a t i n g w a s t h o u g h t to s h o w t h a t
as the l evel o f b o a t i n g a c t i v i t y i n t e n s i t y increased,

a

c o r r e s p o n d i n g i n c r e a s e in the n u m b e r of u n f a v o r a b l e r e ­
sponses w o u l d occur.

T h e sq u a r e of the m u l t i p l e c o r r e ­

lation c o e f f i c i e n t u s e d to m e a s u r e h o w m u c h v a r i a t i o n in
the d e p e n d e n t v a r i a b l e

(UAI)

above the v a r i a t i o n w h i c h

m a y be a c c o u n t e d for by its mean,
by a d e p e n d e n t v a r i a b l e
for Union,

Cass,

can be a c c o u n t e d for
2
(SCSC or I C ) . T h e R 's d e r i v e d

and O r c h a r d lakes w e r e

f r e q u e n t l y found

n o n - s i g n i f i c a n t w i t h the o v e r a l l a n a l y s i s of v a r i a n c e at
2
the 5 p e r c e n t level.
T h e R 's w e r e low (less than .34)
in all c a s e s w i t h a m a j o r i t y as c o n s t a n t terms.
g r e ssion e q u a t i o n s

for e a c h lake w e r e p l o t t e d and is p r e ­

sented in A p p e n d i x G2 a nd G4.
SCSC a n d UAI-IC)

The re­

T h e two c o m p a r i s o n s

(UAI-

for U n i o n L a k e on A u g u s t 24 i n d i c a t e d a

tendency for the b o a t i n g level to i n c r e a s e as the n u m b e r
of u n f a v o r a b l e r e s p o n s e s
two c o m p a r i s o n s
points

increased.

T h e p o i n t s on the

f o l l o w e d a g e n e r a l l i n e a r curve.

(as d i s c u s s e d in C h a p t e r VI, Phase,

were n o t pres e n t .

Extreme

I, P r o c e d u r e

1)

A c o m p u t e r p r o g r a m was u s e d to d r o p

high U A I - l o w SCS a n d low U A I - h i g h S C S C in future analysis.

108
T h e first: c o m p a r i s o n
comparison

(UAI a n d IC)

Appendix Gl and G 3 ) .

(UAI a n d SCSC)

showed similar R

The author

2

and the second

values

(see

judged that either

SCSC or t h e IC w h e n c o m p a r e d w i t h t h e U A I m e a s u r e s
level of b o a t i n g .

The SCSC was

the
the

s e l e c t e d b e c a u s e it r e ­

quired fewer arithmetical c o m p u t a t i o n s .
T h e U A I —P a n d t h e S C S C - P w e r e u s e d to t e s t the
first h y p o t h e s i s o n U n i o n ,
observation p e r i o d s .

1

Cass,

The R

2

and Or c h a r d lakes

was

for all

u s e d to d e t e r m i n e

the

s i g n i f i c a n c e of the r e l a t i o n s h i p a t t h e 5 p e r c e n t l e v e l
2
(see A p p e n d i x G 5 ) . T h e R
d e r i v e d for U n i o n , C a s s , a n d
O r c h a r d lakes w e r e

.35,

.34,

and

.21 r e s p e c t i v e l y .

The

e q u a t i o n for e a c h l a k e r e l a t i o n s h i p w a s p l o t t e d a n d is
p r e s e n t e d in A p p e n d i x G 6 , G 7 , a n d G 8 .
P o i n t s o n the Y X p l a n e b e t w e e n the UAI a n d the
SCSC s h o w e d an i n c r e a s e a t a n i n c r e a s i n g r a t e
and S C S C for the t h r e e
at a d e c r e a s i n g r a t e
O r c h a r d lakes.
i n c r e a s i n g rate.

The points

then increased

for h i g h e r U A I a n d S C S C o n U n i o n a n d

Cass L a k e had p o i n t s d e c r e a s i n g at an
The points

all lake r e l a t i o n s h i p s .
UAI on the t h r e e

lakes.

for l o w U A I

fit t h e

line fairly wel l

for

T h e m a j o r i t y of v a l u e s o f the

lakes ranged from

.10 to

.35.

The

low

indices m a y h a v e b e e n the r e s u l t o f o n e o r m o r e o f t h e
f ollowing s i t u a t i o n s :

son

(1 ) b o a t e r s w e r e r e l u c t a n t to

1E x t r e m e U A I *s a n d S C S C 's p r o d u c e d i n t h e c o m p a r i ­
( p reviously d i s c u s s e d ) w e r e e l i m i n a t e d .

109
answer or did not: u n d e r s t a n d questions p e r t a i n i n g to user
attitudes,

(2 ) boaters from the m e t r o p o l i t a n area are u s e d

to i n t e n sively u s e d lakes, and

(3) data m a y be m i s r e p r e ­

sented by the UAI-P as pr e v i o u s l y discussed.
Riparian Owner
The U A I - P and SCSC-P were used to investigate
relationships b e t w e e n riparian owner attitudes a n d b o a t i n g
conditions.

The procedures were modi f i e d for analyses

of total lake conditions

(responses w e r e not comp a r e d

by lake z o n e s ) .
2
The R
d e r i v e d by the least squares d e l e t i o n r o u ­
tine w e r e used to test the significance of the r e l a t i o n ­
ships.

Union, Cass,

and Orchard lakes w e r e found signifi2
cant at the 5 per cent level.
The R 's for Union and C a s s
2
lakes were .49 and .46.
The R
for Orch a r d Lake was a .09.
The equations for each lake relationship were p l o t t e d and
are p r e s e n t e d in A p p e n d i x G9 and G 1 0 .
Points on the YX plane b e t w e e n the UAI and SCSC
for Union and Cass lakes indicated that as the c o n s u m p t i o n
of water space increased,

the number of un f a v o r a b l e r e ­

sponses increased.

Orc h a r d Lake exhibited a p o o r fit to
2
the regression curve.
The low R was attributed to a
large number of points c l u s t e r e d at low UAI and h i g h SCSC
coordinates.

E x a m i n a t i o n of the questionnaires r e v e a l e d

that a very small p r o p o r t i o n of respondents indicated u n ­
favorable b o a t i n g conditions

for high use p e r i o d s .

110
T h e p u r p o s e of c o m p a r i n g r i p a r i a n o w n e r a t t i t u d e s
w i t h b o a t i n g c o n d i t i o n s w a s to d e t e r m i n e if any d e f i n i t e
re l a t i o n s h i p s existed.

A h i g h n u m b e r of r e s p o n s e s i n d i ­

cating u n f a v o r a b l e b o a t i n g c o n d i t i o n s r e l a t i v e to tot a l
responses w a s disclosed .

T h e m a j o r i t y of the UAI d e r i v e d

from r i p a r i a n owners w e r e h i g h e r than the UAI d e r i v e d f r o m
the p u b l i c ac c e s s users.
Inverse R e l a t i o n s h i p of the N u m b e r o f A c r e s
P e r B o a t to the L e v e l of B o a t i n g
Activity Intensity
T h e se c o n d h y p o t h e s i s t e s t e d in this s t u d y wa s
that an inv e r s e r e l a t i o n s h i p e x i s t e d b e t w e e n the s p a c e
consumed by b o a t e r s and the level of b o a t i n g a c t i v i t y
intensity.

T h e d e t e r m i n a t i o n of the e x a c t n a t u r e of this

relat i o nship is the final s t e p in p r o v i d i n g a m e t h o d of
evalua t ing r e c r e a t i o n a l b o a t i n g c a r r y i n g capacity.

The

least s quares d e l e t i o n r o u t i n e w a s u s e d to t e s t the
hypothesis.
Number of A c r e s Per B o a t
The n u m b e r of a c r e s of s u r f a c e w a t e r in e a c h lake
zone was d i v i d e d by the n u m b e r of b o a t s
every f l i g h t interval.
acres p e r boat.

in the zone for

The q u o t i e n t is the n u m b e r of

T h e m e t h o d w a s e m p l o y e d to give s u r f a c e

waters a n u m e r i c a l a c c o u n t i n g of boat i n g .

T h e n u m b e r of

acres p e r b o a t and the SCSC w e r e u s e d to s h o w t h a t as the
area used for b o a t i n g a c t i v i t y d e c r e a s e d ,
boating increased.

the level of

Ill
T h e m e t h o d of o b t a i n i n g n u m b e r o f a c r e s p e r b o a t
and the S C S C - P u s e d a l l o b s e r v a t i o n d a t a
and O r c h a r d

for U n i o n ,

Cass,

lakes in d e t e r m i n i n g the s i g n i f i c a n c e o f t h e

relationships.

The derived R

2

's for t h e t h r e e

lakes w e r e

found s i g n i f i c a n t b y t h e o v e r a l l a n a l y s i s of v a r i a n c e
the 5 p e r c e n t l e v e l
Union, C a s s ,

(see A p p e n d i x G i l ) .

and Orchard

re s p e c t i v e l y .

lakes w e r e

The equations

.72,

The R
.65,

2

for

's for

and

.79

for e a c h lake r e l a t i o n s h i p

were p l o t t e d a n d are p r e s e n t e d in A p p e n d i x G l 2 , G13,

and

G14.
The points

on the Y X p l a n e

for t h e n u m b e r o f a c r e s

per b o a t a n d S C S C d e c r e a s e at a n i n c r e a s i n g r a t e
high n u m b e r of a c r e s p e r b o a t a n d l o w S C S C 's .

for a

The points

then d e c r e a s e a t a d e c r e a s i n g r a t e for l o w n u m b e r of a c r e s
per b o a t a n d h i g h S C S C 's .
planes of e a c h

A

l a r g e n u m b e r of p o i n t s o n Y X

lake r e l a t i o n s h i p o c c u r r e d at a l o w n u m b e r

of a c r e s p e r b o a t a n d a l o w SCSC.
a t t r i b u t e d to the d i f f e r e n c e s

These coordinates were

in e a c h lake zone a r e a . ^

A M e t h o d for D e t e r m i n i n g R e c r e a t i o n a l
Boating Carrying Capacity
The recreational boating carrying capacity of
surface w a t e r s

is d e p e n d e n t u p o n the a t t i t u d e s o f p a r t i c i ­

pants as t h e y m a y be m o d i f i e d b y

levels of use intensity.

^For i n s t a n c e , a w a t e r skier consumed three acres
of w a t e r s u r f a c e in a ten a c r e lake zone.
Another water
skier c o n s u m e d t h r e e a c r e s of w a t e r s u r f a c e in a 1 0 0 a c r e
lake zone.
T h e n u m b e r of a c r e s p e r b o a t in t h e f i r s t z o n e
is ten a nd t h e s e c o n d zone is 100.
T h e S C S C is .33 f o r
the f irst zone a n d .06 for t h e s e c o n d zone.

112
One of the o b j e c t i v e s of this study was to d e v e l o p a
recreational b o a t i n g c a r r y i n g c a p a c i t y m e t h o d that c o n ­
sidered user attit u d e s and levels of b o a t i n g a c t i v i t y i n ­
tensity.

T h e m e t h o d c o u l d ena b l e lake mana g e r s to justify

management of the a m o u n t of r e c r e a t i o n a l b o a t i n g use on a
given body of water.

C h a n g e s in the levels of use i n t e n ­

sity can be b r o u g h t a b o u t b y m a n i p u l a t i n g a v a i l a b l e r e ­
sources to achieve a d e s i r a b l e s a t i s f a c t i o n level for a
given number of users w h i l e m a i n t a i n i n g b o a t i n g safety
and m i n i m i z i n g r e s o u r c e deterioration.
Application
Union, Cass,

and O r c h a r d lakes w e r e u s e d to

illustrate the a p p l i c a t i o n of the carr y i n g c a p a c i t y m e t h o d
for d e t e r m i n i n g cha n g e s in level of b o a t i n g acti v i t y i n ­
tensity.

The p r o c e d u r e s for o b t a i n i n g indices of user

attitude,

c o e f f icients

intensity,

for level of boating,

acti v i t y

and acres per b o a t are d e s c r i b e d in C h a p t e r IV.

The significance of the r e l a t i o n s h i p s was d e t e r m i n e d b y
the analysis of v a r i a n c e in the re g r e s s i o n analysis d i s ­
cussion in C h a p t e r V.

T h e results w e r e in t e r p r e t e d b y use

of the square of the m u l t i p l e c o r r e l a t i o n coefficient.
W i t h i n the UAI and SCSC r e l a t i o n s h i p is a range of
boater attitudes for d i f f e r e n t levels of use.
SCSC there is an array of U A I 1s .

F o r ea c h

T h e array d i s t r i b u t i o n

includes all a c t i v i t y r e s p o n s e s to various levels of
boating acti v i t y intensity.

T h e v a r i a t i o n of the arrays

113
about: t he b e s t

fit c u r v e d e t e r m i n e s

the l e v e l o f the R

2

.

2

A wide array distribution accounts

for a low R
while a
2
narrow array distribution produces a high R
value.
Each
a r r a y is i n t e r s e c t e d a t t h e m e a n b y t h e c u r v e o f b e s t fit.
T h e n u m b e r o f a c r e s p e r b o a t a n d the S C S C r e l a t i o n s h i p
exhibit similar characteristics.

For each SCSC

interval

an a r r a y of a c r e s p e r b o a t is d i s p l a y e d .
2
T h e R 's f o r t h e U A I a n d S C S C r e l a t i o n s h i p w a s
c o m p u t e d as

.35,

.34, a n d

.21 for U n i o n ,

Cass,

and Orchard

lakes r e s p e c t i v e l y a n d is p r e s e n t e d i n A p p e n d i x G5.
low R

The

2

indicate that the user attitude indices have wide
2
a r r a y s for e a c h SCSC.
T h e R 's c o m p u t e d for r e l a t i o n s h i p
b e t w e e n the n u m b e r o f a c r e s p e r b o a t a n d the S C S C w e r e
.72,

.65, a n d

spectively

.79 for U n i o n ,

Cass,

(see A p p e n d i x G i l ) .

a n d O r c h a r d l a k e s re2
The high R
indicate that

the n u m b e r o f a c r e s p e r b o a t h a v e n a r r o w a r r a y s
SCSC.

The plotted relationships

Orchard

lakes,

are p r e s e n t e d

and G 1 2

through G 1 4 .

for U n i o n ,

Cass,

and

in A p p e n d i x G 6 t h r o u g h G 8

S t e p 1 .— T h e c a r r y i n g c a p a c i t y o f Un i o n ,
O r c h a r d lakes w e r e

for e a c h

i n t e r p r e t e d in s e v e r a l steps.

Cas s ,

and

The

first s tep i n v o l v e d s e l e c t i n g m a x i m u m a n d m i n i m u m u s e r
attitude indices

as s h o w n in A p p e n d i x G 6 , G 7 , a n d G 8 .

s u g g e s t e d m e t h o d is

to b r a c k e t the a r e a

UAI a n d S C S C c o o r d i n a t e
UAI of

.50).

to t h e m i d - p o i n t

A

from the largest
(obtained from a

T h e t w o s e l e c t e d U A I 1s i n c l u d e t h e r e s p o n s e s

114
of 50 p e r cent: o r m o r e

of the boaters

satisfaction with a particular
S t e p 2 .— T h e

section

fit.

to extend the

The

s e l e c t e d U A X *s t o t h e

SCSC were derived

(see A p p e n d i x G 6 , G 7 , a n d G 8 ) .

and 1.00 w e r e

selected

ing activities.
.25 t o

level of boating.

seco nd step in i n t e rp r e t i n g the

carrying capacity was
curve of b e s t

indicating a di s ­

.92;

fro m the i n t e r ­

The UAX of

.50

f o r d e r i v i n g S C S C 1s for a l l b o a t ­

The ranges

o f S C S C 's w e r e :

Cass Lake,

.33 t o 1.22;

3 .— T h e

step

Uni o n Lake,

O r c h a r d Lake,

.57 t o

.73.
Step
SCSC*s

to t h e

acres p e r b o a t

final

involved

second relationship

for c o n v e r s i o n into

(see A p p e n d i x G 1 2 , G13,

range o f c a r r y i n g c a p a c i t y

standards

activities combined on

three

6 to

11 a c r e s p e r b o a t ;

Orchard Lake,

is:

5 to

U n i o n Lake,

9 acres per boat;

carrying capacity standards

ational surface w a t e r s

have usually been

twenty-five

boating activities

limited by

users of t h e a r e a

terms

skiing b o a t ) .

for t h e c o m b i n e d

implies that no single

capacity exists on a w a t e r

for r e c r e ­

in s i n g l e

acres per water

T h e u s e of a c a r r y i n g c a p a c i t y r a n g e

c a p a c i t y is

The

for all b o a t i n g

lakes

Cass Lake,

and G 1 4 ) .

4 to 9 a c r e s p e r bo a t .

Previous

(for e x a m p l e ,

the

t r an s f e r ri n g the

surface over

s t a n d a r d of

time,

since

levels of satisfaction by all b o a t

in q u e s t i o n .

The

relationships

used

in

115
d e t e r m i n i n g c a r r y i n g c a p a c i t y a l l o w the lake m a n a g e r to
examine c h a n g e s in levels o£ b o a t i n g use.

Controlling

the n u m b e r of boats or p r o v i d i n g a d d i t i o n a l f a c i l i t i e s on
surface w a t e r s s u b s e q u e n t l y aff e c t s u s e r s a t i s f a c t i o n .
The a l l o w a b l e change in u s e r s a t i s f a c t i o n b e c o m e s a
m a n a g e m e n t decision.
C o m p a r i s o n of A t t i t u d e s T o w a r d B o a t i n g
C o n d i t i o n s by R e s p o n d e n t s w i t h
D i f f e r e n t Socio-Economic'
Characteristics
As b o a t e r s p a r t i c i p a t e in a c t i v i t i e s o n s u r f a c e
waters,

t h e i r a t t i t u d e t o w a r d the c o n d i t i o n o f u s e c a n b e

expressed as favor a b l e or u n f a v o r a b l e .

The third h y ­

pothesis t e s t e d was t h a t s e l e c t e d s o c i o - e c o n o m i c c h a r a c ­
teristics of b o a t e r s i n d i c a t i n g u n f a v o r a b l e a t t i t u d e s
toward c o n d i t i o n s of use d i f f e r f r o m the c h a r a c t e r i s t i c s
of those i n d i c a t i n g f a v o r a b l e a t t i t u d e s
of use o v e r time.

towards conditions

T h e c h i - s q u a r e a n a l y s i s w a s u s e d to

test the hypothesis.
General C h a r a c t e r i s t i c s of
the Public A c c e s s User
D a t a c o n c e r n i n g the s o c i o - e c o n o m i c c h a r a c t e r i s t i c s
of the p u b l i c ac c e s s users w e r e o b t a i n e d f r o m 2,025 r e ­
spondents d u r i n g the s u m m e r p e r i o d o f J u l y 4 t h r o u g h
September 1, 1969 on Union,

Cass,

a n d O r c h a r d lakes.

A pprox i mately 80 per c e n t of all b o a t u s e r s a t the p u b l i c

116
sites w e r e

interviewed

obtained fro m the

(see T a b l e

"head"

1).

The

responses were

o f th e b o a t i n g p a r t y .1

The head of the boating parties was

predominantly

Caucasian;

two were N e gr o and two were

The sex of

the bo ating party head was dominantly male

(98 p e r c e n t ) .
head was
29.6.

The range of ages

seventeen

of o t h e r races.

for the b o a t i n g party

to seventy-two.

The average age was

The number of b o a t i n g party members

ranged

one to s e v e n t e e n ; t h e m e a n n u m b e r o f m e m b e r s w a s
The a g e of e a c h b o a t i n g p a r t y m e m b e r

ranged

one-year-old

the

to s e v e n t y - e i g h t years;

the m e m b e r s w a s

27.4.

Approximately

boating party heads were
three-fourths of
less t h a n

less

the members

fifty years

than

from
4.2.

from less than

average age of

two-thirds

of the

fifty years old,

of the boating party were

old.

A l m o s t o n e —half of the b o a t i n g p a r t y heads
annual

incomes of

ceived over
fourth)

less

$15,000.

while

than

$15,000,

and one-fourth

The remaining respondents

did not disclose

their annual

had
re­

(one-

incomes.

Five per cent of the boating party heads had c o m ­
pleted e i g h t yea r s

or

less of e l e m e n t a r y education;

cent h a d c o m p l e t e d

some high school;

20

per

7 per

cent had

1T h e h e a d o f t h e b o a t i n g p a r t y w a s g e n e r a l l y
i d e n t i f i e d as t h e h e a d o f t h e h o u s e h o l d , t h e p e r s o n s e e m ­
ingly ir. c h a r g e o f a b o a t i n g p a r t y , o r t h e o w n e r o f t h e
boat.
The interviews were obtained mostly from persons
that s t o o d o u t to t h e i n t e r v i e w e r s as t h o s e in c h a r g e o f
the b o a t i n g p a r t y .
T h e r e m a i n i n g m e m b e r s of the b o a t i n g
party w e r e n o t interviewed.

117
completed high school; and 30 per cent w e r e college g r a d u ­
ates or had some college work.

A b o u t 5 per c e n t h a d a d ­

vanced degrees or p o s t doctorate work,
cent w e r e students.
cent)

and a l m o s t 8 pe r

The r e m a ining respondents

(25 per

did no t disclose their education.
T w e n t y per cent of the boa t i n g p a r t y heads w e r e

craftsmen;

17 p e r cent were prof e s s i o n a l persons;

cent were managers;
were in sales;

7 per cent were students;

7 per cent w e r e technicians;

had m i s c ellaneous occupations.
(26 per cent)

10 per

5 per ce n t

and 8 p e r c e n t

The r e m a i n i n g responde n t s

did not disc l o s e their occupation.

The socio-economic factors related to the h e a d of
the b o a t ing party judged by the author as b e i n g m o s t likely
to influence the p a r t i c i p a t i o n in w a t e r - o r i e n t a t e d out d o o r
recreation are income, education,
pation,

sex, race,

and amount o f leisure time.

ables are interrelated,

age, o c c u ­

Some of these v a r i ­

and the combined effects m a y be

more important than individual relationships.

However,

the purpose of this section of the study is to touch
briefly upon some of the correlations b e t w e e n the s o c i o ­
economic characteristics of boaters
party)

(head of the b o a t i n g

and their attitudes toward b o a t i n g c o n d i t i o n s . ^

Income, education,

and o c c u p a t i o n were selec t e d for c o m ­

parison .

1A p p r o x i m a t e l y 25 per cent of the boaters i n t e r ­
viewed did not disc l o s e their income, education, or
occupation.

118
I n c o m e .— A s
In I n c o m e sc a l e ,
sponses
l evel

b oth the unfavorable and favorable r e ­

(in p e r cent)

i n c r e a s e t o the $ 1 0 , 0 0 0

(highest p e r cent),

$24,000
come

-the h e a d of the b o a t i n g p a r t y m o v e s u p

level,

level

then

to $14,999

d e c r e a s e to t h e $ 2 0 , 0 0 0

to

increase to the $25,000 and over in­

(see A p p e n d i x E l ) .

The chi-square analysis

c o m p a r e d the t o t a l i n c o m e d i s t r i b u t i o n of t h e r e s p o n d e n t s
who indicated unfavorable boating conditions with

that of

the r e s p o n d e n t s w h o i n d i c a t e d f a v o r a b l e b o a t i n g c o n d i t i o n s .
The income distributions were
e n t a t the 5 p e r c e n t
lakes

found significantly d i f f e r ­

l e v e l for Union,

Cass,

and Orchard

(see A p p e n d i x E 2 ) .
The data indicates

(less t h a n $8,0 0 0 ) ,
report unfavorable
increases

t h a t for l o w e r i n c o m e b o a t e r s

a h i g h e r p e r c e n t o f the r e s p o n s e s
than

favorable conditions.

( g r e a t e r t h a n $8,00 0)

sponses reporting

As

income

the p e r c e n t of r e ­

favorable conditions becomes

greater

than the p e r c e n t r e p o r t i n g u n f a v o r a b l e c o n d i t i o n s .
E d u c a t i o n .— A s y e a r s of s c h o o l i n g i n c r e a s e ,
types of r e s p o n s e s

(in p e r cent)

school g r aduate level
c r e a s e for h i g h e r

(see A p p e n d i x E l ) .
the t o t a l y e a r s

i n c r e a s e to the h i g h

(greatest per cent r e s p o n s e ) , d e ­

l e v e l s of e d u c a t i o n

w o r k ) , then increase

both

(post g r a d u a t e

for a d v a n c e d d e g r e e s a n d s t u d e n t s
The chi-square analysis compared

of e d u c a t i o n d i s t r i b u t i o n o f t h e r e ­

spondents w h o indicated unfavorable boating conditions

119
with that of those respondents w h o indicated favorable
boating c o n d i t i o n s .

The educa t i o n d i s t r i b u t i o n was found

significantly d i f f e r e n t at the 5 per cent level for Union,
Cass, a nd O r c h a r d lakes

(see A p p e n d i x E 2 ) .

The data indicates that for boaters w i t h some h i g h
school e d u c a t i o n and for h i g h school g r a d u a t e s , a h i g h e r
per c e n t of the responses report favorable than u n f a v o r a b l e
conditions.

A s education increases,

the p e r c e n t of r e ­

sponses repor t i n g unfavorable conditions b e c o m e s g r e a t e r
than the p e r cent reporting favorable conditions.
O c c u p a t i o n .— The chi-square analysis c o m p a r e d the
occupational d i s t r i b u t i o n of the re s p o n d e n t s w h o i n d i c a t e d
unfavorable b o a t i n g conditions w i t h that of those r e s p o n ­
dents w h o indicated favorable b o a t i n g c o n d i t i o n s .

The

occupation d i s t r i b u t i o n was found s i g n i f i c a n t l y d i f f e r e n t
at the 5 per cent level for Union, Cass,

and O r c h a r d lakes

(see A p p e n d i x E 2 ) .
T he data indicates that for the f o l l o w i n g o c c u ­
pations of boaters a higher per cent of r e s p o n s e s r e p o r t e d
favorable then unfavorable conditions:
clerical, craftsmen, operators,
sales personnel,

and students,

p r o f e ssional,

and service.

For man a gers,

a hi g h e r p e r c e n t of r e ­

sponses reported unfavorable conditions than r e p o r t e d
favorable c o n d i t i o n s .

CHAPTER VIII
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
T h i s s t u d y has a t t e m p t e d to p r o v i d e lake m a n a g e r s
w i t h a m e t h o d for e v a l u a t i n g the r e c r e a t i o n a l c a r r y i n g
capacity of s u r f a c e w a t e r s .

P r e v i o u s e m p h a s i s on c a r r y i n g

capac i t y has b e e n d i r e c t e d towards p h y s i c a l r e s o u r c e v a r i ­
ables.

T h i s study vi e w s a t t i t u d e s t o w a r d the r e c r e a t i o n a l

experi e nce as of e q u a l i m p o r t a n c e in terms of e v a l u a t i n g
ca r rying capacity.
T w o b a s i c r e l a t i o n s h i p s w e r e investigated:

(1)

the r e l a t i o n s h i p b e t w e e n the level of u s e r d i s s a t i s f a c t i o n
and the i n t e n s i t y of use,
between space a v a i l a b l e

and

(2 ) the i n v e r s e r e l a t i o n s h i p

for b o a t i n g a n d the i n t e n s i t y of

use.
T h e level of b o a t u s e r d i s s a t i s f a c t i o n was
to be d i r e c t l y r e l a t e d to the i n t e n s i t y of use.
of user d i s s a t i s f a c t i o n

(user a t t i t u d e index)

was

found

T h e level
inter­

preted as the r a t i o b e t w e e n the n u m b e r of h o u r l y r e s p o n s e s
by boaters i n d i c a t i n g u n f a v o r a b l e b o a t i n g c o n d i t i o n s and
total h ourly r e s p o n s e s .

T h e u s e of the surface w a t e r b y

120

121
all a c t i v i t i e s

(space c o n s u m p t i o n s a f e t y c o e f f i c i e n t )

r e p r e s e n t s t h e i n t e n s i t y of use.

The user attitude

a n d the s p a c e c o n s u m p t i o n s a f e t y c o e f f i c i e n t w e r e
s i g n i f i c a n t l y r e l a t e d w h e n c o m p a r e d b y lake,
a nd f l i g h t i n t e r v a l

index

found

l a k e zone,

for a l l o b s e r v a t i o n s o b t a i n e d d u r i n g

the summer.
The space available
p e r boat)

was

sity o f u s e

for b o a t i n g

(nu m b e r o f a c r e s

f o u n d to be i n v e r s e l y r e l a t e d t o t h e i n t e n ­

(space c o n s u m p t i o n s a f e t y c o e f f i c i e n t ) .

space a v a i l a b l e

The

for b o a t i n g w a s c o m p u t e d as t h e a v e r a g e

acres o f w a t e r s u r f a c e u s e d b y one boat.

Th e number of

acres p e r b o a t a n d t h e s p a c e c o n s u m p t i o n s a f e t y c o e f f i c i e n t
w e r e c o m p a r e d b y lake,

lake zone,

and flight interval

all o b s e r v a t i o n s o b t a i n e d d u r i n g t h e s u m m e r .
ship w a s

for

The relation­

found to b e h i g h l y s i g n i f i c a n t .
The carrying c a p acity and the effects

ment practices on surface waters

of m a n a g e ­

for r e c r e a t i o n a l b o a t i n g

can be s a t i s f a c t o r i l y p r e d i c t e d f r o m t h e t w o r e l a t i o n s h i p s .
A m e t h o d w a s d e v e l o p e d for t h i s p u r p o s e .

The results are

a p p l i c a b l e t o the a r e a s t u d i e d .
T h e a p p l i c a t i o n of the c a r r y i n g c a p a c i t y m e t h o d to
Union, Cass,

and Orchard

attitude index procedure,
were less t h a n

.35.

lakes revealed,

t h a t a m a j o r i t y o f t h e U A X 1s

The m a j o r share of b o a t e r s u s i n g the

p ublic a c r e s s i t e s d u r i n g t h e
accept h i g h

t h r o u g h th e u s e r

levels of boating.

s u m m e r of

1969 a p p e a r e d

O n t h e o t h e r ha n d ,

the

to

122
m a j o r i t y of r i p a r i a n owners p a r t i c i p a t i n g d u r i n g h i g h use
b o a t i n g p e r i o d s , indicated u n f a v o r a b l e u s e .
owners of Union, Cass,

The r i p a r i a n

and O r c h a r d lakes appear m o r e c o n ­

cerned a b o u t h i g h levels of b o a t i n g use than did the p ublic
access users.
S e l e c t e d s o c i o - e c o n o m i c charac t e r i s t i c s of boaters
indica t i ng u n f a v o r a b l e co n d i t i o n s of use w e r e comp a r e d
with those of boa t e r s indicating favorable conditions of
use over time.

T h e s e l e c t e d variables c o n s i d e r e d in this

study w e r e income, education,

and occupation.

The distri­

butions of e a c h v a r i a b l e w e r e c o m p a r e d b y the type of
responses.

T h e c h a r a c t e r i s t i c s of boaters i n d i c a t i n g u n ­

favorable c o n d i t i o n s of use w e r e sign i f i c a n t l y d i f f e r e n t
from those of b o a t e r s in d i c a t i n g favorable conditions of
use.
Recomm e n d a t i o n s
T h e use of h i g h oblique aerial pho t o g r a p h s p r o ­
vides a p r a c t i c a l m e t h o d for e n u m e r a t i n g boats and d e t e r ­
mining a c t i v i t i e s u n d e r t a k e n on a w a t e r surface.

Con­

structing the one p o i n t p e r s p e c t i v e q u a d r i l a t e r a l

grids

and i n t e r p r e t i n g the p h o t o g r a p h s i n v o l v e d a good deal of
time in this study.

T h e accuracy of the acti v i t y location

is d e p e n d e n t u p o n k n o w n flight elevations.

A n e f f o r t was

made to fly at 500 feet above the w a t e r surfaces w h i l e
photographing a c t i v i t i e s .

A n y v a r i a t i o n in the flight

elevation c o n s i d e r a b l y alt e r e d the grid construction.

Air

123
t u r b u l e n c e s o f t e n c a u s e d the a i r c r a f t to fly at d i f f e r e n t
e l e v a t i o n s a n d c o n s e q u e n t l y a f f e c t e d the a c c u r a c y of inter
p r e t i n g the b o a t locations.
Recommendation 1 :

It is r e c o m m e n d e d t h a t r e ­

searchers c o n t i n u e to u s e 3 5 m m a e r i a l p h o t o g r a p h y in o r d e r
to i n v e n t o r y b o a t l o c a t i o n s and u s e p a t t e r n s b y activity.
V e r t i c a l p h o t o g r a p h y s h o u l d be u s e d if at all possibl e .
The v e r t i c a l p h o t o g r a p h s p e r m i t d i r e c t m e a s u r e m e n t of
a c t i v i t i es and the a c c u r a c y is c o n s i d e r a b l y b e t t e r than
high o b l i q u e e x p o s u r e s .

M o s t i m p o r t a n t is the r e d u c t i o n

in time s p e n t for i n t e r p r e t i n g the p h o t o g r a p h s .
A d d i t i o n a l i n f o r m a t i o n on b o a t i n g spe e d s can be
obtained by vertical exposures
sequentially photographed.

if the a c t i v i t i e s are

B o a t i n g speeds w o u l d i n t r o ­

duce a n e w v a r i a b l e into i n v e s t i g a t i o n s of use p a t t e r n s .
T h e u s e r a t t i t u d e index p r o c e d u r e a t t e m p t e d to
q u a n t i f y the a t t i t u d e of boa t e r s t o w a r d v a r y i n g levels of
use.

A t t i t u d e was d e f i n e d as the r a t i o of u n f a v o r a b l e

responses to total r e s p o n s e s

for a g i v e n time interval.

The u s e r a t t i t u d e i n d e x r a n g e d from

.00 to 1.00.

The

U A I 's w e r e c o m p a r e d w i t h levels of u s e as m e a s u r e d b y the
SCSC.

It was a n t i c i p a t e d t h a t the n u m b e r of u n f a v o r a b l e

r esponses w o u l d i n c r e a s e as the level of use increased.
Instead,

the d a t a s h o w e d low U A I 's a s s o c i a t e d w i t h i n ­

c r eased levels of boating.

T h e c o m p a r i s o n of UAI w i t h

124
SCSC r e s u l t e d

in low or no correlations

lakes.

i t is a s i m p l e

Since

i n d e x is e q u a l l y

ratio,

the u s e r attitude

(For e x a m p l e ,

five unfavorable

sponses

for t e n b o a t e r s

of

an identical UAX would result

unfavorable responses
The majo r i t y of
of t h e day;

nate e x t r e m e

from twenty-five

from fifty boaters

low responses

A

interviewed.)

occurred during early hours

responses were

obtained mainly

computer program was developed

indexes

and coefficients derived

n u m b e r of r e s p o n s e s .

re­

interviewed w o u l d provide a UAX

the unfavorable

from fishermen.

three

affected by a large number of responses

as a s m a l l n u m b e r .

.50;

for the

to e l i m i ­

from a

low

T h e outcome of the comparison b e ­

tween the m o d i f i e d UAX

and

the SCSC was

a higher corre­

2:

i t is r e c o m m e n d e d t h a t t h e

lation.
Recommendation
user a t t i t u d e
tiating the

index procedure be re-examined by differen­

indices derived by

low number of responses

a nd h i g h n u m b e r o f r e s p o n s e s .
The differentiation process would
weight

factor to each UAX

(i.e.,

s c a l e of

assign a scaled
0 to

10).

The

weight factors w o ul d be based upon a predetermined e m pi ri ­
cal r e l a t i o n s h i p b e t w e e n
observed boats,

the type of response,

a n d U A X 1s .

r i v e d b y t h e r a t i o of

five u n f a v o ra b l e

t otal r e s p o n s e s w o u l d h a v e
x a weight

factor of

Therefore,

2).

a new value
A UAX

of

n u m b e r of

a UAX of
responses
of

1.0

.50 d e ­
to ten

(.50 U A X

.50 d e r i v e d b y t h e

125
ratio of twenty-five unf a v o r a b l e responses to fifty total
responses w o u l d have a value of 4.0
factor of 8 ).

(.50 UAI x a w e i g h t

The approach for d i f f e r e n t i a t i n g UAI

attempts to place high indices obtained by low n u m b e r s
of responses in perspective.

Es s e n t i a l l y the a p p r o a c h

e limin a t es conflicts reported by a small nu m b e r of
p artic i p ants u s i n g the water surface d u r i n g low levels
of use.
T h e rel a t i o n s h i p b e t w e e n U A I 's and S C S C 1s atte m p t s
to p r o v i de lake managers w i t h a method for a s s e s s i n g the
recreational b o a t i n g carrying capacities of surface
waters.

The met h o d is applicable to the area studied.
Recommendation 3 :

It is recommended t h a t the

user a t t itude index and space c o n s u mption s a f e t y c o e f ­
ficient procedures be applied to other w a t e r b o d i e s

in

order to further test this method.
S e l e c t e d socio-economic c h a r acteristics
education,

and occupation}

(income,

of boaters in d i c a t i n g u n f a v o r ­

able c o n ditions of use were compared w i t h the s o c i o ­
economic characteristics of boaters indicating f a v o r a b l e
conditions of u s e .

The dist r i b u t i o n of e a c h s o c i o ­

economic vari a b l e was compared for the type of r e s p o n s e
and tested significantly d i f f e r e n t by c h i - s q u a r e analysis.
This type of statistical analysis is useful, b u t does not
allow for q u a n t i f i c a t i o n of the net effect of e a c h

126
variable.

Nor does

lb m e a s u r e t h e e f f e c t of i n t e r r e l a t i o n ­

ships a m o n g the c h a r a c t e r i s t i c s .
Recommendation 4 :

It is r e c o m m e n d e d t h a t a

d e t a i l e d a n a l y s i s of i n t e r r e l a t i o n s h i p s b e t w e e n a l l s o c i o ­
e c o n o m i c v a r i a b l e s a n d the a t t i t u d e s

for b o a t e r s i n d i c a t ­

i ng e i t h e r u n f a v o r a b l e o r f a v o r a b l e r e s p o n s e s

to c o n d i t i o n s

of u s e b e u n d e r t a k e n .
Important limitations on carrying capacities of
water bodies

for b o a t i n g r e c r e a t i o n u s e a r e s e t b y t h e

a t t i t u d e of b o a t e r s

towards

m a n a g e m e n t a n d use.

These

overcome,

the area and towards
limitations

its

are d i f f i c u l t to

partly because different groups hold incompati­

ble v i e w s a n d p a r t l y b e c a u s e w e k n o w
t hese a t t i t u d e s a r e

little about how

formed and how they can be c h a n g e d .

The c o n t i n u o u s e x a m i n a t i o n o f the i n t e r a c t i n g s o c i o ­
economic characteristics

of the attitudes

a p p r o p r i a t e m a n a g e m e n t of t h e a r e a s
a t t i t u d e s c a n l e a d to a m o r e

and

t o t a k e a c c o u n t of

flexible view of densely

used w a t e r b o d i e s a n d h i g h e r r e t u r n s
resources.

of u s e r s

from alloc a t i o n of

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O u t d o o r Re c r e a t i o n -! U.S. D e p a r t m e n t of A g r i c u l t u r e ,
Ec o n o m i c R e s e a r c h Service in coo p e r a t i o n w i t h the
M i s s o u r i A g r i c u l t u r a l E x p e r i m e n t Station, 1967.
U.S. D e p a r t m e n t of Agriculture.
U.S. Fo r e s t Service.
W o r k Plan for the N a t i o n a l Forest R e c r e a t i o n
Survey~I Washington, D . C . : G o v e r n m e n t P r i n t i n g
O f f i c e , 1959.
U.S. D e p a r t m e n t of Interior.
B u r e a u of L a n d Management.
B u r e a u of L a n d M a n a g e m e n t M a n u a l . Washington,
D . C .:
Government" P r i n t i n g Office, 1963.
_________ . Bu r e a u of O u t d o o r Recreation.
Nationwide P l a n ,
M a n u a l — P l a n n i n g and Surveys Series"! Washingt o n ,
D .C .:
G o v e r n m e n t P r i n t i n g office, 1964.
Un p u b l i s h e d Materials
Chubb, M.
"Outdoor Recreation L a n d Capacity:
Concepts,
Usage, and Definitions."
U n p u b l i s h e d Mast e r ' s
thesis, M i c h i g a n State University, 1964.
Crysdale, D.
"An Anal y s i s of Spatial Rela t i o n s h i p s and
Resource Requirements for W a t e r s k i i n g ."
Unpub­
lished study proposal on file at the D e p a r t m e n t
of P a r k and Recrea t i o n Adminis t r a t i o n , N o r t h
C a r o l i n a State University, 1969.
Hopkins, W a l t e r S.
"Impact of Recreation on C o m p e t i t i o n
for Use of Water."
Paper p r e s e n t e d at the W e s t e r n
Conference, Un i v e r s i t y of Colorado, Boulder,
Colorado, 1963.
Peterson, G. A.
"An A p p l i c a t i o n of W a t e r R e c r e a t i o n
C a p a c i t y to R e s e r v o i r D e v e l o p m e n t Planning."
U n p u b l i s h e d M a s t e r 1s t h e s i s , Texas A & M U n i ­
versity, May, 1968.
Porter, K. R.
"The C r i t e r i a and T e c h n i q u e s for E s t i m a t ­
ing O p t i m u m Recreational C a p a c i t y at W a t e r R e ­
source Projects."
Un p u b l i s h e d M a s t e r ' s thesis,
Texas T e c h n o l o g i c a l College, 1969.

130
Other
L e t t e r f r o m S. K. Swener t o n , L i e u t e n a n t (j.g.), I n v e s t i ­
g a t i n g O f f i c e r , U n i t e d St a t e s C o a s t Guard, D e t r o i t ,
M i c h i g a n , M a y 4, 1970.
Ruble, W i l l i a m L . , and Rafter, M a r y E.
C a l c u l a t i o n of
L e a s t S q u a r e s R e g r e s s i o n P r o b l e m o n the L. S.
R o u t i n e . S T A T . S e r i e s D e s c r i p t i o n N u m b e r 7.
E a s t Lans i n g , M i c h i g a n :
Michigan State U n i ­
vers i t y , A g r i c u l t u r a l E x p e r i m e n t Station,
N o v e m b e r , 1969.
D a t a P l o t t i n g a n d C u r v e D r a w i n g o n the C a l c o m p
P l o t t e r . STAT. S e r i e s D e s c r i p t i o n N u m b e r 16.
E a s t L a n s i n g , M i c h igan:
Michigan State U n i ­
vers i t y , A g r i c u l t u r a l E x p e r i m e n t Station, July,
1966.
_________ . S t e p w i s e D e l e t i o n o f V a r i a b l e s f r o m a L e a s t
S q u a r e s E q u a t i o n . S T A T . Se r i e s D e s c r i p t i o n N u m b e r
57 E a s t Lansing, Michigan:
Michigan State U n i ­
v e r s i t y , A g r i c u l t u r a l E x p e r i m e n t Station,
N o v e m b e r , 1969.
S t a t e of M i c h i g a n L a w E n f o r c e m e n t M a n u a l . Lansing,
M ichi g a n :
D e p a r t m e n t of: C o n s e r v a t i o n , Boat,
W a t e r S a f e t y Section, 1967.

and

APPEND I C E S

APPENDIX A
LETTER,

I N T E R V I E W SCHEDULE,

AND QUESTIONNAIRE

APPENDIX Al
COPY OF LETTER REQUESTING AGENCIES AND UNIVERSITIES
FOR INFORMATION ON CARRYING CAPACITY

Michigan State University
D e p a r t m e n t of R e s o u r c e D e v e l o p m e n t
Natural Resources Building
East Lansing, Michigan
48823

November

19,

1968

Cloverland Regional Planning Commission
Cloverland Metropolitan Park District
Cloverland, Ohio
D e a r Sir:
T h i s D e p a r t m e n t has ju st c o m m e n c e d a t w o - y e a r i n v e s t i g a t i o n
of the c a r r y i n g c a p a c i t y o f w a t e r a r e a s f o r v a r i o u s t y p e s
of r e c r e a t i o n .
T h e s t u d y is b e i n g c a r r i e d o u t for t h e
S t a t e o f M i c h i g a n u n d e r a c o n t r a c t w i t h Mr. K e i t h W i l s o n ,
D i r e c t o r of the W a t e r w a y s D i v i s i o n , M i c h i g a n D e p a r t m e n t o f
N a t u r a l R e s o u r c e s (for m e r l y the M i c h i g a n D e p a r t m e n t o f
Conservation).
We w i l l b e u n d e r t a k i n g f i e l d i n v e s t i g a t i o n s o f a c t u a l
r e c r e a t i o n a l use p a t t e r n s on a n u m b e r of h i g h - u s e l a k e s
in the s o u t h e r n p a r t of the state.
It is a n t i c i p a t e d
that a e r i a l p h o t o g r a p h y w i l l b e e m p l o y e d in c o n j u n c t i o n
w i t h g r o u n d o b s e r v a t i o n to m e a s u r e t h e a m o u n t s a n d p a t ­
terns o f use.
Personal interviews will investigate user—
p e r c e p t i o n of c r o w d i n g , c o n f l i c t s , a n d s a f e t y p r o b l e m s .
On b e h a l f o f the M i c h i g a n D e p a r t m e n t o f N a t u r a l R e s o u r c e s ,
we s o l i c i t y o u r a s s i s t a n c e in a d v i s i n g u s if y o u r d e p a r t ­
ment, o r a n y of its s u b d i v i s i o n s , h a s b e e n i n v o l v e d i n
i n v e s t i g a t i o n s o f t h i s type.
If i t has, p l e a s e c o u l d y o u
131

132

N o v e m b e r 19,

1968

Page 2
supply us w i t h the names and addresses of the personn e l
c o n c e r n ed and send us copies of any w r i t t e n m a t e r i a l that
is
available.
W e w o u l d a l s o w e l c o m e copies of your c u r ­
rent B o a t i n g S a f e t y Re g u l a t i o n s and inf o r m a t i o n on capac i t y
coeffi c ients or o t h e r p l a n n i n g crit e r i a of this natur e that
may be e m p l o y e d b y your r e c r e a t i o n area d e s i g n e r s .
Any a s s i s t a n c e y o u can give w i l l be m u c h app r e c i a t e d and
will be p r o p e r l y a c k n o w l e d g e d in our final report to the
state.
S i n c erely yours.

Peter 6 . A s h t o n
Recrea t ion R e s e a r c h and P l a n n i n g U n i t
Room 323, N a t u r a l Resources B u i l d i n g
PGA/cs

AP P E N D I X A2
COPY OF INTERVIEW SCHEDULE USED AT
PUBLIC ACCESS SITES

DATE
1.

TIME
Have we

LAKE

INTERVIEWER
* Y e s ______

interviewed you before?

No

W h a t time d i d y o u a r r i v e a t this l a k e today?

W h a t t i m e a re y o u

*4a.
b.

l e a v i n g this

lake to d a y ?

H o w m a n y p e o p l e are i n y o u r b o a t i n g p a r t y ? ___________
C o u l d w e h a v e y o u r age a n d the s e x a n d age o f t h e
o t h e r s in y o u r p a r t y ?
Member
Interviewed

2

3

4

5

6

7

8

9

Sex
Age
*5.

How many boats
Boats

a r e in y o u r p a r t y ?

Horsepower

Length

1
2

3

133

Type

A.
B.
C.
D.
E.
F.
G.
H.
I.

Cruiser
Sailboat
Fishing
Water skiing
Drag boat
Houseboat
Canoe
Runabout
O t h e r (Specify)

134
*6 .

W h a t w a s t h e m a i n r e a s o n y o u p i c k e d ___________________ ___
Lake today?
(close t o h o m e , o p e n w a t e r , o t h e r l a u n c h
r a m p s c r o w d e d , g o o d f i s h i n g , etc.)

7.

Do y o u own p r operty on

8.

Are you a guest of a person who owns
lake?
Y e s ______
N o ______

*9.

this

lake?

Y e s ______

N o _______

p r o p e r t y on this

H o w m a n y d a y s h a v e y o u u s e d _________________________ L a k e
this summer?

*10.

H o w m a n y days ha v e you spent b o a t i n g this
( a n y w h e r e ) ___________________

*10A.

How many times have you used
between M onday and Friday of

*11.

Place of residence:
Zip
or street and
c i t y ______________________ o r c i t y a n d c o u n t y _______________

*12.

A p p r oximately h o w long did y o u spend on the following
activities today?
(Approximate q u a r t e r - h o u r s ) .
(Hand t h e b o a t e r a card.)
**Ask specifically:
A.
B.
C.
D.
E.
F.
G.

Water skiing
Motor boat
cruising
Fishing
Sailing
Picnicking
Sunbathing
Swimming

J.
K.
L.

*13.

OVER

_ _____________ _______ L a k e
this p a s t week?

** H .
**I.

summer?

W a i t i n g in l i n e
to launch boat
W a i t i n g in line
to load o n r a m p
T i e d to priv a te
dock
P a d d l i n g or
rowing
Other

On the other side of the card would you please show me where your activities
took place today?

2
3
4
5
6
7
8
9

Other

Swimming

Su n
bathing

Picknicking

Sailing

WHY
(ask why they
selected these
areas as to
other areas)

LEAVE FOR
#18 OPEN

135

1

Fishing

Lake
Zone

Motor b o a t
cruising

Activity

Water
skiing

13.

136
*14a.

H o w d o y o u feel a b o u t y o u r e x p e r i e n c e o n t h i s l a k e
today?
(Do n o t a s k a b o u t c o n f l i c t s o r c r o w d e d c o n ­
d i t i o n s a t first, t h i s is m i s l e a d i n g the b o a t e r 11
If b o a t e r i n d i c a t e s c o n f l i c t s or c r o w d i n g , t h e n a s k
his perc e p t i o n of the p r o b l e m 1)

b. W h a t t h i n g s s t o o d o u t in y o u r m i n d as y o u u s e d t h e
lake tod a y ?
c. D o y o u h a v e a n y o p i n i o n s ? ________________________________

15.

Employment

16.

(Hand the b o a t e r a s e c o n d c a r d a n d a s k ) :
Would you
p l e a s e g i v e m e the l e t t e r w h i c h c o r r e s p o n d s w i t h
y o u r t o t a l f a m i l y i n c o m e ? ________________________________

17.

O n t h e r e v e r s e s i d e o f the card, w o u .1 3 y o u p l e a s e
g i v e me the l e t t e r w h i c h c o r r e s p o n d ? vith y o u r
___________________
c o m p l e t e d e d u c a t i o n ? _______________

VERY G OOD I
*18.

(specific)

JUST ONE FINAL QUESTION 1 1

D u r i n g a n y of the a c t i v i t i e s y o u d i d to d a y ,
e v e r n o t i c e or feel t h a t y o u w e r e c r o w d e d ?
to #13 O P E N to a n s w e r question)
a.

A s k w h i c h a r e a s d i d y o u feel c r o w d e d in?

b.

W h a t t i m e in e a c h a r e a d i d y o u b e g i n to fee l
crowded?

T H A N K Y O U V E R Y M U C H F O R Y O U R A S S I S T A N C E 11
BOAT R E G I S T R A T I O N N U M B E R
MC

did you
(Refer

or,

IF S A I L B O A T ,
NO.

G O O D DAY,

ETC.

TRAILER LICENSE

APP E N D I X A3
C O P Y OF Q U E S T I O N N A I R E US E D BY
RIPARIAN OWNERS
D A T E ________________
Have y o u c o m p l e t e d this q ue s t i o nn a i r e before?
Y e s ______
N o ______
If Y e s , c o m p l e t e
questionnaire.

only questions

D o y o u o w n or r e n t
______ O w n
Do you

this property?

Rent

reside here

how many?

______ w e e k s ,

17 o f

this

(ch e c k one)

Guest

the entire year?

If No, o n t h e a v e r a g e , h o w
residence each year?
______ m o n t h s

11 t h r u

Y e s _______

long do you occupy

N o __
this

or if only weekends,

______

Please com pl e t e the following i nformation c o n c e r n i n g
your permanent residence:
zip code
How

city

county

long have y o u o w ned or rented this p r o p e rt y ?

______ y e a r s

______ m o n t h s

Why did you choose

to live on this

How m u c h frontage, on the water,
property?
______ f e e t

lake?

do you have with

this

P l e a s e c h e c k all the f a c i l i t i e s w h i c h are p r e s e n t on
this property:
______
______
______
______

Do ck
Boat House
Sand Beach
Anchored float
for s w i m m i n g

How many boats do you own?

Boat hoist
T r a i l e r la u n c h
facility
O t h e r (specify)
_________________________

H o w m a n y of the b o a t s y o u o w n are k e p t a t this lake?
D o y o u k e e p any b o a t s o t h e r t h a n y o u r o w n at this
_____ N o
______Yes , h o w m a n y _________________
lake?
P l e a s e c o m p l e t e the f o l l o w i n g i n f o r m a t i o n a b o u t the
b o a t s k e p t on y o u r p r o p e r t y :
Do y o u own?
(check)
Type

Horse­
Number Length power

Yes

No

Canoe
Sailboat
Fishing boat
Drag boat
Pontoon boat
Houseboat
Water skiing boat
Rowboat
Cruiser
Other
F o r e a c h d a y d u r i n g the p a s t w e e k i n d i c a t e the n u m b e r
of hours that the b o a t s k e p t o n this p r o p e r t y w e r e
a c t u a l l y u s e d for the f o l l o w i n g act i v i t i e s :
Boating
Activities
Cii i
a 1n1o
ei1i n
g**1
't"
• i
Sailing
Fishing
Drag boating
Pontoon boating
House boating
Water skiing
Rowing
Cruising
Swimming
Other

M o n . T u e . W e d . Thurs.
hrs. hrs. hrs. hrs.

Fri. S a t . S u n .
hrs. hrs. hrs.

Is t h e p a t t e r n
use?
Yes

in Question
No

12 t y p i c a l o f y o u r n o r m a l

If No, p l e a s e b r i e f l y d e s c r i b e h o w
your normal u s e .

this differs

from

W h a t factors d e t e r m i n e y o u r typical sche d ul e of
a c t i v i t i e s as y o u h a v e i n d i c a t e d t h e m a b o v e ?

H o w do you feel about your experiences
d ur i n g the past week?

Is t h e r e a n y t h i n g w h i c h
y o u r e x p e r i e n c e s on the
No
Yes
Specify,

WHAT STANDS

WHY DO THESE

Do you boat on other

this

lake

stands out in you r m i n d abou t
lake this p a s t week?

OUT:

STAND OUT

on

Time

Date

IN Y O U R M I N D ?

lakes?

______N o

______ Y e s

W h a t l a k e s ? _____________
_______________
When?
( C h e c k one)
Weekdays
Weekends
H o l i d a y s _____
H o w m a n y t i m e s p e r b o a t i n g s e a s o n ? _________________
If y e s ,

why do you choose another

l a k e ? ___________

Have you used this lake's public access
launch your boat this summer?
______N o
number of times

site to
______ Yes,

140
In order to forecast w h a t future b o a t i n g c h a r a c t e r i s t i c s in
M i c h i g a n w i l l be it is n e c e s s a r y for us to be able to r e ­
late family characteristics to b o a t i n g use patterns.
P l ease
assist us by a n s w ering the following q u e s t i o n s a b o u t your
family characteristics:
19.

W h a t is the age and sex of the “head of your family"?
A g e ____________ years

Male

Female

20.

W h a t is the o c c u p a t i o n of the "head of your family"?
O c c u p a t i o n (not organization)

21.

W h i c h of the following represents the amount of formal
e d u c ation completed by the "head of the household " ?
(check one)
E i g h t h grade or less
Some high school
Hi g h school graduate
Some college

22.

_____
______

C o l l e g e graduate
______
P o s t graduate w o r k _______
A d v a n c e d degree
______
S t u d e n t ______________ ______

W h i c h of the following indicates the total income of
your family in 1969?
(Check one)
$4,999
$5,000
$7,000
$8,000

or under
to 6,999
to 7,999
to 9,999

$10,000
$15,000
$20,000
$25,000

to 14,999
to 19,999
to 24,999
and over

______
_____

23.

Suggestions or remarks co n c e r n i n g b o a t i n g on this
lake:

24.

O t h e r remarks:

THANK Y O U F O R Y O U R COOPERATION.
IF YOU HAVE M I S P L A C E D THE RETURN ENVEL O P E PLEASE SEND THE
QUESTIONNAIRE TO:
Robert Dittrick
R e c r eation Research & P l a n n i n g Unit
Dept, of Park & R e c r e a t i o n Resources
Rm. 131 N a t u r a l R e s o u r c e s Bldg.
M i c h i g a n State U n i v e r s i t y
E a s t Lansing, M i c h i g a n 48 823

APPENDIX B
VALUES

USED FOR CONSTRUCTING

PERSPECTIVE GRIDS

141
A P P E N D I X B1
GRID F O R 400—FOOT ELEVATION
9h
2 .2 )

2,50
2,75
3 .0 0
3 .2 3
3 . 30
3 . 73

4.00
4 .2 3
4 .3 0
4 .7 3
3 .0 0
3 .2 3
3 .3 0
3 .7 3
6 .0 0
6 .2 3
6*3 0
6 .7 3
7 .0 0
7 .2 3
7 .3 0
7 .7 3
1 .0 0
6 .2 3
6 .3 0
6 .7 3
9 ,0 0
9 .2 3
9.311
9 ,7 3
1 0 .0 0
1 0 .2 3
1 0 .3 0
1 0 . 73
1 1 .0 0
1 1 .2 3
1 1 .3 0
1 1 .7 9
1 2 .0 0

A rc T en
• In i
t* .*

r
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 ,9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 8
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6

1 .1 4 3
1 .2 7 0
1 .3 9 7
1 .3 2 4
1 .6 3 1
1 . 776
t ■903
2 .0 3 2
2 .1 3 9
2 .2 6 6
2 .M i
2 .3 4 0
2 .6 6 7
2 ,7 9 4
2 .9 2 1
3 .0 4 6
3 .t7 3
3 .3 0 2
3 .* 2 9
3 .3 3 6
3 .6 6 3
3 .6 1 0
3 .9 3 6
4 .0 6 3
4 ,1 9 2
4 .3 1 9
4 .4 4 6
4 .3 7 3
4.7CXI
4 ,6 2 7
4 .9 3 4
3 .0 6 1
3 .2 0 6
3 .3 3 3
3 .4 6 2
3* 969
3 .7 1 6
3 .6 4 3
3 .9 7 0
4 .0 9 7

46
31
34
36
36

60
62
63
63
66
67
66
69
70
71
71
72
73
73

7m
74
73
73
76
76
76
77
77
77
76
76
76
79
79
79
79
60
60
60
60

( ■ t in )

49
47
24

■"—
3 c ----------(d « | • In )

21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
2L
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21

44
46
39
16
46
09
22
29

31
27

16
06
30
31
09
43
16
49
16
43
11
33
36
19
40
39
16
:i3
32
06
23
36
31
03
17
29
41

49
32
34
37

10
06
43
03

39

09
OU

61
62
6*
63
66
67
66
69
70
71
72
72
73
74
74
73
73
76
76
76
77
77
76
76

7*
7H

1 .1 3 7 1
1 *2 6 6 1
1 .4 1 3 0
1 .3 4 4 6
1 .6 7 4 2
1 .6 0 4 0
1 .9 )3 3
2.11640
2 . 1 9 m)
2 .3 2 3 6
3 .4 3 4 3
2 .3 6 7 1
2 .7 1 9 9
2 .6 4 7 6
2 .9 6 0 0
3 .1 1 1 )
3 .2 4 3 6
3 .3 7 )9
3 .3 1 0 3
3 .6 4 2 9
3 .7 7 6 0
3 .9 0 6 9
4 .0 4 0 6
4 .1 7 6 0
4 *3 0 6 6
*•*4 3 4
4 .3 7 3 b
4 .7 1 1 4
4 .6 4 1 0
4 .9 H I9
) * 11VH
3 .2 3 0 )
3 .3 6 6 8
3 .3 2 0 9
5 .6 6 1 7
5 .7 6 9 *
3 .9 )3 )
6 ,0 4 2 4
6 .1 9 7 0
6 .3 3 7 6

39
09
30
43
30
32
46
39
27
11
32
30
06
39
10
39
06
32
36
19
40

01
20
39

%h
13
29
44
39
12
26
36
30

79
79
79
79
60
60
6 fl
60
61

_

4m

02
__1 -

66*

b h '- r h *

2 .2 7 7
2 .3 )1
2 .7 6 4
3 .0 4 0
3 .2 9 4
3 .3 )0
3 .6 0 4
4 .0 6 2
4 .3 1 6
4 .3 7 )
4 .6 3 0

0 .0 2 7
0 .0 )1
0 .0 3 4
0 .0 4 0
0 .0 4 4

3.U91
5 .3 4 9
3 .6 0 4
3 .6 6 3
6 *1 2 )
6 .3 6 *
6 .6 4 4
6 .9 0 9
7 .1 6 9
7 .4 )1
7 .6 9 2
7 .9 )2
6 .2 1 6
6 .4 7 9
6 .7 4 4
9 .0 0 0
9 .2 7 2
9 .3 )1
9 .6 0 4
H I,U N I
1 0 .3 1 2
1 0 .6 0 1
1 0 ,6 6 3
1 1 .1 4 2
1 1 .3 9 3
1 1 ,6 7 6
1 1 .9 )0
1 2 *1 9 )
1 2 .6 7 2

0,0)0
0 ,0 3 4
0 ,0 6 2
0 .0 6 6
0 .0 7 3
0 .0 6 0
0 ,0 9 1
0 ,0 9 9
0 .1(14
0 .1 1 3
0 ,1 2 3
0 .1 )4
0 ,1 4 4
0 .1 )9
0 .1 6 9
0 ,1 6 1
0 .1 9 2
0 .2 0 2
0 ,2 1 6
0 ,2 2 9
0 ,2 4 4
0 ,2 )0
0 .2 7 2
0 ,2 6 1
0 ,1 0 4
II, i l l
0 *3 3 2
0 .3 3 1
0 .3 6 5
0 .3 9 2
0 .3 9 3
0 *4 2 6
0 .4 1 0
11,44)
0 .4 7 5

i« c
60
1 .3 7 6 3
1 .6 2 9 1
1 .7 3 2 7
1 .6 4 0 2
1 .9 )0 1
2 ,0 6 2 7
2 .1 7 6 6
2 .2 9 )9
2 .4 1 1 4
2 .3 2 9 9
2 .6 )0 )
2 ,7 7 3 6
2 .6 9 6 0
3 .0 1 6 1
3 .1 4 3 )
3 *2 6 6 3
3 ,3 9 4 5
3 *3 2 9 0
3 .6 3 0 2
3 ,7 7 7 7
3 ,9 0 6 1
4 .0 3 4 6
4 .1 6 2 7
4 .2 9 4 1
4 .4 2 )1
4 ,3 )4 3
4 .6 6 1 7
4 .6 1 6 3
4 .9 4 )2
3.1161 1
1 , 71197
5 ,3 4 4 9
3 .4 7 6 6
5 .6 1 0 7
3 .7 4 9 )
3 .6 7 3 1
6 ,0 1 7 0
6 .1 4 4 )
6 .2 7 7 2
6 .4 1 6 0

6 )1 .3 2 .
4 3 1 .6 4
6 9 3 ,0 6
7 )6 *0 6
7 6 0 .0 4
6 2 3 .0 6
6 7 0 .6 4
9 1 7 .3 6
9 6 4 *3 6
1 0 1 1 ,9 6
1 0 6 0 .2 0
1 1 0 9 , 44
1 1 )6 .4 0
1 2 0 7 ,2 4
1 2 )7 .3 2
1 3 0 7 .3 2
1 5 )7 .6 0
14 1 1 .6 0
1 4 6 0 .0 6
1 )1 1,116
1 5 6 2 ,4 4
1 6 1 3 .9 2
1 6 6 3 ,0 6
1 7 1 7 ,6 4
1 7 6 9 .2 4
1 6 2 1 .6 0
1 6 7 2 .6 6
1 9 2 6 .5 2
1 9 7 6 ,0 6
2 0 1 2 .3 2
2<M ) , 8 8
2 1 )7 ,9 6
2 1 9 1 .3 2
2 2 * 4 .2 6
2 2 9 9 .7 2
2 3 3 0 ,0 4
2 4 0 6 .6 0
2 4 ) t . 72
2 )1 0 ,6 6
2 )6 6 .4 0

VS

hv

1 3 .7 6
1 6 .2 9
1 7 ,3 2
1 8 .4 0
1 9 . 30
2 0 .6 2
2 1 .7 6
2 2 .9 3
2 4 ,1 1
2 5 .2 9
2 6 .3 0
27*7 3
2 6 .9 6
3 0 .1 6
31. *3
3 2 ,6 6
3 3 ,9 *
3 3 .7 9
3 6 .3 0
3 7 , 77
3 9 ,0 6
4 0 .3 4
4 1 .6 2
4 2 .9 4
4 4 .2 )
4 5 ,5 *
4 6 .6 1
4 6 .1 6
4 9 .4 3
3 0 .6 1
1*«O V
3 3 ,4 *
3 4 .7 6
3 6 .1 0
3 7 .4 9
5 6 .7 )
6 0 .1 7
6 1 .4 4
6 2 .7 7
6 4 .1 6

3 .0 1
3 .7 1
3*4 1
3 .6 2
3 .6 4
4 .0 6
4 .2 6
4 .3 1
4 .7 3
4 .9 6
3 .2 2
5 .4 6
3 .7 0
5 .9 4
6 .1 9
6 .* 3
6*6 6
6 .9 )
7 .1 0
7 ,3 6
7 ,6 1
6 .0 7
6 .3 3
6 . 39
6 ,6 5
9 ,1 1
9 .3 6
9 ,6 3
9 .6 9
1 0 .1 6
111.41
1 0 .6 9
1 0 .7 6
1 1 .0 4
1 1 . 31
1 1 .5 6
1 1 ,6 *
1 2 ,0 9
1 2 ,))
1 2 .6 2

A P P E N D I X B2
GRID
9h
2 ,2 3
2 .5 0
2 ,7 3
3 ,0 0
3 .2 3
3 .5 0
3 .7 )
4 ,0 0
4 .2 )
4 . 30
4* 73
5 ,0 0
3 .2 )
3 .5 0
3 .7 )
6 , DU
6 ,2 5
6 .3 0
6 .7 3
7 .0 0
7 .2 )
7 .3 0
7 .7 3
6 .0 0
6 .2 )
6 .3 0
8 .7 )
9 *0 0
9 .2 3
9 , 30
9 ,7 3
1 0 .0 0
1 0 ,2 5
1 0 .3 0
1 0 .7 3
1 1 ,0 0
1 1 ,2 5
1 1 .3 0
1 1 .7 )
1 2 .0 0

A r c t h ;—
B ln )

r
1 .9 6 6
1 .9 6 8
1 ,9 6 6
1 .9 6 6
1 .9 6 8
1 .9 6 8
1 .9 6 6
1 .9 6 8
1 .9 6 8
1 .9 6 6
1 .9 6 6
1 ,9 6 6
1 ,9 6 6
1 .9 *4
1,9*1 ■
1 .9 6 6
1 *968
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1*966
1 .9 6 6
1 .9 6 6
1 .9 4 8
1 .9 6 6
1 .9 6 6
1*966
1 .9 6 6
1 ,9 6 8
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 .9 6 6
1 ,9 6 6
1 .9 6 6
1 ,9 6 6

1 .1 * 3
1 .2 7 0
1 .3 9 7
1 .3 2 4
1 .6 5 1
1 .7 7 6
1 *9 0 )
2 .0 3 2
2 ,1 3 9
2 .2 6 6
2 *4 1 )
2 .3 4 0
2 ,6 6 7
2 .7 9 *
2 *9 2 1
3 *046
3 .1 7 )
3 .3 0 2
5 .4 2 9
3 *3 )6
5 .6 6 )
5 . 6 IU
5 .9 )6
4 .0 6 )
4 .1 9 2
4 .5 1 9
4 ,4 *6
4 .3 7 5
4 .7 0 0
4 .6 2 7
4 . 9 )4
3 .0 6 1
3 ,2 0 6
3 .5 5 3
3 .4 6 2
3 *369
3 .7 1 6
3 .6 4 5
3 ,9 7 0
6 .0 9 7

*6
31
3*
36
38
60
62
61
6)
66
67
66
69
70
71
71
72
73
73
74
74
7)
7)
76
76
76
77
77
77
76
76
76
79
79
79
79
60
1 60
60
* 60

49
47
24
44
46
59
16
46
09
22
29
51
27
16
06
30
31
09
4)
16
49
16
4)
11
33
36
19
40
59
16
53
32
06
25
56
31
0)
17
29
41

FOR 450-FOOT ELEVATION
hh 1

11
h h ’ -P h 1

2 .2 7 7
2 .3 5 1
2 .7 6 4
3 ,0 4 0
3 ,2 9 4
3 .3 3 0
3 .6 0 4
4 .0 6 2
* ,3 1 6
4 .3 7 3
4 .6 )0
5 .0 9 1
5 .5 4 9
5 .6 0 4
3 *665
6 .1 2 3
6 .3 6 4
6 .4 * 4
6 ,9 0 9
7 *1 6 9
7 ,4 )1
7 ,6 9 2
7 .9 )2
6 .2 1 6
6 *4 7 9
6 .7 4 4
9 .0 0 0
9 .2 7 2
9 .3 )1
9 .6 0 4
1 0 .0 6 1
1 0 .3 3 2
1 0 *6 0 1
1 0 .6 6 )
1 1 .1 4 2
1 1 .3 9 3
1 1 .6 7 6
1 1 *9 3 0
1 2 .1 9 3
1 2 ,4 7 2

0*037
0 .0 )1
0 .0 3 4
0 .0 4 0
0 .0 4 4
0,11)0
0 ,0 3 4
0 ,0 4 2
0 .0 4 6
0 ,0 7 5
II .0 6 0
0 .0 9 1
0 .0 9 9
0 .1 0 4
0 ,1 1 )
0 .1 2 3
0 .1 3 4
0 ,1 4 4
( 1 .1 )9
0 .1 6 9
0 ,1 6 1
0 ,1 9 2
0 .2 0 2
0 .2 1 6
0 ,2 2 9
0 . 244
0 .2 3 0
0 ,2 7 2
0 .2 6 1
0 ,3 0 4
0 *3 1 1
0 .3 3 2
0 ,3 3 1
0 .3 6 )
0 .3 9 2
0 .3 9 3
0 *4 2 6
0 ,4 3 0
0 .4 4 3
0 ,4 7 )

T nn
(■ In )

(d t|

21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
2t
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
22

49
52
34
37
39
61
62
64
65
66
67
68
69
70
71
72
72
73
74
74
7)
7)
76
76
76
77
77
76
76
76
76
79
79
79
79
60
60
60
60
61

- • ■—-

■ In )
10
06
4)
0)
09
00
39
09
30
4)
30
32
46
39
27
11
52
30
06
39
10
39
06
32
36
19
40
01
20
39
36
13
29
44
39
12
26
36
30
02

J

1 *1 )7 1
I . 2661
1 .4 1 )0
1 .5 4 4 6
1 .4 7 * 2
1 .6 0 4 0
1 ,9 5 5 )
2 .U 6 4 0
2 *1 9 4 3
2 ,3 2 3 6
2 .4 )4 )
2 .3 6 7 1
2 *7 1 9 9
2 -6 4 7 6
2 .9 6 0 0
5 .1 1 1 )
5 .2 4 )6
5 ,3 7 )9
5 .3 1 0 3
3 .6 4 2 9
3 ,7 7 6 0
3 .9 0 6 9
4 ,0 4 0 6
4 ,1 7 6 0
4 .5 0 6 6
4 .4 4 3 4
4 .3 7 5 6
4 .7 1 1 4
4 ,6 4 3 0
4 .9 6 1 9
3 .1 1 2 6
3 .2 3 0 )
3 .3 6 6 6
5 .3 2 0 9
3 *6 4 1 7
3 ,7 6 9 4
3 ,9 3 3 )
4 .0 6 2 4
6 .1 9 7 0
6 .2 )7 6

A rc
-A 1 *3 7 6 5
1*6 2 9 1
1 .7 5 2 7
1 .6 4 0 2
1 .9 3 0 1
2,(1627
2 .1 7 6 6
2 *2 9 5 )
2 * 4 |L 4
2 .5 2 9 9
2 .6 5 0 3
2 ,7 7 3 6
2 *6 9 6 0
3 .0 1 6 1
5 .1 4 3 3
3*2 6 6 )
3 .3 9 4 )
3 .3 2 9 0
3 *4 3 0 2
3 .7 7 7 7
3 ,9 0 6 1
4 . f l1 * 6
4 *1 6 2 7
4 .2 9 4 1
4 .4 2 )1
4 .3 )4 5
4 *6 6 1 7
4 .6 1 6 3
4 .9 * 5 2
3 *0 6 1 3
3 ,2 0 9 7
3 .3 4 4 9
3 .4 7 6 6
3 ,6 1 0 7
3 ,7 4 9 3
3 .6 7 )1
6 .0 1 7 0
6 ,1 4 4 3
6 .2 7 7 2
6 .4 1 6 0

Sl>
HD
7 1 0 .2 3
7 3 3 *0 9
7 7 9 *7 1
8 2 6 .0 9
6 7 7 .5 4
9 2 6 *2 1
9 7 9 , 47
1 0 3 2 *0 7
1 0 6 5 *1 )
1 1 3 6 .4 3
1 1 9 2 *7 2
1 2 4 6 *1 2
1 5 0 3 *2 0
1 )3 9 ,1 4
1 4 1 4 .4 6
1 4 7 0 .7 3
1 5 2 7 .) 2
1 3 6 6 ,0 3
1 6 4 2 ,3 9
1 6 9 9 .9 6
1 7 3 7 .7 4
1 6 1 5 .6 6
1 6 7 3 *2 1
1 9 5 2 ,3 4
1 9 9 0 *3 9
20 4 9 *5 2
2 1 0 6 .7 6
2 1 6 7 .3 )
2 2 2 3 .3 4
2 2 8 6 .3 6
2 3 4 4 .3 6
2 4 0 5 .2 0
2 4 6 3 .4 4
2 )2 4 .6 1
2 )6 7 .1 6
2 6 4 3 .7 9
2 7 0 7 ,6 3
2 7 6 4 .9 3
2 6 2 4 .7 4
2 6 6 7 *»

VS
1 7 .7 3
1 6 ,3 2
1 9 .4 9
2 0 . 70
2 1 .9 3
2 1 .3 0
2 4 .4 6
2 5 .6 0
2 7* 12
2 6 .4 6
2 9 .8 9
3 1 .2 0
3 2 ,5 6
3 3 *9 3
3 5 *3 6
56* 76
36* | 6
3 9 . 70
4 1 .0 6
4 2 *4 9
4 3 ,9 4
4 5 .3 9
4 6 .H)
46*3(1
49*7 3
3 1 ,2 3
3 2 *6 6
3 4 .1 6
3 3 .6 3
3 7 .1 6
3 6 .6 0
6 0 ,1 3
4 1 ,6 3
6 3 .1 2
6 4 ,6 7
6 6 .0 9
6 7 ,6 9
6 9 .1 2
7 0 ,6 1
7 2 .1 0

hv
3 .0 1
3 .2 1
3 .4 1
3 .6 2
3 .6 4
4 ,0 6
4 ,3 8
4 ,3 1
4 *7 3
4 .9 6
3 .2 2
5 ,4 6
3*7 0
5*9 4
6 ,1 9
6 *4 3
6 .6 6
6 .9 )
7 .1 6
7 ,3 6
7 .6 1
6 .0 7
6 ,3 3
6 .3 9
6 .6 )
9 .1 1
9 . 36
9*6 5
9 *6 9
1 0 ,1 6
1 0 , 42
1 0 *6 9
10*7 6
1 1 .0 4
1 1 .3 1
1 1 .3 6
1 1 .6 4
1 2 .0 9
1 2 ,3 )
12*6 2

142
A P P E N D I X B3
GRID F O R 500—FOOT ELEVATION
9h
a .15
2 .5 0
2 .7 5
3 .0 0
3 .2 3
3 .3 0
3 .7 3
4 .0 0
4 .2 3
4 .5 0
4 .7 3
3 .0 0
3 .2 5
3 .3 0
3 .7 3
6 .0 0
6 .2 3
6 .3 0
6 .7 5
7 .0 0
7 .2 3
7 .3 0
7 .7 3
6 .0 0
6 .2 3
6 .3 0
6 .7 3
♦ .0 0

♦ .a s
9 .3 0
9 .7 3
1 0 .0 0
1 0 .2 3
1 0 .3 0
1 0 .7 3
1 1 .0 0
1 1 .2 3
1 1 .3 0
1 1 .7 9

1 A rc t a n
■46)
(♦ •6

(
1
1
1
1
1
1
1
1

I
1
1

1
1
1
1
I
1

1
1
1
1
1
1
1
1
1
L

1
1
1
1
I
1
1
1

I
1
1
1

1 2 .0 0
*

96«
946
960
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
966
9 66
9 66
966
966
966
966
966

1 .1 4 3
1 .2 7 0
1 .3 9 7
1 .3 2 4
1 .6 3 1
1 .7 7 6
1 .9 0 3
2 .0 3 2
2 .1 3 9
2 .2 6 6
2 .4 1 3
2 .5 4 0
2 .6 6 7
2 .7 9 4
2 .9 2 1
3 .0 4 6
3 .1 7 3
3 .3 0 2
3 .4 2 9
3 .3 3 6
3 .6 6 3
3 .6 1 0
3 *936
4 .0 6 3
4 . 192
4 ,3 1 9
4 .4 4 6
4 .3 7 3
4 .7 0 0
4 .6 2 7
4 .9 3 4
3 .0 6 1
3 .2 0 6
3 .3 3 3
3 .4 6 2
3 .3 6 9
3 .7 1 6
3 .6 4 3
3 .9 7 0
6 .0 9 7

49
47
24
44
46
39
16
46
09

46
31
34
36
36
60
62
63
63
66
67
66
69
70
71
71
72
73
73
74
74
73
73
76
76
76
77
77
77
76
76
76
79
79
79
79
60
60
60

22
29
31
27
16
06
30
31
09
43
16
49
16
43

11

I

33
36
19
40
39
16
33
32
06
23
36
31
05
17
29
41

X

21
21
31
21
21
21
21
21
21
21

21
21
21

21
21

21
21
21
21
21
21
21
21
21
21
21
21
71
21

49
32
'4
37
39
61
62
64
65
67
69
70
71
72
72
73
74
7%
73
73
76
76
76
77
77
76
76

21
21
2!
31

21
21
21
21
21
21

66*

■ in )

la in )

76
79
79
79
79
60
60
60
60
61

10
06
43
03
09
00
39
09
30
43
30
32
46
39
27
11
32
30
06
39
10
39
06
32
36
19
40

01
20
39
36
U
29
44
39
12
26
36
30
02

1 .1 3 7 1
1 .2 6 6 1
1 .4 1 5 0
1 .3 4 4 6
1 .6 7 4 2
1 .6 0 4 0
1 .9 3 3 3
2 .0 6 4 0
2 .1 9 4 3
2 .3 2 3 6
2 .4 3 4 3
2 .3 6 7 1
2 .7 1 9 9
2 .6 4 7 6
2 .9 6 0 0
3 .1 1 1 3
3 .2 4 3 6
3 .3 7 5 9
3 ,3 1 0 3
3 .6 4 2 9
3 .7 7 6 0
3 .9 0 6 9
4 .0 * 0 4
4 .1 7 6 0
4 .3 0 6 6
4 .4 4 3 4
4 .3 7 3 6
4 .7 1 1 4
4 *6 4 3 0
4 .9 6 1 9
3 .1 1 2 6
5 *2 5 0 9
3 .3 6 6 6
3 .3 2 0 9
3 .6 6 1 7
3 .7 6 9 4
3 *9 3 3 3
6*0 6 2 4
6 .1 9 7 0
6 .3 3 7 6

t

M l'-P H *

2 .2 7 7
2 .3 3 1
2* 764
3 .0 4 0
3 .2 9 4
3 .3 3 0
9 .6 0 4
4 *0 6 2
4 .3 1 6
4 .5 7 3
4 .6 3 0
5 .0 9 1
5 *9 4 9
3 .6 0 4
3 .6 6 5
6 *123
6 .3 6 4
6 .6 4 4
6 .9 0 9
7 .1 6 9
7 .4 3 1
7 .6 9 2
7 .9 3 2
6 .2 1 6
6 .4 7 9
6 .7 4 4
9 .0 0 0
9 .2 7 2
9 . 331
9 .6 0 4

0 .0 2 7
0 .0 3 1
0 .0 3 4
0 .0 4 0
0 *044
0 *050
0 *034
0 *062
0 *066
0 .0 7 3
0 .0 6 0
0 .0 9 1
0 .0 9 9
0 .1 0 4
0 .1 1 5
0 .1 3 3 '
0 .1 3 4
0 .1 4 4
O , 139
A , 169
I f . 161
0 ,1 9 2
0 *2 0 2
0 .2 1 6
0 .2 2 9
0 *2 4 4
0 *2 5 0
0 .2 7 2
0 .2 6 1
0 .3 0 4

1 0 *9 9 1
1 0 ,3 3 1
1 0 .6 0 1
1 0 .6 6 3
1 1 .1 4 2
1 1 .3 9 3
1 1 .6 7 6
jll. 9 3 0
1 2 ,1 9 3
1 2 *4 7 2

0 .3 5 2
0 ,3 3 1
0*363
0 .3 9 2
0 .3 9 3
0 *4 2 6
0 *4 3 0
0 .4 4 3
0 *4 7 5

a\ V mi\

*
ho

1 *3 2 9 4
1 .6 2 9 1
1 .7 3 2 7
1 .6 4 0 2
1 .9 5 0 1
2 .0 6 2 7
2 *1 7 6 6
2 .2 9 3 3
2 *4 1 1 4
2 .3 2 9 9
2 .6 3 0 4
2 .7 7 3 6
2 .6 9 6 0
3 .0 1 6 1
3 .1 4 3 3
3 .2 6 6 3
3 *3 9 4 3
3 .3 2 0 9
3 *6 5 0 2
3 .7 7 7 7
3 .9 0 6 1
4 .0 3 4 6
4 .1 6 2 7
4 .2 9 4 1
4 *4 2 3 1
4 * 3343
4 ,6 6 1 7
4 .6 1 6 3
4 .9 4 3 2
3 .0 6 1 3
3 ,2 0 9 7
5*3 4 4 9
3 .4 7 6 6
3 .6 1 0 7
3 .7 4 9 3
3 .8 7 3 1
6 .0 1 7 0
6 .1 4 4 3
6 .2 7 7 2
6 .4 1 6 0

7 6 4 .7 0
6 1 4 .3 3
6 6 6 .3 3
9 2 0 *1 0
9 7 3 .0 3
1 0 3 1 .1 3
1 0 9 6 .5 0
1 1 4 6 *7 3
1 2 0 5 *7 0
1 2 4 4 ,9 5
1 3 2 3 .2 0
1 3 6 6 .6 0
1 4 4 6 *0 0
1 5 0 9 *0 3
1 5 7 1 *6 3
1 6 3 4 .1 3
1 6 9 7 .2 3
1 7 4 0 .4 3
1 6 2 5 .1 0
1 6 6 6 .6 5
1 4 3 3 .0 5
2 0 1 7 .4 0
2 0 6 1 .3 3
2 1 4 7 *0 3
2 2 1 6 .0 3
2 2 7 7 *2 3
2 3 4 0 .6 3
2 4 0 6 *1 3
2 4 7 2 .6 0
2 3 4 0 *6 3
2 6 0 4 .6 3
2 6 7 2 .4 5
2 7 3 9 .4 0
2 6 0 5 ,3 5
2 6 7 4 .4 5
2 9 3 7 .3 3
30 0 6 *5 0
3 0 7 2 ,1 3
3 1 3 6 ,6 0
3 2 0 6 ,0 0

15

1 9 ,1 1
2 0 .3 6
2 1 .6 3
2 3 .0 0
2 4 .3 7
2 3 .7 6
2 7 .2 0
2 6 *6 6
3 0 .1 4
3 1*62
3 5*13
3 4 .4 7
96. 2 0
3 7 ,7 2
3 9 .2 9
4 0 ,6 3
4 2 .4 3
4 4 *0 1
4 5 *6 2
4 7 .2 2
4 6 *3 7
3 0 .4 3
52*0 3
3 3 .6 7
5 3 .4 0
36*9 3
56*3 2
6 0 ,2 0
6 1 .9 1
6 3 .3 1
6 3 .1 2
6 6 *6 1
6 6 ,4 6
7 0 *1 3
71*6 6
7 3 .4 3
7 3 .2 1
7 6 .6 0
7 6 ,4 6
6 0 .2 0

hv
3 .0 1
3 *2 1
3 *4 1
3 *6 2
3 *6 4
4 ,0 6
4 *2 6
4 ,3 1
4 ,7 5
4 .9 6
3 *2 2
5 .4 6
5 .7 0
5 .9 4
6 .1 9
6 .4 3
6 ,6 6
6 .9 3
7 ,1 6
7 .5 6
7 ,6 1
6 .0 7
6 .3 3
6 .5 9
6 .6 3
9 .1 1
9 .3 6
9 *6 3
9 .6 9
1 0 .1 6
1 0 .4 2
10*6 9
1 0 *7 6
1 1 .0 4
1 1 .3 1
1 1 .5 6
1 1 .6 6
1 2 .0 9
1 2 .3 5
1 2 .6 2

APPENDIX C
TABLES

SHOWING SAMPLE DISPERSION COEFFICIENTS,

TOTAL DISPERSION C O E F F I C I E N T S , SPACE
CONSUMPTION

SAMPLE COEFFICIENTS AND

SPACE CONSUMPTION TRACING
PAPER COEFFICIENTS

143

A P P E N D I X Cl
SAMPLE DISPERSION COEFFICIENTS AND TOTAL DISPERSION
C O E F F I C I E N T S F O R U N I O N , C A S S , A N D O R C H A R D LAKES
(JULY 17, 1969)
_________
Dl a p a r t to n
L ake

JIB.
U n io n

oooo

TBST

O rc h a rd

“TORT

w

Caaa

orchard

1400

Caaa

1400

Oretiiri

tH a p a ria n
T o ta l

iMpll

IHaporalfin

-

“

"
fc a 2.13
1.30
1*93
2.93
2*33
1 .3 4 . . . - -

1.31
1*97
2 .0 0
1.27
1*03
2.10
1.82
3*90
3 .4 6
3,28
1.60
2.77
2*23
1.61
1.0ft
3 .6 4
4*3?
2.13
2.33
1*69
2.43
2 ,3 9
L IU

• a a p ln

Jl t f l l r l T I

1
,73
1.41

0 .0 0
0 .0 0
1 .24
1.24
0 ,0 0
0 ,0 0
n .io
n. i ft
0 ,6 }
0 .3 6
o .o n
0 .0 0
2.7 4
2*74
_2*oo
. QaAfi------1
0 .4 3
n.-ai
1.7 ft
3 .12
1.84
1.49
n.n o
0 .0 0
o .o o
0 ,0 0
0 .0 0
0 .0 0
U.83
0 .7 2
7.7 ft
2 .76
0 .4 9
___
---------a . u —
0.62
3.14
3.16
1*41
t . ftf t
o.o u
U.00
3*62
3.30
2.13
2.13
2.1ft
2.11
2.11
2.16
2.16
2*12
2.AH
1.41
1.4L
0 .6 ft
0 . 66
0 .0 0
0 .0 0
1*19
1.19
0 .7 1
1.17
■ “
i ;« t —
1.96 ’
3.00
1 .3ft
4 .4ft
3.43
0 .0 0
o .o o
2 .4 0
2.39
2 .2 4
2*11
0.0(1
0.00
0*00
u*uo
1 ,84
2 .2 4 ___
2 .20
* 1 *1 5 — 1
2*79
3 .1 ft
1*53
1 .33
0.97
0 .9 7
3 .17
3.17
2 .09
2 .0 9
2 .1 0
1.30
‘ •‘ i ; 9 r 1*91
1
2.27
1.46
1*09
1*75
1.37
2 ,13
1.11
1 .46
0.72
0 .3 7
2 .1 )
1.33
_ W ? I ___
2. S3
- .........M S 4*03
3.62
4 .1 9
4 .2 ft
4 .3 7
3 .62
3 .13
2 .9 ft
1.92
1 .99
1 .36
2.23
1 .34
1.23
2 .97
4.42
0 ,0 0
0*00
2*74
2*30
2*03
1.36
1.22
1.62
2.83
1.60
2 .26
1,63
1.21
_ t.tt
1 .73
2.2 ft
2.0 ft
1*33
1.19
3.04
2 .06
3 .9 3
3 .3 6
3 .12
2.30
3.41
2*23
1.61
1.30

Lahi

iHUl&iMk.

1.40
1.13
I.U3
1.33
2.17

1.66
7TT"

i.o»
1.23
3 .14
2 .26
2*32

3. 14
K II
3.17
1 .33
2.2ft

1TW I

7.11
ilA0 .9 6

O rc h a rd

'lWHJ

---4

TTST

U n io n

TfBT

"TO

Orchard

-\ -

i
j~

i
.

.1

.1

1
.17
7.01

0 .7 4
2 .33
1*60
1. 79
l.ft'J
2 .28
1.97
■ r ; s v -------1.54
1 ,84
2.21
6.32
1,27
3.27
2. 34
‘ 6 .04
4 .02
7. 79
2*90
3*40
1.08
1 .0 9
l.ft6
3 .3 )
----------r ru ft —
3.31
1 .6 6
1 .1 3
2 .2 3
2. 64
2 ,61
—
htt____
? f2 2 ____
1
1.67
1.73
1.30
1 .3 9
1 .3 9
1*13
:. 9 o
1*23
0 .0 0
0 .0 0
n . ?o
0 .7 0
. . ... .
2 .4 0
1*73
.... - 1 ? * *
3 .4 7
iv w
6.06
2*82
2.40
3*37
3.64
3 .9 ?
2.41
2 .1 0
1*69
2.36
1,01
l.o l
2*10
2 .3L
2 .4 4
TTiJT------—
“ *
3 .0 0
2.30
2*03
1 .3 9
1,94
1*90
2,9 3
3*09
2.97
3.31
2.4 3
3,22

2 .6 4
2 .2 4
1.69
3 .17
2*72
2*53
~
1 .3 *~ “
2.43
2.01
2.41
1.28
1 .3b
3.27
2 .34_
2 ,4 0
4 .13
4*21
4*23
3 .33
1.07
1*09
2.52
3 .0 9
--------' l . W “
2.53
2*05
1*50
2.83

Union

1 .6 1
1 .1 9
2. 14
2 .2 4
0 .9 3
1.34

1.00
imr

1.20

W

A la p o r a lp n
Tot a!

C— £11 c I

APPENDIX C2
SPACE CONSUMPTION SAFETY COEFFICIENTS AND SPACE CONSUMPTION TRACING PAPER COEFFICIENTS
FOR UNION, CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)
' Ipne* CnneMttlnn
W i n
Trnclnf

0*00 I Unlnn

lorn

IfttHltlri)

0.01
0.0T
0.00
0.0*
0.00
0.03
0*07

n

U00

1 Cm *

0.1*
0.00
O.Ot

1000

UMW

*■|.i) 1000

1000

Att«. 1]

Cm *

Orcbnr*

1100 | Onion

00.60

01.1*
00.00
oo. n

00.11
01.**

00.11
00.13

00.1*
00.1*
00.13
00.lt
00.1*

01.10

0.0*
o.»
0.1*

0.11

00.17
01.00
01.**
00.77

0.1*

01.U

0.03
0.30

0.11
0.3*
0.61
o.u

Out. 11 1100' Onion

ob.it

0.0*

0.10
0.11
0.11
0.11

A*. 21 1200 Orcbnrl

00.

0.01
0.01
0.03
0.01
0.01
0.01

0.13
0.U
0.11
0.1*
o.to
o.n
0.1*
0.11
o.oT
0.1*
0.13
0.07
0.06

h *.

23 1100

Cm*

A*. 13 1100 Qretnri

01.*7

wnrl

00.70
01.07
00.31

0.13
0.13

01.13

0.1*

00.**

TTTT

Ukn

Au|. 23 1*00

Orchnrt

An(. 21 1300

Union

An*. 11 1300

I

Con

I
j
I

01.11

0.11 01.0*
0.11 01.10
0.1* 03.13
0.1* Ol.tl
01.Of
0.13
0.10 00.11
0.11 01.70

0.03

0.**
0.10
0.*1
0.13

0.11
0.11

Ao*. 13 1*00

Oslo*

"Of
0.30

01.03
00.00
00.61
00.11
00.**

00.1*

01.31
01.13
TC7T

Tin*

Dtt*

(

tag* ^3

1300

Dtcfcnrt

01.1*
01.lt
01.31
01.63

tog.

U

1*00

Union

0.14

01.31
01.01
00.**
01.31
Ol.tl
00.3*

ul.lt
01.00
ul.tt
01.*»
01.7*
02.01
ot.ot
Ol.SS
ul.ll
inn*'
00.t*
Ol.tt
01.0*

0.11
0.11

0.11
0.1*

00.03

00.01

0.1*
0.17
0.10
0.23
0.11
0.19
0.11
0,16
0.10
0.07
0,07
0.1*
0.07

0.U
0.U

lo*.11 1*00
I

01.*0
Ol.tl

01.09
01.0*

01.1*

01.01

01.0*
00.73
01.**
01.70
01.11

00.*1

0.00
0.11

00.00
01.01

0.3*
0.1*
0.*3

M.0»

0.10
0.10
0.17
0.11
0.12

i
7

01.71
OLOO
01.lt

0.0*

0.*3
0.3*

L

■

Cm *

00.1*

00.43
00.17
10

0.10

1100

00.00

0.00
0.0*
0.0*

O .tl

h*. U

00.19

00.1*
00.0*

'SB*

Tint

00,00 i

0.01

0.17

0*00 T OrcUr*

00.6*!

0.03

0.00
■. ii

00.13 I

Otti

a

Utt

I

TIm

>pic« C n riu a fc ln n
3* 1*13 T r n c ln f
to n *
it M ff lf l* m >

T

1*00

02.1*
03.31

01.43
01.73
01.01

01.12
O l. tl

07.11
01.02

J>U7

An*. 11

1600

Ukn
ton*

1
1
3
*
3
6
7
1
"
I
1
*
3
6
7
0
~f '
2
3
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3
6
7
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1
1
1
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3
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7
1
2
3
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3 !
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1
2
1
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3
6
7
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1
2
1
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3
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7 !

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Intei

(pK* C o m u ^ t l m
lltM)
TtOCit'l
l*t«
0.**
01.3*
01.03
0.30
0.07
01.00
Ol.tl
0.11
01.12
0.20
00,71
0.0*
0.2*
01.23
~n.o*
t. U
01.tt
0.A1
0.10
00 .to
ot.ot
0.30
0.1*
ot.lt
02.0*
0.21
01.7*
0.**
0.3*
Dt.03
0.11 ■"OT.t*
0.15
01.01
Ol.tl
0.**
0.12
Ol.tl
0.11
01.3*
03.07
0.1*
07.11
0.4*
0.2*
02.3*
0.33
03.2*
6.0 ■ ■ n : w
02.70
o.»
0.17
01.(0
01.4*
0.27
0,10
Ol.tl
0.20
Ol.tl
00.7*
0.0*
64.06
0.31
01.**
0.23
01.41
0.37
01.03
02.07
0.17
01.71
0.22
0.2*
01.0*
0.6*
06.70
0.37 ~ 02.H 1
0.10
00.**
0.27
01.1* !
0.**
02.7*
0,3*
02.73
00.93
0.10
03.40
0.4*
0.**
00.20
0.70
ai.ni
0.13
M.U

....

0.1*
0.17
0.13
0.1*
0,11

---- 1________i

00.I*
01.11
02.03
01.13
Ol.tl

Catwtma’ iam

Ukn

A*. 11

•*«. U

An*. 23

As*. 11

An*. 11

Am-

Tim

LU«

lam

1700 Union

1
1
3
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3
t
7
*
1700 Ca m
1
2
1
*
3
i
7
0
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1700 OrchaN 1
1
1
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3
*
7
lift1 Dalm
1
2
1
*
3
(
7
*
1*00 Cm i
1
2
3
*
3
(
7
1

u

1900 Orchard

24

0100 Tr Im

1
1
3
A
3
6
7
1
2
1
*
3
I
|7
r

ten;,
0.3*
0.33
0.4*
0.40
0.33
0.01
0.31
0.1*
6.M
0.11
0.U
0.1*
0.23
0.11
0.1*
0.0*
0.40
0.0*
0.1*
0.27
0.01
0.13
0.20
--0.27
0.1*
1.11
0.17
0.U
0L4*
0.11
0.17
0.10
0.23
0.02
0.23
0.22
0.0*
0.1*
0.00
o.5
0.12
0.1*
0. 0
O.Ot
0.10
0.03
1.(1'
0.23
0.01
0 .M
0.00
0.03
0.0*
0.03

01.7*
02.7*
03.0*
03.0*
01.17
00.10
03.01
04.21
01.11
02.0*
01.02
00.41
01.**
04.20
04.10
01.13
04.03
01.t*
02.11
01.0*
00.13
01.72
01.H
------Ol.tl
n.**
I0L71
01.11
01.30
01.3*
n.u
W.TO
01.11
01.4*
00.33
01.71
01.7*
01.40
02.40
01.11
00.11
01.11
00.07
00.1*
00.31
01.10
00.1*
'W.H
01.10
00.11
01.17
00.00
00.1*
00.33
00.1*

APPENDIX C2— Continued

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4a|. 2*

Tlw
0100

Ao|. 2*

Lak*
Caaa

Orckari

4B|. »

10DQ

Oalaa

fef- 2*

1000

Caaa

i*

ta». >*

1000

lHH

iWo

Orckari

Dale*

1
2
J
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4
7
1
0
1
2
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4
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1
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1
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7
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2
3
4
3
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7
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00,24
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00.32
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0.02
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01.03
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02.17
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01.00
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01.40
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02.43
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04.11

Lak*

4a|. 24

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laf.

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24

4*f. 24

A*f. 24

4*0- 24

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24

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1400 talon

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Zona
I
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3
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1
2
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2
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2
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2
3
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3
4
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1
2
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Spies Canajaptian
Safata
Traclni
[Caafflriant)
00.00
0.00
02.43
0.10
01.42
0.22
02.04
0.27
02.07
O.K
0.21
01.44
0.23
02.00
00,47
0.11
0.20
01.03
01.47
0.23
02.12
0.44
00.17
0,02
00.(2
0.01
03.1(
o. u
01*31
0.31
02.72
0.34
00.3(
0.00
02.20
0.34
02.27
0.14
02.43
0.21
02.(7
0.10
13,(4
0.(0
0.24
01.13
03.11
D.3(
' 6.K " U T . H 01.14
0.31
0.23
01.74
02.23
0.23
02.(3
0.23
01.13
0.13
02.31
0.13
0.41
01,73
0.47
01.14
0.40
03.13
0.71
03.(7
00.17
0.17
02.31
0.30
0.71
03.70
0,34
04.(5
" '4.U04.30
04.41
0.30
02.24
0.34
0.20
02.21
04,02
0.34
03.10
0.30
14.34
O .K
O.K
02.11
04.74
0.(4
i c r
i m r
0.44
01.(2
0.24
02.23
04,(1
0.72
01.07
0.21
0.11
02.10
0.23
02.12
0.40
S . 04
0.43
03.40
0.14
02.14
0.47
04.23
0.20
01.31
02.17
0.10
04.(4
0.44
04.10
0.34

Data

laka
Zaaa

lim

Aa|. 24

1300 Caaa

Aug. 24

IMA Orckari

lat. 24

iwA

4a«. 24

1(00 Caaa

“* 5 n r

id. 14

■WB

balaa

OrcMra

1(00 Oalaa

1
2
1
4
3
4
7
4
(
1 1'
2
1
4
5
4
7
1
2
3
4
3
4
7
1
' I
2
3
4
3
4
7
1
(
1
2
3
4
5
4
7
1
2
1
4
3
4
7

1(00 Caaa
2
1
4
4
7
1
(

tpac* Conai^tlan
Salats
Trad-*

0.47
0.1(
0.47
0.42
0.41
0.33
0.14
0.43
0.30
7i:rr
0.31
0.27
0.34
0.2(

04.41
02,32
02.70
03.35
03.42
03.07
11.44
04.34
07.05
01.lt
03.11
02.32
04.14
02.74

Laka
Zaaa

Tina
in|. 24

0.14
B.U
0,32
0.40
0.71
0.11
0.11
1.11
O.U
0.40
0.41
0.30
0.32
0.31
0.30

03.0(
03.04
01.43.
I
03.23
04.20 j
00.44
01.10
f
07.07
i
04,40
AMA
03.10
03.42
03.32
•
02.H
03.32

0.04
0.40
0.10
0.40
0.20
0.10
0.40
0.20
0.31
0.33
0.11
0.44
0.24
0.14
0.27
0.24
Q.2i
0.30
0.24
0.24
0.21
0.35
0.44
0.31
0.14
0.44

03,41
04.10
n.n
03.24
02.03
02.40
03.(0
02.14
03.44
02.10
02.11
02.04
01.34
01.42
02.24
01.11
02.37
02.17
01.31
01.70
01.07
02.47
02.44
03,00
00.14
04.74

1(00 Orckari

-

*

|
1
1
i
1
|

1
2
3
4
3
4
7

Saac* h r awa'laft
Safat- Traced
0.07
0.10
0.00
0.13
0.2*
0.13
0.20

00.31
00.(4
00.(3
00.(4
01.44
01.11
01.51

145

*i- 2*

tpaca Caoft^ptlan
uk * Safat* - Traclni
In*
ICaafdelate)

APPENDIX C3
SPACE CONSUMPTION TRACING PAPER COEFFICIENTS AND SAMPLE DISPERSION COEFFICIENTS FOR
UNION, CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)

Lak*

Aag* 23

a

i

Oaf. O

0*00

UniM

1
1
3
4
3
*
T

0100

Ciu

1
1
3
*
3
4
7
1

0*00

1000

1000

Orcbar*

HUM

Caaa

l"
1
3
4
3
4
7
" I
1
3
4
3
4
7
1
1
2
3

4

tea. 13

4*. 13

1000

1100

5
4
7
0
0
OrckaH
1
1
3
4
3
t
_ 7....
Doi*a
2
3
4

7
1

0.13
0.44
0.00
0.20
0.00
0.34
0.40

- H0,00r 0.22
0.24
0.04
0.43
0.37
0.10
0.31
1.4*
ITT
0.1*
0.1*
0.33
0.1*
0.1*
0.11
B.B
3.10
0.37
1.00
1.4*
0.77
--—
1.23
D.«]
0.02
2.31
1.01
l.*7
0.4*
1.31
1.42
0.34
■ff.IT1.03
0.00
0.41
0.32
0.4*
O.tt
A.'TT
2.07
0.32
2.10
1.41
3.1*
2.04
1.14

01.41
01.**
00.00
00.44
00.00
00.44
02.04

Oat*
te«. 23

T1m
1200

U ka

space (Sa. ilaparafan
Laka Traclni lapi ’ Saapla
Zaaa

C ut

1
1
3
4
3
4
7
4
*
Orckari “ T
2
3
4
5
*
7
Dalea " !
2
3
4
3
4
7
•
“T
0*4*

. si*7*
00,00
01.73
te,.-n lift
01.44
00.00
01.04
01.41
00.47
00.41
01.34
te|. 13 u u
" oi.67 —
03.17 ]
01.4*
02.33 1
02.73
01.43
02.34
U.H
ta4. 13 IMA
01.41
00.40
01.30
01.44
01.11
....
01.13
BJ.I*
. 06,3*
te(. 23 U00
Orckari
03.*3
03.43
03.13
01.31
01.34
01.01
03.22
la,. 13 i«B n s i M 1'
00.00
02.44
02.11
01.33
01.44
02.10
02.40
L
oi.ii
tag* 23 140(P Caaa
02.47
j
02.*2
1
1
02.17
■
01.40
01.6*
01.43
oo.u

2
3
4
3
4
7
•
t
1
2
3
4
s
6
7
1

I
3
*
S
6
7
S
I
2
3
4
3
6
7
a
J-

03.14
1.34
1.04
03.14
03.44
1.44
1.4*
03.37
1.74
01.04
2.02
02.21
01.14
4.0*
02,13
2.33
44
02,19
1,21
" “ ITTT*' TJTTK
0.4*
03.03
01.43
1.4*
1.0*
01.6*

Data

TiM

Laka

bf. 21

1400

Orchari

la*. 23 iUB

02.21
1.53
02.23
1.13
ISA*
---KXl--- T H . B
01.94
2.*3
02.41
2.11
0**4
01.10
1.0*
01.24
01,07
2.14
3.23
02.30
00.44
1.61
si,n
r*r
b«. 21 1300
0,*1
03.04
1.7*
03.00
03.14
1.34
02.*2
1.16
1.3*
02.03
------01.»
1.43
b*. 23 1400
1.33
02.93
T.TBM.H
02.24
1.71
01.*4
2.00
2.34
01.73
03.47
2.04
0.73
02,24
l.«*
01.34
b*. U 1400
■ i : w ■ "BI.I*
3.33
02.0*
0.91
01.14
-----0.00
00.00
1.41
01.40
01.4*
2.14
1.04
01.73
3.53
44.it
M*. 23 1400
04,7*
1.63
1.73
04.24
1.41
03.1*
1.31
02,72
02.43
1.14
7.12
01.90
3.42
01.49
_.*JI--- . S U B ___

Hiln

Cut

Sptct Con*.
U k* Tr*ein|
Za h
I
2
2
4
J
4
7
T ‘
2
3
4
3
6
7
a
2
3
4

5

Ordin

M«

r

C«M

Orck*n

1
7
a
*
1
2
3
4
S
1
7
1
2
3
4
S
a
7
1
2
3
4
5
4
7
a
a
I
2
1
4
S
6
7

3.34
3.03
1.00
1.41
2.11
0.73
2.23
""J. K
2a39
0.**
4.04
2.44
1.04
1.74
6.13
i aR
1.42
1.93
1.61
1.31
3.07
7.31
1.34
1.2*
J.TB '
2.70
1.40
3.*4
1.14
i.n
0.74

X u

f

1.**
1.43
3.03
2.07
2.71
2.04
4.70
2.**
0.4*
2.24
2.74
2.73
0.V3
3.41
4.11
5.00
ro*—
0,00
1.33
2.03
2.33
l.«l

4*aci Co m . HiparalH
Laka Tracing Pa*a lafll

Diaparsios
Saapte

| 01.44
02.14
02.42
01.31
■ 03.44
i 02.33
02,6*
1■ O
02.9*
02.44
01.47
01.10
01,34
02.07
01.74
03.iS
04.34
01.41
01,77
03.32
01.13
01.34
02.4*
, 03.10
nr:o—
02.27
01.44
02.47
03.42
02.44
£ 5
01.44
02.21
01.10
01.47
01.31
02.24
01.42
03.44
04.34
01.41
03.91
01.44
02.33
01.31
01.94
03.40
ro 2 . n ' 02.34
01.71
02.13
02.4*
02.0*

te|. 21 1700 Oalaa

te|. Z3

1.74
2.74
3.0*
1.04
1.37
0.30
3.01
4.21
2.11
2.04
1.01
1.43
l.*»
4.1*
4.10
1.43
4.03
i:»—
1.41
1.4*
0.33
1.71
1.13
0.00

1
2
3
4
3
4
7
*

Caaa
2
3
4
3
4
7
1
»

K i r n ] 1700 Orckari
2
3
4
3
6
7

s i.

n

TUT W af “
2
1
4
3
*
7
1

4a*. 23

i*4o Caaa

—
1
1
4
3
6
7
4

aa*. 13 1100 OrckaH

te|. 24 0*00 Oaloo
1

t

1
1
3
4
6
7
1
1
3
4
3
6
7
4

1.0
1.M
0.71
1.11
1.14
3.34
1.11
n w —
1.11
1.44
0.33
1.71
1.74
1.40
1.4*
1.11
0:13
1.41
0.47
0.1*
0.31
1.10
0.14
0.41
1.1*
0.13
1.17
0.00
0.14
0.33
0.1*

01.1*
01.44
01.31
01.9*
01.41
00.00
01.03
01.3*
03.97
04,13
04.37
03.17
03.27
02.11
01.34
01.12
01.13
“BTTs
02.43
02.22
01.07
03,13
02.40
00.00
---- 1
01.1*
02.34
01.14
01.71
01.41
01.01
01.4*
■ BC T T "
03.40
02.72
01.11
01.30
01.10
oi.n
01.71
U.43
M.»”
02.43
Ol.*l
03.11
02.4*
02.49
01-4*
01.10
02.11
01.11
02.10
00.00
01.43
01.71
02.00

146

tec. 13

Space C m . H*panlaa
Lak* Tracing Tap< : Sa^l*
Z m

r

APPENDIX C3— Continued
Spaca C m ”

p«tt iit
14

a * . 24

0800

t r a c in g fapai
Io n * Caafflclant
Caaa

0.26
0.3 0
0.33

Orchard

0.1)
0.®
1.01
0.1)
0.M
0.1)
0.))
0.1)
o .»
o.»

0.1)
0.1 4

T.M

*■*.» 1000

0.)t

0.11

11®

Orchard

1
2
3
t
3
6

*». «

11®

Oslo*

1
1
)
4
3
6
7

M .3 6

eOT
01.74
M .«
O l. T t

0).ll
0 2 .3 *

».«
01.))

4®. 14 D M

C m

03.13

01.12
01.®

4a*. 24

14

13®

14®

Orchard

Dnlea

0 3 .1 )

01.4)

0 .74

02.40

02.68
01.®
.h
02.61
01.67

0.92
0 .4 )
0.74

m

1 .M
1.14
).4 1
) .1 4

02.30

Tir ur.ir' An*. 2*

3.3)

01.11
02.1)
01.))
01.®
02.2)
02.)4

3.1)

01.77

1.®
1.2)
2.4)
).46
9.14
2.06
6.31

03.11
01.®
m .«
01.12
01.9)
01.94
0).0)

14®

1
2

Cat

1

00.00
0.®
02.®
1.6)
01.1*
1.41
2.04
01.67
2.07
03.®
02.37
1.®
02.24
2.®
"
Car
TUJ "
0 1 .3 4
l.M
1.67
02.®
01.®
1.02
00.®
0.17
M.61
0.®
01.®
1.1)
01.®
).)!
2.7l
uin
0.))
H.67
1.10
03.6)
03.17
2.27
2.4)
M.61
02.®
2.97
M.M
0.®
01.11
1.13
03.01
3.11
filTts
3.13
01 .))
7.16
0 1 .0 1
1.76
01,1)
2.21
2.®
M.®
02.1)
1.33
2.®
M.M
TH.TT
01. *4
N.2)
M.01
01.1)
01.U
M.22
01. B
4.1004.®
4.61
04.30
2.26
2.2)
04.26
4.®
M.70
>.10
M.3)

Data

Tit

6*. 24

13®

*t. 14 IS®

St- 14 1 UB

4®. 24 16®

4a|. 24 16®

4 4

1
2
)
4
3
4
7
1
)
1
2
3
4
3
6
7
1
2
)
4
)
6
7

01.14

).ll
t.M

3.32

iW tST

fa* 24

Uka

p 9a as >s *s s ■e s a
1

Oatea

Tit

I

Orchard

0.11

r

01.®
00.00
00.00

01.®

1.3)

Data

0 4 .4 )
01.17

01.10

0.6)

, 14

0).))
01.6)

1.M
7.10

l^. 2* 11®

01,18

) .7 )

1.0)

ipaca Can.
Diaparalon
Laka Tracing lapel
Iona Coefficient Cecfficlan

5-*l«

1.T) 01.01
0.J7 n . ®
0 .5 )
01.12
1.0) M .1 9
01.17
2.37
1.^r- oaiia
1 .84
03,40
1 .4 )
0.04
01.®

a*, it 10®

35TTTW

H a p a ra la o

'Bln
4a*. 24 M O M

Laka
Caaa

1
2
)
4
3
6
7
t
)
Orchard 1
2
3
4
3
6
7
Qniea
■1“
2
3
4
3
*
7
*
1
Caaa
2
3
4
3
6
7
1
)
Orchard
1
2
3
4
3
*
7
Halt
is
3

6

7

Aug. 24

24

14®

11®

Orchtrt!
!
I
!
1
[
Unit

‘
1

f
1
2
3
4
3
*
7.
1
2

j
3
!*
! j
*6
1 1
1«

2.63
6.76
).»
).M
2.23
4.6)
1.67
2.®
2.11
3.04
).®
2.1)
4.23
1.31
1.17
4.66
4.30

M.6)
03. *6
01.77
02.44
M.6)
02.®
01.11
M.I1
M.M
M.«
01.14
01.27
01.1)
01.11
, 01.3*
M.14
■M . n

Spat* Cona. Mapcraiac
Laka Tracfrj Tape Saapla
2at

7
6
*®. 24 19®

Caaa

V
2
3
4
3

*
i;
!

1

!

♦

4.41
2.32
2.7)
3.55
3.42
3.07

03.39
M.6)
M.16
M.1)
03.3)
M.4*

4.34
7.03
l.M
3.3*
2.52
4.34
2.76
0.®
3.0)
3.R
3.63
3.13
4.2)
0.64
1.10
7.07
4.®
3.®
3.®
3.®
3.32
2.6)
3.32

01.91
02.93
01.®
02.®
02.1*
01.63
03.1*
00.00
02.15
oz,®
02.43
02.33
02.02
W.7)
®.*1
02.86
02.04
01.22
M.U
03.93
0).42
03.01
02.1)

4.30

03.41__

3.14
L03
2.6)
3.9)
2.®
3,4*

02 !32

Space Cana
Otaparalaa
T r a c is * r a p t
Sa®la

Data

m- 24 IW O

Uka

Orchard

a~
o.si
0.N
0.0

01.12
N.5S
01.®

0.M

M.M

1 .64

1.11
1.31

02.71
M.3)
02. *1
M.®
02.24
“u n * —
01.(1
02.13
01.1)
M.22
01,16
02.31
01.41
DM!
04.3)
04.48
03.61
M.M
02.07
01.02
M.14
M.I3

" !.U '
1.31
2.®
1.3*
I.®
2.26
1.61
2.37
M »
1.31
1.71
1.67
2.67
2.46
).*)
9.6*
4.74

03.0)
02.1)
n.n

•u
>1

APPENDIX C4
SPACE CONSUMPTION SAFETY COEFFICIENTS AND SAMPLE DISPERSION COEFFICIENTS FOR UNION,
CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)
Sput Con* Hipoiloi
Laka Sifity
tcpl*

S|au Cut, Hiynitii
L*hi Safety
3*4,1*

Uka

T1m

Du*

U W

Spue Can*. tt>p*r*lM
Uk * S*f*ty
SMgU
le-«

*t*ca Cm *. h(Marti**
Ut * lafaty
Itgli
Bat*
1

*m - is

two Onfan

0 .0 0

0.03
0.07
0.34

00.*4
03.04
01.71

3
4
3

0 .1 0

t

0 .0 0

0 0 .0 0

6

1

0.04
0.03

01.73
03.40

7
1

0.13
0.13

0 .0 1
0 .0 0
0 .0 1

0 0 .0 0
0 1 .0 0
0 1 .0 1

7

3
*
3
*
7
I
t

n

O MO

Orthgr*

1
1

0

7
1000

<?OlM

1

3
3
4

3

**• u

1666

CM*

13 looo

Orek*r4

*m. 33 1300

Hi*

Cm *

1100

OreluH

A**.23" f i W

1
2

2
2

4
5
6

0 1 .1 0

7

01.07
03.17
03.M
02.33
01.73
01.03
01.34

1

teg. 23 1300

Casa

1
2
3

0.40

01.03

0 .1 0
0 .1 0

a. u

3

0.13
0.33
0.30
0.30

6

0 .0 0

7

0,33

00.31
03. (3
03.34
03.33
01.31
01.30

f

1

0 .1 0

0 1 .0 1

1
2

_ -Wfi.
0.03
0.44
0.41
0.13

1.9 '
0.30
0.04
0.37

3

0.00

0

0.31
0.34
0.24
0.43
0,30.

»

0.11

03.11

1

c o -

KM

3
3
4
3

0.10

03.00

0.13
0.07

01.11

1

01.33
01.40

3
4

*

0.10

01.10

0 .0 0

0.31
0.47
0.14

0 .1 1
0 .1 1

i

i7
S

0 .1 0
0 .2 1

6

l!

t<m.

0.31
0.3*
0 .1*
0.13

0 .1 0

1400 Unloa

1

0 .2 1

3
4
3
7
*M- 13

0.13
0.13
0.14

0 .2 1

7

Ang- 23 1300 Orchard

— o;sr

0.13

1

01.00

0 .1 1

5
6

01.41
0 0 .0 0
0 1 .1 0

0.07

4

n.n

0 1 .1 1

1400 CMS

0,10

3

0.27
0.13

0 .1 0

_Q U O

0

0.21

oi.n

7

0

0,11
0.31
0.03
0.30
0.33
0.34

I
3

0.43
0.34
0.*4
0.44
03.3
0.07

7
|
1

0.01
0.10
0.10

4
3

0.11
0.20

«

2

0.17

0 .0 *
0 .2*

3
4
5

0.10

.i

0.1*

J

Am - 33 1100

.

0 .1 1

4
7
*
"I

1
3
*

%

0 .0 1

0 .0 0

9
'aM . 2 3

00.47
00.03

0.04

0.34
0.34

1

oi.n

0.04

0.27
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.43

AM- 13

1
3
3
4
3

0.13
0.31

0
*

01.07

01.*2
01.17
01.40

01.0*
01.03

00.01
03.14
03.10
01.44
aa.37

02.00
n.n

Aug. 13 1400

Orchard 1

7

0 1 .*0

Aug. 13

1300 I'riM

02.23
01.43
0 1 .**
03.03
01.U
0 1 .**
0 2 .**
0 1 .1 1

Aof■ 23 1300 C m *

01.13

BT.T3 '

0.13
0.43

3
4
3

0 .1 0

6

0 .2 1

7
f

0,44
0.34

1
2

0 .1 2

3
4
3

01.04
02.41
0 1 .1 0
0 1 .1 1

01.07
02.30
00.64
0 2 .*3
03.0*
03.00
03.01
0 2 .*2

1
2

6

7
*
(
am

- 13

1300 Orckir*

1

2
3
3
4

02.03
01.34
01.40
02 .*3

Aug. 23

1*00

CUM

1
2

3
4

02.26
Ol.lt
01.73
03.47

3

0 1 .2 0

23

1(00 Cm *

03.36
01.46
01.04
01.16

0.3*
0.44
0,24
0.33
0.47
0.30
0.17
0.27
0.16
0 .2 0

1

0.(6

I

0.37

2
3

0.10

7
6

01.6*
4m

* 13 1600 Qrchar*

1
2
3

A
3
6
7 I
*M> 23

1700 U*lM

0.32
0.31
0.13
0.37
0.37
0 .2 1

3
*

01.40

01.6*

0 .1 2
0 .1 1

«
7

4

01.03
00.00

03.03
01.64
02.34
02.61
01.31
03.44
02.35
02.64

0.23
0,46

0.0*

01.00

01.73
d>.u
04.74
04.2*
03.14
01.72
02.43
01.40

0.36
0.34

1
2

3
4
3
t
7
g

01.67
02 . »
02.46
01.67

teg- 21

1700 Cm *

1

3
4
3

0 1 .1 0

01,34
02.07
01.74
01,23
04,3*
01.41
01.77
03.32
01.43
01.34
02.4*
03.20
01.43
02.27
02,4*
02.67

6

7
1

Am - 23

1700 Orckart

T
1
2

3
4
3

Ang. 13

1400 Dale*

0 .0 0

0 0 .0 0

0.17
0.3*

01.16
02.34
01 .1*
01.71
01.41

0 .1 1

0.27
0.31
0.46
0.13

o.2>
0.16
0.13

B . W "
03.6*
01.72

4

0 .0 2

0 1 .1 2

3

0.13

(
7

0 .2 2

01.30
01.40

1

1

o.n

01.41
01.(4

3
4

0.14
0.03

0.10

02.11

3

0.06

0.46
0.46
0.71
0.23
0.30
0.14
0.17
0.23

01.33
01.94
03.03

(
7

0.16
0.03
0.06
0.13

0.2*
0.15
0.34
0.33
0.4*
0.40
0.33
0 .0 1

0.31
0.24

6
f
Aug. 13

1400 Orcturg

Aag. 1* 0600 Onion

02.**

02.6*
02.0*
01.36
01.64
02.51
01.4*
01.61
06.00
01.03
01.3*

1
3
3
4
3
(
7
|

02.36
02.3*
01.71
02.23

Am . 24 0400 Cm *

0 2 .0 1
0 1 .0 *

1
2
1

02.*1

01.64
04.36

0 2 .2 2

0.26

0.15

0.17
0.4*
0.34

.an*L _

03.13
01.73
61.41

Q.M.

0 .0 1

0.06
0 .1*
0.06
0 .O1

0.16

0 1 .1 1

7

7
4

01.67
01.31
02.14

0.14,
0.13
0.61
0.14
0 .0 *
0.40
0 .0 *
0.36
0.27

1
2

*

0 2 .2 1
0 1 .1 0

0 .1 1 1

01.(7
04.13
04.17
03.27
03.27
61.21
01.3*

6

3

Aag- 13 1400 Cm *

0.24,
0.23 ;

01.07
0X33
02.46
04.32

3
4

0 1 .(2
0 2 .6 *

03.730 2 .0 *
01.14

l

1
2

3
4

0.01
0,26
0.00
0.03
0.04
0.03
<s;b

0.10
0.06
0.01

3
*

0 .1 1

7

0.01
0.01

6
*

0.31

0.14

0 1 .1 2

01.71
02.43
01. W
02.45
Ol.U

01.11
02.4*
02.60
02 .6*
U.U ■

•1.21
01.11
02.16
00.00
01.43
01.71

02.00
~ a n r
0X1*

01.6*
04.43
02.17
0X00
00.00
OO.HO
•2.34

148

3
*
3

Am - U

0.31
0.30
0.30
0.07
0.07

0 0 .0 0
0 0 .(0
0 0 .0 0

6

%

7

0 .0 0

3
4
3

C m

Cm *

01.41

2

*M- 1) M OO

1100

0.03
0.07

1

APPENDIX C4— Continued

Tim
*1(. 24

0*00

*Bf.

1000

24

A^. 2*

1000

Uk*

Lake
ZoM

Sf*cr Con*. 01ip*rttM
lafl*
LA*

00.00
0.02
01.7*
0.UJ
02.0*
0.01
0 1 .7 2
0.0*
01.12
0.01
02.11
0.01
00.05
0.02
7
■i" - " o r -11 n.ii
Dnfaa
0.07
01.10
2
01.15
0.07
]
0.10
01.02
*
00.00
0.02
]
01.12
t
0.01
02.10
0.*7
7
02.17
|
0.05
0.12
02.1*
1
C*M
04.24
1
0.23
01.40
0,11
1
*
0.10
02.40
0.U
02.00
5
0.10
01.10
6
7
01.12
0.*l
01.02
1
0.20
01.13
t
01.41
Ortkerft
'0.0
1
02.44
0.10
1
02.40
0.11
Ol.U
4
0.00
02.14
0.11
0.07
01.41
02.47
0.0*
7
02.10
Onlaa
0.11
0.10
OLIO
2
02.21
0.20
)
02.23
4
0.01
01.10
5
0.40
01.40
U.ll
t
0.17
02.23
7
02.3*
1
0.*1
01.77
Ch i
1
0.11
0.20
04.50
1
)
0.10 ! 01.12
*
0.20 . 03.40
0.11
02.02
5
0.40 I 01.22
t
7
0.H
01.01
1
0,*«
01.0*
U.07
01.01
1
'1
0 6 1 00.8) “
2
0.11
02.44
1
0.22
02.10
*
0.17
01.47
S
0.20
01.00
1
0.21
02.17
7
0.21
02.14
Orckarft

1
2
3
4
3
ft

An*. 24

1100

**. 24

HOD

to*. 14

1100

Onion

«■. N

«l. »

T W '

1100

1200

I
I
«
I

o.»

Oichorf
1
1
4

24

1400

Onion

P

**.

Int.

1
4
7
1
2
1
4
5
4
7

I
24

1*00

Co**

2*

1400

Orcliri

AnI. 24

1500

Onion

i

•m . »

0.11
0.20
0.15
0.4*
0.02
0.01
0.11
0.51
0.M
0.00
0.14
0.14
0.21
0.10

1
2
1
4
1
4
*
1
2
1
4
5
4
7
1
0

o.»

W I T

Sfact Con*. Dltpcriion
Sn^l*
Uko 4*f*tj
Zoo* Co*fflcl<nt Cn*fflel*»

1
2
1
4
5
*
7
1
0
1
2
1
4
5
4
7
1

2
1
4
5
6
7
8

r

0.24
0.54
0.24
0.11
0.25
0.21
0.25
0.15
0.11
0.41
0.47
0.41
0.73
0.17
0.11
0.71
0.1*
6.2*
0.10
0.14
0.20
0.14
0.10
0.04
0.14
0.94
0.4*
0.44
0.2*
0.72
0.21
0.14
0.21
0.40
0.45
0.14
0.47
0.20
0.10
0.44
0.M

01.40
01.54
02.41
01.40
00.00
00,41
01.40
02,92
01.4*
02.47
01.44
01.17
02.41
02.41
01.4*
02.24
01.01
6i.tr
02.19
02.01
01.41
02.41
02.19
02.14
BI'.U
01.94
02.29
02.01
01.14
01.42
02.12
01,95
01,11
04.04
04.14
03.24
02.70
02.19
01.95
02.83
01.94
01.H
02.4*
02.43
02.04
Ol.U
02.12
02.04

'

—

02761
02,24
02.27
02.15
01.11
01.54
02.14
02.97

DM*

TIs*

U k*

Au|. 2*

1500

Ca§«

An|. 24

1500

OichiH

Ant* 24

1400

UlllMI

I*

1400

C m

tu f

Space Conft. Dispersion
Uka 1iftty
SjapU
Zona
1
2
3
4
5
ft
7
a
9
1
2
3
4
3
ft
7
1
2
3
4
3
ft
7

ft
1
I
\

3

1
7
1
9
*■(. 24

1400

Or Im N

A*. 2*

1400

Onion

An|. 24

1400

Cun

2
3
4
3
ft
7
t
2
3
4
3
ft
7
ft
1
2
3
ft
3
ft
T
•
.. 2 .

0,47
0.19
0.47
0.42
0.41
0.51
0.44
0.45
0.54
0.11
0.11
0.27
0.54
0.29
0.14
0.1*
0.42
0.52
0.40
0.71
0.11
0.11
1.11
0.33
0,40
0.41
0.14
0.11
0.11
0.14
1.14
0.00
0.44
0,19
0.40
0.24
0.14
0.44
0.24
0.15
0.11
0.11
0.4*
0.24
0.14
0.17
0.24
0.24
0.0]
0.24
0.24
0.24
0.51
0.4*
0.11
0.34
0.4*

01.19
04.61
04.14
04.13
01.11
02.44
01.54
01.91
02.95
01.94
02.44
02.14
01.45
01.14
02.14
02.13
62.66
02.41
02.31
02.02
00.71
00.41
02.44
02.04
111.a
04.11
01.91
03.42
01.01
02.29
01.71
00.00
01,41
■.*“
02.52
02.71
02.59
02.41
02.1*
02.24
01.»•
01.44
02.23
01.49
02.22
01.14
02.11
01.41
12.62
04.14
04.44
01.41
02.97
02.07
01.02
02.14
02.45

Du*

Tin*

fa*. 24 1900

u k*
OrcfeiH

if*ca Can. O l a f n l n
Lata Infuy
1^1*
In
1
2
1
4
3
4
7

0.07
0.19
0.09
0.11
0.24
0.13
0.29

02.12
02.51
01.94
02.02
03.05
02.11
01.91

APPENDIX D
T A BLES SHOWING U S E R A T T I T U D E RESPONSES,

INTENSITY

COEFFICIENTS, SPACE C O N S U M P T I O N SA F E T Y
COEFFICIENTS, A N D N U M B E R
OF BOATS

APPENDIX DX

USER ATTITUDE RESPONSES AND INTENSITTf COEFFICIENTS FOR UNION, CASS, AND ORCHARD
LAKES (AUCaUST 23 AND 24, 1969)
Oat«
2*

Uk*
Uniaa

----- Laka
Tlaa I m
DUO

1
2
1
*
I
4
7
•

Can

ORhaH

1
Italoa

idte

t
3
*
3

I
C an

Orekar*

trnln

C an

7
1
I
2
1
a
3
6
7
«
0
1
4
3
4
3
6
7
|
1200
2
3
4
s
6
7
J __
*
2
3
a
3
0
T
______

00.11
. 03.20
01.12
03.14
00.00
01.04
00.tf
00.34
00.43
02.23
02.21
00.02
02.32
02.Of
00.00
00.00
01.34
00.00
00.02
00.41
00.M
00.44
00.34
02.37
t 5. w
02.42
00.34
04.40
00.00
01.21
04.20
00.44
04.3003.02
02.43
■ 02.02
10.44
00.14
01.20
02.34
01.22
■ 'US---11.13'
ot
03.42
00
02.21
Of
01.24
00
02.24
04
01.34
04
00*41
01.34
00
02
02.03
00
04.21
04
10.41
02
07.21
05
03.01
06
02.31
04
03.1f
■ ' 15
—
u m —
02.94
13
01.34
11
14
03.Of
04.71
14
14
12.02
13.37
10

00
00
00
00
00
00
00
00
'■
01
00
02
01
00
00
00
00
00
’ "M “ —
01
01
03
01
01
01
tt""'
00
02
01
01
01
00
00
n

S

03
01
01
01
00
02
W
03
01
04
03
04
01
0]
01
04
03
02
02
01
01
'«■
03
03
04
03
01
01

01
00
01
01
00
00
01
00
"W
03
00
01
00
00
00
04
03
«T'
01
0*
Of
02
Of
02
(K
04
03
04
04
01
04
03
o » - -'
Of
03
01
03
01
04
Of

Data
4«| 24

uk«
Zoo.

Laha
1200

C an

«
9
1
2
3
4
3
0
7

Orcbarf

biiea

X^tuda ilnaaaaaa
Dnfanr.
rim.

1300

—
2
3
4
3
6
7
•

Caaa

i
*
7
1
9
1
2
3
*
3
t
7
1

Orchart

4a*l4

Onlaa

1400

3
4
3
6
7
ft
1
2
3
4
5
4
7

Can

«
Orchar!
1
3
4

1

J

Union

4

_____
! 1300

!

2
3
4
3

4
2
X

■

_

00
03
03
04
04
04
03
03
03
BF
04
03
03
03
02
02
02
KJ
03
07
07
03
02
03
02
04
04
04
04
03
04
03
03
IB
10
0*
01
04
03
05
83
03
03
01
05
04
04
04
04
03
OS
00
03
03
07
12
04
10
11
10
Of
07
07
04

- i . 04

11
11
u
14
If
17
20
01
13
07
“
04
04
04
03
03
03
02
■n—
14
14
14
14
12
14
10
10 „.
, H

Inanalta
CfltfllclHI
02.21
04.30
dO.Ob
0X47
03.0f
07.41
04.11
03.13
03.47
04.21'
03.lt
03.24
04.13
00.00
11.32
04.00
02.32
...

Data
4a* 24

Life
Cut

OrcktrI

hlat

03.41
03.43
01.07
03.74
03.13
24.4*
02.74
Ca n "■
04.03
■M . M
17
04.43
20
04.43
04.71
21
21
04.33
04.44
10
17
04.73
1
" S3.Of '
04
Orckarf
04
OXM
07.3*
03
Of.H
04
04
04.34
03
04.41
04.11
03
03.71
02
10
HtXoi
13
03.3*
14
03.13
02.42
04.13
2
12
03.21
17.11
K
02.*4
Of
tan
03.7*
Of
_
i u ---5S.fl
u
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APPENDIX Dl— Continued
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APPENDIX Dl— Continued

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to

APPENDIX D2
USER ATTITUDE RESPONSES AND SPACE CONSUMPTION SAFETY COEFFICIENTS FOR UNION, CASS,
AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)
lfK> j ™ , |
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APPENDIX D2— Continued
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CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)

1
APPENDIX D3— Continued
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fOM

pact Cana, t s t
U k a Safaty
•f
I*** (Sc.rt.) loua

157
A P P E N D I X D4
U S E R A T T I T U D E INDICES A N D SPACE C O N S U M P T I O N SAFETY
C O E F F I C I E N T S F O R RIPARIAN OWNERS ON UNION, CASS,
A N D O R C H A R D LAKES (AUGUST 23, 24, 30, 31,
A N D S E P T E M B E R 1, 1969)
Jaar

ueituM

In te a
(T o ta l U k a )

(MlA t t l t o t e
Intel

M i » C on*
T o t a l C o o ff .
(T o ta l Laka)

(T a tn l U k a )

Im la n
C aa*

Qatar*.
Q re h a rl
rc h a g d
n io n

Union
O rc lia r

Union
Caaa
U n io n
Caaa
U n io n
Caaa

fifth#**

Union
Caaa

B
kJ
iu
U n io n
Caaa
O rc h a rd
O iilo n
Caaa

t* OMO Uti

Union
Caaa

Orchard
Caaa
O rc h a rd

U n ion
Caaa
O rc h a rd
U n ion
Caaa
O rc h a rd

llnloA

|

Caaa
O rc h a rd
u n io n

“ 15w

O rc h a rd

BESUU
u n io n
Caaa

f
ilSUU
U n io n
O rc h a rd

.Or^hijri
O rc h a rd
U n io n
Caaa
O rc h a rd
U n io n
Caaa
O rc h a rd
U n ion
Caaa
O rc h a rd
U n io n
Caaa

ONbri
U n io n
Caaa

-UOK
bar*
n io n
Caaa
O
r#
U n io n
Caaa
O rc h a rd

fWTlKi
ion
Caaa

P tth d rti
U n io n
Caaa
O ra h a rd

Caaa
O rc h a rd !
U n io n
Caaa

grcha*d4_
U n io n
Caa*
O rc h a rd

B p a c * Cona
T o t a l CoafC
(T o ta l Laka)

APPENDIX E
T A B L E S S H O W I N G F R E Q U E N C Y D I S T R I B U T I O N F O R INCOME,
ED UCATION, A N D O C C U P A T I O N C L A S S E S B Y RESPONSE,
C H I - S Q U A R E ON INCOME,

EDUCATION,

AND OCCUPATION

APPENDIX El
FREQUENCY DISTRIBUTION FOR INCOME, EDUCATION, AND OCCUPATION CLASSES BY RESPONSE
FOR UNION, CASS, AND ORCHARD LAKES (JULY 4 THROUGH SEPTEMBER 1, 1969)
C—

PworibU towoawt
Educulos OcctfiCloo

t
Cod*

i ~c3«

C ot*

ca*

isci

U n e a tio a lO c c o M tla a

w r

001

oo;

Ml

oca

ooo
000

00*

001

oos
oos

002
oos

002

00}
001

00*

002
001

002
) 17

00*

* l o w clu.lHeotim o n (1) **.IM or vote, (2) 55,000 to it,Ml, (J) *7,000 to 7,fM, (*) 5*,000 to I,Ml, (S) $10,000 to 1*,M9, (6) HS.OOO to tl.M*. (7) *20,000 to t*,MI, (I) *»,000 m i m u,
(01 rtfoM*.
* Mocotlon cluiMlcotlou o n (1) «l|btb p i * or ltu, (2) m m bl,b odool, (3) hl,b ukool (rotooco, (*1 l a i calloft, (5) colloft |ro*utt, (i) poot p iluti nrt, (7) otvoocot tofno, (I) ttodoot (eolloc*)
(0) rtfsoo*.
' Denpotloa clontficotloai u i (1) profuolonol, (2) ( c n w o g o n , (3) oootjori, (*) cUrlcol, (SI uloo, (tl croftnos, (7) oporotlnt, (I) print* hHintolt, (I) ootvle*, (10) f*i* boo*,(ll) lokor,
(12) Itaitot, (13) hoaonrlfo, (I*) rotlroo, (13) BtUtorj, (It) lMM^lopot, (17) otkor, (0) nfooot.

158

001

159
A P P E N D I X E2
CH I - SQ U A R E T E S T ON I N C O M E , E D U C A T I O N , A N D O C C U P A T I O N
CLASSES BY R E S P O N S E F O R U N I O N , C A S S , A N D
O R C H A R D LAKES

Lake

Union

Union

Union

Cass

Cass

Cass

Orchard

Orchard

Response

U n f a v orable
F avorable
Unfavorable
F a v o rable
U n f a v orable
Favor a b l e
Unf a v o r a b l e
Favorable
Un f a v o r a b l e
Favorable
U n f a v orable
Favorable
Unf a v o r a b l e
Favorable
Unfavorable
F avorable

Socio-economic
Variable
Income
Income
Education
Education
Occupation
Occupation
Income
Income
Education
Education
Occupation
Occupation
Income
Income
Education
Education

x2

d.f .

13.76
57 .97
7T.73*

8

203.49
10.44
21 J. 3 3*

9

72 .19
41.54
113.73*

17

49 .50
17.52
57.65*

8

55.60
14. 80
TT.'Sff*

9

26.41
11.65
3-ff.OS*

17

43 .40
27 .08
40.48*

8

21.37
9 .19
9

Orchard

U n f a v orable
Favorable

Occupation
Occupation

65.02
103.48
168.50*

17

*Signi f i c a n t l y d i f f e r e n t at the .05 level, tested
by chi-square.
T h e r e is less than five chances in 100 of
the d i f f erences b e i n g the r e s u l t of chance.

APPENDIX F
TABLES AND PLOTS SHOWING LEAST SQUARES DELETION ANALYSIS
FOR SAMPLE DISPERSION COEFFICIENTS AND TOTAL DISPERSION
COEFFICIENTS,

SPACE CONSUMPTION SAFETY COEFFICIENTS

AND SPACE CONSUMPTION TRACING PAPER COEFFICIENTS
AND SAMPLE DISPERSION COEFFICIENTS,

SPACE

CONSUMPTION SAFETY COEFFICIENTS AND
SAMPLE DISPERSION COEFFICIENTS

160
A P P E N D I X PI
L E A S T SQUARES D E L E T I O N A N A L Y S I S FOR SAMPLE D I S P E R S I O N
C OEFFICIENTS A N D T O T A L D I S P E R S I O N C O E F F I C I E N T S
F O R UNION, CASS, A N D ORC H A R D LAKES
(JULY 17, 1969)
I
_

s m

* l

Mo*
O ftoob

L+m

• to y
K *.

9a

■ to n n n rd l
Irro r of
S o tla o ta

¥

»0
■I* .

Toot

J u l y IT

U n io n

94

1

• 9)

0 ,1 4 9 1

13 3 .0 7 1 1 < 0 ,0 0 0 1 -

J u l y 17

U n io n

ii

z

;n

V .H II

1 7ft. 4 99(9 < b .b o 0 3

it

U n io n

! u i?

" ■

j r

—

r ~

b . i4 7 f t

'H i. ljr *

0
3
4
3
ft
0
3
3

Cooo

A3

TT

Cooo

AS

J u l y 17

Cooo

*3

J u ly

i

.M

0 .4 4 * 4

♦§ * “ " B . U T &

3

• f t*

111 .3 1 3 0 < 0 ,0 0 0 1

r tt.u n

4

- 0 .0 1 * 7
1 .3 9 7 *
• 0 .3 0 1 7
0 ,1 0 4 2
• 0 .0 3 1 1
T r .in S t
* 1 .1 * 2 *
o .o n o
• 0 .0 1 2 0

3
ft

1 *114 3
• 0 ,0 0 9 9

< E « a r_

-------- ■--------- “4
J u ly it

P a r t ia l
fto g r o o o ln n
C n n f f le lo n c

V o r.*

{D .B 5 0 9

0
3
_ 4.
9
A
" 0 —
3
5

A

0 .4 3 1 1

“
1

8
3
3

J u ly

IT

O ro h o rd

49

1

• 73

0 .4 4 3 J

3 1 ,7 9 3 * C0 .0 0 0 3

0
3
4
5

J u ly

17

O re h o rd

49

a

• 79

0 . 4393

44 ,4 1 3 7 < 0 .0 0 0 3

0
4
1
ft

■

III.
0 .0 9 7 ft
0 ,7 6 9
< 0 .0 0 0 3
1 9 ,4 0 3 0
1 *1 3 *4
0 .2 9 1
0 .2 7 2
1 .2331
O. 125
2 .4341
X .O M H
S .ftftl
1 1 3 .3 4 0 0
< 0 .0 0 0 3
O .llf tl
0 .7 3 2
3 ,4 4 * 4
— 1 1 ,5 6 6 5 “ — 6 T W J —
3 2 4 ,4 9 1 3
< 0 .0 0 0 5
1 4 0 .7 7 4 *
0 .0 0 0 5

• 0 ,0 1 4 0
O.OOAI
0 .9 3 4
1 ,0 0 4 9
4 ,0 4 9 0
0 .0 1 1
O .lft ll
0 .9 2 1 *
0 .4 7 3
-Q .O A 7 *
1 ,2 9 9 *
0 ,2 5 9
0 .0 0 4 *
1 ,2 2 * 0
0 ,2 7 2
- 5 ,8 7 4 1
*
777219*"* — i r m —
1 1 9 .4 * 4 1
1 .2 * 9 2
< 0 ,0 0 0 9
• 0 .0 2 3 3
3 .7 3 1 0
0 .0 2 0
0 .0 0 1 7
2 ,1 1 0 7
0 .1 9 2
B IT O T " ■
B .T M » 1 .1 2 * 3
3 2 4 ,7 9 0 4
< 0,0009
- 0 ,0 1 0 1
9 2 .2 * 4 7
< 0 .0 0 0 9
0 ,0 7 9 6
0 .3 1 f t)
1 .1 2 2 2
- 0 ,4 3 * 3

n ,0 4 0 7
0 .2 2 4 0
3 .0 * * 3
4 ,7 9 3 *

0 .1 * 2 *
1 .4 1 2 0
• 0 .9 2 0 4
0 ,0 3 0 *

0 ,7 7 4 )
3 1 .2 2 6 )
3 1 .1 * 2 3
2 0 ,9 4 0 *

0 .0 0 7
0 .6 3 9
0 ,0 *6
0 ,0 3 4

4

V a r t a b la * In tr o d u c e d a r « c o n s t a n t * d r a t , i m m 4 , t h i r d ,
oo 0 , 3 , 4 , 3, and ft r o o y o e t lv o ly .

f o u r t h d o g r o t to n a d l i p i n l M

0 ,3 *4
< 0 ,0 0 0 9
< 0 ,0 0 0 3
< 0 .0 0 0 3

t o t a l c o e f f ic ie n t

161

sample dispersion
coefficient

A P P E N D I X F2

total d i s p e r s i o n
coefficient

sample dispersion
coefficient

Plot of sample dispersion coefficient and
t o t a l d i s p e r s i o n c o e f f i c i e n t for U n i o n L a k e
(July 17, 1969)

total d i s p e r s i o n
coefficient

sample dispersion
coefficient

P l o t of s a m p l e d i s p e r s i o n c o e f f i c i e n t and
t o t a l d i s p e r s i o n c o e f f i c i e n t for C a s s L a k e
(July 17, 1969)

total dispersion
coefficient
o■

■

*m

•m

*.«•

s.**

•

•

m

Plot of sample dispersion coefficient and
t o t a l d i s p e r s i o n c o e f f i c i e n t for O r c h a r d
L a k e (July 17, 1969)

162
A P P E N D I X F3
LEAST SQUARES DELETION ANALYSIS FOR SPACE CONSUMPTION
SAFETY COEFFICIENTS AND SPACE CONSUMPTION TRACING
P A PER COEFFICIENTS FOR UNION, CASS, AND
O R C H A R D L A K E S ( A U G U S T 23 A N D 24, 1969)

■ rro r o f

Ho.
U n io n

I»

1

• TT

"o
li
a*

•

ft*
0 .1 0 0 *

iM .ttia

< 0 .0 0 0 9
;

U n io n

1 5 *"'

3

, TT

'"I"' •15

Cooo

0 *1 0 0 9

“ I W . T W l * h4 f l . W W "

o*ioi5

45,ood4

C o oo

133

3

.n

0 *1 0 0 7

1 *1 *3 1 3 0

CD.0 0 0 3

OrtWri

11*

I

•M

0 .0 9 * *

1 4 d .M ll

< 0 ,0 0 0 3

P a r t ia l
la g r a a a lM
V a rf
0
4
11
13
U
- *8 "
4
11
U
6
4
11
13
13
0
4
11
11 .
0
4

11

Orchard

11*

13
13

Orchard ~U* ' i

Virliblii
traclaf

0 ,0 3 * 4

3

.1*

***** C M f l t o l M t

5.

oivf

1 * 7 , 4 7 4 4 < 0 .0 0 0 9

1 * 4 .7 3 * 3

iQ.oddi

'8
4
11
13

"8—
4
13

V .
• 0 .0 1 9 *
Q .3310
- 0 .0 4 1 4
0 .0 0 4 T
• 0 .0 0 0 1
•0 ,0 1 1 1
0 .2 1 3 0
-0 .0 3 9 4
0 .0 0 3 3
•0 .0 1 2 4
0 .1 9 4 4
• 0 .0 3 0 3
0 ,0 0 0 4
0 .0 0 0 0
-0 .0 3 4 ?
0 .3 0 2 4
• 0 .0 2 2 3
0 .0 0 0 4
0 .0 0 3 3
0 .1 3 2 4
-0 .0 0 7 4
-0 .0 0 1 4
0 .0 0 0 7

8:88ir

0 .1 3 0 3
- 0 .0 1 3 1
0 *0 0 0 9
*•0 1 9 *
0 .1 0 * 2
0 .0 0 0 2

0 ,2 3 1 1
4 .7 1 9 *
0 .7 3 0 4
0 .1 4 4 4
0 .0 1 4 1
0 .2 * 4 1
3 1 .2 0 0 1
4 .2 3 7 6

k.iSig
4 0 ,3 9 4 9
4 .1 * 4 4
0 .4 4 4 3
0 .0 * 2 2
2 .7 4 5 1
1 7 0 .3 2 9 7
4 4 .1 1 9 7
3 J*4 *4 *_
0 .0 2 9 0
3 .4 9 4 9
0 .0 1 4 0
0 .0 0 4 4
0 .1 2 5 0

0 .6 3 2
0 .0 0 4
0 .3 4 4
0 .6 4 4
0 .4 9 *
0 .6 1 3
< 0 .0 0 0 3
0 .0 1 4
0 .0 2 3
0 .3 1 4
0 .0 0 0 3
0 .0 0 3
0 .3 9 9
0 *7 4 2
0 ,0 9 7
< 0 .0 0 0 9
« 0 *0 0 0 9
4 0 ,0 0 0 3 _

o.Uo
0 .0 4 4
0 .9 0 *
0 .9 2 7
0 .7 2 *

<:8fl8^ K w j "

2 4 .2 3 * 4
1 .4 1 *4
3 .3 4 0 4

1.11*7

1 * 4 .0 4 2 *
4 .3 1 0 4

< 0 .0 0 0 9
0 .2 3 4
0 ,0 4 *

9.111
0 .0 0 5
0 ,0 4 0

cowtant, flrat, aaeondt third, aai Court Ii 4t|vat tors ifaca cnnatmptfton
Coil«n«tai aa 0 . 4 » U ai3a
13 rna*nctiv«ly.

am*

-

A P P E N D I X F4

space

consumption safety
coefficient

163

space c o n s u m p t i o n
tra c i n g p a p e r
coefficient

space consumption safety
coefficient

P l o t of space c o n s u m p t i o n safety c o e f f i c i e n t
and space c o n s u m p t i o n tracing paper c o e f f i c i e n t
for U n i o n L a k e (August 23 a n d 24 combined)

space c o n s u m p t i o n
tracing p a p e r
coefficient

space

consumption safety
coefficient

I CM

1C 3

'J

P l o t of space c o n s u m p t i o n safety c o e f f i c i e n t
and space c o n s u m p t i o n tracing p a p e r c o e f f i c i e n t
for Cass L a k e (August 23 and 24 combined)

space c o n s u m p t i o n
tra c i n g paper
co e f f i c i e n t
P l o t of space c o n s u m p t i o n safety c o e f f i c i e n t
and space c o n s u m p t i o n tracing p a p e r c o e f f i c i e n t
for O r c h a r d L a k e (August 23 a n d 24 combined)

APPENDIX F5
LEAST SQUARES DELETION ANALYSIS FOR SPACE CONSUMPTION TRACING PAPER COEFFICIENTS
AND SAMPLE DISPERSION COEFFICIENTS FOR UNION, CASS, AND ORCHARD
LAKES (AUGUST 23 AND 24, 1969)
•c r
"1“

Lata

4af. 23

71

hlaa

n

n

Mta

n ■ear

■ n

1*

scwf (n,
tuluti

.11

i.im

■j s r

Otof
■

.11

! '

L.1IB

r
Tut
7.77

10.11

1

.11

1.1101

11.17

I

•14

i.nu

5.11'

“T.—
sit.

rtf

<0.0005

<0.0005

<0.0005

0
5
14
16
0
14
U
0
14
■■■#

0.#1T

1
14

o

tal- U

Cut

Orctart

H - D

^ . 8

Orctart

u

.03

1

t.un

0.007

1.97

0.76

o.ttll

0.516

ii

1 ‘ •03

o.tia

1.01

0.JU

U

1

0.9936

0.11

0.710

Orttar^ u

k b O d s w r
Bf.'H

•13

1

ii
w

1 .01

4

fOri

5
1

*00

T H B
0.42)4
1.4310

* .H
0.00
7.61

~ i .v .

0
5
14
16
0
5
14

tO
“

1.00
40.0005

L , . H Oaio*

u

I

Ai

r . w

4.96

<0.0001

W *1

BaUo

u

3

.13

l.tttt

15.14

<0.0005

t M

71

1

.33

OKhtri

U

tJrctur* g»
1
L. .

1~ '

r I

i
.
1 .10

1
1

1.H

1.139*

~r.ros

1.31

T.iT

5
1*
0
1
0
0
,5
!*
15
16
0

[s
I*
0
15
16
<0.0005 r 0
5
14
15
16
0.170
0
5
14
. 15
16
0.156 I a
1 5
14

»6i

111.

Di m

0.044*
*■*.21
0.013
0.1154
0.7711
•1.9711
0.301
1.6240
0.107
6.5061
1.1*3*
•1.9611
0.261
0,3190 - J L I M t
_
htf. It
0.139
0.0416
-0.10V
0.002
In*. 21
-1,1577
1.1199
0.109
6 14
•0.0113
0.7315
0.05*9
0.779
0.079J
0.0017
0.960
-0.0170
1.0100 24.0960 <0.0005
10.7793 <0.0003
-O.SS01
"
o n w r "5.T4*
ii- n
5.9245
4.6351
0.017
6 24
1.1754
-1.1415
0.079
0.104
0.1743
1.6190
0.319
•O.OZ23
0.4000
0.970
' •0.0164
0.1920
3.0003
0.005
6 14
•1.0171
0.000
7.31*0
9.5450
.
.
Q-«*
-5L0OB.
0.979
0.0147
0.0007
"Im -R
0.7955
1.1117
0.176
6 1*
-1.015*
0.650
0.1075
0.040
0.0410
0.1511
-0.0020
0.0007
0.970
T.IW
a.otii 4 . W '
i.om 0.000
1.1140
tat. ii
0.101
-0.9*64
1.754*
6 14
1.4112
o.m
0.9011
o.JH
w w
0.460*
0.44]
0.5971
0.444*
■0.0017
' t.IW
0.00*
■ W . U
0.9000
0.6*1
0.1171
6 14
1.57*1 140.1400 _4.BJNS}_
0.0917
0.1505
0.761
1.7099
0.6(2
0.1*90
0.6)6
-1,9471
0.11*1
k$. I)
0.3657
1.1*1*
0.435
6 14
•0.4454
0.9*11
0.3)1
0.4109
0.357
0.3490
1,1117
-0,1090
0.1454
0.7710
-0.U67
-0.0*04
31.0091
-17.1505
7.0632
-0.7501
00.0117
1.73151
-0 .1*2 0 ;
0.0141;
0.0275
5.diIs
2.70*9
-0.9506
0.0194

1.00*5
0.31*
1.0)04
0.177
0.574
0.11V
19.4434 <0.0005
14.1627 <0.0005
0.977
0,0000
11.1163 <0.0005
17.7*73 <0.0005
14.6623 <0.0005
12.4*91
0,001
0.0002
0.909
0.569
0.1291
0.0147 1 0.076
0,0000
0.996
0.0045 ; 0.947
0.0002 - 0.900
2.540*1 0.116
1.1175. 0,201
0.4510 1 0.504

it.
Ki*_ Ota.

It*,
■*.

i1

Still* tin
btlatt*

r
ltat

9ixf

OrctaH

56

1

.09

1.1211

2.31

.090

OrtkvS

56

4

.04

1.241*

i.ii

.14*

bOCtafE.

'kl

0
3
14
0
5
0

0.1016
0.0615
1.71(1
4.19*9
-0.3*50
1.(143
I.TK!
J.XB
2.1406
0.5731
i.%73 IX. W T

11*
0.(01
0.045
0.0*9
~s j s t 0.14*
<0.0005

54

3

.000

1.2144

Omlso

133

1

.30

1.1144

13.99

<0.0005

0
5
14
15
If

0.1*57
41.9431
2.4*59
-0.7144
o.nu

0.140*
0.11*2
0.41*9
0.1407
0.004*

0.704
0.723
0.310
0.70*

OklM

135

1

.10

1.30*4

1(,00

<0.0005

0
5
14
15

0.17*3
.0.77*0
2.2254
-0.5623

0.1169
0.41*5
5.6412
).*07*

0.711
0.3U
0.01*
0.006

0
14
15

-0.0*52
1.6477
-0.4432

0.017*
53.21)9
21.320*

0.0*4
<0.0005
<0.0003

Orctatd

0.000 — 1.0*6

tain

1)3

3

.109

1.3045

2*.U

C«ii

152

1

.12

2.6030

3.10

.001

0
55
14
15
16

.0.1716
6.1510
•4.7111
0.963)

0.0447
11.6455
(.6614
6.0605

0,11)
0.001
0.004
0,015
n.AU

OttWd

119

1

.0*

1.10(5

1.0*

.116

0
5
14
15
16

0.0)54
2.4720
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0.1525
'fliflflft

0.002*
1.5475
0.3201
0.0514
0.0013

0.95*
0.216
0.373
0.111
(Ltlt

Onlurt

119

1

.06

1.1017

1.54

.*60

0

0.03*6

0.00)9

0.(50

14
u

•1.0110
0.1209

4.1733
1.7441

0.04)
0.100

0
)
14

0.4932
1.0131
-0.2115

0.7*41
4.7135
3.9441

0.375
0.0)1
0.04*

Orcku*

119

3

.04

1.1110

2.40

<0.0005

.096

4
Vulallo Intretau* <r« csucut, £lr»t, m c m O, tklrS, » < [wrth
cixFftcltnc d*il|UM< u 0,5,14,1), u 4 16 rupactlnij.

<l«a«r»lon i s ^ U

,
1

164

iS d r c W <

ii

16
" 0
1
14

“ 15 7 "
Cm ({.

space consumption tracing
paper coefficient

165
. APPENDIX F 6

sample dispersion
coefficient

space consumption tracing
PaPer coefficient

o

m

l

JO

9

*

a

Plot of space consumption tracing paper coef­
f i c i e n t a n d s a m p l e d i s p e r s i o n c o e f f i c i e n t for
U n i o n L a k e ( A u g u s t 23, 1969)

•s a m p l e d i s p e r s i o n
coefficient

space consumption tracing
paper coefficient

o «*1

Plot of space consumption tracing paper coef­
f i c i e n t a n d s a m p l e d i s p e r s i o n c o e f f i c i e n t for
C a s s L a k e ( A u g u s t 23, 1969)

sample dispersion
coefficient
P l o t of space c onsumption tracing paper c oef­
f i c i e n t a n d s a m p l e d i s p e r s i o n c o e f f i c i e n t for
O r c h a r d L a k e ( A u g u s t 23, 1969)

space consumption tracing
paper coefficient
space consumption tracing
paper coefficient
space consumption tracing
paper coefficient

166
APPENDIX F 6— Continued

i
B

B
A

1

sample d i s p e r s i o n
coe f f i c i e n t

■i

Plot of space c o n s u m p t i o n tracing p a p e r c o e f ­
ficient and sample d i s p e r s i o n co e f f i c i e n t for
Union Lake (August 23, 1969)
i

sample d i s p e r s i o n
coefficient
Plot of space co n s u m p t i o n tracing p a p e r c o e f ­
ficient and sample d i s p e r s i o n c o e f f i c i e n t for
Cass Lake (August 23, 1969)

sample d i s p e r s i o n
co e f f i c i e n t
mm

mm

is

ip

*«b

ip

■■

Plot of space c o n s u mption tracing paper c o e f ­
ficient and sample disper s i o n c o e f f i c i e n t for
O r c h a r d L a k e (August 23, 1969)

167
A P P E N D I X F7
LEAST SQUARES DELETION ANALYSIS FOR SPACE CONSUMPTION
SAFETY COEFFICIENTS AND SAMPLE DISPERSION
C O E F F I C I E N T S F O R U N I O N , CASS, A N D
O R C H A R D L A K E S (AUGUST 23 A N D
24, 1969)
Aa«. 11 ■ataa

n

k « .'n

n

1n

1

**

1

o .»

-. j

.

Ifalaa

te .

,

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K t te j. I n i ■“ f "
■a* M ata
la a t
0,14*1

w

0 .0 )

g . u n 1-

0 .H

S .T iil

17,11

D ,l* 4

o .ia *a

).«

M

1

tea . is Qaaa

at

— r

0*1*

0.1*01

4.IS

' ¥1—

)

0*11

o .i* * a

4 .M

tea . is D n M

♦j

i

0*0*

0.11*1

o.ass

/■a* t i teakarJ

U

i

0*0*

tea . t ) In k a H

U

"y

aaa>

u

(laaa

M a ri

—

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te .K

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■ ■ s n T ii" ■ X l s

o.oodj

b .ilil

ff.O*

0*0001

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n i!!
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9.31

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n

tea. I t

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Braharl

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tea.

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a i*

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a »

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9
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9
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<0,0005
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0,414
> .H 1
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5
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9
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<1.0005
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19
1*
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” 1 .W h .O H l
£.0 00 5
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T .fi4
<J).806S
~ 0 ,W » ‘ — 0 7 w *r
9
0.9*99
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0.9974
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19
0.92*9
. 0.4427
. 0*951
.. .11
0
0,090*
0,0792
0,779
9
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19
•0*02*0 ... 2*4092_
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li
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IS
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o.bos*
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11.19*9
9
1*
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*•124* __ 0,01*
•0.0*19
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037)
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0,799
5
0.2104
0.004*
0.947
0.09*7
1*
0,440
19
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0 .0*1*
1*
0.01*0
0*0441 _ -_fl*794
0.947
0*10*
0
0.0017
0.0009
0.049
9
0,291*
9.000*
0,929
•0.0910
19
0.972*
0.491
1*
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0.4912
Q
0.717
O a ll*
0*6949
4.1)31
9
0.1922
4,2*90
0.0*4
•0*0102
2*4994
0.099
19
0.094
fl* IQ
3.7444
1.4024
0.241
9
olo*oo
0,29*1
" u m
<0.0009
1IT.01M

i
t e a . ii

0
9
1*
19
1*

~ l# * a
« •« » .

19

^

•0 *0 9 7 9

;

0*970
<0*0005
<5*0005

168
APPENDIX F7— Continued

d m

*
11

U k*

n c r
O hk

■ H 3T
N .

llin i.
n*

I r e “ 7 ---------T ill

* « •»
\ l

•U .

»

CaM

i 1»

1

0 i* l

Os t i t *

1 .U

0 .0 0 9

0
9
14
19

• 0 ,0 1 4 1
0 ,4 0 9 0
• 0 .2 0 * 2
0 ,0 3 9 0
^ .n M i

« H

Cm *

IS *

a

0 .0 9

0 .1 1 1 1

* .U

9 .0 0 1

0
9
14
19

0 ,0 1 9 1
0 ,9 3 0 4
- 0 ,0 0 0 9

*

1>
4 1*

B ill

113

* ■ « • 11
D re H c r* 1 1*
4 14

JUi.'TT
4 1*

>refc#r4 1 1*

>

o .o a

0 ,1 1 * 0

3 .4 1

0 ,0 0 3

111.

0 .0 1 9 3
4 ,4 9 1 0
1,
7304
1 ,3 3 0 ?

4-oiao

0 .4 7 4
0 .0 1 1
0 .1 0 1
0 ,1 4 *
0 .9 4 4

0.00??

0 .0 3 1 ?
1 0 ,4 4 1 0
4 ,0 0 0 0
9 *4 4 9 3

0
3
.1 * .

0 *1 1 7 4
o .m i
-O .O M 9

1 9 * 9 144

O .IM
0 ,0 0 3
0 ,0 0 1

2 ,1 2 7 4
10 ,0 4 1 1

0 *4 9 ?
0 *0 0 1
0 .0 1 0
0 ,0 4 9

i

0 .0 4

0 .1 * 3 *

1 **1 3

0 .1 1 1

0
9
1*
11
1*

0 ,0 0 0 *
0 .1 * 9 1
•OsOOTl
• 0 ,0 1 4 0
0 ,0 0 9 0

o .o n v
0 ,3 4 0 1
0 ,0 0 0 4
0 ,1 0 7 1
0 .3 ? * 9

.> .* 1 *
0 .4 5 4
Q .*T ?
0 ,7 * 4
0 ,9 * 4

a

0 .0 4

0 .1 4 3 3

1 ,3 7 9

0 ,0 3 ?

0
3
13
14

0 .0 0 * ?
0 .1 0 4 0
. 0 ,0 9 0 4
0 ,0 0 9 4

0 ,0 1 4 1
7 ,4 1 1 4
9 .4 * * 3
4 ,9 4 0 7

0 .4 *4
0 .0 0 7
0 .0 1 *
0 .0 3 4

V n t i b l M lftC fo 4 » e « 4 i n M M t i M i l l f i t i i M M r i , t h i r d s
t r i c i n g i n n e n f f l c t n t 4 n t d > M « l a# 0 , 1 , 11) 11, n d D

mi

f M f t k 4 * f lt e « t i n
n i f n t l» ily >

n w t r tm ia p i t n

space consumption safety
coefficient

169
t

APPENDIX F 8
«

H

o

I

V
sample dispersion
coefficient:

H
■3

space consumption
coefficient

safety

Plot: of s p a c e c o n s u m p t i o n s a f e t y c o e f f i c i e n t a n d
s a m p l e d i s p e r s i o n c o e f f i c i e n t for U n i o n L a k e
(August 23, 1969)

-s a m p l e d i s p e r s i o n
_coefficient

space consumption
coefficient

safety

Plot of space c o n s u m p t i o n safety c o e fficient and
sample d i s p e r s i o n c o e f f i c i e n t for Cass Lake
(August 23, 1969)
1

t

*

1

i

sample dispersion
coefficient
Plot of space c o nsumption safety coefficient and
s a m p l e d i s p e r s i o n c o e f f i c i e n t for O r c h a r d L a k e
(August 23, 1969)

space consumption safety
coefficient

170
A P P E N D I X F 8- - C o n t i n u e d

sample dispersion
coefficient

space consumption
coefficient

safety

P l o t of space consumption safety c o efficient and
s a m p l e d i s p e r s i o n c o e f f i c i e n t for U n i o n Lake
( A u g u s t 24, 1969)

nmm

a «b

tm

*

sample dispersion
coefficient
»

* -n

space

consumption
coefficient

safety

Plot of space consumption safety coefficient and
sa m p l e d i s p e r s i o n c o e f f i c i e n t for C ass L a k e
( A u g u s t 2 4 , 1969)
H•:

sample dispersion
coefficient
Plot of space consumption safety coefficient and
s a m p l e d i s p e r s i o n c o e f f i c i e n t for O r c h a r d Lak e
( A u g u s t 2 4 , 1969)

APPENDIX G
TABLES A N D PLOTS S H O W I N G L E A S T SQUARES DELE T I O N A N A L Y S I S
F O R U S E R A T T I T U D E INDICES A N D INTENSITY COEFFICIENTS,
U S E R ATTIT U D E INDICES A N D SPACE C O N S U M P T I O N SAFETY
COEFFICIENTS,

U S E R A T T I T U D E INDICES F O R RIPARIAN

OWNERS A N D SPACE C O N S U M P T I O N SAFETY
C O E F F ICIENTS, N U M B E R OF A C R E S PER
BOAT A N D SPACE C O N S U M P T I O N
S A F E T Y COEF F I C I E N T S

APPENDIX G1
LEAST SQUARES DELETION ANALYSIS FOR USER ATTITUDE INDICES AND INTENSITY COEFFICIENTS
FOR UNION, CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)
■s,

Dit<
I! M a

■-_
I Ob*. _**>

1}*

\n

.07

Odf. 23 IhdM :

S t i* I

.07

71

JS tM * O r*

• 0. 1*331

3

I

F

fAit

1

Bg

Cli

CoM

Vg~

0.1070
0.0071
0.0001
-0.0011

1.3203 0,272

I
1-------0. 1010. 1.7037I: 0. 1J0

.

0 10*0
0.0100

71

3

- i --

*0- 23f Mm

.03 0.1023 1. 910* ' 0.133
.02

n*
* ■ * 2 ? C*M

11

1

0. 10*1 1. 60*0 0.107
" n.iwn~ O-OOOP~T.O0 ~

.00

0.1330

1.3*02

,00 0. 13S0 2.0137 0.100
M . 23) Cm«

II

03

3

.01 0.1310 0. 6303; 0.*30
. 00
0.1377 0. 0000. 1.00
,09 1 o.tio*T i.* 6i i ! T ii!

*■. 23 chi
M * 22 Or Im c I. 13

M- 73OrM

63

1.23

63

rst

63

-0* - ^
m i. 2* Mm

.M

3 , .06

■**
t

72

0.1331 2.160 0.121

I 0.1503 I 1.7

0.173

0.1303 2. 0*96 0.131

'

0.1307 2.7171 0.100
« 0-1121 o-oooo US— .
. 3* .0. 261* 7. 1*36 <0.0005

2

. 3*

3

. 3*

~

10
ft
H6A0*
i0
n.3
e0n1i7V7
n
.2
37
!1
<n
0.0001
0. 131* 13. 1*23 <0.0005

.11 • 0. 10*3 ! 1. 20*1 0.077

hi%. 2*1 Orrkrr*

0.0131 i 2.1013
0.112
-0.0022 ; 1.2903 j 0.234
*0.1106
*0.yt3i I W . M W
0.01)2
2.7*71 ; 0.100
0.2263 '* 130.3*0 ~ <tfTM6T

v .m r

■|.UWfHH>

I 0. 1*77 ! 1.32*3 0.221
| -0.0362 0.3*1* I 0.361
o.oo** ; 0.2630 ! 0.60*
} -0.0002 i 0.3171 0.373
^ 0.M2I
: 0 .12*1 . 3
. 0*2* 0.00*
-0.00*9 0. 1*17| 0,663
.. -0. 000? . PUSH | 0.1*2
: 0.0616 0.*«21 0,*04
. 0 .1*75 : I *
.6003 <0.0003|
;-o.oofi ’ 6.1136 6.513
4 0.1*0"* (. 190* 0.01S'*
0.061* 1.01*1 0.006 ■
. 0,00*7 ' 1.3770 0.005 '
| 0.000* ; 7. 6U2 0.007 .
1-0.0000 | 6.1263 0.011 ;
i

1____ 1

l*.tt*l^O.OOOl
3.0362, 0.006

36

.11

0.1106 1,3623 0,100

0.1200 1.7106 0.176

0,1720
: 0.070
4 .0 10
0.020
-0.0000

0.1170
0. 013*
0.0000

2*

OrtWNI

.0* 0.1276 I

36

0- 3*1O itto ir 36
M - 2* OrImNT 3*
62* i M m 133

.00

Tmrn]
42*
t it .

2jj
4 1*

11*

111

1

.00

.10

- 0.0000

I. i>01

0.003 i
'

0
5

> li

2. 3*47 0.112
0.1312 0.0000 1.000
0.2320 6.*31* <0.0003

0.12*7

.17

3.60311 0.03*
-s rw
p
0. 170* *7,1111I 0.0003
* 2* Cu> ! 133
0.0031 0.63031 Q.*30
00.1157 ~ 1*7.2411 <0.0005
B.17T
sr*-# .w *6 *
0. 1*73 2.6300' 0.12*
-0. 0U3 1.37771 0.2*3
h+.TT
0.0032 0.1671 0, 12*
6 2*
11*
16 i -0.0002 fl.W + M IL
- 1 0.1232 3,5311T 0.022
0. 076* 2. 636* 0.110
-0.0131 1.***o! 0.21*
___________
0.315 -T^rn
0.000* 1.0262
0.133* : I*.2911 <0.0003
42* OreUN 119

. 0* '

1

2*1Mm
, 1*: Mm
I

"H

**• 2*| OreUN

M
0
5
1*
13
U

0.2107
0.011*
-0.0000
0.2*27

m

«L.

0.2036 0.006
1.321* 0.223
1.1112
1.1711 0.21*

0.297

JL226-

___ u m
ll.*l« 0.0003
0.731* .

03*0
0.000
ao.a** 0. 63*
0.

36.0600
3.1171

0,020

o-io*

66,3*22<0.0
2.1467 0.112

"B O W

aw ~

0 0,1327 6.0206 0.0*7
3 0. 03*1 0.2162 0.621
0.0110 0.2771 0.600
1*
15 •0.0016 O.M10 0.W0
11 0.000 0.3*1* 0.447
0.2321 *.21*0 <0.0001I 0 t 0. 1*27 13. 623* 0.0003
1* ' 0.0209 12.4313 0.00
IS ■ -0,0026
7.32*4 0.000
0,000 *.*10* 0.010
1*
~r
1.17*) 0.011
0 0.03*3 7. 3*0 0.007
0.1212
5 0.05*3 11.9621 0.001
9.3226 0.002
1* 0.0001
13 • 0.0003 7. 212* 0.00
16 )-0.0000 3. 6*36. 0.011
0. 119* 1. 113* 0.013 0 0.112* 10.24*0: 0.00
3 0.0*31 4.1*01 0.04}
1* 0.0211
2.5*63 5.113
13 0,0021
1. 1*61 0.1*1
1.1079 0.10
16 0.0000
3.6*10 0
0.1*02
.014 0 0. 16*3 23. 70*0<0.000
3 0.0167 2. 3*92 0.126
1* -0.002* 0.470 0.40
13 a.ooao 0.100* 0.732
0.11*7 | 5.5171 0
.005 0 0. 172* 1*.***1 10.000
3 0.0300 7.310 0.007
1* -0.0016 1.7110 0.037
1
--0. 1*13 t 7.1573 0.00*
0.2003 101.211*(0.000
7.1373 0.00
0.0102
-

-

■
VarUblii Introduce* n eoutmt, (Iru, m c o s I, thirl, n O (Mrth ( q m I n Inttulty c m HI c Im *
6nl|ut«* a
, ,14,15, u t 16 nificilaly.

03

171

3

0.021
0. 02*
0.607
0.300

3. 390*
0,0091
0.1327
0. 20*1,

fanifV m
0.0303 0.6131j 0.*33
-0.0011 0.0211 0.113
-0.0001 0.0233■ 0. 17*
0.0000 Q.0IU 0.777
r.wr’"■#.m*
o.Mii
0.0316 5.3133I 0.021
6*10 0.101
>0.0003 2.
1.U 37! 0.176
0.1279 ’i i w i m
0.0170 *.21*1- 0.0*2

0.107

5i*adEr%
*r~
tlClftltt Utt ~
J ib

ISelf

Obfc j Mo.

bi

2.0337 0.136
0.227
1
3 <0.0003
0.2205 31.1202
I 0, 003*
2.0391' 0.007
■ 41.0002 1. 113* 0.130
mIiiiA; <l.M«
1.69*0 0. 1*7
-4.0013

*•0.13 Mm

I
i

172

user attitude

index

A P P E N D I X G2

intensity
coefficient

user attitude

index

P l o t of user attitude index and i n t e nsity
c o e f f icient for U n i o n Lake (August 23 and
24 combined)

I
a

intensity
coefficient

«
u
m

i* o

•a o

user attitude

index

Plot of user a t t i t u d e index and intensity
c o e f f i c i e n t for Cass Lake (August 23 and
(2 4 .combined)

i nten s i t y
^coefficient
• wo

* -a

Plot of user attitude index and intensity
coe f f i c i e n t for O r c h a r d Lake (August 23 and
24 combined)

APPENDIX G3
LEAST SQUARES DELETION ANALYSIS FOR USER ATTITUDE INDICES AND SPACE CONSUMPTION SAFETY
COEFFICIENTS FOR UNION, CASS, AND ORCHARD LAKES (AUGUST 23 AND 24, 1969)
■ii ItaJ"fc* 1 !“■
H
a
* K5
f
e
f
e
f
L 'u •4
faat 1li
t
. *“? C
M* I2
Um
9*09)0 2.2144 0.143
M 240RM 54 1 .17 0.121) 2.4543 0.041 9
3 4*07*4 9*090 0
.
0
0
f
t
1
1
f
t •22.1792 f
t
.
4572 8.014
1
3 44.7)75 5.5491 9.022
1
f
t -IMP! ,_MP* 0*0)0
Mft23
.
0
7
3
f
t 1,0053 0*319
t
,MU 0.0903 0 0
3
f
t 1 .20 0,24*3 f
f
t24 Mm 1
5 2
.
4
0
0
f
t 4.3947 0.034
j
1
4 -5.94*1 1.33)0 0.247
1
5
f
t
.
3
1
7
5
9.4259 0*421
■
j
14 •2.2934 0.3)79 0*303
f
’OJ20O3 0 0.0174 2.52*9 0.114
f
t24 Me* 134 2 .20 0.244) 11*1412<
3 1**013 14*3719 0.091
14 •3
.
1
0
5
f
t 4.3945 0*019
1
1*7144 .MB1 4*0* ^
1
3
••\
f
t
u
t23
0.1310 19.2543 9,092
f
t24 MM 1)4 3 .10 0.2303 14.10420.0095 9
3 9*99*0 13**942COaftUO
1
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91X)
0
.
0
0
0
5
0
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2
1
9
1
)
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.
1
f
t
f
t14 Mi«a
s 9.5422 29.0531<9.0993
|
a
9.0511 1.4309 t+m
f
tH Cat* 112 1 •Of 0.122* 3*4)41 0.007 0
3 1.4930 0.M42 Q.0B
14 .3.933) 3.4352 o*«a
15 4*2339 3*007) 0.033
tt _-J,3002 2.*3*3 9*009
m »
*0912 7.0594 a.oh
*97 9.12)7 3.H339*911 0 0
132
f
t24
.
T
l
f
t
l f
t
*
2
9
5
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t 9.895
3 O
t
f
t •1.1799 3*1547 9.023
15 0*3444 3*54)3 9JH
»
t
O
t
S
f
t
*
f
t
7
*
(49*f
0 9.1395 3
3
,
1
7
4
99
.
0
2
3
0
.
1
2
4
0
3
•
0
9
f
tit Cm 152
5 0.392* 4.4941 9*IU
14 *9.2237 1.4495 9*109
MB
*0119
,
9
4
f
t 0 9*1943 •9.7512<0
f
t24 Cm 132 4 .9) 9.1239 4.03229
.
9
1
f
t
3 0,01)1 4.03X1 0
^ 23
9
.
0
)
1
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f
t2* OttftaNU*
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5 2.520
9
.
0
9
f
t
14 •12*917)
9.1X2
f
t
.
401)
15 3
0.149
1
f
t •10*2919
**2
3
0*lt05 It.NM<9*M
O
f
fj0,1411 2.01479.942 9
f
t24 QrcMft11* 2 •
tita
3 1.0224 3.0*41 t
.1949 tm
t
f
t •2.4070 1
1) U73H 0.5595 •.Mt
ft*o OnftM U* ) •
,1791 XJHfk a w
.*
4
5
2
'0.022 Q 0
0
f
t 0.1409 3
f
tH
.
3
9
9
f
t atu
3 0.92*9 9
t.tJT
5
*
4
0
4
•
0
.
9
2
1
9
W
Ma
.2109 99.9129<t.Mt
.03 0.1424 4.14270.044 • 0
f
t24
0
,1924 4*1427 9.tta
’
l”
n m

M b — fit:"
eM
l*
l.
vbP t
»!■
bn* Uta CM* to* I1 Katlaan Taat
*023
*
1
7
3
f
t 0,01* 0 0.1*40 3.4402 0
% 23Mm n 1 .14 0.143V l
.14*4 0.3444 0.337
3 -11
1
f
t 2.0*72 1.03)5
*240
13 -33.2171 1.3490 0
24.3133 1.2*43 0.259
i
d
.
2
9
4
0
0
o
i
.
i
S
3
4
MB*
O
.
I
B
f
t
t
4
.
1
5
f
t
*
0
.
0
0
*
2
*
1
3
M & Mm n
14 3.743* 2.*437 0.00*
1
3 -17.4301 1.0443 0.17*
1
f
t 1S.0H1 1.4024 0.140
—J
9.0444 <0.0003
l
f
t 0*1434 9,4*4* 0.004 0 0.1434 11
-a Mm 72 1 *
It 2.0030 .7077 0.090
. .__ ..
1
3 -2*3711 1*0311 0.100
.
2
2
2
f
tf
t
i
*
t
t
i
2 <0.0005
n
.
1
1 4.1443 *,0937 0.004 0 0
1
f
t o.tai *.03)7 0.004
S
jSift"0,'iiDr'MU
.
4
4
2
f
t 0.12* 0 ■
Cw n 1 .09 0.134* 1
3 2.4431 3.1540 0.000
.4953 0.197
14 *1.9321 1
15 13.730* 1.0229 0.315
1
f
t *1*3104 0.4331 0.421
0447 J m 0.4*
M a Cm » 1 *00 0*134* 2.2413 0.04* T
.0253 0.020
3 1.4437 5
.
0
1
4
f
t 9.4*43 0.043
M •4
H 3.2441 2.4*43 0.103
.10ftF 4.0S uora
a CM 01 1 •14 0.1341 1.4412 0.141 0 0
0,3013 2,9554 0.0*0
l
.
f
t
f
t
n 0.203
u3
2.2*40 0*134 0 0.1471 24.5031 40*0003
t .O
a Cm tt f
0.1400 1.1*40.
a 0
0.4000 1.000 0 .1057147.2*03 <0.0003
-a»-aCm ~.
0 ton? 'T.W01 “0.4X7o.:i3* o.wf
t
) 1
*ta Orcterif
9.32*
I 3.2*04
14 *24,5993
TOT
13 73*1173 0,3400 0,434
-77.2432 &5079 9.47*
CN
t
,
f
t
f
t
* .M4 CUB
4
f
t 4.1333 0.4*43 f
•.a Mart 43 1 •
3 1,1401 0.5*03 0.442
14 -4,0340 0.2543 9.413
U 4.4101 0.1114 0.401
.IBI
B
f
t 0.1321 1.21471LBI 4 '9
**a MtMcft41 1 •
3 0.4027 1.2M4 0,274
14 -0.0703 0.414 0.404
t .03 0.1513 2.0*13 0.133 0 0.1074
M a Mrtwi 4) f
0 0.2205130.3400 <9.0003
...3„.•* 0.133* 0.0000
*r.oJio 0.793»
f
t 0*3430 7.430* 0*0003 0'.4.0519"
M M Mm 4* 1 •
3 4.71*0 7.34*5 9.00*
14 -11.0507 2.4247 0.111
1
3 11.0042 1.1040 0*201
If *4.0544 0.4194 0*433
f
t 2 •33 0.2421 10.04*7 0.0403 0 0.020“Mftir“-fi.ur
•m a MM 4
3 3.5334 14.5711 <9.0003
14 .4,3459 9
1.1
M05
M4 9*004
0.0313 0.0504 9.330
ata Cm n 1 .11 0.1104 2.03U 0.001 0
3 1.4134 5.3000 9*914
14 -3*7492 3.2*09 0*074
1
5 3
.
0
0
3
f
t 2.27*9 0.154
-1,2054 1.7274 0,193
1
4
a Cm n 2 .«* 0.1112 2.1*31 0.103 0 0,093* 4.2134 0,043
,
0
1
f
t
3 0.720* 5.2099 0
1
f
t -1*1344 3.3770 0.013i
0
.
3
1
*
3
0
.
1
1
1
*
u
Uf
f
t0,0093
•** Cm n 1 •03 0.1123 l.oHo 0,142 3" O
0*2444 3*3*73 0.070I
.
.
.
i
f
.
. -0.L9I0 2.2427i
Cm n *
0.1134 1*43*4 oTzm 0 0,1792 51*0430,.<0*0005J
3 Q.M30 1.4344.0,2)2;
ta* - 4 H i > 1*91
^ 0.113* Vim 1.000 0 0,2047229.0040!<0*0005:

VtflablnliimMci*viautae,fine,a
a
c
a
v
f
t
,UlHt■»*fMiftftpittviMicaCMM^tlN
UfitrcmUUIM4ail|M«<a
f
t0,3,14,15,mi 1
f
tnsractinly.

174

user attitude

index

A P P E N D I X G4

space consumption
safety coefficient

user attitude

index

ipl o t o f u s e r a t t i t u d e i n d e x a n d s p a c e c o n ­
s u m p t i o n c o e f f i c i e n t for U n i o n L a k e (August
:!3 a n d 24, 1 9 6 9 c o m b i n e d )

space consumption
safety coefficient

user attitude

index

P l o t of u s e r a t t i t u d e i n d e x a n d s p a c e c o n ­
sumpt i o n c o e f f i c i e n t for C a s s L a k e (August
23 a n d 24, 1 9 6 9 c o m b i n e d )
i• ■ *

space consumption
•
safety coefficient
■m «■ 4i* a
>e *•« ■^
'■*"■ 1**
P lot of user attitude index and space c o n ­
sumption coefficient for O r c h a r d Lake
( A u g u s t 23 a n d 24, 1 9 6 9 c o m b i n e d )

175
A P P E N D I X 65

|!I
r

L E A S T S Q U A R E S D E L E T I O N A N A L Y S I S F O R U S E R A T T I T U D E INDICES
A N D S P A C E C O N S U M P T I O N S A F E T Y C O E F F I C I E N T S F O R UNION,
CASS, A N D O R C H A R D L A K E S (JULY 4 T H R O U G H
S E P T E M B E R 1, 19 69)
ih M ir
J M

ft.

V a tla fc l* "

O .t.M

M )W

< 0 .0 0 0 3

.3 5

. .H it

1 0 .6 M 1

< 0 .0 0 0 3

aM

o.ln*

0
3
14
15
I*
0
3
14
J3_
0
3

lL

U n lv n

1041

U n i An

16U

,T " I

IP*

1

»
ta a t

1

_
< 0 .0 0 0 3

1*
t ill

I lf 4

( ill
o rc h a rd

V a r t a k la a
U

■.I A l U b a a

1

ii* 9

3

.1 4

0 .1 M

IP

1

•ii

o . llll

ln c » * u c a * i r <
a a

10. H I 5

fl . t

I A . I V

n iu lm ,
.

*

4A

d ra t,

— ■ — -■- - - - *

■m

- ■ ___

em*.

.m U

d

m

t h lr * .

u

n«

13
10
0
3
14
10
0
3
14
0
3
14
13
to

4 4 .A 6 6 I

{0 *0 0 0 3
*T H P ”

fw n b

%

h

P a r t ia l
l« l> il» lin
C M lfie tc n t

.

• 0 .0 4 0 1
4 .0 0 1 0
• 1 1 .7 3 1 0
1 1 .0 2 0 3
• 4 .0 0 3 6
0 .0 3 0 0
3 .3 6 6 3
- 6 .4 3 3 0
3 .3 9 3 2
0 .0 3 2 9
0 .1 9 9 0
- 0 .0 4 2 3
0 .0 0 3 2
- 0 .0 0 0 6

oloSU

0 .1 4 3 3
- 0 .0 0 9 4
- 0 .0 0 0 0
0 .0 0 3 0
0 .1 7 4 3
. 0 .0 0 7 9
0 *0 9 9 3
4 .7 9 3 2
-2 3 *1 9 7 2
4 4 *9 7 3 2
-3 2 * 7 1 0 1

01a.
0 *0 7 9 6
7 .4 1 0 2
2 .7 0 4 7
1 .1 9 2 1
.0 * 0 1 0 3
O a O ilf
1 0 .7 7 1 6
9 ,1 0 2 1
6 .2 0 0 1
0 *172 1
1 .7 0 2 3
0 .3 4 2 3
0 .2 6 0 3
0 .3 7 1 3
0 .6 3 4 $
3 *0 0 4 2
0 .1 9 7 1
0 .1 5 9 2
0 .4 9 9 2
. 4 .7 0 0 3
7 .3 0 3 1
2 .3 4 1 2
0 .9 9 2 3
6 .3 7 0 2
3 .9 6 1 9
3 .9 4 4 2

0 .7 6 3
0 .0 0 0
0 ,1 1 9
0 .2 6 9
0 .4 3 2
0 .0 3 9
< 0 .0 0 0 9
0 .0 0 4
0 .0 1 6
0 .6 4 0
0 .2 3 2
0 .3 7 1
0 .6 1 9
0 .9 7 9
0 *« 6 2
0 .0 9 3
0 .6 6 4
0 .6 9 9
0 .4 9 9
0 .0 0 5
0 .0 1 4
0 .1 3 9
0 *0 0 7
0 *019
0 .0 2 3
0 .0 3 2

t a n a a , a » « . n a u a * t lo n a . f a t a c o . r r i c l a . 1t
w

Index

APPENDIX G6
f
3
9

user

attitude

0

I
c
0
*

J

&
1

e
I
o
176

s

0
t

0
8

e
I
&

a
0

&
Q
e
0

oa

Plot of user attitude index and space consumption
safety coefficient for Union Lake (July 4 through
September 1, 1969}

x ea

j,q *

space consumption
safety coefficient

index

F

attitude

i

user

APPENDIX G7

J
b

0

r
o
0

r
0

i
0

I
177

5
O
t
0
i

0

I
0
3

0
G

o
8

o

OQfi 0&

C 1?

on

0B

c

Plot, of user attitude index and space consumption
safety coefficient for Cass Lake {July 4 through
September 1, 1969)

I 03

im

space consumption
safety coefficient

!

index

APPENDIX G8
f

0

9

user

attitude

0

I
0

f
0
«k

i
o
s

0

I
o
178

1
0

I
o'

a
o
2

o
£
0
8

o
CX

*

17

0X

a

0 —

Plot of user attitude index and space consumption
safety coefficient for Orchard Lake (July 4
through September 1, 1969)

C -0

0%

0 -C.

c.

0

space consumption
safety coefficient

179
A P P E N D I X G9
LEAST SQUARES DELETION ANALYSIS FOR USER ATTITUDE INDICES
AND SPACE CONSUMPTION SAFETY COEFFICIENTS FOR RIPARIAN
O W N E R S O N U N I O N , C A S S , A N D O R C H A R D L A K E S { A U G U S T 23,
24, 30, 31, A N D S E P T E M B E R 1, 1969)

[?

a *b a r
La h a
t ln ltf i

49

1

V t'e n J A r J
■ rv p i • (

P
Teat

" f
IU

11.3*10

40.0009

»*
•

33

1.9016

P a r t ia l
A a g r a ic lo n
C o e ff ic ie n t

V ir n b U *

0
3
4
3

U n io n

49

a

.34

1.BH4

13.1993

40.0009

U n i an

43

3

.40

i.m s

14.444*

4 0 .0 0 0 5

Ca«e

49

<30

1

3.0309

*.3330

<0.0009

4

4
9
4
}
0
3

4
9

C ast

49

• 49

a

11.9043

3.0031

<0.0003
9

3
C aea

49

.49

3

3.0497

19.9190

<0*0009
3

O v « lM v d

43

.13

l

1.40T3

1.34*0

0.370
3

4
9
O rc h a rd

ki

...j

..

• 13

1.4300

6
"

i

:h m

4
3
O rc h a rd

43

3

.1 1

1.4400

3.3041

0.0 *4
3

O rc h a rd

V iflillic
4
«
a

43

4

• 10

L.4339

lM r * 4 u e H m « e o n lt a n tf
t a c a a r f,
m
0 , 9 , 4 , 5 , and 0 r e s p e c t iv e ly .

4,331*

th lv li

0.044

and f o u r t h

"""

.

9. *403
130.443*
1 4 * , 0*71 1 .9 4 * 9

109.02**
- 4*2.4409
1*49.2942
•14*0.9641
9.9290
9.2600
240.5304
373,1*43
4. 3434
323.940*
3.0377
- 23.3*70
331,0301
-1999.4144
2413.4004
1T969*

t f . ’l W

4
0
*

d a a ra a l y w i

Tot

M i.

4.3036
0.3010
1.71*3
2.1403
. 2.27*4
20.1494
0.7094
9.2359
3.0064

9.3B14
• 93**440
439.9334
*2619.3144
_2L7_Z* f * 0 * .
4.14*4
339,4930
-1223.9724

R .m

k‘

0,039
0,491
0.190
0.152
0,139
4 0,0003
0.005
0,027
0 f Q30
« 0.0005 ........
40.0009
0.004
— v . m ------0.173
0,106
0,130

i

17.212*
9.3294
T . tt* S “

1.9297
1.0197
2.3943
2.01*3
5 .4 « « “ ”

. 2.2302
47.3062
19.10*0

.

<

1.9990
Q*1259
0.2139
0.0246
0.4761
il.f it a

0.4313
00,490*
0.6474
- 42*.4547
— 1241, 6 3 7 4 . .-..0*9346
43.7930
2.4449
0.7072
• 111.4406
2.4120
112.0402

c o n itfv tlo n

a ih ty

_91.3410
a .« ? «

0 .1 0 1

0,740
0,140
0.142
< 0.0003
0.0009

0 .1 1 2 0
2 .1 0 1 *

,

.

4.3219

c o e f fic ie n t

0.170
0.725
0.647
0,372
0.494
0,601
0.306
0.426
0. 340
40.0009
0.409
0,263
4076603

0.044

‘

180
A P P E N D I X G10

!

»

o

r.

'S
.5 *
G 0) id*
.-t

S’

Pi*
•H "
(d M a
H

41

+1

01
01

3

space c o n s u m p t i o n
s a fety c o e f f i c i e n t
P l o t of user attitude index and space c o n s u m p t i o n
c o e f f i c i e n t for r i p a r i a n owners o n U n i o n L a k e
A u g u s t 23,24,30,31, and September 1, 1969)

i
i
S
G
•H

if
9

01

T3

5 idK
■H a
v
a M:

id

u
0)
01
3

space c o n s u m p t i o n
saf e t y c o e f f i c i e n t
P l o t of u s e r attitude index and space c o n s u m p t i o n
coe f f i c i e n t for riparian owners on Cass Lak e
(August 23,24,30,31, and September 1, 1969)

i
i
x
0)
•c
G

§

•H

1

•H Scu
."
+1 -H

id
M

01
01

3

space c o n s u m p t i o n
safety coefficient
P l o t of user attitude index and space c o n s u m p t i o n
c o e f f i c i e n t for riparian owners on O r c h a r d Lake
(August 23,24,30,31, and September 1, 1969)

181
A P P E N DI X Gil
LEAST SQUARES DELETION ANALYSIS F O R THE N U M B E R OF ACRES
P E R BOAT AND SPACE CONSUMPTION SAFETY COEFFICIENTS
F O R UNION, C A S S , A N D O R C H A R D L A K E S
(JULY 4 T H R O U G H S E P T E M B E R 1, 1969)

Lah«
IM tw

M h ir
O W a r v a t lt M

>M »

M

1000

lf
1

,7 1

Im r •(
B a tlM ta

. *
T «t

*•*4 4 0

9 1 3 .0 1 4 0

Y a r l'h U *
4 0 ,0 0 0 3

0
3
7

0

0
10
Om i

11S0

1

.* 3

1 4 .0 9 9 1

4 1 ) . TOT*

0

ll»

2

*0 3

1 4 ,0 * 4 0

3 1 1 ,4 3 1 3

? 0 .0 0 0 3

«
10
0

7

o n h irt

900

~

10

t

.n

1,1111

0

~W«.V3lfl

3

7

0
9

10

V a r l a S l i a i n t r M u c « * m w * c m a t a a t , V t n t , i t aM , t k l r i , f a w t t i ,
I I U I m c i « i l | M t a 4 a i 0 , 3 , 7 , # , 9 , a M 10 r a i f a a t l v a l y i

c m

4 ,7 9 * 7
* * ,3 9 0 0
-1 9 4 .4 * 4 *
4 2 4 .9 1 2 9
- 1 9 2 ,4 4 1 2
0 .4 3 9 )

tiiim

< 0 .0 0 0 9
3
r

CM* •

ra rtta l
I w r a a a la n
f lM fd a iM ta

id i I h v it m

4 « n rH

*b .
9 .9 7 *0
1 2 .9 3 1 7
7 .3 * 3 1
1 1 9 .9 2 1 4
1 2 .9 * 2 *
7 4 1 .4 2 4 0

U t.Im

• 1 1 4 ,9 4 4 *
1 4 .3 0 * 0
1 0 9 .1 9 7 7
3 .1 3 0 9
- 1 2 9 .4 3 7 0
0 ,0 1 * 7
3 0 . *7 0 3
0 .2 3 4 4
_____p j i n ___ ~ U 2 a * f t + 2 .
2 7 ,9 9 1 9
2 )2 .0 1 3 1
4 4 .9 2 7 *
- 1 0 2 .4 3 7 4
1 9 .1 7 7 4
1 3 4 .0 4 4 4
- 3 0 ,3 1 0 0
4 .4 0 9 2
0 .9 9 )7
9 )3 .9 1 4 0
2 .4 9 3 4
1.1400
1 0 1 .1 9 3 2
7 .3 3 0 9
4 1 4 ,9 0 4 3
4 .0 0 * 0
1 3 0 4 .9 9 0 4
9 .9 2 0 0
4 ,4 7 9 2
- 9 0 9 .1 1 3 9
0 .4 9 3 )
1 1 9 0 .4 2 4 0

ta n

■U .
0 .0 0 2
4 0 .0 0 0 9
4 0 .0 0 0 3
4 0 .0 0 0 9
4 0 .0 0 0 3
< 0 .0 0 0 3
4 0 .0 0 0 3
4 0 .0 0 0 3
0 ,0 7 3
0 ,3 * 9
0 .4 2 0
4 0 .0 0 0 9
< 0 .0 0 0 9
4 0 .0 0 0 3
4 0 .0 0 0 9
0 .0 1 1
4 0 .0 0 0 3

0.171
0 .0 0 7
0 ,0 0 9
0 .0 1 *
0 ,0 3 3

<0.000$

c a n a u ^ t l« n a a l a t y

APPENDIX G12
boat

i

number

of

acres

ff

per

t •

*

1
a

* \
• . !

o
ft

0

i
0

i
182

0

i
i
0

i
D

5
Q
5
B
►
ft

0M

o*»

e

Plot of the number of acres per boat and the space
consumption coefficient for Union Lake (July 4
through September 1, 1969}

4.

i

4Qi

space consumption
safety coefficient

I

APPENDIX G13
I-.

.

r!t
per

a

acres

■|

sn

V

-

number

of

r
I
8

a
183

i

e
i
o

s
0

9
e
a
8
a
qn

C

a

o»

o -a

0

plot of number of acres per boat and space
consumption safety consumption for Cass Lake
(July 4 through September lr 1969)

a a»

L01

i i-

190

space consumption
safety coefficient

number

of

acres

per

boat:

APPENDIX G14

a
0

I

B
a

o*- a n
o
3»
0 4
Plot of the number o£ acres per boat and the space
n u»

consumption safety coefficient for Orchard Lake
(July 4 through September 1, 1969)

av

3?

space consumption
safety coefficient