1.cx#)lls
I 1.1.2.11) .

k.

.'.l
.41 (5...!
If.» .4...»
altitle _ .3...
3.13.2.5... r
.1233}: i:
3::
E. .
1:33.:
_ I:
.. 3:53...
R53...» o.
.2. t :1
[’1‘

13...-..2...» tin:
£512.}. :5 .XV .2
«9.2.1:...215! at... .1...)
SEZF! {10...}...‘5Euv? .. 35..
.ifflil §!:.¥l35l;‘!v’13‘ltl‘ . '.H-.v 31 .
:SZfiFI-{lri tltfiuaigatiarzrwi 2.1.525! safil‘lz‘iu. :‘Av >33.
,v....V..-a!.3. 33.2.2.3... .. 5’16 2-. 2.3.1-1... 2.....2...Z...a.....‘
.{araicszrw.....§..!...v..u.::. .33....5..£\

filiulittla
it,

.A. strefiiiifx 1.7.11...
Ilivlvx:lta v.3...llxttvlflvrav
v :BIT'CI:
) irrii

5.2.; :591..’|n

31:11:15.:

.. iii: . V .
....V¢Il..7lb7tz!:ar).l.

vrltfx: ..n 5.91..)otif‘9 ll

. .1.
East‘s... . c .l..rl:.l.r§|zixul
. El-

: I! .2... i=2;

Ao.y...~.:I..I..:91xv:1iiy.z . I) ,
:lyKIIrizrlnlev-ic 731:37Iil:v‘.. t.
. it! )alirlvlvnt2|..¢..
. III . . .

50n- I-C2-" v
. :32 5...-..
R...z§2.¥i§
3-1.3.: .I:

$3.21»:
1...!)2

. £3.
7.. .07.;

)k.)l£l’).
....t...¥l ,

”Kw. .

:
1..iuvl.~.y. .

. 53.. .. .1. 1121...}..1‘
t. .. y . + .quavu'lsisilizgg tn.
5...... gavégmcmfidkflntah $43.... 3.9;... . u
:«1::.: 1-1 ,1
5:. ,x.1..é-r,

 

 

 

3.1.1:..1.
L2 3} i

 

I— ,

inabib

I. ”37;: g; .1 37’. y

Whijilf-Ep
K.

ta tC

1..Cy

 

 

 

 

 

ABSTRACT

TRACTION PERFORMANCE CHARACTERISTICS
OF TRACTORS ON AGRICULTURAL SOILS

by Kenneth Walter Domier

The low pressure pneumatic tire has been used on
tractors for approximately thirty—five years. During this
time extensive testing of tire performance has been
carried out. DeSpite this extensive testing it is still
difficult to predict the performance of a given tractor
under practical use.

The greatest variation in tractor traction is due to
variations in soil conditions. No soil strength character—
istics are presently available which permit calculations
of tractor output. The hypothesis tested in this research
is that the traction characteristics of a field surface
can be determined from tests with a "standard tractor" and
that the results can be used for the prediction of the per—
formance of other tractors.

A two wheel drive tractor equipped with 13.6—28 tires
on the rear and 6.00—16 tires on the front was instrumented
to record drawbar pull, front wheel rolling resistance,
weight transfer, rear wheel input torque, rear wheel speed
and actual forward speed. Drawbar load was provided by towing
another tractor fitted with a gate valve on the engine

exhaust.

   

Kenneth Walter Domier

Traction studies were made with the instrumented
tractor on several field surfaces. One series of tests
was made to determine the effect of varying percentages
of maximum allowable load for an inflation pressure of 14
psi (load factor influence). Additional tests were made
with the maximum allowable load for inflation pressures
of 14, 16 and 18 psi.

Field surfaces used for this part of the study
included Osborne clay fallow and stubble, Almasippi sandy
loam and Sperling silty clay loam.

Additional tests determining drawbar pull and actual
forward speed were made on several tractors equipped with
varying sizes of rear wheel tires. The tractor with the
13.6-28 tires was used as a standard in each test. Field
surfaces were Osborne clay fallow and stubble with varying
bulk density and moisture content.

The measurements made were recorded on light sensi—
tive paper by an optical light beam recorder. Power was
supplied by a portable generator. A truck outfitted with
a shade protection for the recorder served as a mobile
instrument vehicle.

The results obtained were analysed according to the
following performance parameters: coefficient of net
traction, coefficient of gross traction, coefficient of
rolling resistance, tractive power coefficient, tractive

efficiency and travel reduction.

 

Kenneth Walter Domier

For a given tire on a firm field surface a common
set of performance curves was suitable for most combina-
tions of weight and pressure. Where the field was loose,
higher performance was obtained with less weight on a
tire.

A straight line relationship between measured weight
transfer and rear wheel torque was obtained. This rela—
tionship was relatively independent of the traction sur—
face. Reasonably good agreement between measured and
calculated weight transfer was obtained.

The traction characteristics of two surfaces were
determined for the standard tractor. After corrections
for load factor and diameter were applied, the performance
of both smaller and larger tractors on these two surfaces
was calculated. The measured performance in most cases

agreed very closely with the calculated performance.

Major Professor

Approved filly %"L

Depa ment Chairman

TRACTION PERFORMANCE CHARACTERISTICS

OF TRACTORS ON AGRICULTURAL SOILS

By

Kenneth Walter Domier

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1967

 

645607?

2/22 W

ACKNOWLEDGMENTS

I wish to express my gratitude to Dr. S.P.E. Persson
for the advice and assistance given during this study.

Thanks also go to the Agricultural Engineering Staff
of both Michigan State University and the University of
Manitoba for assistance given in the preparation of equip—
ment and carrying out of field tests.

I would also like to thank Massey Ferguson Industries
Ltd. for providing the test tractor.

Appreciation is also given to my wife Selma, and
children Calvin, Sharon and Linda who have Spent many

evenings without the company of their father.

ii

 

 

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . V
LIST OF FIGURES . . . . . . . . . . . . Vi
LIST OF APPENDICES . . . . . . . . . . . X
Chapter
I. INTRODUCTION . . . . . . . . . . . 1
1.1 The Problem . . . . . . . . . 1
1.2 The Objective . . . . . . . . . 1
II. REVIEW OF LITERATURE . . . . . . . . 2
2.1 Tractor Tire Research 1930—1938 . . . 2
2.2 Tractor Tire Research (Applied)
1939—1967 . . . . . . . . . A
2.3 Tractor Tire Research (Soil Dynamics) . 10
III. TERMINOLOGY AND INDICATORS OF PERFORMANCE . 1”
IV. EXAMPLES OF TIRE PERFORMANCE——AN ANALYSIS OF
PUBLISHED TEST RESULTS . . . . . . . 21
V. EQUIPMENT . . . . . . . . . . . . 37
5.1 Equipment Used by Other Investigators . 37
5.2 Equipment Used in This Study . . . . 39
5.3 Calibration of Equipment . . . . . A7
VI. TESTING PROCEDURE, RESULTS AND DISCUSSION . 57
6.1 Preliminary Tests . . . . . . . 57
6.2 Field Studies . . . . . . . . . 57
6.21 Preliminary Field Testing of
Equipment . . . . . . . 58
6.22 Field Test Procedure . . . . 59
6.3 Analysis of Data . . . . . . . . 61

iii

 

Chapter

6.A Presentation of Data . . .
6.41 Part I. Performance of the
"Standard" Tractor

6.A2 Part II(a). A Comparison of the

Performance Characteristics of
Several Sizes of Rear TraCtor
Tires Under Similar Field
Conditions

6.43 Part II(b). A Prediction of the

Actual Field Performance of
Other Tractors Based on the
Traction Characteristics of
the "Standard" Tractor

VII. RECOMMENDATIONS FOR FURTHER WORK

VIII. SUMMARY OF RESULTS

REFERENCES

APPENDICES

iv

Page
65
65

77

8A
107

109

111

116

   

Table

LIST OF TABLES

Surfaces used in traction studies
Sand, silt and clay analysis

Weights and pressures of tractor tires tested
in the field

Tire Specifications (taken from a tire
handbook)

Page
66
66

79

79

 

Figure

10.

11.

12.

LIST OF FIGURES

(a) Basic forces and velocities on the wheel,
(b) The concept of gross traction and rolling
resistance

Drawbar pull vs. travel reduction for three
tractors with 23.1—26 tires. (Nebr. Test Rep.
824, 835 and 836) . . . . . . .

Coefficient of net traction vs. travel reduction
(same tractors as in Figure 2)

Drawbar pull vs. travel reduction for three
tractors with 18.4—34 tires. (Nebr. Test
Rep. 806, 839, 8A9) . . . .

Coefficient of net traction vs. travel
reduction (same tractors as in Figure A)

Coefficient of net traction vs. travel reduction
for eleven tire sizes (Nebraska Test).
Inflation pressure and load factor in
parenthesis

Coefficient of net traction vs. travel reduction
(from Walters and Worthington, 1956)

Drawbar pull vs. travel reduction (from SAE
Coop Tests 1938)

Coefficient of net traction vs. drawbar pull
(calculated from Figure 8)

Coefficient of net traction vs. travel reduction
singles vs. duals (from NIAE Test Report RT
49/50088) . . . . . . . . .

Coefficient of net traction vs. travel reduction;
singles vs. duals (from Sauve, 19AO)

Top—Instrumented tractor (with 13.6—28 tires)
and load tractor,

Bottom——Adjustab1e drawbar with pull transducer
and frame for extra weights

vi

Page

17

23

2A

26

27

29

31

32

33

3A

36

AO

 

Figure Page

13. Equipment components (a) weight transfer and
rolling resistance transducers, (b) rear
wheel speed indicator, (c) fifth wheel speed
indicator, (0) fifth wheel or forward speed

indicator (d) mobile recording . . . . . A2

1A. Calibration of rolling resistance trans-

ducer . . . . . . . . . . . . . A8
15. Rolling resistance calibration, MF 150

tractor . . . . . . . . . . . . A9
16. Calibration of torque transducer . . . . 51
17. Torque calibration, MF 150 tractor . . . . 52
18. Calibration of weight transfer, MF 150

tractor . . . . . . . . . 5A
19. Calibration of drawbar pull transducer . . 55
20. Typical record chart from Honeywell

Visicorder . . . . . . . . . . . 62
21. Typical graph plotted by the data plotter . 6A
22. Performance parameters for Osborne clay

fallow (a) load factor influence (b)

pressure influence . . . . . . . . 67
23. Performance parameters for Osborne clay

stubble (a) load factor influence (b)

pressure influence . . . . . . . . 68
2A. Performance parameters for Almasippi sandy

loam stubble (a) load factor influence (b)

pressure influence . . . . . . . . 7O
25. Performance parameters for Sperling silty

clay loam stubble (a) load factor influence

(b) pressure influence . . . . . . . 71
26. Measured weight transfer vs. measured torque

input (clay fallow and aSphalt) . . . . 73
27. Calculated weight transfer vs. measured

weight transfer . . . . . . . . . 75

vii

 

Figure Page

28. Performance parameters for Osborne clay
stubble vs. coefficient of net traction
(pressure influence) . . . . . . . 76

29. Performance parameters for several tires on

Osborne clay stubble . . . . . . . . 80
30. Performance parameters for several tires on

Osborne clay fallow . . . . . . . . 82
31. Performance parameters for several tires on

roto—tilled Osborne clay fallow . . . . 83
32. Performance parameters for several tires on

Osborne clay fallow (higher m.c.) . . . 85

33. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay stubble (9A80 1b. tractor) . . . . 87

3A. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay stubble (7820 lb. tractor) . . . . 89

35. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay stubble (10,030 lb. tractor) . . . 90

36. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay fallow (5510 lb. tractor) . . . . 91

37. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay fallow (7820 lb. tractor) . . . . 92

38. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay fallow (10,030 lb. tractor) . . . . 93

39. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay fallow (6790 lb. tractor) . . . . 9A

A0. Predicted and measured values of drawbar
horsepower and travel reduction on Osborne
clay fallow (6790 lb. tractor with a dif—
ferent load factor) . . . . . . . . 95

viii

 

Figure

Al.

A2.

A3.

AA.

AB.

A6.

A7.

A8.

A9.

50.

Predicted and measured values of drawbar
horsepower and travel reduction on roto—
tilled Osborne clay fallow (5510 lb.
tractor) . . . . .

Predicted and measured values of drawbar.
horsepower and travel reduction on roto—
tilled Osborne clay fallow (7820 lb.
tractor) . . . .

Predicted and measured values of drawbar
horsepower and travel reduction on roto—
tilled Osborne clay fallow (10, 030 lb.
tractor) . . .

Predicted and measured values of drawbar
horsepower and travel reduction on high
moisture content Osborne clay fallow
(5510 lb. tractor)

Predicted and measured values of drawbar
horsepower and travel reduction on high
moisture content Osborne clay fallow
(7820 lb. tractor)

Predicted and measured values of drawbar
horsepower and travel reduction on high
moisture content Osborne clay fallow
(11,310 lb. tractor)

Predicted and measured values of drawbar
horsepower on high moisture content
Osborne clay fallow (7820 lb. tractor,
gears 1,2, 3) . . . . .

Predicted and measured values of drawbar
horsepower and travel reduction on higher
moisture content Osborne clay fallow
(3700 lb. tractor, gears 1 and 2)

Predictedznuimeasured values of drawbar
horsepower and travel reduction on higher
moisture content Osborne clay fallow
(11,310 lb. tractor)

Predicted and measured values of drawbar
horsepower and travel reduction on higher
moisture content Osborne clay fallow
(11,310 lb. tractor, gears 1, 2 and 3)

ix

Page

97

98

99

100

101

102

103

10A

105

106

 

Appendix
A.

B.

LIST OF APPENDICES

Analysis of Nebraska Tractor Test Reports

Specifications of the Standard Test
Tractor . . . . . . .

Analysis of 13.6—28 Tire Test Results
Analysis of Several Sizes of Tractor Tires

Calculation of Drawbar Performance of Other
Tractors Based on the Standard Tractor

Page

117

122
12A

128

133

 

I. INTRODUCTION

1.1 The Problem

 

The low pressure pneumatic tire has been used on
tractors for approximately thirty—five years. During this
time extensive testing of tire performance has been carried
out. Despite this extensive testing it is still difficult
to predict the performance of a given tractor under practi—

cal use.

1.2 The Objective

 

The objective of this thesis was to find background
data for interpretation of given test results for practical
farm use and tractor size recommendations. The prediction
of the field performance of a given tractor operating in a
given soil should be the end result.

To fulfill the objectives given above, the following
was proposed:

1. To instrument a "standard" tractor to record
tractive performance in the field.

2. To study the performance of a given tire sub—
jected to different weights (loads) and
inflation pressures.

3. To evaluate the influence of tire diameter.

A. To determine with the "standard" tractor,
traction characteristics for a number of soils.

5. To predict the field performance of tractors of
several sizes and compare with measured values.

 

II. REVIEW OF LITERATURE

"No other single change in farm tractor design has
so improved their efficiency, increased their utility and
promoted their popularity as has the advent of low pressure

pneumatic tires" (Walters, F. C., and W. H. Worthington,

1956).

2.1 Tractor Tire Research 1930—1938

 

In the early years of the pneumatic or rubber tire,
tests were carried out to compare rubber tires and steel

wheels. A review of the Journal of the American Society of

 

Agricultural Engineers shows no less than twenty—two articles

 

on the topic "Rubber tires vs. steel wheels" for the years
1930-1935. In the majority of articles, rubber tires were
shown as superior to steel wheels under average farm con-
ditions. Duffee (193A) stated, however, that Wisconsin
farmers might not derive enough of the benefits of rubber
tires to warrant the cost of changing from steel wheels to
rubber tires.

The majority of the tests conducted during the above
period consisted of drawbar pull-slippage tests and towed
rolling resistance tests. The equipment for measuring draw-
bar pull usually consisted of a hydraulic cylinder connected
to an indicating or a recording pressure gauge. Slippage

tests were made by either measuring travelled distances for

 

 

load and no load tests or by mounting automobile distributors
on the rear wheels. Counters were connected to solenoids
actuated by the interrupted current. The data obtained were
averages over a considerable distance, in some cases, 500

to 1000 feet. Thus, large areas subject to wide variations
in soil uniformity were required for tests. Differences
obtained in drawbar pull or slippage for a change in a vari—
able may have been due to a change in soil conditions.

By the year 1936 rubber tires were generally accepted
as being superior to steel wheels except under adverse con-
ditions or at extremely low speeds.

The acceptance of rubber tires led to many problems
concerning the choice of tire size, inflation pressure and
weight for different soil types and conditions. The Society
of Automotive Engineers Tractor and Industrial Power Equip—
ment Activity Committee appointed a subcommittee in 1935 to
consider the whole problem and arrange for field tests. A
series of tests with eleven tire sizes was conducted on six
surfaces ranging from concrete to loose sand. The Society
of Automotive Engineers Cooperative Tractor Tire Testing
Committee Report (1938) listed four main conclusions that
still form the basis for any discussion on tractor tires.
These are:

l. The most important factor affecting the
drawbar performance is the soil itself.

2. For a given soil, the most important factor
affecting drawbar pull is the weight that
the tire carries.

 

 

3. Tractors with high horsepower to weight
ratios have to travel faster to utilize the
available horsepower or use added weights to
operate at lower speeds.

A. Inflation pressure has an effect, lower
pressures being advantageous on loose, sandy
soils. This advantage disappears on firmer
soils.

The information obtained provided answers to some of

the problems but the data again was based on averages and
considerable variation was present.

2.2 Tractor Tire Research
(Applied) 1938-1967

 

 

The possibility of traction loss due to wear was
investigated by Barger and Roberts (1939). Their tests
showed a general loss of traction on all field surfaces
used, although at light to medium drawbar loads worn tires
gave good performance. At high drawbar loads, where the
farmer may Operate only a small percentage of the time,
worn tires generally cannot penetrate or dig down to a
firmer traction surface.

Another area of tire performance that received con—
siderable attention was that of rolling resistance.
McKibben and Davidson (19A0) carried out extensive tests on
towed pneumatic tires at various loads and inflation pres-
sures. A definite relationship was obtained between the
outside diameter and rolling resistance for given inflation
pressures and field conditions. McKibben and Hull (19A0)
found a correlation between rolling resistance and soil

penetrometer readings. This marked the first time that any

 

 

index of soil strength was used as an indicator of soil
properties which affect wheel performance.

Dual tires were introduced as a means of obtaining
better flotation (less sinkage) and possibly better trac—
tion under adverse conditions. As many of the tests were
made with different sizes of tires and weights, the infor—
mation obtained was only applicable to the tractor and soil
condition tested. However, as-a general rule, although
duals did provide better flotation, the pulling ability of
the dual equipped tractor was not always increased as com-
pared to the same tractor equipped with single tires.

Sauve (1939) obtained less pull with duals than with single
tires for the same rear wheel weight. This was probably
due to the high inflation pressure (20 psi) used in the
duals as compared to the single tires (12 psi). Lowering
the inflation pressure increases the traction area and
decreases the rolling resistance. Later tests by Clark and
Liljedahl (1963) on model tires indicated that duals per—
formed better than singles (at equal normal weight) in
loose soils at travel reductions less than 30%. On firmer
soils, an advantage could only be obtained by decreasing
the inflation pressure of the dual tires below that of the
single tire. These results, although quite valid for the
artificial soil they were obtained on, were not verified by
the authors in actual field tests.

McLeod et_al. (1966) obtained better tractive per—

formance from duals on the soil bins at the National Tillage

 

Laboratory at Auburn, Alabama. The difference between
duals and singles was less pronounced in clay than in
sandy loam.

Kucera and Jamieson (1963) found duals to be advan-
tageous on clay soils only at high drawbar pulls and at
high rates of travel reduction (above 20%).

The effect of different tractor tire design on tire
performance was investigated by Reed and Berry (19A9).
Certain tire designs were better than others depending on
the drawbar pull at which the comparison was made. The
effect of lug height on tire performance was studied by
Reed and Shields (1950). Low-lugged tires (0.5 inch) per-
formed better than high—lugged tires (1.75 inch) on a sandy
soil. On a clay soil there was no advantage for high or
low lugs. The effects of rim width on tractor tire per—
formance was studied by McKibben et_al. (1952). No sig—
nificant difference was found in the performance of lA—26,
6 ply tractor tires on sand when mounted on 12, 1A, 16 and
18 inch rims and operated at the same inflation pressure,
with the same total load on each tire.

The performance of farm tractor tires weighted with
liquid and cast—iron wheel weights was studied by Sauve and
McKibben (19149) and by Reed still. (1953). Very little dif-
ference between the two methods was obtained when the infla—
tion pressure of the liquid—filled tire was adjusted to
include the increase in pressure due to increased rear

wheel weight as drawbar pull was increased. Kucera and

 

Jamieson (1963) found no significant difference in wheel
slippage of tires ballasted with liquid, dry powder or
cast-iron wheel weights.

As the need for increased pulling power arose, tires
with larger diameter were used. For a given tractor this
resulted in a reduction in drawbar pull in a given gear, a
decrease in clearance between integral implements and
tractor parts and problems in hitch linkage. This question
of oversize tires was studied by the SAE Tractor Tire Sub—
committee in 195A and the test results reported by Walters
and Worthington in 1956. Tests were made with (a) tires with
the same bead seat diameter, but with increasing section
widths, outside diameters and rolling radii (b) tires with
increasing section widths, approximately the same outside
(iiameter and rolling radius, but with varying rim diameter,
arni (0) tires with the same rim diameter, approximately
tflle same outside diameter and rolling radius, but with sec—
tfixon widths greater than that of the basic tire. The normal-
Siazed tire supplied with a tractor was called the "basic"
tirwe and tires with increasing section width were called
"OVHersize tires." The three main conclusions from this

St tidy were:

1. When basic and oversize tires were loaded
to the rated capacity of the basic tire,
basic tire performance was slightly better.
(There were, however, several cases where
contradictory results were obtained).

 

 

2. With each tire loaded to its individual rated
capacity no significant difference was found
among the values of traction coefficient
(pull plus front wheel rolling resistance
divided by dynamic weight on the rear wheels)
of any of the tires tested.

3. When flotation is adequate, the traction
advantages resulting from the use of oversize
tires are directly proportional to their
loading.

Reed (1956) reported results from similar tests con-
ducted at the National Tillage Laboratory at Auburn,
Alabama. Oversizing by method (b) above resulted in better
performance. Additional data indicated that there appeared
to be an interesting relationship between inflation pressure,
load and drawbar pull in sand.

When a tractor tire exerts a pull, additional sidewall
deflection occurs which changes the axle height (above a
given datum point) and the effective or dynamic rolling
radius. Steinbrugge and Bruwer (1958) measured the variable
rolling radii of tractor wheels. Some variation (approxi—
Inately i 1 inch in 29 inches) was detected at zero drawbar
pull and the variation increased as drawbar pull increased.
The average effective rolling radius of each wheel decreased
with increased pull due to increased deflection. Wann and
Reed (1961) found in a series of bar table tests that the
effective rolling radius of a loaded tire depends on the
average effective circumference of the section of the tire

in contact with the surface. Reed (1962) studied the

effects of inflation load and drawbar pull on axle height

and rolling radius. Measurements of tires under load on a
concrete surface showed that the rolling radius was greater
than the axle height but less than the no load radius of the
tire. The axle height varied proportionately to the total
amount of deflection whereas the rolling radius varied only
by the amount the deflection changed the effective average
radius of the tire in the contact area. The use of the
term "axle height" is only academic as it is practically
impossible to measure the axle height under practical field
conditions.

Another aSpect of traction that has been studied is
traction aids. Bailey (1956) and Southwell (1965) reported
on the performance of various traction aids (strakes, cage
wheels, etc.) under actual farm conditions. Bailey found
that the use of retractable/extendable strakes more than
doubled the drawbar pull in a wet soil surface covered with
a green crop but underlain with clay. Southwell concluded
that the most effective means of reducing wheel slip (travel
reduction) was by the use of wheel strakes or half-tracks
with additional weight on soils of low shear strength or
where absolute maximum pull was required.

Tractive performance of radial—ply and conventional
tractor tires was investigated by Vanden Berg and Reed
(1962). The conventional tractor tires had cords crossing
in alternate layers at near 80 degrees and at 50 degrees to
the center—line of the tire. The radial—ply tires had two

sets of cords, one set of cords running radially from bead

 

10

to bead and the other running tangentially. A significant
increase in traction was obtained by the radial—ply tire
in the range of 0 to 30% travel reduction.

Four—wheel drive tractors with (a) all four wheels
the same size or (b) smaller wheels (tires) on the front
have been tested by Franke (1963), Sonnen (196A) and
Southwell (1966). In general, the results favour the four-
wheel drive combination (a) with alternative (b) conSidered
superior to a two—wheel drive tractor of the same weight
and available horsepower. However, the test results ob-
tained were not analyzed on a dimensionless basis and, as
such, cannot be transposed or used to compare other combina—
tions of weights and tires.

2.3 Tractor Tire Research
(SoilADynamics)

 

 

A logical approach to the prediction of tractor draw—
bar output would be to make calculations based on basic soil
strength characteristics and tractor specifications.

Because the relationship between soil strength and tire per-
formance has not been developed to any degree of accuracy
the author does not wish to present a thorough review of
the literature. Certain studies however, will be mentioned.

In reviewing the history of soil vehicle mechanics,
Reece (196A) listed the development by Morin (18A2), Reynolds
(1875), Bernstein (1913), Goriatchkin (1936), Micklewaithe

(19A9) and Bekker (1956).

11

Micklewaithe applied Coulomb's classical soil mechaniCS

equation.

3 = c + p tan 0
where s = soil shear strength
0 = cohesive strength
p = unit vertical load
gy= internal angle of friction

to the ground contact area (A) and weight (W) of a vehicle
to predict the maximum possible tractive effort or gross

thrust (H).
H = Ac + W tan 0

An expression for the drawbar pull (D) of a vehicle

is

where H is the gross soil thrust and R is the rolling
resistance.

In an effort to obtain an analytical approach to the
gross thrust that would incorporate the stress-strain or
soil deformation relationship of the soil into the Coulomb
equation, Bekker (1956) and others have used the following

equation:

s = (c + p tan 0) (1 — eIJ/K)
The shear diSplacement (j) and the modulus of shear

deformation (K) are obtained from a shear stress-shear

displacement diagram.

 

 

 

12

The rolling resistance (R) can be approximated by
assuming that the work expended on rolling resistance equals
the work involved in making a rut. Bekker (1956), Janosi
(1963), Reece (196A) and others have studied this area of
soil dynamics. The equations developed fit experimental
results in sandy soils but do not apply too well in other
soils.

In terms of soil trafficability, the U.S. Army Engi—
neers Waterways Experiment Station have developed a standard
cone index rating for prediction purposes. According to
Foster £3431. (1958), the cone index rating of an area can
be used to predict whether a given vehicle will be able to
cross the area once, whether 50 vehicles can cross in the
same path, how heavy a load the vehicle can tow through the
area, or how steep a slope the vehicle can climb. It has
not been shown that this method can accurately predict the
output of farm tractors.

The area of stress—strain relationships for soil has
been investigated by many researchers in the last five
years. Wills (1963), Taylor (1966), Dunlap (1966), Wilkins
(1966) and others have studied the relationship between
shear stress and shear displacement. Correlation between
their results and actual traction performance of a traction
member has not yet been attained.

If it can be shown that the performance of any tractor
can be predicted for a given soil on the basis of tests with

a standard tire, this will most likely simplify a prediction

 

It
I .u .U .3 w a. . PI
:.. .... r .s u

13

based on soil strength parameters when such a prediction
becomes possible. On the other hand, the knowledge about
the relationship between soil strength and tire performance
when available, will likely improve the prediction of dif—
ferences in standard tractor and evaluated tractor per—

formances.

 

III. TERMINOLOGY AND INDICATORS

OF PERFORMANCE

"Of the principal ways of transmitting tractor-engine
power into useful work—belt, power take—off, and drawbar——
the least efficient and most useful method is the drawbar"

(Tractors and Their Power Units, 1963, Barger et al. p. 272).

 

In the transmission of power from the engine to the
drawbar, a driving force, called traction, must be developed
by the traction device as it acts upon the surface. In
this investigation the tractive performance of a pneumatic
or rubber tire will be studied.

The traction process can be considered from an energy

standpoint as follows:

Power Input = Drawbar Power Output + Losses

The power input to the traction member (in this case
to the axle of a rubber—tired driving wheel) is the engine
power minus losses in the transmission and differential.
The power output is the useful drawbar power obtained. The
losses result from travel reduction, front wheel rolling
resistance and rear wheel rolling resistance.

The common definition of travel reduction is given in

equation form:

1A

 

15

(A—B)

A 100

 

Travel reduction (per cent) =

ID
II

where advance per revolution with zero pull

00
II

advance per revolution with pull

Zero travel reduction can be determined at zero
drawbar pull of the vehicle (only enough input torque to
achieve motion) or at zero net pull of the drive wheels or
at zero drive wheel torque (in the latter two cases the
vehicle has to be towed). In this study zero travel
reduction was determined at zero drawbar pull.

Vanden Berg et_al. (1961) have described two distinct
phenomena related to travel reduction: (1) the relative
movement at the contact surfaces which in the case of a
rubber tire includes flexing of rubber, deforming of soil,
sliding of rubber surface on soil surface and twisting or
bending of lugs, and (2) the actual distance travelled
forward. They define slip (slippage) as the actual rela—
tive movement that occurs between the surface of the trac—
tion device and the surface of the soil. Slip values are
less than travel reduction values, however, slip is not
uniform over the contact area. The actual value of slip
cannot be separated from the other sources of travel reduc-
tion and thus cannot be measured. The travel reduction is
based on the actual distance travelled forward, and can be
accurately determined and will be used as a performance

parameter.

 

16

The energy losses due to rolling resistance include
power required to bulldoze, compact and displace the soil,
shear and flex the tire and other losses that do not con—
tribute to useful drawbar pull.

Wheel performance, according to Persson (1966) can
be defined by a relationship between the five quantities
acting on a wheel. These quantities are: the weight V on
the wheel, the pulling or braking force H it provides and
the resulting forward velocity v of the wheel center, the
torque T applied to the wheel and the rotational speed w.
These quantities are shown in Figure l.

A set of parameters, completely describing the perfor-
mance of a wheel as outlined by Persson are as follows:

The parameter, coefficient of net traction (u), is
the ratio between the net pull (H) and the vertical (dynamic)

weight on the wheel (V).

1:
ll
<|m

The gross traction or gross thrust (P) is the torque

T divided by the rolling radius rO

The coefficient of gross traction (uT) is the ratio

between the gross thrust (P) and the vertical weight V.

 

l7

pmmocou mfiB ADV

.mocmpmammu mafiaaou 0cm coapomuu mmoum mo
.Hmmxz mnp co mmflufloon> can mmouom oawmm Amv

 

 

 

 

 

 

 

 

 

 

a musmflm

 

 

 

 

 

 

 

18

The rolling resistance of the tire (Br) is defined

as the difference between gross traction (P) and net pull

(H).

The coefficient of rolling resistance (p) is the
ratio of rolling resistance force (Br) and the vertical

load (V).

<§O—H>=%<p_H>=uT—u

D
II
<1Il—’

It is important to state at this point that the
rolling radius (r0) is for zero drawbar pull with only
enough torque exerted to move the tractor. This is an
arbitrary choice of radius, done for practical reasons
because this radius can be determined relatively easy,
gives simple equations and is consistent with the defini—
tion for travel reduction.

The definition of the rolling radius (r0) for zero

pull is:

<

_ O

r —_
O w

0

 

 

19

where V0 is the forward velocity and mo the angular velocity
of the wheel at no pull.

Travel reduction is defined as:

_ _V .‘39_=_V
S — l _ ( v ) ( w l r w

0 O

 

where v and w are the forward velocity of the axle and the
angular velocity respectively.
Other performance parameters are derived from the

basic parameters. These include:

va
O

Tractive power coefficient (n) = Vv w = ngw
0 o

 

 

= u (1—s) = uT (1- §—) (l—s)
T

This parameter indicates how much output power a
wheel with a given vertical load produces when driven with
a given rotational Speed (given gear). The maximum value
of n for a given combination of wheel and soil indicates
when maximum drawbar power is developed and is considered
by Persson (1966) to be probably the most important measure
of wheel performance from a tractor design standpoint.

Tractive efficiency is the ratio of drawbar horse—

power to input wheel horsepower.

TT

II
II
A
H
I
U]
v
II

(1 — 3—) (l—s) = ——
“T “T “T

 

20

Tractive efficiency is not influenced by rO and thus
can be considered as a basic performance parameter.

The performance parameters can be related by using
(a) the travel reduction or (b) the coefficient of net
traction as the independent variable. Method (a) is con—
sidered the conventional method, however, method (b)
illustrates better the relationship between pUll, maximum

power and maximum efficiency.

 

 

 

. rd I"
- -~—4

' _ I}
J‘s-'1

:1 13'.

 

IV. EXAMPLES OF TIRE PERFORMANCE——AN

ANALYSIS OF PUBLISHED TEST RESULTS

In order to provide a preliminary check on traction
performance parameters several sources of tractor test
results were analysed. The primary parameters used in the
analysis were the coefficient of net traction and the
travel reduction. These are usually the only ones available
or derivable from the reports.

One of the best known sources of information on
tractor performance is the Nebraska Tractor Tests which are
conducted on a concrete test surface at the University of
Nebraska. For the majority of tests the drawbar load (pull)
is adjusted to keep the engine at its rated speed. The test
results include maximum power take—off horsepower at rated
speed, maximum drawbar horsepower at rated Speed, drawbar
pull, forward speed, travel reduction and fuel consumption
for certain tests. Tests with different tractor weights
are made.

As certain basic information was not available in the
Nebraska Test Reports, several assumptions had to be made
as follows:

1. the front and rear wheel rolling resistance

coefficients were assumed constant throughout
each test. A value of 0.025 was used as a
reference coefficient for 6.00-16 front tires
and 0.019 for 18.A—3A rear tires. These

values were derived from McKibben and Davidson

21

 

22

(19AO) and Kucera and Jamieson (1963).

Coefficients for other tire sizes were

calculated in inverse proportion to the
loaded radii.

2. the total rolling resistance of the tractor
did not change during a test.

3. the torque input to the rear wheels was equal
to the drawbar pull plus total rolling
resistance multiplied by the loaded radius
of the rear wheel. This assumption was
necessary for weight transfer calculations.

Values of drawbar pull and per cent slip (travel
reduction) and additional data such as front and rear axle
weight, wheelbase, drawbar height, etc. were taken from
the test reports and punched on data cards. The basic
equations and definitions used to obtain the performance
parameters are contained in Appendix A.

Figure 2 shows drawbar pull versus per cent travel
reduction for three tractors (tested at Nebraska) having a
rear tire size of 23.1—26. Two of the tractors were of
the same model but differing in the type of engine (diesel
and LPG). The horsepower available at the power—take—off
for all three tractors was within 2.5% of each other.
Thus, it may be assumed that the power input to the rear
wheels of the three tractors was also within 2.5%. However,
one of the tractors, the Oliver 1900 Series B Diesel,
carried an extra 3600 pounds on the rear wheels and was
able to develop nearly 2000 more pounds of drawbar pull
than the other two at a travel reduction of 1A.5%. If,

however, the test results are shown as the coefficient of

net traction versus travel reduction (see Figure 3), one

 

23

.Aomm was mmm .emm .mmm umme .snmzv
.mmuep omua.mm nuss muopomup essay
now SOHDUS©wH Hm>mup .m> Hasm HMQBwHQ N musmflm

o\o 2078381 4w><mk

9 S m. N. __ o. m m h m m ¢ m N _
a _ _ . _ _ _ _ q _ _ d . . s

on: m0h-w 22 o
.330 moww .22 q
.935 m mocom 00m. .525 o

l

l

 

266

000.0

0006

000K

000d

956

09%:

9X2

000d.

RES

(581) Tlnd avamvaa

 

COEFFICIENT of NET TRACTION

 

2A

 

Figure 3

0 Oliver |900 Series 8 Diesel
A MM. G-705 Diesel
0 MM G-705 LPG

l l I L l l l l l I J
4 5 6 7 8 9 D II m l3 M
TRAVEL REDUCTION (°/.)
Coefficient of net traction vs. travel
reduction (same tractors as in Figure

2).

 

25

common curve will describe the tractive performance of all
three tires.

Figures A and 5 are drawbar pull vs. travel reduction
and coefficient of net traction vs. travel reduction graphs
for three other tractors equipped with 18.A-3A tires with
quite a wide difference in power take—off horsepower and
weight. In this case one common curve for the coefficient
of net traction does not at first seem adequate to describe
the performance of all three tires.

If the curves in Figure A are extrapolated (straight
line) down to zero pull the travel reduction should be zero
by definition. For the John Deere A020 Diesel tractor this
does not appear to be the case. A correction of the travel
reduction figures for this tractor of + 0.7 seems there-
fore, justified. This will bring all three curves in
Figure 5 together up to u = 0.7.

The method of presentation of the data overemphasizes
small inaccuracies in the determination of zero travel
reduction. The remaining difference may be due to (a)
difference in tire lug height, (b) different rubber compo—
sition and tire design, (0) errors in the estimation of
weight transfer, (d) effect of different inflation pressure—
weight combinations and (e) effect of weather conditions
on traction characteristics of the concrete surface and the

rubber tire.

 

DRNWBAR PULL (LBS)

[0,000

8000

6000

4000

2000

 

26

 

O IHC 806 Dmsd
A Oliver I800 Gasoline
C) John Deere 4020 Diesel

41 I I I I I #J
2 4 6 8 l0 I2 I4
TRAVEL REDUCTION °/o
Figure 4 Drawbar pull vs. travel reduction
for three tractors with 18.4-34 tires.
(Nebr. Test Rep. 806, 839, 849).

    
    
  

NET TRACTION

0 MC 806 Diesel
A Oliver 1800 Gasoline
Cl John Deere 4020 Diesel

As Reported

x John Deere 4020 Diesel
Corrected to Zero Travel
Reduction

COEFFICIENT of

   
 

4 6 8 l2
TRAVEL REDUCTION %
Figure 5

Coefficient of net traction vs. travel
reduction (same tractors as in Figure
4) .

—

 

 

 

.-

 

 

 

28

Figures 3 and 5 Show that when tractors with the same
tire size are compared, sometimes a good agreement between
the parameters is found (Figure 3) but not always (Figure 5).
Tests with other tire sizes showed similar variations even
in a case where four tractors of the same model and horse—
power were compared.

Figure 6 contains the coefficient of net traction vs.
travel reduction curves for eleven different tire sizes
taken as an average for a number of tractors tested with
each size at Nebraska. Considerable differences in the
coefficient of net traction curves are apparent, however,
seven of the eleven tire sizes could be represented by a
common curve with limits in u of i 0.025. The larger tire
sizes such as the 23.1—3A and 2A.5-32 seemed to outperform
the other tire sizes.

The reasons cited for the difference between the
three curves in Figure 5 would also apply to Figure 6.

When tractors are tested at Nebraska the lug height at the
start of the test must be at least 65% of the original
height but there is no minimum lug height required there—
after. Some of the tires, therefore, can have a larger
surface area because of wear. This larger surface area

can result in increased drawbar pull as shown by Taylor

and Williams (1958) who found that the maximum drawbar pull

increased as lug height decreased.

 

COEFFICIENT of NET TRACTION

 

29

 
      

“60.0.78” 23.I x 34

      
 

/
? l3.6 x 38(l6.6,l.027l
/ l2 4 x 28 (:34 0976)
. I49 x 24 (I3) 0.925)
O :49 xZBIISO 0.984)
// l69 x 30(160 0920)
/’ i5..5x38(i96l.OI3I
/’///’ 6.4 x34 (:90 0986)

23.l x 26 07.5 0.934)

I|65,0.838I24. 5 x 32

  

      
   

I I I I I

4 6 8 IO l2 l4
TRAVEL REDUCTION °/o
Figure 6 Coefficient of net traction vs. travel

reduction for eleven tire sizes (Nebraska
Test). Inflation pressure and load factor
in parenthesis.

30

Natural soils, in general, do not provide as uniform
a traction surface as concrete. Although the results are
quite variable, it is possible to obtain coefficient of
traction curves that tend to characterize the soil. Walters
and Worthington (1956) drew a graph (see Figure 7) summariz—
ing their entire series of tire tests. The coefficient of
net traction curves were described as representing the over—
all performance characteristic for different types of
surfaces. The following statement by Walters and Worthington
serves as a focal point for tire performance studies: "An
interesting facet of this study is the close conformity of
tractive performance applying to each soil and surface con—
dition, irreSpective of tire section width."

That each soil can at least be partly characterized
by one coefficient of net traction vs. travel reduction
curve is shown by an analysis of the 1938 SAE tractor tests.
Figure 8 is a travel reduction vs. drawbar pull graph as

reported in the text book Tractors and Their Power Units

 

by Barger gt_al. showing the effect of added ballast on
drawbar pull. 'By making an assumption that the weight
transfer in these tests was one fifth of the drawbar pull
the coefficient of net traction curves shown in Figure 9
were obtained. A common curve with limits of i 0.02 would
suffice for all four rear wheel weights.

Application of the same assumption to drawbar pull—
travel reduction data obtained in England using single and

dual tires results in a curve as Shown in Figure 10. On

 

31

.Aomma .coumCHAOAOZ 0cm mumuamz
Eoumv coflu09©mu Hm>muu .m> cofiuomuu umc mo unmAUAMMmOU h madman

o\o ZOEbDomm 4w><mh

 

 

 

 

 

mm 8 ...o. om m. N. m e o

q A _ 1 . . a . 0

saw as: m M

2:20 8.....5 e. l N.

....flam .62.; .m

32.2.0585 .m 0
2520 26.268 8.2.4 e m
3-3m 8.22 .n ...
29850 N l m. .1...
x09; 33. Oxmognmz ._ m
N
l
0..

l v.
N
3
II.
I.
w
.w ... m m
m
N

m
l w.
.v
.m
l N.

 

 

32

..mmma 60009 0000 mam
Eoumv coHHUSCmu Ho>muu .m> Hana Hmn3mnn

o\o zo_._.oDomm 4m><m._.
om mm om m. o_

m wusmflm

 

_ _ _ q q

.mmq Omtuodo... 9.3.5 30134 .xflz
>440 >mo

an. N_ ¢N i mm:

 
 

 

 

mm... Omm.

.mmq O¢m_

   

mm... 0mm.

.mmA GEN

         
     

 

00m

000.

009

OOON

00mm

000m

'ni'ld HVBMVHO

I881)

 

COEFFICIENT of NET TRACTION

 

33

 

 

I390 lbs. II.25- 24 l2 psi

 

’ ----- I640
---—-|89O
—-- — 2:40
/ Dry Clay
I l I I I J
5 IO I5 20 25 30
TRAVEL REDUCTION %
Figure 9 Coefficient of net traction vs.

draWbar pull (Calculated from
Figure 8).

 

3A

..mmoom\me am unommm umme mmHz scum.
mango .m> mmHmGHm coau0500n awkmuv
.m> coflpumnu no: mo pcmfiofimmmoo

o\o ZOEbDomm 4m><m._.
mm ON 9 O_

OH wusmflm

 

_ _ _ _

>06 0600 :0 000.305

.8 N. .309: .84 NNNn 3.: .25
.3 N. am. 00...: mm... .05 we: .25
.8 N. .3. 00.5 .8. Nva me: 295
.8 N. 8.700.... mm. .00» we: 6.25

0x00

 

 

NOIIOVHI J.3N IO lNBIOIddBOO

 

 

 

NM

36

.Aoema .w>smm Eoumv mamst .m> mmamcflm
“coflu050ou Hm>muu .m> cofluomnu umc mo #cmNOmemoo

o\o 20....030mm .._m><~...:.

mm 0N ON 0. N.
_ . _ _ _

28.. 96m 8 232m .60
_80N...8.._.¢e-00.m 8.: .68 .
.8 0N.umNm_.ev-00.m we: .25 o
.msN_.¢~mt.0m- 00.0 9: 225 e
.8 N....mNm_.0m-00.m 2: 205m 0

Ha ousmflm

      

 

NOLLOVELL .LEIN I0 .LNEIIOIddEOO

V. EQUIPMENT

5.1 Equipment Used by Other
Investigators

 

 

Measurements made‘by tractor tire researchers during
the period 1930 to 19A0 were usually drawbar pull, actual
forward speed and rear wheel slip or travel reduction.

Equipment for the measurement of drawbar pull generally
conSisted of a hydraulic cylinder with an indicating or
recording pressure gauge. The cylinder was inserted between
the tractor drawbar and the load (pull). The drawbar pull
obtained was the product of the average pressure and the
net cross—sectional area of the cylinder.

The actual forward Speed was obtained by measuring
the time required to travel a prescribed distance. This
measurement combined with drawbar pull produced drawbar
horsepower.

Travel reduction or wheel slip was determined by
counting the number of wheel revolutions over a set distance
for both load and no-load conditions. Mechanical counters
using automobile distributors to interrupt an electrical
current were used to record wheel revolutions. The travel
reductions obtained were an average for the set distance.

This method of testing had the disadvantage that only
one drawbar load (pull) was used in each run. To cover a

range of drawbar loads a large field and considerable time

37

 

38

was needed. Non—uniformity of field conditions resulted
in widely varying results.

Of Special interest is that the type of equipment
described here is still used at the University of Nebraska
Tractor Testing Station. Tests are made on a surface that
presumably does not change. The drawbar pull is kept
quite constant throughout each test and therefore the
average results are considered reliable.

Additional measurements including torque input and
weight transfer were reported by O'Harrow (l9A7). This
was one of the first studies made to measure torque input
and actual weight transfer. Torque measurements are neces—
sary for comparison with available engine power, for
stability studies and for determination of rolling resis—
tance losses.

The widespread use of strain gauges together with
recording strain indicators (oscillographs) and cameras
made it possible to instantaneously record all measurements.
The use of such equipment, instruments and testing methods
has been reported by Walters and Jensen (195A) and Vanden
Berg (1966). The National Tillage Laboratory (1966) has
instruments and equipment for very extensive tire studies
in controlled soil bins. Continuous recording combined
with on-line data reduction on an analog computer has
resulted in immediate calculation and plotting of the para—
meters making it possible to vary the load continuously

during a test. One test run can therefore give the

39

relationship between the parameters for the full range of
interest. The method of variable loading had not been

used in the field before the study reported here.

5.2 Equipment Used in This Study

 

Measurements made in this study were (a) torque input
(to left rear wheel), (b) drawbar pull, (0) weight transfer
(from front to rear wheels), (d) front wheel rolling
resistance, (e) rear wheel speed and (f) actual forward
speed. The equipment used to indicate or record these
variables consisted of the following:

1. Test Tractor: Massey—Ferguson 150 gasoline
tractor, serial number 6A2000 AA5 equipped with
6.00—16 front tires and 13.6-28 rear tires.
Frames for additional weights were installed on
the lift arms. A complete description is given
in Appendix B.

2. Drawbar Loading Unit: A used Massey—Harris 55
Diesel tractor serial number 55D51A09 was modi—
fied to provide variable drawbar pull for the
test tractor. A hitch was added to the front
axle to provide 10, 1A, 18 and 20 inch hitch
point heights to keep the line of pull level
between the test tractor and load tractor. A
large gate valve was installed in the exhaust
line of the load tractor to assist in varying

the load. The tractors are shown in Figure 12.

   

Figure 12

A0

 

 

Top — Instrumented tractor (with
13.6—28 tires) and load tractor,
Bottom - Adjustable drawbar with
pull transducer and frame for
extra weights.

 

A1

Rolling Resistance Transducers: Two steel

rings, three inches in outside diameter, 0.185
inch thickness and one inch wide were installed

in the tie-rods of the test tractor. The trans—
ducers were fitted with 120 ohm SR—A strain

gauges so that the action of the rolling resis—
tance force would have two gauges in tension and
two in compression. The gauges in each transducer
were joined together in a Wheatstone bridge
arrangement with the lead wires connected to a
5—prong female connector (mounted on a plexi—glass
cover) as Shown in Figure 13(a). Five-wire
shielded cable was used to connect the transducers
to the amplifier.

Torque Transducers: A torque transducer built by
Berlage (1962) was installed in the left rear
wheel. The torque input to the left wheel was
measured as a force in a compression cylinder.

The four 120 ohm SR—A strain gauges on the com—
pression cylinder were in a Wheatstone bridge
arrangement with two gauges in compression and two
gauges in tension (Poisson arrangement). The five—
wire shielded cable from the torque transducer

was connected to a 5—pin female connector.

Pull Transducer: A ring—type strain gauge pull
transducer with four 120 ohm SR—A strain gauges,

two in tension and two in compression, was inserted

 

Figure

A2

 

Equipment components (a) weight
transfer and rolling resistance
transducers, (b) rear wheel speed
indicator, (c) fifth wheel or
forward speed indicator (d) mobile
recording

 

A3

between the drawbar of the test tractor and the
load tractor. The Wheatstone bridge arrangement
was connected to a 5—pin female connector

(Figure 12).

Weight Transfer Measurement: Four 120 ohm SR-A
strain gauges were placed on the front axle of
the test tractor so that two gauges were in
tension and two in compression (Wheatstone bridge
arrangement). The wires from the bridge were
connected to a 5—pin female connector mounted on
the front axle as shown in Figure 13(a).

Travel Reduction Indicator: Two direct current
generators whose output voltages were directly
proportional to Speed of rotation were used. One
generator indicated rear wheel Speed and the
second generator driven by a "fifth wheel" indi-
cated actual forward speed. Travel reduction was
calculated as:

(Rear Wheel Speed — Actual Forward Speed)

Rear Wheel Speed X 100

(a) Rear Wheel Speed Indicator: This unit con—
sisted of a D.C. generator driven from the
left rear wheel by a bicycle chain through a
10:1 gear box as Shown in Figure 13(b).
The output terminals of the generator were

connected to a 2—pin connector.

 

AA

(b) Fifth Wheel Forward Speed Indicator: A 26
inch bicycle wheel with a balloon-type tire
was used for the fifth wheel. A 22—tooth
Sprocket was fitted on the input shaft of a
1:27 gear box. A Barber Colman Model FYLM
73920—51 D.C. generator was connected to the
output shaft of the gear box by flexible
tygon tubing (pinned to both Shafts). The
bicycle wheel (with a A8—tooth Sprocket) and
the gear box generator assembly were mounted
on a frame and connected with a standard
bicycle chain. This frame was attached to
the right front side of the tractor as shown
in Figure 13(0). The attachment was such that
the wheel was free to move vertically and to
castor. A hook was installed on the tractor
to hold the fifth wheel off the ground when
not in use or when the tractor was driven in
reverse. The output terminals of the genera—
tor were connected to a 5—pin female connector.
Weights in the form of 1 inch square iron
bars and 1 pound lead bars were added to the
frame to ensure adequate traction. Air
pressure in the tire was 1A psi.

8. Drawbar: A drawbar was constructed so that the
height of the line of pull above ground could be

varied from 10 to 20 inches.

 

A5

Recording Equipment: The recording equipment was

manufactured by Honeywell Controls and consisted

of the following basic components plus associated

plugs, wires, etc.:

(a)

(b)

(C)

(0)

Gauge Power Unit: supplied D.C. voltage for
the four Wheatstone bridges (strain gauge
transducers).

Four Gauge Control Units: allowed control

of D.C. voltage (7.8 volts maximum) and out—
put zero (for initial balance). Calibration
resistors of 178K and 357 K were provided.
(1) Four Accudata 10A—l D.C. Amplifiers: 0
to 250 times amplification of output from
Wheatstone bridges.

(2) One Accudata 10A—2 D.C. Amplifier: 0 to
10 times amplification of output from the
rear wheel speed indicator (D.C generator).
(3) One Accudata 10A—3 D.C. Amplifier: 0 to
1.25 times amplification of output from the
fifth wheel speed indicator (D.C. generator).
One 1508R—1B678HK Visicorder equipped with
the following:

(1) One M—1100 Fluid—damped galvanometer with
0—600 cps flat frequency response and a sensi—
tivity of 10.9 inches per volt (for torque

transducer).

 

A6

(2) Five M—l650 Fluid—damped galvanometers
with 0—1000 cps flat frequency response and
a sensitivity of A.A9 inches per volt.
(3) A mercury vapour lamp; ultra violet
light was reflected by the galvanometer's
mirrors, transmitted through an optical
system and focused directly on ultra violet
sensitive recording paper.
(A) Record drive system: A-Speed transmis—
sion (1, 2, A, 8 inches per minute) with
multipliers of 0.1, 1.0 and 10.0).
(5) Timing System: time line intervals of
0.01, 0.1, 1.0 and 10.0 sec.
(6) Grid Line System: grid lines 0.1 inch
apart along the length of the record were
produced simultaneously with data traces.
(7) Trace Identification: light beam inter—
rupter of each channel every 8 inches.

10. Portable Power Source: Zeus Series APJ 1250 Watt,

120 volts A.C.

The equipment described in 3 to 8 above was installed
on the test tractor. Fifty feet of Shielded cable was used
to connect the four 5—pin male connectors to the recording
equipment. Two—wire cable was used for the D.C. generators.
A 26—pin quick disconnect coupler was used to facilitate
field hook—up of the equipment. The Agricultural Engineering

Department's 1/2 ton truck was outfitted with a Shade

   

A7

protection for the Visicorder and thus served as a mobile

instrument vehicle (Figure l3(d)).

2,3 Calibration of Equipment

 

To ensure that the output from the strain gauge ampli—
fiers was constant from day to day for a given input, the
built—in controls mentioned in Section 5.2 were used. A
calibration resistor shunted across one gauge produced a
Simulated strain which resulted in a certain galvanometer
deflection on the chart depending on the galvanometer,
bridge voltage and amplification selected. A predetermined
calibration deflection was maintained throughout the tests
by varying either bridge voltage or amplification or both.

1. Rolling Resistance Transducers: Two l/A inch

thick steel plates 2A inches long and 16 inches
wide were placed between a set of rollers and a
pair of wooden shoes which conformed to the curva—
ture of the front wheels. The rear wheels were
raised to the same height as the front wheels. A
Dillon pull meter and a quarter—ton winch were
inserted between the two Shoes and a A" x A" wooden
beam placed behind the rear wheels as shown in
Figure 1A. The simulated rolling resistance pro—
duced by the winch was read on the Dillon pull
meter and as output on the recorder. Figure 15

shows the calibration curve obtained.

 

A8

.uoosmmcmup mocmpmflmou qcaaaou mo CONDMHQNHMU

ea mosses

 

W

 

 

 

On

20...; :0... 5.05 m

.202 ..an. 8:5 0
503020;. mocofimmm 3:61 0
0.2a .005 m

005m c0000; 4

 

 

 

T:

H!

....W

Ir I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A9

00m

.uovumuv

 

oma m2 .coHpmnflaamo oocmwmfimou mcaaaom ma musmam
.mmn. . muzqemfiwm 02340.”.
08 OON 00. 00. On
_ . a . a q

muooscmcmne monopmflmom
mafiaaom Mo cofivmuflaamo

 

N.

(Nouvasnvo II'ON UO 33m 99)

IO SBNH

NOIIVHB I‘IVO

(”“1 IO)

50

Torque Transducer: A static calibration was made
by attaching a lever arm to the left rear tractor
wheel. The lever arm was constructed so that each
front tractor weight (83 1/3 lbs) attached to it
added 500 lb. ft. of torque. The arm itself pro-
duced a torque of 1A5 1b. ft. Calibration con—
sisted of raising the left rear wheel off the
floor, locking the brakes and adding weights to
produce a range of torques from zero to AlA5 1b.
ft. (Figure 16). Lines (tenths of inches) of
chart deflection were recorded and plotted against
torque as shown in Figure 17.

The calibration curve was quite linear from
2000 lb. ft. to AlA5 lb. ft. From 0 to 2000 lb.
ft. a curved line was obtained. This was an
inherent characteristic of the transducer as indi—
cated also by the calibration curve given for the
same transducer by Berlage and Buchele (1966).
The same curve was produced in both loading and
unloading indicating that the non—linearity was
probably not due to friction.

The transducer was calibrated in the same direc—
tion as the torque was applied in the field. This
was done to reduce any influence of rotational

direction sensitivity.

 

51

Hoosomnmuw osvnou mo :OvanQflHmo

0H 09:3...

 

   

52

009».

000.4
..

 

comm

uouomuu oma m2 .cofiumunfldmo mzvuoe SH ouswflm

...L. .m:. MDOmOk

000m 00mm OOON com. 000. 00m
_ _ a 1 . q

$0.5de 0m. ...:2
..mmrz, admm ......mn
20...<mm...<o NDOmOH

 

8 ‘2 E (I) q-
11 "1:10 uo SEINl'l 07.2 ‘ (HONI :') Nouoa'uaa :0 SBNI’l

N

CD
N

53

Weight Transfer: A platform scale with a range
of 0-1250 lbs. was used for calibration. A hydrau—
lic jack placed between the scale and the front
axle was used to take weight off the front wheels.
Lines (tenths of inches) of chart deflection were
recorded and plotted against weight transfer as
Shown in Figure 18.

A straight line relationship was obtained over
the complete range of weight transfer. Engine
vibration produced cyclic chart deflections, the
amplitude of which depended on the R.P.M. of the
engine. Maximum peak to peak amplitude was one
line (.1 inch) however, the average deflection
could easily be determined.

Pull Transducer: Preliminary calibration tests
were made in the Agricultural Engineering Depart—
ment in the range of 0 to 690 lbs. Final calibra—
tion of the pull transducer was made in the
Materials Testing Laboratory,Department of Civil
Engineering. The final calibration as shown in
Figure 19 was very linear.

Travel Reduction Indicators: Calibration con-
stants to convert lines (0.10 inch) of deflection
to miles per hour for both the rear wheel and
fifth wheel speed indicator were determined ini—
tially on an asphalt surface. Both Speeds were

set equal to tractor forward speed when the tractor

5A

000.

00v.

”Spoon“ om.” m2 ummmcmunv named»? mo coflpmunflnamo

OON.

ma masses

.mm:. . mmmmzqm... ......0.m>>

000.

00m

00m 00¢ OON

 

_

—

a _ _

mOPodm... Om. ...s.
$9.525... F1003 *0 20....4mmjdo

 

O.

N.

.v.

w.

0
N
[IRVO U0 SBNI'I O'Ol

(HONI :0) NOLLOB'HEIO :0 83er

55

0000

0000

000k

.uoUSGmcmnu Hana HMASmHU mo COHuMHAHHmu ma ousmflm
.mml. . .330 m<m 35.0
0000 0000 000? 000m OOON 000.

O

 

   

_ — _ fi fi _

  

mmoaomz<mk :39. 532550 00 20....4mm...<0

       
  

 

s s 2 0
II "IVO U0 SBNI'I O'OI (HONI I'OI NOLLOB'HBO IO SBNI'I

0
q-

0
It)

00

56

developed no drawbar pull. Further tests were
made in the field to determine the calibration
constants for each particular surface.

A A0 mf capacitor was placed in parallel with
the output of the rear wheel Speed indicator to
minimize the effect of the a—c ripple (given by
the manufacturer as 3% rms (root mean square) of
the average D.C. component or 2 x 3 x l.A = 8.A%
peak to peak ripple voltage). An R—C filter of
1000 ohms resistance and two capacitors (150 mf
and 100 mf) was used for the fifth wheel speed

indicator.

VI. TESTING PROCEDURE, RESULTS

AND DISCUSSION

6.1 Preliminary Tests

 

The review of literature in the field of traction
commenced in October, 196A, continuing until June, 1965.
Construction of research equipment and preliminary testing
took place on the campus of Michigan State University dur—
ing July and August of 1965. A progress report was sub-
mitted to Dr. S. P. E. Persson on November 29, 1965,
describing the equipment, calibration, preliminary field
trials and results, changes to be made in equipment and
procedure and an outline of work to be done at the Univer—

sity of Manitoba in 1966.

6.2 Field Studies

 

The field studies were divided into two parts. The
first part (after the equipment had been field tested)
dealt with the effect of weight and inflation pressure on
a "standard" tire. The second part involved a comparison
of the field performance of other tractors with widely
varying weights and tire sizes and a prediction of the
actual field performance based on the traction character—
istics of the "standard” tire (tractor). Actual field

measurements provided a check on the prediction.

57

 

6.

58

Preliminary Field Testing of Equipment.-—Field

testing of the transducers and Speed indicators resulted in

several modifications and changes in procedure. These were:

1.

The addition of extra weight to the fifth wheel
Speed indicator to reduce the bouncing of the
wheel.

The zero position of the weight transfer record—

ing was made easier to determine by:

(a) driving the test tractor ahead several feet
at the start of each run. This helped to
counteract stresses set up in the front
axle during the backing up portion of the
test run.

(b) turning the steering wheel as little as
possible during the test run to minimize the
influence of steering corrections on the
output from the weight transfer transducer.

Steering corrections, the direction of motion,

reduction of front axle weight and surface irregu—

larities produced an irregular output from the
rolling resistance transducer. However, by follow—
ing the precautions given in point 2 above, the
output from the rolling resistance transducer at
zero drawbar pull was linear and reproducible over
the range of front wheel weights used. A study

of the front wheel rolling resistance results

reported by McKibben and Davidson (1940) indicated

 

 

59

that within the range of speeds and weights
encountered in these tests, the coefficient of
rolling resistance could be considered constant
for a given surface and equal to the value

obtained at zero drawbar pull.

6.22 Field Test Procedure.——(a) Tests with the stand—

 

ard tractor (MF 150). A typical field test was carried

out as follows:

1.

The test tractor, portable generator and load
tractor were serviced for fuel, oil, etc.

The portable generator was started, the recording
equipment turned on and allowed to warm up.

The prescribed weight and pressure for the front
and rear tires of the test tractor was checked.
Zero pull rolling radius was determined from
measurement of the distance travelled in five
wheel revolutions.

The test tractor was positioned at the end of

the 50 ft. cable. The transducers were connected
to the recording equipment through the 26 pin
connector. All transducers outputs were balanced,
calibrated and zeroed or positioned at Specified
positions on the recording paper. The outputs
from the two speed indicators were likewisee set

at specified positions.

 

10.

11.

12.

60

A trial run with zero drawbar pull at approxi—
mately 2 m.p.h. was made to check the coefficients
for the rear wheel and fifth wheel Speed indicators.
A chart Speed of 8 in./min and a time—line interval
of 1.0 sec. was used for all runs.

The test tractor was driven in reverse (in its

own wheel tracks) to the starting or initial
position such that the next run was made on un-

disturbed soil.

.- The load tractor was connected to the drawbar of

the test tractor (at a specified height) with a
10 ft. chain.

The test tractor was driven at 2 m.p.h. (approxi-
mately). Drawbar load (pull) was applied
gradually by (a) decreasing the forward speed of
the load tractor, (b) closing off the valve in
the load tractor's exhaust line and (c) applying
the brakes if necessary. The load (pull) applied
caused travel reductions from zero (at no pull)
to approximately 60% during 80 feet of travel.
Both tractors were driven in reverse to the
initial position as described in (8) above ready
for the next test.

After visual inSpection the record chart was
rolled up and periodically cut off to be stored
away from the sun's rays for proper chemical

processing.

 

61

13. Soil samples and other measurements were also
taken.

(b) Tests with other tractors. Field testing of other
tractors mainly followed the procedure for the standard
tractor. Three tractors were connected (test tractor—-
load tractor——standard tractor) to facilitate forward
speed and drawbar pull measurements. The fifth wheel on
the standard tractor recorded the actual forward speed.
The pull transducer was mounted on the drawbar of the test

tractor.

6.3 Analysis of Data

 

The record charts from the "Visicorder" were developed,
fixed, washed and dried in the Photographic Unit of the
Faculty of Agriculture, University of Manitoba. For the
majority of tests the zero location of the light beams
(outputs from amplifiers) were as shown in Figure 20 which
is a photographic copy of a typical record chart.

The record charts for the tests of the MF 150 test
tractor were analysed as follows:

1. The zero pull charts were analysed for (a)

rolling resistance coefficient, (b) rear wheel
Speed coefficient and (c) fifth wheel Speed
coefficient.

2. The deflections for torque, pull, weight transfer,

rear wheel speed and fifth wheel Speed were read

from the chart, for approximately 16 points from

 

62

.Omm. H

.Howuooflmfl>
Haozhmgom Eoum pusso Unooou HMUHQNB

ON ousmflm

02$: Es L
03%. .3..-»
80% as. -..

. man... :32. -6 .
anna-s
macmoe-e

 

63

zero travel reduction (no pull) to approximately
70% travel reduction. The one second time lines
provided convenient reference points for deflec—
tion determinations.
The deflections for each run and other pertinent
data were punched on computer cards and analysed
with the computer programme shown in Appendix C.
The results were printed on data sheets and
punched out in data decks. It should be noted
that zero drawbar pull was defined to give zero
travel reduction.
The output data decks were programmed into a data
plotter which joined the calculated points for
each parameter to curves for each run. An example
of the graphs plotted by the data plotter is Shown
in Figure 21 (scales added afterwards).
Normally four to six complete test runs were made
for each tire and soil combination. An average
curve for such a set was then drawn for each
parameter.

The record charts for the tests on the other
tractors were analysed in a manner Similar to
that used for the standard tractor. Exceptions

to the above method are given in Part II.

 

 

Figure 21 Typical graph plotted by the data plotter.

65

6.A Presentation of Data

 

6.A1 Part I. Performance of the "Standard" Tractor.—-
The performance of the 13.6—28 tires on the instrumented
Massey-Ferguson 150 tractor, the "standard" tractor was
studied. The tests were carried out on four field surfaces
namely Osborne clay fallow, Osborne clay oat stubble,
Almasippi sandy loam rape stubble and Sperling silty clay
loam oat stubble. Moisture contents and bulk densities of
the soil are given in Table l and a mechanical analysis
in Table 2. The effect of weight inflation pressure and
surface was determined by:

(a) tests with varying percentages of maximum

allowable static load (load factor) for a

constant inflation pressure of 1A psi.

 

Total static rear weight (lbs) Load factor (%)
A860 100
3990 82.2
3OAO 62.6

On the Osborne clay fallow tire performance was
better at low load factors (Figure 22(a)). The increase
in coefficient of net traction (u) at 30% travel reduction
was approximately 5% for the 82.2% load factor and 17% for
the 62.6% load factor.

On the Osborne clay stubble (Figure 23(a)) the load

factor had no apparent influence.

 

66

TABLE l.——Surfaces used in traction studies.

 

% Moisture Bulk Density

 

 

 

Date Surface 0-3" 3—6" 0—3" 3—6"
Aug. 11 Osborne clay fallow 38.2 39.9 0.85 1.15
Aug. 19 Osborne clay fallow A2.8
Aug. 26 Osborne clay fallow A2.6 0.93
Sept. 7 Almasippi SL stubble 1A.? 20.2 1.32 l.A6
Sept. 8 Almasippi SL stubble 1A.7 20.2 1.32 l.A6
Sept. 9 Sperling SiCL stubble 35.2 35.7 0.95 1.1A
Sept.23 Osborne clay stubble 26.0 37.8 0.98 1.22
Sept.2A Osborne clay stubble 30.5 35.5 1.01 1.16
Oct. 6 Osborne clay stubble 2A.A 3A.0
Oct. 12 Osborne clay fallow 25.7 38.1
Oct. 12 Osborne clay fallow 25.7 38.1

(roto—tilled)
Oct. 20 Osborne clay fallow 38.A .61
Oct. 25 Osborne clay fallow A3.7 .60
TABLE 2.—-Mechanical analysis.
Soil Type Sand % Silt % Clay %

(>.05 mm.) (.05—.002 mm.) (<.002 mm.)

 

Almasippi Sandy Loam 70.1 1A.2 15.7
Sperling Silty Clay Loam 1A.9 A9.6 35.5

Osborne Clay 6.1 32.1 61.8

 

67

.mucmsfimcfl whammoum

cmoa .0.

o\o 20....030mm 4m><mh

00 00 0¢ Om ON 0. 0

 

 

end we .mnH ompm::-:. :
n00 ma .mnH ost..-:
and ea .mna opme.|:|
means 0N:0.mH
BoHHmm kmau wcuoflmo oo\ma .ms<

 

AD. mungchA nouomw
BOHHmm mmao ocuonmo How mumvaMHmm wocmEnomnwm

NN unseen

o\o 20...030mm 4m><m:.

 

.mQH oomv.l-li

.mQH ommm ::.:
.mna ovom Ill:
and ed .mmnna mmup.mH
Sofiamm kaU ocuonmo o©\aa .md<

 

 

0.

68

.wocmsawcH unawmmnm 3. 00:09.30; Houomm
pmoq Am. wanflsum wmao wcuonwo How mumumfiwumm wUEmEuowumm mN ousmfim

o\o 20....030mm. .. m><m._.

$0. 3 .82.. 0$mIII ..
00 0H 0.: oeNmiII
00 3... .03.. 80.. II
00000 mm-0.ma

03030 930 00.880 SEN .0000

 

 

o\o ZOEbDQMN. ..m><m.r

 

 

    

/
.mnH oome.::-::/HM//
.mna 000m.:.::. :
.mna oeom.:::::
000 ea .mmuna 0N10.MH
mannsum smflo 0000900 00\MN .pamm

IQI
\

 

0..

69

On the Almasippi sandy loam stubble and the Sperling
silty clay loam stubble the load factor had a slight influ—
ence on the coefficient of net traction (Figures 2A (a)
and 25(a)). Percentage increases in the coefficient of net
traction were approximately 2.5% and 5% at 30% travel reduc—
tion for the 82.2% and 62.6% load factors respectively.

The load factor consequently appeared to have a con—
siderable influence on traction in loose soils such as
fallow. On firmer surfaces the influence was less and one
common set of curves could be used to characterize the tire
and soil combination.

On Osborne clay fallow a decrease in the load factor
resulted in an increase in the coefficient of rolling re—
sistance p. This would be similar to a tire operating in
sand where a decrease in pressure results in lower rolling
resistance. On the other three surfaces there was no
apparent influence. The p values were obtained by subtract—
ing the coefficient of net traction from the coefficient of
gross traction and thus the results were heavily influenced
by measurement inaccuracy.

(b) tests with three inflation pressures for a

constant (100%) load factor.

 

Pressure (psi) Total static rear weight (le)
1A A860
16 5270

18 5630

 

 

 

 

mocmnamcH «unnumum AD. mochHch uoyuww 0000 Am.

 

 

7O

 

     

  
  

 

maflnspm Emoa macaw NmmflmmEHd How mumumamudm musmEuomumm vmnmnsmam
......o 7.0...030mm 4.10.200; o\o 20....onomm :.m><m._.
00 on 00 om ON 0. O on 00 on 0.» 0m ON 0. 0
. o e e e . a 7 .
N.
v.
0.
000 NH .20 omme-I m. .8: come l-| l
.00 0... do: 0st ...:i: .3.” 000m. ll:
000 ea .mna some .mna oeom
Nmm 0H .mmHHH mN:w.ma Hum 0H .mmuah mmlo.ma
.00 83065.4 00>. .0000 c .00 0.000692. 00> .008
0. l

 

 

0.

71

 

.mucmsawcfl 00500000 .3. mucmdamcfl HOOUmw 000A .00

 

manflsum Emoq mmau muafim mcflauwmm How muoumemumm mocmEuowumm mu musmfim
o\o 20....030mm ..m><w:. o\o 20:.030mm ..m><m._.
on 00 on o¢ om ON 0. O on cm on 00 on ON 0. o
o _ . . _ . 0 . o

 

  

124,
/
1//I\. I. m.
.000 0000.II-I: /.

.000 000m II I
.000 0000 :IIII
000 ea 00000 mNI0.mH
0000 00000000 00\m .0000

 

000 00 .000 om00::-:l
000 00 .000 ost.:.:::
000 00 .000 0000.:IIII
00000 0NI0.m0

0000 00000000 00\m .0000

 

 

L o._

72

The effect of increased pressure and corresponding
increased weight was similar to the effect of increased
load factor. However, only on the Osborne clay fallow
were the differences quite noticeable (Figure 22 (b)). On
the other surfaces the differences were so small that a
common curve with limits of i 0.02 for u would represent
all three combinations (Figures 23 (b), 24(b) and 25(b)).

On Osborne clay stubble the rear wheel rolling co~
efficient p decreased as the weight and pressure increased
(Figure 25(b)). On the clay fallow a slight tendency in
the opposite direction was observed. On the other surfaces
there was no apparent influence as the curves tended to
intertwine.

In both Part I (a) and (b) increased weight had an
unfavorable influence on tire performance especially where
the field surface was loose. Only for the 100% load factor
series (Part l(b)) on Osborne clay fallow, however, was the
decrease in performance, as expressed by the parameter u,
sufficiently large to offset the increase in pull due to the
increased weight, i.e., in most cases the overall pull still
increased with increased weight.

A straight line relationship between measured weight
transfer and rear wheel torque was obtained. This relation—
ship was independent of the traction surface (Figure 26).

The measured and calculated weight transfer agreed
quite well although the measured weight transfer was consis—

tently lower than the calculated weight transfer at low

73

 

.Awamflgmm Ucm Bbaamm

 

hmaov MDQCH 035000 p0HSmm0E .0> 00w00000 0:0003 00050002 om 0Hsmfim
3mm1>> mzo mo“: H0. .m._ ,.Sn_z_ mnemon.

0000 00mm 000m comm 80m 009 000. 00m

_ 0 _ _ a 0 _ _
x

o
x
29.304 0 o

ZQFE >20 x

 

OON

oom

000.

881‘ HEdSNVHl iHOlBM

 

74

values and higher at the high values (Figure 27). These

differences could be due to:

(a)

(b)

error in locating zero point for measured
weight transfer.
inaccuracies in determining torque (especially

at low torque values).

The discussion up to this point has been based on the

coefficients of net traction and rolling resistance con—

sidered with travel reduction as the independent variable.

Figure 28 shows the relationship of the basic parameters

considered with the coefficient of net traction as the

independent variable. This method of presentation does not

yield any more additional information than the other method

but it does indicate more clearly several important relatiOn—

ships. These are:

(a)

(b)

(C)
(d)

the highest tractive efficiency is obtained

at very low values of u (which means low drawbar
pull).

the maximum tractive power is obtained at high
values of u.

torque input is represented by 0T.

the farmer's dilemma in whether to achieve high
tractive efficiency and low travel reduction
which means low drawbar pull or to obtain maximum
drawbar power or drawbar pull which means higher

travel reduction and lower tractive efficiency.

75

 

OO

 

mmumzst ._.Io_m>> ommzm<m2
00m 00m 00.0. 00m 08 00v 00m OON oo_
_ 0 fl _ 0 0 0 0
..u0wwzmuu u£m003 600000000: .m>
0000:0000 HE00003 0000006000 sm 0.000000
0
O
o
o
o
o
O \
o \
oo

 

 

O8

CON

.LHOIBM GBLVWDO'IVD

ERASNVHJ.

76

.000c0camafl 0usmm0nmv
00000000 #00 mo 0:0HUHMM0OU .0> mannnum

>000 0cuonmo How 000008000m 0uc0Euomu00 mm 005mfim
29.—.0de ...mz no Hzmaiumoo
O. m. w. v. N.

 

_ _

 

 

.000 00 .000 0000.I.u: ////,///unbr1\0\\\

.000 00 .000 ohmm..u..

.000 00 .000 0000 It.
00009 0010.00
0H£Q50m mmau 0cmogmo
00\0m .0000

 

 

 

O;

 

6.

77

Part II (a). A Comparison of the Performance

 

Characteristics of Several Sizes of Bear Tractor Tires Under

 

Similar Field Conditions.——As the input data in these tests

 

only consisted of drawbar pull, actual forward speed and

other physical constants, several assumptions were made to

have the results in the same form as that obtained with

the MF 150 standard tractor. The assumptions made were:

1.

the engine rpm decreased 10% linearly from
zero drawbar pull to maximum drawbar pull.
Nebraska test results and field results
supported this assumption.

the front and rear wheel rolling resistance
coefficients were assumed constant throughout
each test and inversely proportional to the
loaded radii in comparison to the standard
tractor. The rolling resistance coefficients
of the standard tractor were obtained on the
same surface.

the total rolling resistance of the tractor
did not change during a test. Results from
the standard tractor supported this assumption.
the torque input to the rear wheels was equal to
the drawbar pull plus total rolling resistance

multiplied by the zero pull rolling radius of the

 

78

rear wheel. This assumption was necessary
for weight transfer calculations.

Values of drawbar pull and forward speeds (recorded by
both the rear wheel of the standard tractor and the fifth
wheel) as well as additional data such as front and rear
static weight, wheel base, drawbar height, etc. were punched
on data cards. The computer program, definitions relating
to the program and a sample print—out are contained in
Appendix D. In plotting the data only the values based on
fifth wheel Speed were used.

As mentioned earlier the tests with different tractors
were carried out on only one soil type. The surface condi—
tions varied from loose cultivated fallow land to firm stubble
land. The MF 150 tractor with 13.6-28 tires and 100% load
factor was used as a standard for all tests. The tires on
the other tractors were either new or with fairly good lugs
except for the 23.1-26 tires on the 10,030 lb. tractor which
were worn considerably. The tractors had different load
factors and inflation pressures as shown in Table 3. Other
tire data are shown in Table U.

The comparison in this first section (a) is made only
on the traction parameters which permit an easy comparison.
An independent comparison in actual performance between pre—
dicted and measured values follows in section (b).

Figure 29 shows the comparison on Osborne clay stubble.
The larger tires (both in diameter and contact area) out-

performed the standard tire. The load factor had been shown

 

79

TABLE 3.——Weights and pressures of tractor tires tested in

 

 

 

the field.

Tire Max. load @ % of Max. Pressure Tire

Size Rec. Press Load Used Used (psi) Condition
12.4 x 28 1890 @ 12 65.8 11 Good
13.6 x 28 2430 @ 14 100.0 14 New
114.9 x 24 2700 @ 14 82.0, 92.8 114 Good
14.9 x 38 3330 @ 14 90.3 14 Good
16.9 X 30 3620 @ 14* 51.3 23, 14 New
18.4 X 30 4320 @ 14* 66.0 14 Good
23.1 x 26 6190 @ 14* 62.1 11 Worn
23.1 x 30 6600 @ 14* 67.5 13 New

*Estimated

TABLE 4.——Tire specifications (taken from a tire company

 

 

 

handbook).
gig: $120. 0.0. $335: Is‘éiied 13:32:: Cstq.
Inches Inches Inches ¥igggs Inches
12.4 x 28 12.7 49.4 22.8 13.4 140
13.6 x 28 14.1 51.5 23.5 14.7 153
111.9 x 20 15.0 50.0 22.0 16.4 181
14.9 X 38 15.0 64.0 29.4 16.4 215
16.9 x 30 16.4 58.2 26.0 17.8 243
18.4 X 30 18.8 61.4 27.5 20.7 290
23.1 x 26 23.2 62.5 27.1 24.7 342
23.1 x 30 23.1 67.2 30.0. 24.7 398
*By personal communication with R. W. Ellis, The

Goodyear Tire and Rubber Company.

 

80

.maflnsum mmHU

 

 

mauOQmO co mwnflp Hmum>mm MOM mumumfimumm mucmEHOmumm mm musmflm
o\o ZOpoDQmm 4m><m._. o\o ZOEbDQMK 4m><mk
ON 8 Om OW Om ON 0_ 0 ON om Om OV Om ON 0_ O
a _ a a. _ _ _ o _, a _ q _ a 1 o

 

.XT\\\®\\WAYIII¢III¢IIIAY\I¢. IIIIIIIIII¢lll\¢\IlIkAv IlYllllotl

/
O.
\V

/
‘\
\
\
\
(0

\s

a
\
/

 

O\\\\\ \ // N
1--- . ..lm .
R mm X 0 ma \ X . I:
\ a x ..x MM .. $1.--
mm x m.valll .\\
\ mHQQSpm mmao mCHOQmO
m
BOHHmm K.nmau canon o o©\mm.pmmm

 

 

.000
oo\o ; 01 L o;

 

 

 

81

in Part I (a) to have very little influence on this surface
and the differences must be considered quite significantly
an effect of diameter. The worn lugs on the 23.1-26 tires
probably prevented penetration to slightly denser soil and
consequently the coefficient of net traction started to
level off more for this tire at high travel reductions.
This is in agreement with the results of Barger and Roberts
(1939) where worn tires gave good performance at light to
medium drawbar loads.

The coefficient of rolling resistance could be deter—
mined only for the standard tractor and is included for‘
reference.

Figure 30 shows the performance of five tire sizes on
Osborne clay fallow. Although there is considerable inter—
twining of the curves, the larger diameter tires with the
exception of the 23.1—26 at high travel reductions outper-
form the standard tire. The worn lugs of the 23.1—26 tires
again resulted in a levelling off in the u curve at high
travel reductions. In Figure 30 the 14.9-24 tires with a
diameter 5% smaller than the standard tire outperformed the
standard tire. The differences obtained can be accounted
for if the load factor effect found in Part 1(a) is con—
sidered.

Figure 31 is for Osborne clay fallow that was roto—
tilled 4 inches deep, 24 hours prior to testing. The per-

formance obtained was similar to that mentionedl above~

 

.BOHHmw %mau

 

 

82

 

 

 

mCHOQmO co mmuflp Hmum>mm How mummemumd mUCMEHomumm om musmflm
o\o zocbzomm Jw><me o\o zoFoaomm 163$:
ow on O? on ON 0_ o on om Om 0v om ON 0. o
a _ A 1 L n o 1. u, A _ _ A _ o
\
IIIYIII®\\\LTIII®II119\\\ mi
m l
.?
...} m
3‘ ... a
/ c: x.“ t
n. o \.\ \
./ . . c .. \o i
/ lol u u u \\s. x
/ //I I I \\\ o \\ L. LG
.. \
:F . x 3
a .. \\ _
1 v \V _
,. . \ 1‘
\. IO \ s 1
\\ I u c I. w
:\ \..\\x n s Q
o\ n a a \
\v. \\ /II“W\
\H\Iw! \\ \
. o
x . .
1 m. mmxmmn1 m
A.p3 .me mo fimmv VNXm.VH!-I. omX4. 1-:
A.03 .xms mo xmmv vmxm.va-aa mm ..mm
mmXo.malll mmxm walll.
BOHHmm hmfiu mayonmo Boaamm hmHU\mcHonmm
. .10 .00 NH .pu
8}; + o 1 o." 1 0..

PW . 7,,

 

 

83

.BOHHmw hmau mauonmo
co mmuflu.dmuw>mm mom
mumumEmumm mucmEuomumm Hm madman

o\o zozbnomm nix/4E.

 

 

. \\ . \
\\w\\\ mm x o.ma9|l¢

. Om x m.caa-a.1 m‘
omvma.mmsan

mm x m.¢alll
pmaaflpsowom

BCHamm hmau mauoflmo
oo\ma.puo

 

 

84

Figure 32 is for Osborne clay fallow that was culti—
vated and harrowed. Fall rains raised the moisture content
as shown in Table 1. In Figure 32 (left) the large diameter
tires outperformed the standard tire. The performance of
the 23.1—30 tires compared to the 14.9—38 and 16.9—30 tires
indicate again that factors other than diameter had an
influence for this tire. Figure 32 (right) shows the effect
of many factors in that a small diameter tire (12.4—28)
considerably outperformed the large diameter tire (23.1—30).
The influence of load factor alone cannot explain the dif-
ferences obtained. The inability of the large tire to
penetrate, along with cleaning problems combined with both
the load factor and diameter effect, resulted in lower
performance.

6.43 Part II (b). A Prediction of the Actual Field

 

Performance of Other Tractors Based on the Traction Char—

 

acteristics of the "Standard" Tractor.——In the prediction

 

of drawbar performance the following assumptions concerning
the influence of load factor and tire diameter were made.
These assumptions were not made on the basis of the results
mentioned in Part II (a).
(a) the coefficients of front and rear wheel
rolling resistance varied inversely with the

diameter.

 

85

. 10.5 8:35 3033

 

 

 

 

 

 

 

 

kmao wauonmo no mmuflp Hmum>mm How mumpmamumm mocmEuomnmm mm madman
o\o 20....030wm 4m><m._. o\o ZO_._.ODOmm 4w><mk
Ox. 00 On 8 0m ON 0. O Ox. Om Om O¢ Om ON 0_ O
T q _ A _ m _ O _ _ a a O A a O
._
. m
o I. N.
/c. III .. m c
/ II A \ \
a II Atul \ c \
.5; xx\
\ \ ..
. \ x
\
u \
R u xvi/la
R . xxx /.
. . \\\\
1 . -\ 3026.271. 1m.
mm x 6.3.1 \ om x m.cali.
mm x v.manll 0m x H.mmlnl
0m x 1mm mm x 0.:
BoHHmm mmau mauonmo Bodamm mmao mauonmo
.©o\mm 1.60 L O._ .Oo\om ...«UO 1 O_

 

86

(b) the correction for diameter of the coefficient
of net traction from the standard tractor on a
firm soil as the Osborne clay stubble was one—
half the relative difference in diameter multi—
plied by the coefficient of net traction (u) at
30% travel reduction. This correction was added
uniformly to the u curve of the standard tractor
to obtain the calculated u' curve for the com—
parison tractor. Kliefoth (1964) used a similar
approach to correct for tire diameter.

(c) a correction for load factor on a loose soil as
the Osborne clay fallow was based on the results
from Part I (a). This correction was added to
obtain u' for the particular tractor.

Values of u' and corresponding travel reduction for
each surface and other physical tractor data were punched
on data cards. The computer program, definitions relating
to the program and a sample print—out of predicted tractor
performance are contained in Appendix E. The measured draw—
bar horsepower was evaluated by modifying the computer pro-
gram in Appendix D. The traction characteristics of the
soil as determined by the standard tractor are also included
in Appendix E.

On Osborne clay stubble (Figure 33) the predicted
horsepower of the 9480 lb. tractor was below the measured
values at maximum drawbar pull. The predicted and measured

drawbar horsepower of the other tractors tested on this

 

 

87

.AH0#omnu .QH
om¢mv mHQngm mmao wcuonmo co sofluUSOmu Hm>muu paw

 

 

 
  

 

nw3ommmnoa Hmnzmup wo mmSHm> pmMSmmmE tam ©060flpmum mm musmflm
mm... . .338 $53me
OOOO OOOm OOOq OOOM OOON 000. AU
_ H i _ _ . .
o
0 3’ JV
cozosumm 33¢
no
“H
V.
m
Lm V
“d
m
a U
. 3
5308901 63390 im. %
M.
o .d
60.218028 no
0 pmpmHDUHmu.lu
o wmufls omnv.wa.1m_
.mna ommm Hmwm
x .2: omsm uaoum
he 0 0 £3.33 Houumue
96 o mannspm mmau mcuonmo
m o o 0 mm .085

 

 

O
N

8

CO

NOIlOflGEH WBAVHJ.

°/o

 

 

88

surface agreed well up to maximum drawbar horsepower
(Figures 34 and 35). In Figure 35 the engine speed of the
tractor was pulled down from 1400 rpm at idle to 800 rpm
at maximum pull. The measured forward speed and drawbar
power (at maximum pull) was therefore less than the pre—
dicted values which were calculated from travel reduction
alone. With this exception the measured travel reductions
for all three tractors were usually slightly lower than the
predicted values.

On Osborne clay fallow the field performance of four
tractors was predicted from the standard tractor (Figures
36, 37, 38, 39 and 40). In two cases (Figures 36 and 38)
the predicted performance was 10% and 15% respectively
higher than the measured values. In the other three cases
the agreement was good. The tire pressure of the 5510 lb.
tractor (Figure 36) with 16.9—30 tires was 20 psi or 6 psi
above the recommended 14 psi. According to Kliefoth (1964),
higher tire pressure decreases the performance of a tractor
operating on agricultural soils. Worn tire lugs on the
10,030 lb. tractor (Figure 38) prevented penetration to
denser soil and thus contributed to decreased performance.
The effect of changed weight distribution is shown in Figure
40 where higher maximum drawbar pull was predicted and
obtained as compared to the same tractor with less rear

wheel weight (Figure 39).

 

 

89

.Auouomup .QH
ommbv mHQQDum hmHu mcuonmo co cofluUSUmu Hm>muu paw

umBommwu0£ HMQBmup mo mmfiam> UGuSwmmE paw pmuuapmum Vm musmflm

.mmJ .....Dn. m<m>><mo

0000 GOOD OOO¢ OOOn OOON 000. O

 

_ a _ _ _ _

 

” UmusmmmZoo
fifigm pmumasoamo I
o mmuee mmum.¢a1

o .mha meow ummm
.mba meme ucoum
uzmflmz nouomue

o oo mabhsum smao mcuonmo 66\e .uooL

$30380: conical.
o

 

Q

Q

HBMOd BSBOH ave/mac

 

ON

Om

NOIlOflOBH 13mm

96

 

 

90

OOQN

.AHOpUmuu

.QH omo.oav mHQQUum wwau mCHOQmO co :oflOUSOGu Hm>mup
cam umBOmeHO£ uwfl3mup mo mmsam> pmuammma paw pmpoflpmum

OOOm

.mmq 133a m<m>><mo

000v

AXXE

nOON 000

mm 9.53m

 

UOMSmmeOO

pwwmasoamo I
mmHHB ONIH.MN

.mQH owON Hmmm

  

.mfla Ommm ucoum
uflmfimz Houomue
maflflsum xmau mayonmo

O©\©

. poo

 

HBMOdBSHOH BVBMVHG

OV

 

Ov

Om

Ow

NOLLDOGBH WBAVHI

°/o

 

 

91

00mm

.QH OHmmV Bofifimm %mau ozuoemo

Hm3omwwuoe

OOOm

 

m HMQBme mo mosfim

.Auouomuy
co COHuUSUQM Hw>mha paw
> pmhzmme pcm pmwoflpmnm om whfimflm

mmq .4431 m<m3<mo

OOmN OOON

OOm_ 000_ 000
: 0

530830: 283 05
pmuzmmmzoo
twystonOIl
meHB Omlm.©H
, .mQH mHhm Hmwm
.wQH mama #GOHM
b£mfiwz uovomuB
Sofiamm amao mcuonmo
©O\NH .UUO

<1-

HBMOdBSBOH HVBMVHO

O.

C)
OJ
NOUDHOBB WEAVHL

C)
v.

96

OO

 

 

 

.AHOOUMHu
.Qa ommhv BOHHmw mmHu mcuonmo co COHOUSOmH Hm>muu paw
HOBOmeHOL umflBmup mo mmsHm> pmuSmmmE tam pmuUfipmnm mm musmflm

.mmu. 40:8 mamgamo

92

Comm

OOmv

OOOV 00mm OOVN

com. 08 . o

 

a

cozoaomm

M

_ d

65¢

$30890: Lonzolo

C.)

      

pmuflmmflZoo
pmwmasoamu I
meflB mmlm.va

.mhe mace 086m .4

.mfla momH ucoum
ufimflmz HOpUMHB
BOHamm %mHO mcuonmo

oo\ma .poo

 

N.

m_

BVBMVEIO

BBMOd BSHOH

 

ON

0v

om

lBAVHl

NOIlOflOBH

°/o

 

 

93

OOOw

.AHOprHu
.QH omo.oav BOHHMM xmfio mayonmo so :ofluosomu Ho>muu
paw umzomowuog Hankmup mo mosam> pmufimmmfi tam Umpoflpoum mm musmfim

mmn. . 443a m<m>><mo

OOON OOOO OOOm COO? OOOm OOON 000. O

 

       

141 _ fl _ In

  

cozoaoom

 

6‘6;

5308301 53305 .

  

pmusmmmz oo
pmpmasoamo I
money ONIH.mm
.mQH omon “mom 1
.mna ommm ucoum
pgmfloz Hepomue
BoHHmm >ma0 wagonmo
oo\ma .uoO

 

 

0_

ON

vm

H 3M0d BSHOH HVBMVBO

 

ON

OV

Om

NOLLOnOBH WEAK/Bl

°/o

 

 

 

.Auouumuu
.QH omhwv BOHHmm hmao mcuonmo :0 cofluospwu Hm>muu tum

Hm3bm0mHO£ HMQBMHU MO mosam> Ownsmmwfi paw wwwoflpmum mm wusmflm
mm: . fine Ems/4mm
00mm 000m 8mm 88 oo.“ 89 8o.

 

q _ _ L _ A

  
    
      

cozoaumm 320:.

94

3383.5: EnZEQ

pwuzmmmz oo
twvmasoamo I
mouse VNIm .va

.mQH momm uconh

o 0:303 0300.3.
Boaamm mmao mcuonmo

©o\ma .puo

.mQH mNVfl Hmmm I

 

O_

HEMOd BSHOH HVBMVHO

 

ON

NOIlDflOBéi WEAVHL

°/o

 

9.5

. 300000 003 3000030 m :0?
uowomuu .QH omhmv Sodamm undo mcuonmo so Gawuuscmu Hm>muu

 

can HmzbmmeOA Hmnzmuw mo mosam> pmusmmmfi paw pmpoflpmum ow musmfim
mm: . 0.50 ~133me
80¢ 8mm 80m 08m 88 com. 08. com
a fi _ n 1 _ 0‘ m
o
\

  

 

cozuacom .05..»

5380201 .3265

monummmzoo
pmpmasoamo I
mmuaa wmlm.¢a
. o .8: 03m 80m

.mna omna acoum

unmamz uovumue
o BOHHMh mmao mcuonmo
oo\ma .900

000

 

O_

HVBMVHO

BBMOdBSHOH

 

ON

ow

NOllOnOBH WBAVHl

°/o

 

 

96

On the roto—tilled Osborne clay fallow (Figures 41,
42 and 43) the agreement between predicted and measured
values was good.

Other tests were made on moist loose fallow (Figures
44, 45, 46, 47, 48, 49 and 50). The rear tire pressure of
the 5510 lb. tractor (Figure 44) was reduced to 14 psi,
however, the measured maximum drawbar pull was still less
than the predicted value but within 5%. The measured
drawbar horsepower and travel reduction of the 11,310 lb.
tractor are lower than the predicted values eSpecially
near the maximum drawbar pull (Figures 46, 49 and 50). The
high moisture content of the soil especially in Figures 49
and 50 combined with the lug design may have prevented
penetration to denser soil. This might be attributed to the
tires (23.1—30) of this particular tractor. Figures 44, 45,
47 and 48 show good agreement.

Considering that the correction factor for Osborne
clay fallow was based on the effect of load factor obtained
two months earlier, the comparison between predicted and

measured values was reasonable.

 

 

 

97

 

. Ahouomuu on: oammv 30:23
hmau 098an pwaaflvlonvon so cofluuspmu Hog/mun tam

 

umBomwmuoa HmflBmuU mo mosam> UmHDmmmE 0cm pmpoficwum aw wusmflh
.wm._ . 4.5a m<m>><mo
00mm 80m 80m OOON 00m. 000. 000
_ _ _ _ _ _ 4
N
8:030: .03..» O
a
V
o M
330330: 8030.5 c avU
a
o
00 W
H
o 3 o E
o o m M
o o o M
o o o nonhummmzoo 3
o o 8
o empmasoamonI
o . mmufla omIm.oa
0 0 00: masm 80m m

 

 

   

.83 was” uconm
##mflwx HO#UMHB
Boaamm pwaaflulogom
hmHU $58an

00\NH .000

   
   

 

O_

 

CO

on

NOILOI'IOBH 13AV31

°/o

 

 

00mm

. 300.0000 .0: 03$ 30:00
mmau wcuoflmo pmaafiulouou co coflpUSOmu Hm>mup

cam nmzomwmuog HmQSmup mo pmusmmmfi tam pmuoflpmum mv musmflm
.mmq . 1330.. m<m>><mo

 

98

oomv OOOV OONm OOVN 009 OOm
_ _ _ _ _ fiI

      
 

8:809; 63:.

0
03000901 000305
0 pmHSmmmEoo
e 00008000'
0 o o o 0002.. 0010.3
0 .05 A0400 00m
o .mfl mom: 00000
O o

pnmfiwz Houumua
30Hamm pmaaflulouom
hmao wcuonmo

om\wd .#00

N_

 

m.

HBMOdBSUOH HVGMVUO

 

8

NOILDHGBH WBAVHL

0
@-

°/o

 

 

99

.AHOpomup .QH Omo.oav 30Hamm
awau mCMOQmO pmaaflpIOpou co cofiuUSUmu Hw>mn# cam

HwBOQmmHox HMQBmup mo mmDHm> pmuzmmmE paw pmpUflpme mv madman

Mm4 .4430 m<m3<mo
OOON OOOO 000m 000? OOOm OOON OOO.

 

O

 

_ _ 4 _ _ _ .

  
  
   

   

8.820% 55;

002000901 00030:“

0 pmuzmmmZQO
o umpmHDUHMUII

o 00020 0N1H.MN

00 .00a 000s H00m

o .mflfl ommm “noun

0 o pfimflwz Houomua

onH0m emflausnouom

hmao mcuonmo

oo\NH .uoO

O.

in.

 

HVBMVHO

UBMOdESHOH

 

8

NUIOOGBB WBAVHI

C)
v

90

 

 

 

100

   

 

.A0000000 .00 00004 300000 0000 0000000
0:00:00 0050m00§ £m0£ 00 000005000 Hm>m0u paw

 

 

       

 

0030Q0000£ 0093000 00 m05Hm> ©00SmmmE Cam 000006000 00 m0smflm
mm: . 4.50 0830.00
000m ooom OOmN 000m oom_ 000_ 000 0
4 4 _ 4 4 4 .
o o o
o
O
cozosnom 4006.0

  

0
o
0
0 00300090: 000305 0

0 o o 0 0005000200
0 o 0000000000|I
o o o 0 00000 0010.00
o .000 mabm 000m
o .000 00: 00000

ufloflmz 0000008
300000 >000 mc0onmo
®o\om . HUO

 

N4

HEMOdBSHOH HVGMVHO

 

ON

O0

00

NOLLOHGBH "IE/WELL

°/o

 

 

 

101

0000

 

.00000000 .n0 omwmv 300000 0000 0:0oomo

0000:00 00:0m0oe LM0: :0 CO0005000 00>000 0:0

 

00zom0m0o: 0003000 00 m0300> 000:000E 0:0 000000000 m0 003w0m
mmg 00:0 m<m3<mo
0000 0000 000M 000m 0004 O
4 0 4 4 4 4

Icogzumm .920

00300090: Enseol

o

 

0005000200
0000050000 I

00009 wmlm.¢0

.000 m0oo 000m

.000 mom0 0:00m
000003 0000008
30000m >000 0000000
00\0m .000

Q

 

0

83M 0:! BSHOH HVBMVHO

 

O
N

NOUOHGBH WBAVHL

0
¢

96

 

102

 

300000 0000 0:000mo 0:00:00 00:0m0oE LW0: :0 :00003000

.00000000 .00 00m.000

 

 

00>000 0:0 003000m0o: 0003000 mo m0500> 0005m00E 0:0 000000000 ow 005w0m
mm; 0030 m<m3<mo
0000 0000 0000 0000 0000 000m OOON 000_ o
7 4 4

4
4

unicozosumm _0>00r

a

    
  

0005000200

0000050000 I

m000B omu0.mm

032$90:.503&ol .mp0 comm 000m
.0 00000

0 o 0mm0mwvmo0u00e
300000 >000 0c0onmo
00\0m .000

 

04

0

0m

mm

HBMOdBSHOH HVSMVHG

 

0?

00

NOIiOflG 33 WEAVHJ.

96

 

 

103

 

.Am .N ‘0 00000 .0000000
.00 ommS 300000 >000 0:00000 0:00:00
00d0w00E £000 :0 0030000000 0003000

 

mo m0500> 0005000E 0:0 000000000 00 005000
.000 . .330 $03me

0000 0000 009» 0000 0000 000_
0 _ _ 0 _ 0

m 0000 x

N 0000 0

005802 _ 0000 0

02030.00 I

o
o o o
o oo o
00x 0
0

0000.0. 09.0.00

.000 m000 000m

.090 m000 0:000

000003 0000008

3000mm x000 0:00000

x o 0030 .000

.X

 

O_

9

ON

mm

H 3M0d BSHOH 8V8 MVHO

 

 

 

.Am 0:0 0 00000 .0000000 .QH oonmv 30aa0m >000
0:00900 0:00000 0000000E 00£00£ :0 000005000 00>000

 

 

 

Mug“ ngommmuog «HMGHBMHU MO mmfldmmr CmHgmme USN mquUflmumHam w? whgmfirm
me . .330. mdmgdmo
OOVN OO_N OOQ 00m; OON_ 00m 000 00m
_ _ 0 _ a 0 -II Lvl“!
\\|\lll.
COT—030$, _®>O.Cu 0-\‘\t\.\\‘0\t
. & \£fi\\ O. O

101.L

 

m_

OT

 

_Om

NOLLOHO 38 WBAVH i

°/o

m 0000.

$0 0 00050002 A 00000
0 V 00000500001].

00009 mmlv.ma

.mfla mmmm 000m

.090 mnaa 0:00m
0:000; 0000009
BOHH0m m0au 0:00900
00\mm .000

HBMOdBSBOH HVBMVHG

 

 

105

 

.0000um00 .00 00m~000 3o0000 0000 ocuonmo
0000:00 0050000E 003000 :0 :00005000 H0>000 0:0

0030000003 0003000 00 005H0> 00050006 0:0 000000000 mv 005000
03 . .38 «403400
080 cook 008 080 ooov 800 800 08.

 

 

_ _ ~ _ _

    
   
  

.0 0
8580.0 .2600

0038005: 80320

O O
0 0005000200
o 0000050H00Il
o 00000 omu0.mm
.MQH 00mm 000%
.mQH Odvm #Goum
0£m003 0000005
3oaa0h hmau 0:00000
®o\mN .000

O.

9

ON

 

mm

UBMOdBSHOH HVBMVHO

 

ON

O¢

NOUDflOBH WBAVHL

°/o

 

 

106

 

.Am 0cm 0 .0 .m0mmm .0000000 .00 00m.00v 3O0000
>000 0:00000 0:00:00 00500008 000000 :0 :00005000 00>000

0:0 0030m0000£ 0003000 00 005H0> 00050005 0:0 000000000

.mmq

000m 0000 0000 0000
_ 0 0 0

 

D

0:. ..m \
‘\\\\\

n

.330 0.495me

0000 000m OOON 009
0 0 _ _

mQIm D
mqlm 0
00050002 mQIH 0

0000050000.!!
00008 omla.mm

.000 comm 000%

.000 00¢N 0:000
0£m003 0000008
300000 x000 0:00000
©©\mm .000

00 003000

 

om

3V8 MVHO

HBMOd BSHOH

 

VII. RECOMMENDATIONS FOR FURTHER WORK

Based on the results obtained in this study the

following further work should be undertaken:

1.

Correction factors for tire diameter and load
factor and their possible interaction should

be investigated, preferably under well con—
trolled conditions.

The standard tractor in future tests should be
closer to other tractors in tire size and load
factor (75 — 80% seems better justified).

An extended study of the critical conditions of
farm field work, e.g., very soft spring field
conditions, including an investigation of the
relative occurrence and importance of these con—
ditions.

Correlation of traction characteristics of a
soil with a simultaneous determination of the
draft requirements of several tillage machines
for these same soil conditions.

Relationship between tire performance and soil
strength characteristics.

Performance characteristics and drawbar horse—

power of a range of tire sized offered as options

107

 

108

to tractor purchasers included in a systematic
analysis of preferable choice.

Determine methods for finding the optimum
dynamic (or static) weight on drive wheels for

a particular soil condition and type of work.

 

 

 

VII. SUMMARY OF RESULTS

An instrumented test (standard) tractor was used to
determine the effect of different tire loads and inflation
pressures on tractive performance. The field results
obtained with the standard tractor indicated that a de—
creasing "load factor” of a tire increased the coefficient
of net traction on loose surfaces. On firm surfaces one
common set of performance parameters represented most load 0
factor ratios. The effect of increased pressure and cor—
respondingly increased weight on loose soils was similar
to the effect of increased load factor.

Only for the 100% load factor series on loose clay
fallow, was the decrease in coefficient of net traction
sufficiently large to offset the increase in pull due to
the increased weight, i.e., in most cases the overall pull
still increased with increased weight.

A straight line relationship between measured weight
transfer and rear wheel torque was obtained. This rela—
tionship was independent of the traction surface.

In other tests with tractors and tires of different
diameter, increased tire diameter resulted in increased
tire performance except for one particular case. On a firm
soil surface the effect of diameter was apparent and the

"load factor" effect on the standard tractor was minimal.

109

 

 

110

However, on the loose soil surfaces the increase in per—
formance characteristics of larger tires could be accounted
for by the ”load factor" effect.

The drawbar horsepower of seven tractors was pre-
dicted from basic parameters obtained with a standard
tractor. Field measurements indicated that the accuracy
was normally within t 2 per cent up to the maximum drawbar
horsepower except for three cases out of a total of eight—
teen. An interaction between tire pattern and soil moisture
was indicated for one tractor. For high drawbar pulls the
predictionvws more uncertain. The agreement between pre—
dicted and measured output was reasonable taking into con—
sideration the inaccuracies of the testing procedure and

natural soil variability.

 

 

 

 

 

REFERENCES

 

Ill

 

REFERENCES

Bailey, P. H. (1956). The Comparative Performance of
Some Traction Aids. Jour. Agr. Engr. Research lzl,
l2—23.

Barger, E. L. and J. Roberts (1940). Effect of Tire
Wear on Tractor Performance. Agric. Eng. 20:191-
19A.

Barger, E. L., J. B. Liljedahl, W. M. Carleton and E. G.
McKibben (1963). Tractors and Their Power Units.
John Wiley and Sons, Inc., New York, 524 pp.

Bekker, M. G. (1956). Theory of Land Locomotion——The
Mechanics of Vehicle Mobility. University of
Michigan Press, Ann Arbor, Michigan, 495 pp.

Berlage, A. G. (l962). Vehicular Mechanics of a Tractor
Operating on a Yielding Soil. Thesis for the degree
of M. S. Michigan State University, East Lansing.

Clark, S. J. and J. B. Liljedahl (1963). Model Studies of
Single and Dual Powered Wheels. Paper No. 63—603
presented at the Winter Meeting of the American
Society of Agricultural Engineers, Dec. lO—13.

Duffee, F. W. (1934). Wisconsin Observations of Rubber
Tire Performance. Agric. Engineering l5z58—59.

Dunlap, W. H., G. E. Vanden Berg and J. G. Hendrick (1966).
A Comparison of Soil Values Obtained with Devices of
General Geometrical Shape. A.S.A.E. Trans. 9:6:
896—900.

Foster, C. R., S. J. Knight and A. A. Rula (1958). Soil
Trafficability. Proceedings of Seminar on Tillage
and Traction Equipment Research, United States
Department of Agriculture, Agricultural Research
Report No. A2-l6.

Franke, Rudolf (1963). Four Wheel Drives. The Institution
of Agricultural Engineers 19:25—31

Heroe, P. (1956). Measurements of the Sidewall Deflectiorx

of a l2—28 Tractor Tire. Unpublished M. Sc. Thesis,
University of Nebraska, Lincoln.

112

 

 

 

 

   

113

Janosi, Z. (1963). Theoretical Analysis of The Performance

of Tracks and Wheels Operating on Deformable Soils.
A.S.A.E. Trans. 5:2: 133—134.

Kliefoth, F. (1964). Die Ermittlung Der Zugfahigkeit Der

Kucera, H. L. and W. Jamieson (1963). Tractor Tire Ballast
McKibben, E. G. and J. B. Davidson (1940). Effect of Out—

McKibben, E. G. and D. 0. Hull (l9UO). Soil Penetration

McLeod, H. R., I. F. Reed, W. J. Johnson, and W. R. Gill
(

National Tillage Laboratory (1966). United States Depart—

O'Harrow, C. T. (l9A7). Traction Efficiency.S.A.E.

Persson, S. P. E. (1966). Parameters for Tractor Wheel

Reece,

Reed,

Reed,

Ackerluftreifen. KTL Schleppertest, Grundlagen and
Berechnung des Berichtes ffir die Landwirtschaft K.T.L.
Ber. 81:16—25.

Compared. Paper No. 63—605 presented at the Winter
Meeting of the American Society of Agricultural
Engineers, Dec. lO—l3.

side and Cross—sectional Diameters on the Rolling
Resistance of Pneumatic Implement Tires. Agric.
Engr. 21:57—58.

Tests as a Means of Predicting Rolling Resistance,
Agric. Engr. 21:231—23A.

1966). Draft, Power Efficiency and Soil Compaction
Characteristics of Single, Dual and Low Pressure
Tires. A.S.A.E. Trans. 9:1:A1—A4.

ment of Agriculture, Agricultural Research Service
u9—9—2, Washington, D.C., 12 pp.

Quarterly Transactions 1:1:71—75.

Performance. Paper No. 66—142. Presented to 59th
Annual Meeting of the American Society of Agri—
cultural Engineers, June 26—29.

A. R. (196A). Problems of Soil Vehicular Mechanics.
Land Locomotion Report No. 8A70. U. S. Army Tank
Automotive Center, Warren, Mich.

 

I. F. and M. 0. Berry (19A9). Equipment and Pro-
cedures for Farm Tractor Tire Studies Under Controlled
Conditions. Agric. Engr. 30:67—70.

I. F. and J. W. Shields (1950). The Effect of Lug
Height and Rim Width on the Performance of Farm
Tractor Tires. S.A.E. Journal AO—Al.

 

114

Reed, I. F., C. A. Reaves and J. W. Shields (1953).
Comparative Performance of Farm Tractor Tires
Weighted with Liquid and Wheel Weights. Agric.
Engr- 34:391—395, 399.

Reed, 1. F. (1956). Excellent Correlation Between Field,

Laboratory Test Data. S.A.E. Transactions 64:405—407.

Reed, I. F. (1962). Effects of Inflation Pressure, Load
and Drawbar Pull on Axle Height and Rolling Radius
of Six Tires. A.S.A.E. Transactions 5:2:125, 132.

S.A.E. Co- -operative Tractor Tire Testing Committee (1938).
The Traction of Pneumatic Tractor Tires. S. A. E.
Transactions 42:13- 26.

Sauve, E. C. (1939). Traction Tests of Single Pneumatic
Tires vs. Dual Pneumatic Tires. Michigan Agric.
Exper. Sta. Quart. Bu11., 22:59—71.

Sauve, E. C. and E. G. McKibben (1945). Studies on Use
of Liquid in Tractor Tires. Michigan Agric. Exper.
Sta. Quart. Bull. Vol. 28 No. 1.

Shields, J. W. (1952). Selecting Rear Tires for Farm
Tractors. Agric. Engr. 33:485—486

Sonnen, F. J. (1964). Erganzenden Beitrag Zu Den Au
Ausfuhrungen Von F. Kliefoth. KTL Schleppertest,
Berechnung des Berichtes fur die Landwirtschaft,
K. T. L. Ber. 81: 26— 29.

Southwell, P. H. (1964). An investigation of Traction and
Traction Aids. A.S.A.E. Trans. 7:2:190—193.

Southwell, P. H. (1966). An Investigation of Four—Wheel
Drive and Tandem Tractor Arrangements. Paper No.
66—108 presented to 59th Annual Meeting, American
Society of Agric. Engr. June 26—29.

Steinbrugge and Bruwer (1958). Measuring Variable Rolling
Radii of Tractor Wheels. Paper No. 884 Journal
Series, Nebraska Agricultural Experiment Station,
Lincoln.

Taylor, J. H. (1966). An Annular Shear Device. Paper No.
66—307 presented to the 59th Annual Meeting of the
American Society of Agric. Engr., June 26—29.

Taylor, P. A. and N. Y. Williams (1959). Traction
Characteristics of 11—36 Agricultural Tractor Tyres
on Hard Surfaces. Journal of Agric. Engr. Research

4:3—8.

 

115

Vanden Berg, G. E., I. F. Reed and A. W. Cooper (1961).
Evaluating and Improving Performance of Traction
Devices. Proceedings No. I of the Int. Conf. on
Mechanics of Soil Vehicle Systems, Turin, Italy.

Vanden Berg, G. E. and I. F. Reed (1962). Tractive Per—
formance of Radial Ply and Conventional Tractor
Tires. A.S.A.E. Trans. 5:2:126—129, 130—132.

Vanden Berg, G. E. (1966). Continuous Analog Techniques
in Experimental Research. A.S.A.E. Trans. 9:5:661—664,
668.

Walters, F. C. and J. K. Jensen (1954). Instrumentation
for Evaluating the Operating Performance of Farm
Tractor Tires. S.A.E. Paper No. 352. Presented at
S.A.E. National Tractor Meeting, Sept. 13—16.

Walters, F. C. and W. H. Worthington (1956). Farm
Tractors and Their Tires. S.A.E. Transactions 64:
394—405.

Wann, R. L. and I. F. Reed (1962). Studies of Tractor
Tire Tread Movement. A.S.A.E. Trans. 5:2:130—132.

Wilkins, D. E., W. L. Harris and S. H. Taylor (1966).
Effect of Rate of Displacement on Shearing Stress
of Soils as Measured with a Torsional Shearing
Device. Paper No. 66—144 presented to the 59th
Annual Meeting of the American Society of Agricul—
tural Engineers. June 26—29.

Wills, B. M. D. (1963). The Measurement of Soil Shear
Strength and Deformation Moduli and a Comparison of
the Actual and Theoretical Performance of a Family
of Rigid Tracks. Journal of Agric. Engr. Research.
8:1:115—132.

 

 

APPENDICES

116

ii...

 

 

II.

III.

IV.

APPENDIX A

ANALYSIS OF NEBRASKA TRACTOR TEST REPORTS

Definitions Relating to Appendix A

Forces and Distances Used in Tractor
Analysis

Computer Program for Analysis of Nebraska
Test Reports .

Typical Data Print—Out From the Computer

117

Page

118

119

120

121

 

 

 

PF

PR
SFWT
SRWT
STOWT
FRR
RRR
DBH
FWRRC

WHLBS
CGDIST
RWRRCO

PULL
SLIP
RRTOTL
TORQUE
CALWTR
RRFW
THRUST

DRWT

U
GRTRST
RRRW
RWRRC
TRVRAT
UT

PIE
TREFFY

II II II II || II II II II

II II II

|| || II II II II II

II II II II H II II II II

A—I. Definitions Relating to Appendix A

pressure in front tires, psi.

pressure in rear tires, psi.

static front wheel weight, lbs.

static rear wheel weight, lbs.

total weight of tractor and operator, lbs.
front wheel rolling radius, ft.

rear wheel rolling radius, ft.

drawbar height, ft.

front wheel rolling resistance coefficient,
dimensionless.

wheelbase of tractor, ft.

horizontal center of gravity of tractor, ft.
rear wheel rolling resistance coefficient,
dimensionless.

drawbar pull, lbs.

travel reduction, per cent.

total rolling resistance of the tractor, lbs.
calculated torque input to the rear wheels, 1b. ft.
calculated weight transfer, lbs.

rolling resistance of front wheels, lbs.
drawbar pull and front wheel rolling resistance,
lbs.

dynamic rear wheel weight, lbs.

coefficient of net traction, dimensionless.
drawbar pull and total rolling resistance, lbs.
rolling resistance of rear wheels, lbs.

rear wheel rolling resistance coefficient, lbs.
travel ratio, dimensionless.

coefficient of gross traction, dimensionless.
tractive power coefficient, dimensionless.
tractive efficiency, per cent.

118

 

 

119

 

mflmmamcm MO#omnw SH poms mwocmomflp Usm moonom

 

1:5 .30 - ...m

a

 

3 mm
mmu-mmm

 

 

mam

mmDIE

.HH-<

L

M

 

 

 

 

 

 

 

 

 

120

A-IIIComputer program for analysis of Nebraska Test
Reports. (a) input data, (b) transformation
into performance parameters.

DISK OPERATING SYSTEl/360 FORTRAN 360N-FO-6Sl 21

DI“ENSION DAYEIll).0LOC(7).SURF(1).DDATE(7).PULL(zoleLlPIZO).
ITREFFVIZOI. TORQUEIZOIOCALHTRIZOIIRRFHIZOIoTHRUSTIZOIyDRHTIZOII
ZUIZOIpGRTRSTIZOI'RRFHIZOI' RHRRCIZOI'TRVRATIZOIcUTIZOIcPIEIZOI

FORNAT IIXOIZoIDAAI

‘ORNAT Il‘A‘v5A‘)

FOR'AT IIXIFToODFbozI

FOIIAI (1x.2F§.0.F6.0.2F1.0.1F6.3D

FORMAT IIHIvl/IIZOXvIDAAv/II

FURNAT I/l' LOCATION I5 'TAAO'SURFACE IS '5A41'TEST DATE 'SAAI/II

1° FORMATIIXn' PF PR SFHT SRHT STOUT FRR RRR DBH FHRRC
I UHLDS CGDIST RHRRCO'II
II FORNATIlio' TORQUE PULL CALOTR SLIP U RHRRC TRVRAT UT PIE
ITIEFFY RRRU “RF. N'I/I
12 FORMAT IIXpJFboooFS.206F6o3'2F6oIvZXIIZI
l3 FORMAT IIZ)
I 99 READ (1'1) NODSoIDATEIJIoJ'IvIB)
READ I102) IDLOCIJI'J'IpTIO ISURFIJIoJ'IvSIoIDDATEIJIvJ'IISI
READ I105) PFO'R'sFuTOSRHT9STOHTOFRR'RRR'DBH'FHRRC'HHLBS'CGDIST'
{RURRCO
’READIIo3’ IPULLIKIcSLIPIKIoK'10NODS)
RRTOTL =SFHT‘FHRRC 9 SRHT’RURRCO
DO 6 K'IoNOBS
TOROUEIK) - I'ULLIKI 9 RRTOTLI .“RR
CALHTRIKI ‘ S‘UT‘ISTOUT‘CGDIST 0 IRRE-DDH)‘PULLIKI-TORQUE(K)I
IIIUHLD$°IFHRRC.IRRR-PIIIII
RRFHIKI ' ISFHT'CALHTRIKII‘FHRRC
THRUSTIK) ‘ PULLIKI O RRFHIK)
b DRUTIK) ’ SRIT 0 CALHTRIKI
UIK) 3 THRUSTIKI/DRHTIKI
GRTRSTIK) I TOIOUEIKI/RRR
RRRUIKI ' GRTRSTIKI'TNRUSTIKI
RHRRCIK) = RRRHIKIIDRHTIK)
TRVRATIK) 3 [.00 ' (SLIPIKIIIOOo.
UTIK) 3 GRTRSTIKIIDRUTIK)
PIEIKI ' UIKI‘TRVRATIKI
6 TREFFYIKI ' PIEIKI/UTIK)
HRITE I308) IDATEIJIvJ'IclaI
IRITE I399) IDLOCIJIoJ‘IoTIvISURFIJIoJ'IoSIvIDDATEIJ)oJ‘l.5)
HRITE (3'10)
HRITE I3|4I PF.PR.SFHT.SRHI.STOHY.FRR.RRR.DBH.FHRRC.HHLBS.CGDIST.
IRHRRCO
"RITE (3011)
K ' 0

OOOUNF

DO 7 K' I. NOBS
KKIKK OI
1 HRITE (3.12) TORQUEIK).PULLIK)'CALHTRIK)nSLIPIK).U(K).RHRRCIK)v
IIRVRATIK)pUTIKIoPIEIK).IREFFYIK).RRRHIK)yRRFHIK)oKK
READ (1.13) NEJOB
IF (NEJOD-99) 99.98.99
98 CALL EXIT
END

 

 

 

121

 

«.0m
0.~n
~.-
m.m~
0.0—
~.0

0.0m
F.0N
¢.¢~

dNNQU‘OFQO‘

2

m.00~
0.00u
0.~h~
0.m-
0.N0~
n.00~
«.m0u
b.00u
0.0hd

.popsmsoo map 8090 pSOIchgQ

000.0
000.0
000.0
000.0
000.0
0m0.0
000.0
000.0
000.0

3001 3010 >uum¢b
0N0.0 0~h.~ 000.h ¢~0.0 00~.~ m~n.~ 0m~.~ .mmm0

00¢¢3¢ hmuoou 004:3

00\N >405 wh40 ham»

0‘ x 00.0 00 x m.m~

-~.0
000.0
m~¢.0
“00.0
000.0
0h0.0
0h~.0
000.0
0~¢.0

w—m

0m~.0 000.0
~hn.0 ~00.0
¢h¢.0 «m0.0
000.0 0~0.0
000.0 000.0
000.0 000.0
h0M.0 000.0
mn¢.0 000.0
0mm.0 m~0.0
h: h<¢>¢h

01030 I00

001

whwcuzou m— 0010000

n00 hwwb (1040002

0~0.0
0N0.0
0N0.0
~N0.0
~N0.0
~N0.0
0N0.0
0N0.0
0N0.0

00110

000

0~N.0
Nmn.0
000.0
0mm.0
«00.0
00~.0
00N.0
m~¢.0
000.0

0 a~40 «h30<0
.m00s

hxuhm

sumo Hmofiohe

.~.m .~n.
mm.. ..oo
o... .moo
m~.m .~oo~
oo.-.o~m~
.o..~.nmo~
oo.m ...m
-.m .m~m
so.~ ...od

plum

.000N

bzmm

.000~
.~¢0~
.0-m
.mom¢
.0000
.mwmh
.~h-
.nwem
.00m¢

.>HL<

.0s¢¢
.mmws
.0000
.-m-
.mo¢¢~
.mm0u.
.h00m
.0000
.0u00~

4430 wnozch

.0~

«a

.0~

ma

<¥w<¢0wz mu ZO~h<000

4mmw—0 0000 0000

 

 

APPENDIX B

 

122

 

 

Specifications of the Standard
Test Tractor

 

 

Make and Model: Massey—Ferguson MF 150
Serial Number: 642000 445
Weight: Front—~Variab1e from 1250 to 2390 lbs.

Rear ——Variable from 3040 to 5630 lbs.
Dimensions: Wheel base-—82 inches
Rear tread—-56.5 inches

Front tread—-78.0 inches

 

Steering: Power Steering

Engine: Model Z—145 Gasoline

Clutch: 2 stage dry disc
Transmission: 12 speeds forward, 4 reverse

Advertised speeds (mph):

First 1.38 Seventh 5.51
Second 1.80 Eighth 7.20
Third 2.07 Ninth 8.28
Fourth 2.70 Tenth 10.81
Fifth 3.79 Eleventh 15.17
Sixth 4.96 Twelfth 19.82

Reverse 1.88, 2.45, 7.51 and 9.81
Tires: Front 6.00—16, 4 ply
Rear 13.6—28, 4 ply
Nebraska Test: Not tested as MF 150. MR 135 with
same engine, tires, transmission,

etc. was tested and results reported
as Nebraska Tractor Test 899.

123

 

II.

III.

APPENDIX C

ANALYSIS OF 13.6—28 TIRE TEST RESULTS

Definitions Relating to Appendix C

Computer Program for Analysis of 13.6—28
Tire Test Results . . . . .

Typical Data Print—Out from the Computer

124

Page

125

126

127

 

   

RRRW
RWRRC

TRVRAT
UT

PIE
TREFFY

II II II II II II II II II || II II II II II II II II II II II

II II II II

C-I. Definitions Relating to Appendix C

multiplier coefficient for rear wheel speed.
multiplier coefficient for fifth wheel speed.
pressure in front tires, psi.

pressure in rear tires, psi.

static front wheel weight, lbs.

static rear wheel weight, lbs.

total weight of tractor and operator, lbs.
front wheel rolling radius, ft.

rear wheel rolling radius, ft.

drawbar height, ft.

front wheel rolling resistance coefficient,
dimensionless.

wheelbase of tractor, ft.

horizontal center of gravity of tractor, ft.
torque input to left rear wheel of MF 150 tractor,
1b. ft. (evaluated manually from calibration chart) 3
lines (deflection) of pull. ‘
lines (deflection) of weight transfer.

lines (deflection) of rear wheel Speed indicator.

lines (deflection) of fifth wheel speed indicator.

total rolling resistance of the tractor, lbs.

drawbar pull, lbs.

measured weight transfer of MR 150 tractor, lbs.

rear wheel Speed mph.

fifth wheel speed, mph.

travel reduction of rear wheels, per cent.

calculated weight transfer, lbs.

rolling resistance of front wheels, lbs.

drawbar pull and front wheel rolling resistance, lbs.
dynamic rear wheel weight, lbs.

coefficient of net traction, dimensionless.

drawbar pull and total rolling resistance, lbs.

rolling resistance of rear wheels, lbs.

rear wheel rolling resistance coefficient,

dimensionless.

travel ratio, dimensionless.

Coefficient of gross traction, dimensionless.

tractive power coefficient, dimensionless.

tractive efficiency, per cent.

 

125

 

126

 

DISK UFEIIYTNU‘KVSYEI7IIO"FDITIIfi"—_350N:FU:ISI ZI"‘-

DIHENSION DAVE!16).DLOC(7).SURFI7).DOAYE(7).T¢20).AIZOD.B(20I.CIZO
_-__ " ‘““1):DI2617PU[E120)..uttatzo).nusvotzo:.rusoo¢2o».xuspo¢20).Spr(20).
zansutzo).tunusttzoa.onuttzo».utzo).cntn5ttzo:.naau¢zo:.aunnc(2o».
BTRVRAIIZOI.UIIZOD.RURRKIZOD.PIECZO).YREFFYIZOI.CALHIR(20!
1 taunt? IIH .IZ.16|§I ‘"‘*‘ “ ‘"‘—‘"“
2 FORHA! c1¢aa.5n¢a
3 FORMAT (xx .ro.o..rs.1:
‘ b FORHAY (1H .2F..0.3F6.o.6r6.3:
D FORHAT IIHIO/I/oZOXoIbAAo/II
9 FORNAI III 0 LOCAIION IS 01.... suarnce IS '7...' test oars 'SA6./
III
to sauna: (IN .0 vs pa srut scat Stout can can can ruuac an
ILIS ccoxsr'./:
—————~—n-ruun lf.‘ velour mu Hum nusvo rusvo sup ‘ 0 MI: WW"

 

 

I UT PIE TREFFY CALUIR IAIU AURA“ “'9!!!
[2 FOAIAT II” 9336000276.).F5.Iob‘bo3oF6.OQZX.FT.D.ZI.F6.3.2!.IZI
I77 ‘5'. ' 'I ' '.F1.‘?IU!3'“!2“- 'OF’0‘977'

0
I! FOIIAI (I?!
I6 ODQIAI I257ofil

 

 

99—!!1D‘IIIII “O'DIIDATDIJIOJ'IQI‘T A
READ IIoZIIDLOCIJIoJ'IoIIoISURFIJIoJ'IoTIoIDDATEIJIoJ'IcSI
READ IIOIAI IIQXZ
III” IIO‘I IF.FI.IFIY.SIUT.SYUIY.FII.lll60l83FIllcSIRIUS?CEDISY
“DAD IIODI IIIK).A¢uI.IIKl.CCII.OCKD. ‘3IQNODSI

 

DD 5 IIIoIOIS
__—‘““—“——__—'U[ITKIIAIKI‘I‘S.
INIIIIRI-DIAIODD.
IUSPDIKIOCIII’II
0 FIS'DTKT‘DT‘IUIZ” "’“"”"""“

- q—mad_dh“~____.-_ ___

 

 

l
a,
I
I
b
i
c

 

00 6 I-I.~OIS
IISDDCII-ICRUS'OIID-IISPOCKOII IISPOIIOIOIOO.
SKI'tKl-XHS'DIII
all! III -C3¥b! - until!!!) 0 tunic
INIUSIIKII PULL!!! o IIIUCII
“‘"‘""“"‘“DIIT I!) - SUIT o‘IlTTIt!)
0‘!) - IHIUSIUIO I OIUVCID
G'IRSIIII'IIIIIIIIAIOZ.
Illhlxi - GIIRSICuI - tHIUStCII
nuanccn) . RRRuIKI I cluttni
tavaAllnl- 1.00 -(SLIPCIDIIOO.D
'UTIK) - GRYISYIKII DflhtIK)
nunnucno - VIII) - Uta!
'lEIx) - 0‘s) 0 tavnattnl
VIEFFVIK)- PIE!!! I 01‘!)
CALulaInl- Isle-t 0 CODIsI . (can -aano 0 PULttxi -(1IKIOZ.IDII
IIHLBS - (Funk; 0 (aha-fiat)!
6 cllUtIIKI-SFiI-cnthtllxl ‘“

 

 

 

IIITE I’vDI IDAIEIJIoJ'IoIOI
U‘ITE I399I IDLOCIJIoJ'IoTIc‘SUIFIJIoJ'IoTIpIDDATEIJIoJ'IOSI
bAITE I39I5I II.12
ODIIE I30IOI
“RITE I’Q" PF.Pfl.Sfut.Ska!.SVCI!.FRK.RRI.OBE.FURRC.UHlBS.CGDlSI
_TTW‘TUITTE '3OII’
KA'O
DO 7 K‘IoNUOS
KK-KKOI
7 “RITE IJoIZI IIKI.PULLIKIohHTIRIKI.RHSPOIKIoFHSPCIKIQSLIPIKI.UIKI.

IOURRCIKIoIKVRAIIKI.UIIKI.PIEIKI'TREFFYIKI.CALHTRIKIoRRRHIKI
zoR'RRKIKIoKK

i... an‘t‘IZ'lHOQ3H Iv§H 0000‘“ 1000‘"- oIo‘H I0I03H 6.93” 60'9” .2
l.«n .2)
IRIIE ((.lb) Nous

4L7 I7 FORFAT III. WIL.II
l:g;;£ I2.I7) (UIKI.TRVRATIKI.PIEIKI.TREFFYIKIoRHRRCIKI.UTIK).K=I.
I

18 FORMATIIZvIH593H IOSH-I000'6H I00000AH- .IQQH IoIv3H 60'3H 6..“H
I .204" .ZI

I9 FLKNATIIXoFbolo‘OFbo3I '

_, . HRIID (2.19) I5LIPIK).PIEIKIvTREFFYIKI.RHRRCIKloUIKI.K=I.kCBSI

READ II.I3) NEJCB
IF INEJOB‘99I 99.96.99

98 CALL EXIT
END

C—II. Computer program for analysis of 13.6—28 tire test
results (standard tractor). (a) input data, (b)
calculation of physical data, (c) transformation
into performance parameters using equations in

Section III.

 

 

 

dNM‘U‘OF-QO‘

127

000.0
50~.0
000.0
050.0
000.0
000.0
000.0
000.0
000.0
000.0
000.0
000.0
~00.0
0-.0
000.0

050.0

x0131

I'll

.00~:

.-0
.5~0
.ume
.000
.000
.00u
.000
.000
.N00
.~0~
.000
.000
.0~0
.05N
.000

31¢: 153440

.05h

.0N0

Iwn¢5

.«05
.005
.~¢5
.0~0
.~0m
.050
.uem
.000
.000
.000
.000
.0¢~
.0¢~

 

.meSQEoo map

000.0
000.0
000.0
000.0
000.0
~00.0
000.0
000.0
000.0
5~5.0
505.0
005.0
0N5.0
000.0
005.0
0¢~.0

>muw¢5

000.0
500.0
000.0
~00.0
000.0
~00.0
0~¢.0
000.0
050.0
050.0
000.0
00~.0
~0~.0
~0~.0
000.0
0~0.0

mun

Scum

005.0 000.0.
005.0 500.0
0N5.0 ~00.0
~05.0 -m.0
0N5.0 000.0
00520 000.0
m~0.0 0N5.0
500.0 005.0
000.0 005.0
0~m.0 0a0.0
000.0 000.0
~0¢.0 000.0
000.0 0~0.0
000.0 ~00.0
00~.0 000.0
00~.0 000.~
50 5<¢>¢5

pSOIchLQ mpmu
.000.0

50~.0
000.0
050.0
000.0
000.0
000.0
000.0
000.0
000.0
000.0
000.0
~00.0
0-.0
000.0
050.0

01030

md~.c.

500.0
~50.0
500.0
000.0
000.0
~0m.0
~0¢.0
0am.0
500.0
-¢.0
«00.0
000.0
0¢N.0
00~.0
0N0.0

D

5.00
0.00
0.00
0.00
0.00
0.00
0.0N
0.0N
N.0~
~.0~
5.0a
5.0a
5.0
0.0
0.0
0 0

amam

awoflsz

00Q10.000.~
0~0.~ 5«0.~
000.~ 5~0.~
~00.0 5~0.~
5mo.~ m00.~
-~.~ 050.~
000.~ 050.~
~0¢.~ 050.~
00¢.u 000.~
000.~ 000.~
000.— 000.—
000.~ n50.~
055.~ 000.~
050.~ 000.~
000.~ 000.~
5m0.~ 5mo.~
00030 00030

.HHHLQ
.QN013.00N£.
.0N0 ..0000-
.000 .0550
.0N0 .0000
.000 .0000
.0N0 .m~00
.000 .00N0
.0N5 .000N
.000 .mm5N
.000 .n0¢~
.000 .m5uN
.000 .005u
.000 .0~m~
.000 .00—a
.000 .005
.00 .0
«5511 4435

.co..
.non.

.oo~.

.o.n.

.oo~.

.mao.

.oomn

.oson

.m._n

.o~o~

.m~m~

.om-

.moo~.
.oom~

.oc-

.owm

000005

000.~ 000.0 00~.0 m0~.~ 0~0.~ N0«.~ .MNNO .0000 .m00~ .00 .0N

5m~000 00413 00030 100 00¢ «am 53050 5300 5300 at us
0000.0 n NX 0000.0 u ax
00\¢N 5000 0540 5005 0- 040—& 0400350 500 m— wotuzam ~20: ~10040 «002040 m~ 20~5<000

0‘ x 00.0 0~ x 0.0a 1050405 0m~mt 20~50<¢5 w¢~5

 

II.

III.

APPENDIX D

ANALYSIS OF SEVERAL SIZES OF TRACTOR TIRES

Page

Definitions Relating to Appendix D . . . 129
Computer Program for Analysis of Several

Sizes of Tractor Tires . . . . . . l3l

Typical Data Print—Out from the Computer . 132

128

 

   

WHLBS
CGDIST
RWRRCO

T9!-

A

B

C

D
RRTOTL
PULL
WHTTR*
RWSPD
FWSPD
SLIPRW

SLIPFW

TORQUE
CALWTR
RRFW

THRUST

DRWT

U
GRTRST
RRRW
RWRRC

ll

ll II II II

D—I. Definitions Relating to Appendix D

 

multiplier coefficient for rear wheel speed.
multiplier coefficient for fifth wheel speed.
pressure in front tires, psi.

pressure in rear tires, psi.

static front wheel weight, lbs.

static rear wheel weight, lbs.

total weight of tractor and operator, lbs.

rear wheel rolling radius, ft.

drawbar height, ft.

front wheel rolling resistance coefficient,
dimensionless.

wheelbase of tractor, ft.

horizontal center of gravity of tractor, ft.

rear wheel rolling resistance coefficient,
dimensionless

torque input to left rear wheel of MF lSO tractor,
lb. ft.

lines (deflection) of pull.

lines (deflection) of weight transfer.

lines (deflection) of rear wheel speed indicator.
lines (deflection) of fifth wheel speed indiactor.
total rolling resistance of the tractor, lbs.
drawbar pull, lbs.

measured weight transfer of MF 150 tractor, lbs.
rear wheel speed, mph.

fifth wheel speed, mph.

travel reduction based on rear wheel Speed, per
cent.

travel reduction based on fifth wheel speed,

per cent.

calculated torque input to the rear wheels, lb. ft-
calculated weight transfer, lbs.

rolling resistance of front wheels, lbs.

drawbar pull plus front wheel rolling resistance,
(net pull) lbs.

dynamic rear wheel weight, lbs.

coefficient of net traction, dimensionless.
drawbar pull plus total rolling resistance.
rolling resistance of rear wheels, lbs.

rear wheel rolling resistance coefficient,
dimensionless

 

*
Data not used in this analysis.

129

 

 

TRRTRW
TRRTFW

UT
PIERW

PIEFW
TREFRW

TREFFW

130

travel ratio based on rear wheel speed,
dimensionless

travel ratio based on fifth wheel speed,
dimensionless.

coefficient of gross traction, dimensionless.
tractive power coefficient based on rear wheel
speed, dimensionless.

tractive power coefficient based on fifth wheel
speed, dimensionless.

tractive efficiency based on rear wheel speed,
per cent

tractive efficiency based on fifth wheel speed,
per cent.

 

 

 

D—II.

 

131

DlSl OPERATING SVSTEI/Jbo FORTRAN 360N-FD-‘51 21

DIIENSION DATEIlb).DLOCITI.SU!‘I7I.ODATEIT)'T(20l.A(20’vB(20I.CIZO
I).DIZOI.PULLI20).hHITRIZOI.RhSPDIZOI.FHSPD(10). SLIPRHI 20). SL

2410 0). DROU!(20).CALHTRIZOI.RRFHI20I.THRUSTIZO) DRdTIZOI
3.0(20).GRTRSTIZOI.RRRHIIU).RhflKCIZOI.TRRTRH‘ZOI.TRRTF#(20I.UTI20Iv
6AIARKI20).PIERHIZO).PIEFHIZOI.TREFIHIZO).TIEFFH(20)

.1)
A FURNAT IIXOZFA. U.SFA. 0' TEA. 3’
U FORMAT ‘lHlo/IIoIUXI16A4/II
' ‘ofluAT (II. LOCATION Is :7A§" SURFACE IS 'TAzo'TEST DATE 'SAA'III
E0 FOIIAYIIX.' '5 PR SFUT SIHT STOUT FIR DBH FHRRC HHLB
IS CGDIST IUIICO")
AI EOKIATIlXo' PULL RHSPD E050? 5LIPRH SLIPFN TORQUE CALHTR U
IRIAKC TIRTRH TRRTEE UT PIERU PIE'H TREFRH TREFFH N'I/I
ll EORHAT IIXI15600.2Fbo392F6.I.ZF9.019F6.3'2X0I2)
l3 FOIIAT ‘12
IA 'OAIAT ‘2‘10"
IS FOIRAI ‘I/ol’lo. I! I 'oFToAgloXo. X2 ' '0‘7qu//’
99 READ IIOII “0551‘DATEIJ’0J'I'I6’
READ (1.2) TOLOC‘J’0J=I'7"ISU§F‘JI.J'Ip 7’.IDDATE(J"J'lv5,
READ ‘Ell.’ ll!
READ ‘E'.’ 'fo':oSFIT'$RIT|STOUTt'I‘olflluoaflvFNIRCvUHLBS'CGOISTO
1"“. £0
.EAO ‘10,) ‘T(:"A“’o.‘I'QC‘K:QDE‘I'KIIINOBS’
lulu Tl '5' IT FIRKC 0 SR'T0Rfl MC
wb‘ll'm
'ULLIK) ' AIII.IA5c
UNT’I‘I’ ' .‘K’..°o
IISPDIII ' C“'.ll
'US'D‘AIID‘IE.X2
SLIPQIIK) ' 9h..IIISPU‘II - RUSPD‘KII/KHSPOII)
SLIPOIIK) I 90.:‘EISPC‘I, ' flSPD‘:DI/'ISPOIII
TORQUE‘I’ I IPU LII) 9 “REUTl I.
CAL'T‘E" - S" “STOUT.CGDIST 0 I22“- DBNIUPULLIKI- TORQUE‘I)’

TIlTRuIK) I [.00 -|SLIPR:Ill/I00.l
TRITFIIK) - .00 -ISLIPFIIK)IIOO.I
UTIKI I uITlpl(KIIDRhT‘II

Allik“) l UWIK I U

'IEIIIAI ' U“II.T;ITIIIK)

 

UNITE I309, IDLOCEJ'IJ'E:TI:‘SURFIJIoJ'loT’vIDDATEIJ’vJ'leI
“I E ‘,015' Ali]:

‘ITE (391°,

IRITE ‘30A’ 'Fo'l.SFIT-SRHTvSTOhT.FIA.RRR.OBH.EIRHC.HNLBS.

I CGDISTcfliiRCO

“RITE [3711)

I i 0
00 7 I I I.NDIS

KI I ll 9
7 HRITE ‘5.IIIPULL(K)IRISPDIKlvFISPDIKI'SLIPRVIKI.SLIPFHIKIV
l TDIOUEIK).LALITR(K)IU(KI. RHRRCIKI.lRRTIHIKIoTRflTFIIKIy
2 UT“I.'IEKI‘KI.'IEFIIKIoTREFKHIKI'TREFFUIKIpKK
I. FORRAYIIZ.IN6.3M lp‘H Co°v§H 1000‘“- olv‘N Tole," 6.03" 600‘" .1
I

hm O
RITE (2.16) NOBS6

I? FORMAT (IX. .3)
IRITE (2.17) (UIKI.TRKTFhIK).PIEFIIKIpTlEFFh(Kl.RHRRCIKI.UTIKI.KII
I. I0.

I. FORNATIItulNSvlfl IvSh-lO-Opbfl 100.0.£N- .|.6H 1.1.3” 6.93“ 6.9‘"
0 Q 0
19 FORMATIlloFo. Itha
“RITE (2.19) ISLIPF:(K).PIEkulK).IREFFU(KI.RHRRCIK)vU(KIvItI.NOBSI
KEAD (I.I3l NEJUB
IF lNEJOB-99399.96.99
98 CALE EXIT

Computer program for analysis of several sizes

of tractor tires. (a) input data, (b) calculation
of physical data, (c) transformation into perform—
ance parameters using equations given in Section
III.

 

 

132

 

 

000.0 000.0 000.0 000.0 000.0 450.0 000.0 500.0 000.0 .NONd .00000 0.N0 0.50 ~00.0 NNu.u .00—0
4u0.0 040.0 ~50.0 N~0.0 000.0 000.0 400.0 500.0 005.0 .0004 . .0uN0u N.00 0.00 040.0 500.4 .0500
~00.0 050.0 000.0 0‘0.0 400.0 000.0 0~0.0 500.0 000.0 .0-~ .0000n .0.00 0.00 0-.~ 000.4 .0000
000.0 050.0 400.0 000.0 000.0 000.0 0N0.0 000.0 ~55.0 .0N04 . .500Na (0.00 ~.50 u~0.< ~00.~ .0000
000.0 ~00.0 000.0 000.0 0N0.0 ~00.0 000.0 000.0 ~05.0 .0004 .-5~4 0.00 0.00 500.~ 000.~ .0000
0—0.0 500.0 000.0 000.0 500.0 000.0 000.0 000.0 005.0 .~00~ .0000u 4.00 0.00 0~N.~ 000ou .0000
000.0 000.0 ~00.0 0~0.0 000.0 ~00.0 000.0 500.0 0~0.0 .0004 ..5~500 0.00 0.00 000.4 ~N0o~ .00N0

-oa0ut¢-0o~coo-0w-°UF‘0|D
fldO-‘ado-IF‘

000.0 050.0 000.0 ~00.0 405.0 000.0 ~05.0 000.0 005.0 .000 .500Nu 5.00 0.0N ~50.~ 050.0 .0000
~05.0 0N5.0 0~0.0 000.0 005.0 000.0 000.0 000.0 000.0 .000 .0000~ 0.0~ 0.0a 050.~ «00.~ .0~00
~05.0 ~05.0 000.0 000.0 000.0 400.0 0N0.0 000.0 000.0 .NNO .~0~0~ 0.04 0.0~ 000.0 500.~ .0550
005.0 005.0 050.0 040.0 500.0 000.0 050.0 000.0 400.0 .005 .0050 0.00 5.~4 050.4 000.5 .0000
505.0 000.0 0~0.0 000.0 000.0 000.0 ~00.0 000.0 000.0 .000 .5005 «.04 0.5 0~0.~ 05~.N .0055
000.0 000.0 00N.0 ~00.0 050.0 000.0 ~50.0 000.0 040.0 .000 .00N0 0.0 0.~ . ~0N.~ 000.~ .000—
N05.0 ~05.0 00~.0 00N.0 N~0.0 N00.0 ~00.0 000.0 00N.0 .000 .0N00 0.4 0.0 500.N 500.N .0004
050.0 050.0 500.0 500.0 0-.0 000.~ 000.~ 000.0 500.0 .50" .000~ 0.0 0.0 000.N 000.N .0

2 300005 300005 300—0 300—0 5: 305005 305005 00030 0 051400 000005 300~40 300040 momxu 00030 4409
N00.0 000.0 050.0 ~00.0 000.~ 00~.~ 00N.~ .0000 .0000 .0050 .0~ .05

ouxaxx hm.aou mo4zz uxazu :oo «ca «an pzohm hzam .30m «a an.
ammo.o » ~x mmoo.o . 0x

00500 5500 0500 5005 (N4 040—0 0400050 500 0— 0000000 4200 ~00040 0042040 0— 20—50004

04 x 00.5 00 x 0.0a 005 0000 20_50005 0005

 

II.

III.

IV.

APPENDIX E

CALCULATION OF DRAWBAR PERFORMANCE
OF OTHER TRACTORS BASED ON THE

STANDARD TRACTOR

Definitions Relating to Appendix E

Traction Characteristics of the Soil as
Determined by the Standard Tractor

Computer Program for Calculation of Drawbar
Performance of Other Tractors Based on
the Standard Tractor

Typical Data Print—Out from the Computer

133

Page
134

135

136
137

 

 

 

PF

PR
SFWT
SRWT
STOWT
FRR
RRR
DBH
FWRRC

WHLBS
CGDIST
RWRRCO

FWSPD
U

SLIP
DRWT
DFWT
THRUST

DBHP

E-I. Definitions Relating to Appendix E

 

pressure in front tires, psi.

pressure in rear tires, psi.

static front wheel weight, lbs.

static rear wheel weight, lbs.

total weight of tractor and operator, lbs.
front wheel rolling radius, ft.

rear wheel rolling radius, ft.

drawbar height, ft.

front wheel rolling resistance coefficient,
dimensionless.

wheelbase of tractor, ft.

horizontal center of gravity of tractor, ft.
rear wheel rolling resistance coefficient,
dimensionless.

forward speed at zero pull, mph.

corrected coefficient of net traction,
dimensionless.

travel reduction (from standard tractor curve),
per cent.

dynamic rear wheel weight, lbs.

dynamic front wheel weight, lbs.

drawbar pull plus front wheel rolling resistance,
lbs.

drawbar horsepower.

 

13A

 

135

 

 

.LOQoMLp Upmpswpm

osp mp ooQHEhopoo mm HflOm map 00 moapmflgopomhwco QOflpowa

o\o zoioaomm 4m><E
00 O5 00 00, 0+» 00 ON 0_ O

 

 

 

 

 

 

_ 14 _ fl _ 0 _ a O
\ N \K \N
\\ \ \ \ H88 93.
am he 90 9.19% 2:9 t 28:38 L N
O J8 0% 9 nc
/ v oi 01 0v
ow $0 .... %y Am].
04 ... 02/ p» m,
a, o a» fl.
1..
”no .00 1 v.
9//. 8
,m «o.
0
0//
44
35:0“; mm to
30:05 8.60 ‘ \ 1 m.
22-29 .32Ev m. to
36:0“: N200 \\\ 5:8:
5: o €22 mo
E329 o to 0 t o

 

6.829 MN .68 L m,

.HHlm

 

136

DISK OPERATING SYSTEM/360 FORTRAN 360N-FO-451 21

IMENSION DATEI16)oDLOC(7)oSURFI?)gDDATE(7),U(20)oSLIPIZO)o

D
DRHTIZO)aDFHT(20)oTHRUST(ZO)yRRFHIZO)9PULLIZO),DBHPI20)

IHHTTRIZO).

1 FORMAT (1X012916A4)
2 FORMAT (14A4o5A4)
3 FORMAT (1X9F6.4¢F6.3)
4 FORMAT I1X¢ZF4.0.3F6.0.7F6.3)
8 FORMAT (1H1o/llo20X916A4a/I) A

9 FORMAT (ll' LOCATION IS '7A4o' SURFACE IS '7A40'TEST DATE 'SAkt/l)
10 FORMATIIX.’ PF PR SFHT SRHT STOHT FRR RRR DBH FHRRC HHLB

IS CGDIST RHRRCO'l)
11 FORMATIIX.'HHHTTR DRHT THRUST RRFH PULL DBHP SLIP U N'/’)

12 FORMAT IIX.5F6.092F6.2.F6.3912)

13 FORMAT I12)
14 FORMATIFbo4)

99 READ (191) NOBSoIDATEIJ)vJ=1916)
READ (1.2) (DLOCIJ).J=1.7).(SURFIJ)oJ=197)oIDDATEIJIoJ=195)
READ (1.4) PFcPRoSFHToSRHTgSTOHT,FRRgRRRgDBH,FHRRC.MHLBS¢CGDIST9

IRHRRCO
READ (1.14) FHSPD
READ (1.3)(UIK). SLIPIK) gK=loNOBS)

DO 6 K = IQNOBS
HHTTRIK)=(IRHRRCO*RRR + DBH*U(K))lIHHLBS-FHRRC*IRRR-FRR)

I ‘IRHRRCO*RRR) ’ DBH*UIKI))*SRHT
DRHIIK)= SRHT +HHTTRIK)
b DFHTIKI =$FHT 'HHTTRIK)
THRUSTIK) =DRHTIKIFUIK)
RRFHIKI =DFHTIK)‘FNRRC
PULLIK) =THRUSIIKI'RRFNIKI
6 DBHPIK)= PULLIKIFFHSPD‘II'SLIPIKIIIOOoI/37So
“RITE I398) IDATEIJIOJ31916I
HRITE (309’ IDLOCIJIOJ‘ItT)oISURF‘JIQJ'191I.IDD‘TEIJ’OJ'IOSI

HRITE (3910)
WRITE I394) PFQPRQSFHTvSRHTQSTOHTOFRRQRRRoDBHQFHRRC0HHLBSO
I CGDISIQRHRRCO
HRITE (3911)
KK = 0
DO 7 K = IoNOBS
KK = KK * I
7 HRITEI3vIZ) HHITRIK). DRHIIKIQ THRUST‘KIcRRFHI‘IO'ULLIKIQDBHP‘K’Q
ISLIPIKIvUIKIvKK
READ ‘1913’ NEJOB
IF INEJOB‘99I99v98999
98 CALL EXIT
END

E~III. Computer program for calculation of drawbar
performance of other tractors based on the
standard tractor. (a) input data, (b) calcula—
tion of drawbar performance using assumptions
and equations in Section 6.M3.

 

7.
3
l

 

 

.popSQEoo map 809% @501pcflhm dump HwOHazB

mm~oo o~.~¢
mmooo ooomw
mmm.o o~.o~
mmtoo Oh.N—
mmn.o omoo
mm~oo ooo~
anaoo oo.a

ANMOMOF

D a—gm

z
Noooo 09m.m o~¢.o ~00.o 00m.~ oo~.~ m¢Noa .ow¢o

001131 hmuoou mmJIJ uaazu xmo

.00\0~ificww whdc hmwh (Na cam—u wamoabm #40 m— wu<u¢3m

o— x omoh on x «.oa

.>HLm
oo.o~ .fimo¢ .mmN .aao¢ owooo .Noo
mocha .ommm .~o~ oom—¢ o¢¢mo o¢wo
~N.O~ .~m~m .o- .~n¢m o~—¢o o-h
amom— o¢¢¢N .~ON ocflhw .OQNO .OOm
m¢ood .mohd .Nom .moo~ oeodo .¢h¢
mace coaud oNgm on~¢u .hcoo chmn
doom cop: omNn odon .¢mom oeeN
QIQO 443$ lama hmnxth h3g0 abhrsl
.OOOm oo¢hm o¢_ oON
mam dam plohw Flam hlwm do us
~ZD¢ .xUDJQ (wJZwJO m~ ZO—h<904

om~ wm<u 20~huddh wmnh

 

 

 

 

 

3,9 ,

 

 

 

'. ‘ 9 '. 5‘
3’1Q‘fl5?§ [:2 37F?! F: “fig? M 1:; gr;