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MEASUREMENT AND- ANALYSIS OF SOIL
PRESSURE DISTRIBUTIW UNDER TRACTOR
AND IMPKEMENT TRAFFIC IN AN
ARTIFICIAL FIELD

Theda fee The Dogma mi M. 5.

MICHIGAN SYATE UNIVERSITY

Gian Edwin Vanden Berg
1956

......

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1HESI§

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

3 1293 00076 5291

 

 

 

‘bvisSIUJ RETURNING MATERIALS:
PIace in book drop to
LIBRARIES . remove this checkout from
.—:—. your record. FINES WIII
~ — be charged if book Is
returned after the date
stamped below.

 

 

 

 

 

 

.IEASIIRSICLCNT AND AI‘GAIVSIJ OF SOIL PIIISSSURE
iDlSTRIBUTION UNDER TRACTOR AND JNPLEhENT

TRAFFIC IN AN ARTIFICIAL FIELD

by

Glen Edwin Vanden Berg

AN ABSTRACT

Submitted to the Nichigan State University of
Agriculture and Applied Science in Partial
Fulfillment of the Requirements

for the Degree of

MASTER OF SCIENCE

Department of Agricultural Enfiineering
Year 1956

Approved by NLL) 0% m - W ._ .... _M.- -

3~S’Lo

TH 5515

 

Glen Edwin Vanden Berg

AN ABSTRACT

Twelve strain page pressure cells (transducers) were
built to make soil pressure readings under traffic in Nau-
mee sandy loam soil. The traffic was provided by a plowing
demonstration which was part of Powerama staged by the Gen-
eral Motors Corporation in Chicago, Illinois, from August 51
to September 25, 1955.

The cells were placed at various depths in the soil per-
pendicular to the direction of travel, and pressures were
recorded with a six channel, direct-inking recording oscillo-
graph. The necessary measurements to locate the cells with
reapect to the tires of passinc tractors and implements were
made and recorded on the oscillocraph charts. Contact areas,
weights, pull of implements, and other necessary information
were measured to enable calculation of loads carried on each
tire or implement.

The data from the charts was put in tabular form using
only the maximum “ressure readinas for each cell durinfi each
pass. It was assumed that the maximum pressure occurred un—
der the center of the tires. On the basis of this assumption,
the maximum pressure readinns for the same tire were plotted
on a graph representing pressure versus depth. A smooth curve
was drawn throuflh the points and called "center of tire."

The readings of cells adjacent to the cell indicating a maxi-

.um reading were averaged and plotted on the same graph as

mentioned above. The smooth curve drawn through these points
represented the pressures 0.4 of a foot from the center of
the tire since that was the spacing of the cells. This was
continued until zero pressures were encountered with average
readings from each pair of cells determining a curve repre-
senting pressures at the same distance from the center of

the tire as were the cells. This was done for each tire
where pressures had been measured over a large enough span

in depth to permit drawing good curves from the contact sur-
face to the depth of soil at Powerama.

Values from the averaging curves were then used to deter-
mine isobars under the tires. The resulting family of iso-
bars gave a good visual picture of the distribution of
pressure under the tires for the given soil conditions at
Towerama. A formula develOped by Froehlich and applied to
soils by Soehne was used to calculate theoretical pressures
under the center of the tires. These pressures were compared
with measured pressures.

The following indications for the conditions at Powerama
seemed true: greater pressures were transmitted through loose
soiksthan through dense soils; the lugs on the rear tractor
tires carried the majority of the rear tire load even in
freshly plowed soil; the plow bottoms applied a small nega-
tive pressure to the soil; the peak pressure under a tire

always occurred ahead of the wheel's axle; applying a load

in small scattered areas <ihi not cause as much pressure in

the soil as applying the same load in one area.

0]

MEASURELENT AND ANALYSIS OF SOIL PRESSURE
DISTRIBUTION UNDER TRACTOR AND II-‘PIEI‘I’ENT

TRAFFIC IN AN ARTIFICIAL FIELD

by

Glen Edwin Vanden Berg

Submitted to the Michigan State University of
Agriculture and Applied Science in Partial
Fulfillment of the Requirements

for the Degree of

MASTER OF SCIJNCE

Department of agricultural Engineering

1956

A CK N OLI'L {EDGTT EN T

The author wishes eSpecially to thank Dr. Jalter R.
Carleton under whose guidance and leadership this project
was carried out. The author also eXpresses his sincere
appreciation to Professor H. F. McColly for his assistance
and to Dr. A. N. Farrell who approved the assistantship
that made this work possible.

A special vote of thanks is also due kr. A. W. Coorer,
who helped with the measurements and analysis of the data
presented here. His efforts contributed immeasurably to
the completion of this work. The author is grateful to
Offner Electronics, Inc., of Chicago, Illinois, who loaned
the recording equipment which aided the work immensely.

The efforts of Kr. James Cawood and his staff, who assisted
in building the pressure cells, are sincerely appreciated.

A sincere thank-you is extended to the author's wife,
Phyllis, who typed and helped edit the thesis and whose loyal
support was given throughout the work. The author wishes to
thank all the others who contributed in any way to this work,
especially those connected with the plowing demonstration

of the General Motors' Powerama.

TABLE OF CONTENTS

Tit l2 ' Ease.
Introduction ------------------------------------------- 1
Review of Literature ----------------------------------- 5
Description of equipment ------------------------------- 5
Procedure ---------------------------------------------- 9
R e s u l t s ----------------------------------------------- l 5
Pressure Distribution Under Tractor Tires ---------- 22
hagnitude of Pressures in Loose Soil --------------- 35
Effect of Lugs on Rear Tire ------------------------ 55

Location of Point of Maximum Pressure with

Respect to wheel Axle ------------------------------ 59

Pressures Under Plow Bottoms ----------------------- 42
Conclusions ------------------------------------------- 44
Recommendations for Further Studies ------------------- 45
Literature Cited -------------------------------------- 47
Other References -------------------------------------- 47
Appendix ---------------------------------------------- 49

ii

IIST OF FIGURES

 

Page
Half aperture Angle Under a Circular Load ------------ 4
Type A Soil Pressure Cell ---------------------------- 6
Offner Dynograph Hecordin: Assembly ------------------ 7
Replacing Noisture Lost from the Soil --------------- lO
Compacting the Soil with Sheeps-Foot Tamper --------- ll
Smoothing Surface with Pneumatic Tired Roller ------- 12
Placing Cells to Wake Pressure Readings ------------- 15

Recordinn Soil Pressures Under Tractor and Plow -----14
Sample Data Page ------------------------------------ 16

Pressure Distribution Under Front Tractor Tire
in Dense Maumee Sandy Loam Soil Placed on Paving ----25

Pressure Distribution Under Rear Tractor Tire in
Dense Maumee Sandy Loam Soil Placed on Paving ------- 26

Isobars Under Front Tractor Tire in Dense Soil
Placed on Paving .................................... 28

Isobars Under Rear Tractor Tire in Dense Soil
Placed on Paving ---------- - ------------------------- 29

Comparison of Theoretical and Measured Pressures
Under the Center of the Front Tractor Tire ---------- 52

Comparison of Theoretical and Measured Pressures
Under the Center of the Rear Tractor Tire --; -------- 34

Pressure Under Front Tractor Tire in Dense and

Freshly Plowed Naumee Sandy Loam Soil Placed on
Paving ---------------------------------------------- 36

iii

17.

LIST OF FIGURES (continued)

Pressure Under Rear Tractor Tire in Dense and -
Freshly Plowed Maumee Sandy Loam Soil Placed on

Paving ---------------------------------------------- 57
Weight Distribution of Tractor Under Static

Conditions ------------------------------------------ 49
Weight Distribution of Tractor While Plowing -------- 50
Tire Contact Area ----------------------------------- 51

Circular Curve Representing Drum of Sheeps-Foot
Tamper ---------------------------------------------- 52

iv

II.

III.

IV.

VI.

VII.

VIII.

IX.

LIST OF TABLES

Page
Summary of Loads Carried, Contact Areas and
Pressures Measured in Naumee Sandy Loam Soil
Placed on Paving -------------------------------- 18
Soil Pressures Detected Ahead of and to the
Rear of the Tractor Axle While the Tractor
Was Moving Over the Soil ------------------------ 41

Pressure Cell Readings Under Front Tractor
Tire in Dense Sandy Loam Soil Placed on Paving --54

Pressure Cell Readings Under Rear Tractor Tire
in Dense Sandy Loam Soil Placed on Paving ------- 55

Pressure Cell Readings Under the Center of
the Front Tractor Tire in Freshly Plowed
Maumee Sandy Loam Soil Placed on Paving --------- 56

Pressure Cell Readings Under the Center of the
Rear Tractor Tire in Freshly Plowed Maumee
Sandy Loam Soil Placed on Paving ---------------- 56

Theoretical Pressure Distribution Under the
Center of the Front Tractor Tire ---------------- 57

Theoretical Pressure Distribution Under the
Center of the Rear Tractor Tire with 5.00"
Radius ----------------------------------- -- ----- 58

Theoretical Pressure Distribution Under the
Center of the Rear Tractor Tire with 5.16"
Radius ------------------------------------------ 59

Summary of Static Loads, Loads Carried, Pull
and Semi-Axes of Contact Areas for Tractor and
Implement Tires --------------------------------- 60

INTRODUCTION

With the development of a strain page cell (transducer)
for measuring pressures in soil (2)1, techniques and methods
for using the cell were needed. Particularly in field appli-
cations, the procedure for usina the cell and analyzing
data collected with the cell was not established. A rare
Opportunity to develop these procedures as well as partially
investigate the distribution of pressures in soils was pre-
sented when the General Motors Corporation staged its 26-
day Powerama in Chicago, Illinois from August 51 to Septem-
ber 25, 1955. The Powerama consisted of a technoloaical
circus, and exhibits and demonstrations of every application
for which General Notors produces diesel engines.

One of the many exhibits was the plowing demonstration
put on by the Detroit Diesel Engine Division of General
Motors and the Oliver Corporation. hey imported 14 train—
car loads of Laumee sandy loam soil which was placed at
Powerama in an area approximately 286 feet long and 60 feet
wide to a depth of about 15 inches over the central 40 feet
of width. This soil was plowed, moisture added if lost

durinc plowina, and recompacted to orininal bulk density on

-- *0-

 

“ A. -
'— ._..—-.—.—- .—-—-“--—.—~ “~- ...._-—.-.—- o—---

1. Numbers in parenthesis refer to references listed
in literature cited.

CO

the average of approximately 11 times a day for the 26 days
of Powerama.

Pressure readings were made under all traffic in this
artificial field. In this thesis the methods and tedhniques
used at Powerama and the analysis of the data collected there
will be presented. Wherever possible, the results of the
analysis will be compared with Soehne's (1) theoretical

observations on pressure distribution in soil.

(fl

REVIEH OF IITERATURE

Althouph much work has been done dealing with various
aSpects of the soil such as NcKibben (5), Nichols (4)(5),
and Baver (6) have reported, very little is available on
distribution of pressure in the soil. The primary reason
:for this has been the lack of a physical means of measuring
3 oil pressures .

Soehne (1) took cmperical formulae that had been
<ieveloped by Boussinesq and modified by Froehlich to calculate
‘theoretical pressure distribution in the soil. The formulae
<3f Boussinesq were developed for use in an isotropic homo-
ggeneous body which obeys Hooke's law. Froehlich modified the
:formulae for use with a plastic body similar to the soil.

Some of the theoretical observations by Soehne are:

l. The more pliable a soil the more concentrated,
will be the compressive stresses towards the center.
This is primarily due to the lateral giving way or
flowing of the soil from under the load. Thus we would
expect greater pressures transmitted through a pliable
soil than through a dense soil.

2. In a dense soil the pressure bulbs or isobars
tend to be circular whereas in a more pliable soil the
isobars will be slender and reach farther down.

5. Pressure at a point in soil is determined both

by the magnitude of the unit pressure applied and the

area over which the unit pressure is applied. Thus if
the same unit pressure is applied over one area twice
as large as another, there will be more pressure under
the larger area at a given depth than under the smaller
area.

4. The difference in pressure under a luv of a tire
and the slots between lugs would be slight in a pliable
soil.

5. Under a circular load surface in a dense soil,
the pressure under the center of the load at a certain

depth is given by the formula

C\z': F%(?~Cosqafl

where:

Ci? 3 pressure at a point in the soil

f%,: average pressure applied to the surface
of the soil

cg : the half aperture angle of a circular
cone with its apex at a point under the
center of the load and where the base of

the cone is the circular load itself, as

illustrated in Fig. l.
I p
i

v
I .-. --

- -.ll_,l)/il~_iaaai.l_
3 I
\ 'a/
\§:/fl\

Fig. 1. Half Aperture Angle Under a Circular Load

DESCRIPTION OF EQUIPMENT

Twelve strain gage pressure cells of the type designed
by the Agricultural Engineering Branch, Agricultural Research
Service, U.S. Department of Agriculture, and the Agricultural
Engineering Department of Michigan State University (Fig. 2)
were built to make the pressure measurements. Each cell had
two SR-4 strain gages (type A-lB) cemented to the underside
of the 0.025 of an inch thick stainless steel top. The
strain gages used were l/8 of an inch in length, 120 ohms
in resistance and had a gage factor of 1.75. Two more gages
of the same lot were cemented to the sides of the brass body
of the cell to complete the wheatstone bridge.

This arrangement provided perfect temperature compensa-
tion. Thirty feet of four wire rubber covered shielded
cable was connected to each cell. Breakaway connectors
(Cinch-Jones series 400) were placed in the cables approxi-
'mately 25 feet from each cell to protect the recording
instrument in case the Cells were caught by the plow.

Each cell was individually calibrated in a water pres-
sure chamber usinn a Young strain indicator to record strain.
£1 mercury manometer was used to record pressures in the
Vvater chamber. each cell was calibrated in increments of ten
11p to 60 inches of mercury. This was repeated three times

I?or each cell and an average computed. A calibration curve

 

 

 

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i BRASS FITTING
WITH TAPERED THREADS

SOLDERED

‘SHIELD SOLDERED

’“‘“ TYPE A-l8 5R—4
STRAIN GAGES
CEMENTED To

STAINLESS sTE'EL.

COVER AT 90° TO EACH

OTHER AS NEAR CENTER

AS POSSIBLE

 

 

 

AND SOLDER

 

asa—
DETAIL. oF MODIFIED
STANDARD BRASS FITTING-

FIG. 2
TYPE A SOIL PRESSURE CELL

SCALE-ACTUAL. SIZE;
Aueus‘r I955
mac qt bail

 

 

 

was plotted for each cell with strain in the metal

(,a. in./in. x 10) on the ordinate and pressure (psi) on the
abscissa. These calibrations were linear for each cell
within a range of O to SO'psi. Two of the cells were later
calibrated up to 60 psi and found to be linear to approxie
mately 50 psi.

A six channel direct-inking recording oscillograph *

was used to make all pressure measurements at Powerama.

 

Fig. 5. Offner Dynograph Recording Assembly

7.. - .. w .. - ._. —. ...—... --«< - , .. * _—.V- -‘a - a... ._ — -2 —.- _ a ‘5‘...-

* The oscillograph was a six channel Dynograph Record-
ing Assembly loaned to this project by Offner Elec-
tronics, Inc., Chicago, Illinois.

The instrument was calibrated according to the formula:

C __ / fl? é? . f“;

N - I. ) .)) }_ ,_
S : indicated strain ,xx in./in.
R ::resistance of active gage
Rc::resistance of calibration resistor
N ::number of active gages
GF ::gage factor
171th the strain gages used in the cells, the formula reduced

to: s: 406» /Zo _.

g. Lia-(500,000 :55) - //5/c¢/:)7./)')L
lflie instrument was calibrated so that each line of the chart
zeepresented five xx.in./in. strain in the metal. With thts
calibration, each line represented approximately 0.25 psi;

liowever, this varied sliphtly for each cell.

C3

PR OCEDURE

The plowing demonstration was conducted as follows:

An Oliver Super ‘39 G122 tractor'was used to pull a .6 bottom
16 inch plot: which plowed an 8 feet strip with each pass.
The center 40 feet of the artificial field were plowed in
five passes which took less than five minutes. After the
soil had been plowed, another Oliver Super 99 GB: tractor
pulled a BOO-gallon capacity high pressure sprayer which
replaced any moisture lost during plowinft. The same tractor
then recompacted the soil to its original bulk density by
first pulling? a 38-inch diameter sheeps-foot tamper and then
a pneumatic tired roller.

To make the pressure readings, six of the cells were
buried at the same depth, spaced 0.4: of a feet apart on cen-
ter, and in a line perpendicular to the direction of travel
Of the traffic. The cells were placed five times durinp; the
25 days of Powerama, always below depth of plowing. Three
of the locations were with the cells resting on the pave-
ment and the remainins two were suSpended in the soil. These
plaeements were distributed periodically throughout the
dol'I'lonstration, the times being: approximately the beginning,
middle and end. During the intervals en readings were not
being made, the cells were removed from the soil. Large
010213 were carefully avoided when covering: the cells and the

305-1 was packed as tirthtly as possible by tampinrtti‘lith feet.

10

Except for one location, a cycle of the plowing demonstra-
tion was completed before readings were taken.
To obtain pressure measurements at less than plowing
ciepth, the cells at three of the previously mentioned loca-

'tions were placed so that one dead furrow during the plowing

<1peration was over the center of the cells. On the next

 

Fig. 4. Replacing Moisture Lost from the Soil

338433 this permitted the front and rear wheels of the tractor
Puhninp; in the furrow to pass over the cells with as little
‘is one inch of soil between tires and cells. To obtain pres-
3111%: measurements at maximum soil depths, the cells were

:pldiced on the remaining two locations so their center line

ll

fell under tractor's wheels not in the furrow. By this

-arrangement it was possible to make pressure readings under

 

Fifi. 5. Compacting the 8011 with Sheeps-

(7

foot Tamper

tlme front and rear wheels of the tractor while plowing at
shallow as well as deeper depths.

Pressures were also recorded under the wheels of the
lilcmm and plow bottoms. Pressures were recorded under the
fr Ont and rear wheels of the auxiliary tractor while water-
11191. tamping and rolling and under the sprayer wheels, tamp-
1135: feet and roller wheels. During each location of the

cells, several plowing demonstration cycles were followed by

12

recording pressures under all traffic that passed over the
cells.

When the cells were placed for a series of recordings,
the distance to the cells from the inside of the fence sur-
rounding the demonstration area was measured with a steel
tape. On each pass over the cells by traffic, a measurement
was taken from the fence to some reference point of the
passing implement. In the case of plowing, the furrow wall

was the reference point and all wheels were located with.

 

Fig. 6. Smoothing Surface with Pneumatic
Tired Roller

respect to the wall. In watering, tampinfi and rolling, the

13

center of the outside tamper foot or roller wheel nearest
the fence was used.

It was observed that the depth of soil above the cells
changed during every demonstration cycle. Therefore the
total depth of soil was measured after each demonstration
cycle had been completed. The depth of soil, distance to
reference point, wheel identification, direction of travel,

and other necessary remarks were recorded directly on the

 

Fig. 7. Placing Cells to Make Pressure Readings

oscillograph chart.
A small hydraulic cell dynamometer was used to deter-

mine the average force required to pull each implement.

l4

Necessary distances were measured to enable calculation of
weight transfer during each Operation. The Oliver Corporation
provided the total weights of the tractors and implements

as well as the weight on each wheel of the tractor. The con—
tact area between the ground and the tires and tamper feet

and ground were measured as accurately as possible.

 

Fig. 8. Recording Soil Pressures Under
Tractor and Plow

RESULTS

To facilitate handling, the data recorded on the charts
was put in tabular form (Fin. 9). Only the values indicated
by the maximum deflections of the pens were recorded in the
tables. The weight transfer from front to rear wheels of
the tractors and individual loads on each wheel and imple-
ment were calculated for each Operation. The average amount
of water in the Sprayer tank was used in calculating the
total weight of the Sprayer. In the analysis, each front
wheel and each rear wheel of the tractor were assumed to
have the same weight for each given Operation.

Except for the rear tractor tires, all wheels were as-
sumed to have an elliptically shaped contact area. Soehne (1)
also made this assumption in his analysis. In dense soil
such as was the condition of the soil while plowing, the lugs
on the rear tire did not penetrate the soil enough to allow
the slots between the lugs to touch the soil. Consequently,
only the portion of the lugs of the rear tires in contact
with the soil was considered as contact area. The contact
area varied so much for the tamping and rolling operations
that it was impractical to try to obtain these areas. In
the analysis the average unit pressure applied by each tire
or implement was calculated by dividing the load carried by

the contact area. A summary of this information is presented

l6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 9.

Sample Data Page

 

 

 

 

7; C)Lm/i rlél
(TVCLCIOK from?” WhPEU
TEST CELL lCHART PRESSURE CENTER POSITION DEPTH OF I
NUMBsR NUMBER READING OF TIRE OF CELLS selt Asova
(div) (psi) (ft.) (ft.) CELLS
‘ (in.)
SEE/ES 3 9/04/15"
11: I O O /‘i~8£3 /0,0
2 O O
7 o 0 L32 1.
i 8 ’ 4 [.0 -92L
9 // 2,4 :JaL
/0 l5 3-3 .1 EL
III / o i o /é.57 43/? 3.0
2 28 7‘7 .esfi
7 85’ i 20.6 .37L
£3 %_ CD I C3 '77’é_ _4
9 3: O O 1 g
/o o 4 o If
t“* r‘ ~ ~r~wi~~~o~ ——-~. »—7»~ .—.~L.~ .. -_a%
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-._‘ __ ... _.._..__ _,__._-_._-_i,e_. .. i. ..-i .... .....i
L_. -e,._._,_._.._..._____._... _ _____-_..l_. __..__s

 

17

in Table 1.

Most of the items in the summary table are self-explana-
tory; however, additional information about some items seems
necessary. The major and minor axes of the elliptical con-
tact areas were measured as accurately as possible, but the
contact areas may not have been exactly elliptically shaped.
Also the contact areas were probably varying considerably
throughout the tests. This was esrecially true when the
soil was loose. Consequently the contact areas can only be
considered as close estimates. It should be noted that the
contact area of the rear tire while watering contains lug
area plus the area of slots between lugs whereas the con-
tact area for plowing consists only of lug area. For the
sheeps-foot tamper and the straight wheeled roller, the
total area of the implements in contact with the soil was
used as contact area.

The pressures in the soil under the tires were average
values ten inches below the centers of the tires. Where
possible the values were taken from curves: otherwise a
statistical average was computed. The average pressure under
the tamper feet was determined by averaging all the cell
readines recorded under the feet. The maximum pressure was
determined by averaging the largest single pressure reading
for each pass over the cells. Under the straight wheeled
roller, the average of all readinés was usea.

To try to get some means of comparinp the different

18

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19

tires and loads directly, a ratio of load on tire to mea-
sured pressure ten inches below the center of the tire was
calculated. The ratio was obtained by dividing the load on
each tire by the measured pressure. This ratio may not seem
to be of much value since it is not a true dimensionless
ratio. However, recalling that pressure in the soil at a
point below the center of a load is determined both by the
magnitude of the load and the area over which the load is
distributed, it can be seen that the ratio may mean somethinr.
Two factors will determine the magnitude of the ratio*—-the
contact area and the soil itself. For a given soil condition,
dividing the load by the pressure measured results in a ratio
number which reflects variation in contact area. The contact
area in turn will be influenced by physical characteristics

of the tire such as flexibility and size. Therefore, the
ratio number will reflect physical characteristics of the
tire and a lower number will indicate more pressure trans-
mittal.

Considering the effect of the soil on the ratio, for a
given tire a lower number indicates the soil transmits more
pressure or.the contact area changes so more pressure is
transmitted or a combination of both. But certainly the
contact area is dependent on the soil condition, as the con-
tact area is increased in looser soils. However, since the

same tire is considered, the change in contact area will be

20

influenced by the change in soil. Thus, whether the higher
pressure results from contact area change as the soil changes
or the soil change itself or a combination of both, a lower
number means more pressure was transmitted because of soil
change. Therefore whether a constant tire or a constant soil,
a lower number indicates more pressure was transmitted
through the 5011. Consequently, the ratio number does have
a significant meaning, even though it is not dimensionless.

The ratios indicate some interesting things. The front
tire of the tractor in every case has a lower number than
the rear tire. Thus, since the soil conditions were the
same, the front tire caused more applied pressure to be trans-
mitted than the rear tire. The number for the sprayer wheel
was the smallest of all the ratios calculated. Thus more
applied pressure was transmitted below the surface than for
either tractor tire. The sprayer tire was an eight-ply tire
with an internal pressure of 51 psi. The front tire of the
tractor was a four-ply tire carrying 56 psi, while the rear
tractor tire, also a four—ply tire, had only 16 psi. Thus
it seems possible that the flexibility of the tire may have
something to do with the magnitude of pressure transmitted
through the soil.

Ratios were not calculated for the tamper or roller
since they would be meaningless. It was possible to double

the load carried on the tamper or roller without increasing

the value of the measured pressure since not all of the

load was contributing to the pressure at a given point.
This was caused by not havinm the total load in one concen-
trated area as was the case for the tractor and sprayer tires.
It is interesting to note that the pressure measured in
the soil under the tampinp feet was considerably less than
under the rear tractor tire while plowing. This was true
even though much of the time the tampinc feet penetrated
the soil so they were probably much closer to the cells than
the tire was. The estimated contact areas for the rear tire
while plowing and the tamper feet should be quite accurate;
thus the applied pressures should be quite accurate. Both
the tire and tamper applied about the same unit pressure, but
the measured pressure in the soil was much less under the
tamper. This bears out Soehne's observation that the pres-
sure at a point is determined both by the applied unit pres-
sure and the contact area of the applied pressure. With the
rear tractor tire the pressure was applied over a fairly
large area compared to the tamnina feet. The contact area
of the rear tractor tire was 84 square inches but the contact
area of each tamper foot was only 6.5 square inches. The
center of the next adjacent area was 12 inches away since
the tamrine feet were spaced one feet apart on center. Thus
the small scattered contact areas did not cause as much pres-.
sure at a given depth in the soil as the sinple larger con-
centrated contact area even though all areas applied approxi-

mately the same unit pressure.

(O
(‘0

It should be noted that the observations made from the
ratio numbers and applied unit pressures were not accented as
fact, but only as indications of what appears to have oc-
curred. Further investiqntions under varying soil conditions

would be necessary before definite conclusions could be made.

Pheasurmeistrihution. .Unssr. Tracie: .T.i.I’.°§.

It was hoped at the start of this project that the pres-
sure distribution under the tractor tires could be determined.
The investigators believed it would be possible to plot the
pressure cell readings with resoect to vertical and horizon-
tal distances from the center of each tire and thus have a
visual picture of the pressure distribution. Such an attempt
was made but variations in the data would not permit connect-
ing points of equal nressure with a smooth curve. The vari-
ations in the measurements could have been due to inability
to measure accurately the horizontal and vertical distances
between tires and cells, the variation in soil from test to
test and the position of maximum apnlied pressure by the
tires with respect to their centers.

One reason for the uncertainty of the distance measure-
ments was that in all operations the actual tracks of the
tractor Wheels were disturbed bv the trailinp implement.
Also, time did not permit precise measurement to each wheel

track but only to some reference point. Thus, if the

{‘0

implements were not perfectly aligned behind the tractor
when passing over the cells, the measured location to each
wheel would be in error. Similarly, time did not permit
measuring the depth of soil between tires and cells during
each pass. Therefore, the total depth of soil was measured
at the end of each demonstration cycle. By measuring depth
of plowing or depth of wheel track, a close approximation of
soil depth under each wheel was possible. During plowing

it was felt that these measurements were quite accurate
since the tires did not penetrate the soil.

Inspection of the data showed that in every case where
the tire passed near the center of the cells, one of the
cells had a higher reading than the others. The two adjacent
cells had lesser readings and the further the cells were
from the highest reading the lower pressures they indicated.
‘The only exception was under the rear tractor tires when less
than three inches of soil separated tires and cells. Under
this condition it was observed on occasions that two peak
readincs occurred instead of one. Under the rear tractor
tires at shallow depths, the peak readina depended on where
the lugs made contact with the soil above the cells. At shal-

low depths it was possible for two lugs on opposite sides of

the tire to cause two peaks.
Since usually one cell clearly indicated a peak reading,

it was decided to arbitrarily assume that this cell was

under the center of the tire even though horizontal measure-
ments might not indicate it was under the center. This
assumption seemed justified for two reasons. First, even
though the highest reading was not under the center of the
tire, it was probably under the center of the load applied
by the tire. Secondly, by assuming the highest reading was
under the center, average values of pressure under the cen-
ter should result from a number of readings. This procedure
was followed separately for each tractor tire using only
data in which a single peak was indicated by the readings.
These points were plotted with recorded pressure (psi) on
the ordinate and depth (in.) on the abscissa. A smooth
curve was drawn through the points and labeled "center of
tire" (Figs. 10 and ll.)

Similarly the average pressure recorded by the two
cells adjacent to the one having the highest reading was
plotted on the same graph. A smooth curve was drawn through
these points and labeled "O.4-of-a-foot-from-center” (Figs.
10 and ll.) Since the cells were spaced 0.4 of a foot
aspart, this curve would represent the average pressures 0.4
of‘a foot from the center of the tire. A similar procedure
VVas used on the next pair of adjacent cells and the result—

:inq curve labeled "O.8-of-a-foot-from-center." This pro-

cedure was followed until zero pressures were encountered.

It was believed that by plottind in this way and drawing a

25

    

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27

smooth curve through the points an average value of the pres-
sures would be represented by the curves.

The distribution of pressures under the tires was hard
to visualize from the above mentioned curves (Figs. 10 and
11.) Thus it was decided to take values from these curves
and use these values to determine isobars under the tires.
This was done for both the front and rear tractor tires.

The isobars were plotted on a graph having depth below the
tire on the ordinate and distance from the center of the tire
on the abscissa (Figs. 12 and 15.)

To plot one isobar, a chosen single pressure value was
selected. On the pressure versus depth graphs (Figs. 10 and
11) the chosen value was followed across the graph and if
crossed by the "center" curve, a point was plotted on the
isobar graph (Figs. 12 and 15) under the center of the tire
at a depth indicated by the ”center” curve. If the pressure
value was also crossed by the "O.4-of-a-foot-from-center"
curve, a point was plotted on the isobar graph 0.4 of a foot
from the center of the tire at a depth indicated by the
~"O.4-of-a-foot—from-center” curve. This was continued until
all points from curves that crossed the chosen pressure value
liad been plotted. A smooth curve drawn through these points
‘was the isobar renresenting the chosen pressure value. Other
isobars representing other pressure values were drawn in the

same manner. Since the pressure versus depth curves did not

28

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Dense Soil Placed on Paving

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identify a left or rihht of a tire, the pressure distribu-
tion was assumed to be symmetrical and a point was plotted
'both to the left and right of the tire's center. lsobars
under tractor tires could not be located for operations
other than plowinfi because all pressure readings were made
10 indhes or more below the tires except while plowinr.

All isobars were determined by points from at least twO
curves except at shallow depths under the center of tires.
There, because the distribution of pressure at the Contact
surface was not known, the isobars were drawn to the tire's
contact surface arbitrarily. Since the family of isobars
under each tire plotted smoothly the method of drawing them
seemed justified.

The Ea see sandy loam in which these pressures were
measured was very densely compacted. The soil itself prob-
ably was influenced by the supporting paving and so could not
represent a normal soil. However, the general distribution
and magnitude of the pressures were probably an indication
of what would be found in a similarly loaded field soil of
the same physical characteristics. It is interesting to note
that the general shape of the isobars is a sort of flattened
circle. Soehne (1) observed that in a dense soil the isobars
would be circular. Certainly this same soil at other moisture
contents would have given different results. Thus the most

we can say is that these isobars represent only the conditions

31

at l‘owerama. However, the techniques used in this study
should be useful when applied to other projects which have
general aims related to effects of pressure on soil compac-
tion.

The formula CEI: Pm (p. C054“) was applied to the
front and rear tires of the tractor while plowing. The
radius of a circle whose area was equal to the contact area
of the front tire was used in calculating the angle 0C for
the front tire. The radius used was 35.26 inches. The tan-
nent of 0< was equal to the radius of the area divided by
the distance below the tire. The average pressure applied
Was 29.8 psi and this was used for Pm in the formula. The
values calculated by this formula represented the theoretical
pressure distribution under the center of the front tire
While plowing. These values were plotted in Fig. 14 along
With the measured pressure values under the center of the
tire.

A similar procedure was followed for the rear tire ex-
cept for the radius used. The radius of a circle whose area
is 84 square inches is 5.16 inches. Using. this in the for-
mula results in a curve which indicates higher pressures than
Were measured. However, since the lugs applied the pressure
under the rear tire, the contact area must have been scattered
Somewhat. Thus, considering: the load as concentrated in one

area does not truly represent the conditions under the rear

32

    

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53

tire. Therefore a smaller radius - 3.0 inches - was arbi-
trarily selected. Using 3.0 inches with Pm : 53.6 psi
results in a curve which aprroximates very closely the mea-
sured pressures. The fact that a smaller radius was needed
to get a close approximation of the measured pressures shows
the same effect as was noticed under the tamper feet. There
the spread feet resulted in lower pressures, which is appar-
ently what occurred under the rear tractor tire. This same
effect may be the cause of the higher ratio numbers under
1ihe rear tractor tire than under the front tractor tire.

UThe curves for the rear tire are shown in Fig. 15.

-*.—d ‘ _.

Magnigmdeoof_£ressures in Loose Soil

 

,—_. ...... _.____.————-o

It was observed by Soehne (1) that the more pliable a
53011 the more concentrated will be the compressive stresses
tzowards the load axis. This is primarily due to the lateral
Ffivinp way or flowinn of the soil from under the load. Thus
lure would expect to record larger pressures under the center
fo a tire in loose soil. Such was the case during the water-
iixaq operation. There the tractor was traveling over freshly
Fjilowed soil which Was very loose compared to the unrlowed
53<3i1. Two graphs (Fins. 16 and 17) were drawn showinw the
Inéaximum pressures under the center of both the front and
3P13ar tires of the tractor while plowinw and while waterinm.
:[ti can be readily seen that the pressures recorded while

W2lterine were hicher for both front and rear tires.

54

 

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It is true that the front tractor tire had a larger
load while watering than plowina. The opposite is true for
the rear tire but waterinq pressures were still higher than
plowine pressures. The fact that watering pressures were
higher was also shown by the ratios in the summary table.
Rememberinc that the lower the number the more pressure
transmitted to the cells, we see that for the front tire
while plowinfi this number was 282. Jhile watering the num-
ber drOpned to 233, indicating a hisher transmittal of pres—
sure. Similarly, the number for the rear tire was 360 while
plowing and 294 while watering. Thus it seemed conclusive
that larger pressures were transmitted deeper through a
pliable soil than through a dense soil. It should be remem-
bered that while waterina the cells were still in a dense
soil. The pressure was transmitted through the loose soil
to the depth of plowinn and the last few inches through the
dense soil to the cells. This undoubtedly lowered the value

of the indicated pressure slightly.
Effect of lugs on Rear Tire

Soehne (1) also stated that in a very pliable soil the
difference in pressure under the luvs and under the slots
between the lues of a tire while in contact with the soil
was very slight. It was easily seen that the luas alone ap-

plied the pressure in a dense soil since the luqs did not

 

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2 mi

penetrate the soil enoueh to permit the slots between lugs
to touduthe soil.

Usina the total contact area of the rear tractor tire
while watering, the calculated mean pressure applied was
10.4 psi. Obviously, more pressure than 10.4 psi must have
been applied bv the tire. Thus the load carried by the con-
tact area could not have been uniform. Either the lugs
carried more weight than the slots between the lugs or the
pressure under the center of the tire was much greater than
the mean applied pressure or both.

The area of the lugs in contact with the soil while
plowine was 84 square inches. The elliptical area, includ-
ing the space between the lugs, was 332 square inches. If
we assume only the lugs supported the load while waterine,
the area of lugs in contact with the soil would be 84/333
of the measured elliptical area (59 square inches) since
the ratio of lug area to total area is a constant. assuming
this lug area supported the load, the calculated applied

pressure is 41.1 psi which seems much more loqical in View

*3
5'
H.
U)

[—10

of the measured pressure in the soil. ndicates that
the load carried by the slots between lugs of the tires
must hwve been small. Thus it seems likely that the lufis
carried the majority of the load even in loose soil.

The apparent reversal of Soehne's findinrs does not
indicate his work was in error, since the heiaht of luqs

on the tires he used is not known. The lugs on the tires

r]
(3

at Powerama were one and one half inches hifih, which may
have been higher than the lues on the tires he used. Thus
it is entirely possible that for a lower lus height Soehne's
findines could be right. However, we must conclude that
under these soil conditions, with 3 lug height of one and
one half inches, most of the load is supported by the luvs,

even in loose soil.

LogatiOnMoI‘- 1" 0.1 nt.- of- Limimyajrassyrs
With Heepect to_wheel;§xlg

 

Three tests were run to try to determine the location
of the point of maximum pressure under the tractor tires
with relation to the axle of each tire. Each test was
conducted in the following manner:

A transit was set up so that its vertical hairline
determined the vertical plane in which the line of pressure
cells laid. The chart Speed on the recordina instrument was
set at ten centimeters per second. One observer held a pen-
cil near the ends of the tracinn pens and close to the chart.
Another observer sighted throush the transit and have a ver-
bal signal when the center of the rear axle of the passing
tractor was in the vertical plane determined by the transit.
As quickly as possible after hearing the signal, the first
observer made a mark on the chart. Although this method was
crude, its simplicity probably permitted reasonable accuracy

at the slow tractor sreeds used. also time lost in human

4O

reflexes was partially compensated for, since the pencil
could not be held exactly adjacent to the points of the
pens. Thus the chart had to travel a short distance before
the exact point representinp the axle was under the pencil.

The speed of the tractor as indicated by the tachometer
on the tractor was also recorded on the chart. It was heped
to use the speed in determinins the relation between dis-
tances representind the tractor and those recorded on the
chart. An attempt to do this was only partially successful.
It was noted that small changes in the recorded Speed of the
tractor would alter the results considerably and it was felt
that the speed of the tractor had not been measured precisely
enough.

Therefore a different approach was tried. Pen traces
were recorded under both the front and the rear tractor tires.
Assuminn the point of peak pressure occurred the same dis—
tance ahead of the front tire as the rear tire, the distance
on the chart between the two peaks would represent the wheel-
base of the tractor (BC inches.) Thus a ratio was established
so that all distances on the chart could be converted to dis-
tances representing the tractor. Using the ratio, all dis—
tances on the chart could then be measured from the line
locating the axle and converted to distances representing
the tractor. This was done by averagine the three cells

nearest the center of the tire to obtain each value recorded

in Table II.

41

.moeocH NH 0» OH Haoa eo enema eomeHpma

.30 a o % amp
emcee was HwOm exp m pmoe H p U was

.UeBOHQ hasmoaa mes HHow on» m use A name "opoz

.5 -1 =1, . o - ,:;Vl
.A‘ | uliav

   
   

 

‘I

_
aaxgl v. stthx KJe¢
a tJe\n\ ..4 oak ems.snw_ _
km... rink 76* W CH

,EsaukkOLodxt w
we Coioof. T

.maxd esp mo Geese pmaasooo wmaSmmead seed Had :

3.
\O

 

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W m.¢e m.mm w.em e.ma mm.) a, omsgmpa
m.me m.om m.em m.ea em.m H e.m aka
a a
W s.¢e n.Hm m.am s.HH em.m l ms.H mtg
al h M
m.me H.mm s.em >.sH ee.m _ m.a w H W
a, w ll
A.aac A.aav A.eav A.nav A.cac m Angel N w
amom paonh nmmm nachm paom _ m
_ meme mmmpmmmxm memes easemema a mmeoeeme we:
AHom moama wszDQ BmmHm nae mmbmmmmm AHom Mme 2H mmbmmmmm
wozaemHm He>ema qeeoe mona ea mozaemHo mama means as ezHom swamm same

 

 

 

QHOm WEB mm>o UZH>OE mi; moeofima HEB qume magma moeutme
mme mo mdmm HEB OB 92¢ m0 Gamma QflBomBHQ mfimwmmmmm HHow

HH mamde

42

It was noted that the peak pressures always occurred
ahead of the axle. From this we must conclude that the
major portion of the contact area lies ahead of the vertical
plane containing the rear axle. This seems logical when
remembering that the tire is compacting soil ahead of it as
it moves over the soil. This would be eSpecially true in a
loose soil and that fact is observed in the data since dur-
ina Test 2 the point of peak pressure ahead of the tractor

was less than during the other two tests.
P38582398. Pads? flow .3 stat oms

Pressures under the plow bottoms were recorded while
the plow was Operating. These values were negative since
the pen traces indicated a reduction in pressure. It was
possible for the cells used to indicate such a reading since
they were under a small pressure load while in the soil;
this lead would not be present if the aflls were out in the
atmOSphere. Thus the cell: indicated a negative pressure but
in reality the neaative pressure was a reduction in pressure
already applied by the soil. At a depth of from 2.5 to 5.5
inches below the plow bottoms, the average of 24 cell read-
lnRS was nemative 1.05 psi with the maximum being 1.9? psi.

Not all pressures observed under the plow bottoms were
neeative. Small positive pressures were observed which.may

possibly have been caused by the fallinn of overturned soil

45

from the adjacent plow bottoms. The pen trace would jump

up and down with great variability whereas the pen trace

under the tractor tires was relatively smooth. Thus the

impressed pressures under the plow bottoms changed very

rapidly. Also rather large pressures were noted under the as
plow tires. Some of the pressures were as great in magni-
tude as those under the tractor tires. Therefore under the
conditions of the tests, it seems that nearly all of the I'
load on the plow was carried by its wheels whereas the plow *
bottoms did, in fact, create negative pressures. No attempt
to include the plow tires in the analysis was made since the
load carried by the tires was unknown.

The author feels that a characteristic of the pressure
cells used to make the soil pressure readings should be men-
tioned. These cells measured only soil pressures that were
normal to the face of the cells. It is highly probable that
the pressures in the soil were not always vertical; thus the
cells indicated only the vertical component of the soil pres—
sure. However, under the center of the tires the soil pres-
sures probably were vertical and there the cells indicated
the total pressure. Also the soil pressures probably were
close to vertical until they were past the edges of the tires.
Therefore, the pressures indicated by the isobars beyond the
tires' edges may be lower than actual pressures present in the

soil. Other parts of the analysis would not be affected since

pressures under the‘center of the tires were used.

44

CONCLUSIONS

The use of strain name pressure cells with a multiple
channel recorder provides an effective and rapid means
for measurina pressures in soils.

The ratio number may be a quick way of evaluating effects
of different tires in the same soil, or different soil
conditions for the same tire.

The graphical analysis used to plot isobars results in a
family of smooth curves clearly showing the distribution
of pressures under a tire for a given condition. Since
in any field work one would expect variations in soil
conditions and loads applied as well as pressure meas-
ured, the method of graphical analysis may be a simple
way to obtain smooth curves representing average values.
Froehlich's formula as used by Soehne apparently gives
close approximations of pressure under the center of a
tire.

The more pliable a soil the more pressure it transmits.
The high lugs on rear tractor tires carried the majority
of the load in the Naumee sandy loam soil.

loads applied over scattered contact areas caused less
pressure in the soil under the center of the load than
loads applied over one continuous area.

The maximum pressure always occurred ahead of the axle

on each wheel.
The plow bottoms applied a slight negative pressure.

The greatest part of the load of the plow was carried

by its wheels.

RECOinNDJTIONS FOR FURTWJR STFDIES

Determine the distribution of pressure at the contact
surface of tires.

Determine the distribution of pressure in a normal field
under various soils and soil conditions.

Investigate the effect of varying contact area for a
given load on pressure in soil.

Investinate the possibility of using vector analysis to
develOp mathematical relationships representing pres-
sure distribution in soil.

Determine the extent of soil compaction due to pressures
in soil.

Investigate and develOp means for lowering pressures in
the soil under tires by using scattered contact areas

or greater tire flexibility.

47

LI 'PEJRATUR :1 C] TED

1. Soehne, Halter. Druckverteilung in Boden und Bodenver-
formung unter Schlepperreifen. (Distribution of
Pressure in the Soil and Soil Deformation under Trac-
tor Tires.) Grdlpn d. Landtechn. 5:49-65, 1955.

2. COOper, A. N. Investigation of and 1nstrumentation for
Measuring Pressure Distribution in Soil. Unpublished
Ph.D. thesis, Nichipan State University, 1956.

5. McKibben, E. G. The Soil Dynamic Problem. Page 412,
Agricultural Engineering, December, 1926.

4. Nichols, M. L. Dynamic Pronerties of Soil I. Page 259,
agricultural Engineering, July, 1951.

5. Nichols, M. L. Dynamic Preperties of Soil II. Page 521,
Agricultural Engineering, August, 1951.

6. Baver, L. D. Physical Preperties of Soil. Page 524,
Agricultural Engineering, December, 1952.

OTHER REFERENCES:

7. Randolph, J. w. and Nichols, M. L. A Method of Studying
Soil Stresses. Page 154. agricultural Engineering,
June, 1925.

8. Kummer, F. A. The Dynamic Properties of Soil. Page 75,
Agricultural Engineering, February, 1958.

9. Seaton, L. F. Compaction of Soil Due to Tractors. Page
68, Agricultural Engineering Transactions, 1916.

10. McGeorqe, H. T. and Breazeale, J. F. Studies on Soil
Structure. Pages 411-447, Arizona Station Technical
Bulletin No. 72, 1958.

11. Cooper, A. J. and Kummer, F. A. The Dynamic Properties
of Soils. Agricultural Engineering, January 1945.

12. Randolph J. W. Tractor Lug Studies on Sandy Soil.
Page 178. agricultural Engineering, May 1926.

14.

15.

16.

17.

Gilboy, G. Soil Mechanics Research. American Society
of Civil Engineering (N.Y.) Proceedings 57,
No. 8PP 1165—1188, 1951.

Jensen, J. K. Experimental Stress Analysis, Agricul-
tural Engineering, September, 1954.

Lee, G. H. an Introduction to Experimental Stress
Analysis. John niley a Sons, Pages 114-147, 1950.

Lucas, D. B. Plowing Draft Tests on Fertilizer Plots.
Page 555, Agricultural Engineering, November, 1928.

Schwantes, A. J. flowing with Rubber Tire Equipped
Tractor. Page 66, agricultural dngineerinfi, February,
1954. -

Jilliams, Ira L. Keasurement of Soil Hardness. Page

25, agricultural engineerinr, January, 1959.

Nichols, N. L. Shear Values of Uncemented Soil. Page
47, Agricultural Enaineerina Transactions, 1952.

pun. .mp5. Fug
-.-- '. , ‘H "r

.- ._ —._...--..u

49

{if} 1.51%D1X
The weight transfer in the tractor while plowing was
calculated as follows: /Cfi980’¥

Vérf’f cal F/in a of
##CPGfer 0; 9r,v;f,

 

 

I
lé—--——- - - _ at 7
l
l V
i
l
_ __ ground IFVF/
7V "_ — _ "'- F’ _ —'
(.— - 8'3, ——._. _ )
“r .v
2930 8030
fro/1" M/hPE/

 

I’Eckf' WUPFI

F€CL- xon r~eac+lon

Eig. 18. Weight Distribution
of Tractor Under Static Conditions

To determine location of center of gravity from

Fig. 18:
25/“4 =5? ='€3C>5CDA 8<‘- /O‘?8:?A‘1

fronftvnaei

E%O:TC>W<9:3
/O?80

H

CL

 

2 58-0 /‘/7.

Distance from rear axle to center of gravity will

be 80” - 58.6” I 21.4"

SC

 

 

 

.. 13
[0480
_ U ‘
eral-4 w :000 a
' :9
W , T fl

....-. «up-......“ .
fix ‘0-

l
|
il
‘l
I
l
U)
oil
I
|
l
L-4

J
no

Fig. 19. Weight Distribution
of Tractor while Plowing
To determine front tire reaction while plowing from

Fig. 19:
- EMR203 /098OX21.9~—5000x15.5‘——F)(80
F:

_Q980x3L4-5boyw56 . +
8C) _/969

F: /770 raundpa of;

5V=O'=/0980—/97o—R
R 2 9010/0.
Thus each rear tire carried 4505 lb. and each front
tire carried 985 lb. weight transfer for other operations

was calculated in a similar manner.

The elliptical contact areas were calculated by use of

the formula:

flI‘STTCL-b

(\
Ky

Fig. 20. Tire Contact Area

 

where a and b are semi-axes of an ellipse. Thus for

the front tire on a hard surface:

Area-I TTxg—X—g-E— :: 33.01%;

The weight of water in the Sprayer tank was determined
as follows:

at the start of the watering process the amount of

waterwas _35X69>(4E. ‘_ 53 7 7574.3
1728 "

The amount of water at the end of the watering process

was approximately 20 X69 X 43

:3
I 7‘25; 2 3 3:f7fff

 

Average water in the sprayer was than

58.7 + 3 3-5

 

52

The weight of water in the sheeps-foot tamper was

calculated as follows:

Equation of curve
would be:

26+)”; m"-

X = i- ‘//72.— y?

 

 

Fig. 21.
Drum of Sheeps-Foot Tamper

Circular Curve Representing

From the calculus we know the area would be:

/2 PW: [2 ’19
: ° 2"“
A f dX 0/) : f X] '0’)’
_/9 —/9

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[,3 M36, ”.149 + 36/ s/‘ndfl—gfl—E + 36/s}n”/(‘{_;’.)]

-'
-

/77 +36/(gg) — 36/{-afl) : 993 me

Jach drum (two drums on the tamper) was 40 inches long.

Therefore total volume was:

:3 92 X a (so)

60 7‘3
/723 4} f

H

46.0x 62.4 : 2870 Ho OfWCU‘W

54

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TAB] ..3 V

PRESSURE CELL RMDINGS UNDER TiiE CENTER OF THE FRONT TRACTOR
TIRE 1N FRESUIY PLOHSD LAUMEE SANDY LOgh SOIL PLACED ON PAVlNG

 

 

 

 

 

 

 

 

Depth Cell Readings Depth Cell Readings
(in.) (psi) (in.) (p81)
9.8 5.7 10.2 5.8
10.0 8.1 11.8 5.8
10.0 5.1 12.8 5.5
3 10.0 4.7 14.7 4.1

 

 

 

 

 

 

TABLE V1

PRESSURJ CELI READIKGS UNDER THE CENTER OF THE REAR TRACTOR
T186 IN FRDSHLY PLOJED NAUMEE SANDY LOAN SOIL PLACED ON PAVING

 

 

 

 

 

 

 

 

 

Depth Cell Readings Depth Cell Readings
(in.) (psi) (in.) (psi)
9.8 11.4 10.0 15.5
10.0 12.5 10.2 12.5
10.0 12.5 11.8 15.7
10.0 17.5 12.8 12.8
10.0 12.4 14.7 11.8 I
.. a

 

 

 

 

.. - 00 A.” ..--scan 1“

57

TABLE VI 1

DI:5TRIBI“T10N ULJDISR THE
TIRE a

THEOREPICAI FRASSUIMS
CENTER 01“ TEE; FRUIT 'I‘R;‘«.CTOR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Depth tancx b 0“ COSa\ cos4¢~ Pressure
(in.) (degrees) (psi)
‘ 2 1.65 58.5 0.522 0.074 27.5
5 1.09 47.5 0.676 0.209 25.6
L 4 .815 59.2 0'775_ 0.560 19.1
E 6 .545 28.5 0.880 0.600 11.9
if 8 .407 22.2 0.926 0.755 7.9
E 10 .526 18.0 0.952 0.822 5.5
E 12 .271 15.2 0.965 0.867 E 4.0
E 14 .L .255 E 15.1 0.974 0.900 ¥T 5.0
E 16 I_ .202 E 11.4 0.980 0.922 2.5
2. Calculated from formula C:'= F5n(/":osfi“)

b.

with Pm:: 29.8 psi and effective radius

0\ is arc tan

and x is depth.

1’

.— '2
_ L).

26 in.

where r is effective radius

 

58

T1218 V111

THEORETICAL PRSSSURE DISTRIBPTION UNDSR THE

CEKTflR 0E Tum RRAR TRACTOR TIRE WITH 5.00" RADIUS a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:Depth tancfl b 7’ coscx cos4d9 Pressure
(in.) (degreeS) (psi)
2 1.50 56.5 0.555 0.095 48.5
5 1.00 45 0.707 0.250 40.2
4 .750 56.9 0.800 0.410 51.6
6 .500 E 26.5 0.885 0.614 20.7
I
s .575 E 20.6 0.956 0.768 12.4
10 .500 16.7 0.958 0.842 8.5
12 .250 14.0 0.970 0.885 6.2
. ..11_1.““4.
14 .212 12.0 0.979 0.919 4.8
-r-~—-— -r---—~- »«~— -—~-
16 .187 I 10.6 0.985 0.954 5.5
., Q C\=P (/—cos"a\}
a. Calculated from formula 2 ’”
with Pm : 55.6 psi and effective radius : 5.00 in.
b.

GA is are tan i where r is effective radius and

x is depth.

THEORETICAL PRESSLRE DIJTRJBDTION UNDER THE

TABLE 1X

C (‘3
l 13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CENTER OF THE 8818 TRACTOR T1RE 91TH 5.16” 840105 3
Depth tancfi b C‘ 00384! c034d1 Pressure
(in.) (degrees) (psi)
2 2.58 68.8 0.562 0.017 52.7
5 1.72 59.9 0.500 0.062 50.5 _J
F 4 1.29 52.2 0.615 0.141 46.1#]
E7 6 .860 40.6 0.759 0.552 55.8 E
E 8 _ .645 52.8 0.841 0.499 26.8 E
’ 10 ET .516 27.5 5 0.888 0.622 20.2 E
; 12 e; .450 i 25.5 E 0.925 f 0.752 14.4 E
{—14 E .568 .9 20.2 E 0.958E 0.774 12.1 E
##16 E .522 _*17.8 £0,952 E 0.821 9.6 E
8. Calculated from formula 575" FT"(/-COS I“)
with Pm::55.6 psi and effective radius ._ 5.16 in.

b.

x is depth.

cx is are tan E

where r is effective radius and

SUILIGzafiY 0F STATI C I 01sz , LOADS CARR I LCD,

TABLE X

PULL

60

A ND

SEEI-AXES 0F CONTACT AREAS FOR TRACTOR AND IMPLELENT TIRES

 

Tire or I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Static Pull Causing Working Major Minor
Implement Load Weight Transfer Load Axis Axis
1b. lb. 1b. in. in.
F t T
P§2$1n81r° 1465 5000 985 7 6
Eigxifiére 1 4025 5000 4505 - -
n . f 1
agggfiigére ; 1457 900 1550 17 g 7.5
1 i
. f
Ezggrfige ; 4040 900 4127 28 ' 18
T 1L
Front Tire 1 ‘
Tamping i 1457 1800 1265 e j
fizigigér° 4040 1800 4212 - i -
rent Tire ’ 1
Rear Tire : Z 1
s 7 1 ‘1
mgizyer 2852 - 2852 11 ; 8 a
L : .
i T T
.eet ; 8550 - 8550 . 5.25 : 2.03
C T
Efiier 4565 - 4565 8 j 6

 

 

 

 

 

a. Rectangular area calculated.

b. 24 feet in contact with soil.
column were pneumatic tires.

c. 8 tires on the roller.

All other items in

MAR 19 1962 N"

' 1
u"
,.;

 

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