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TESTING AND ANALYZING THE ADAPTABILITY OF
CERTAIN IMPLEMENTS TO ONCE-OVER TILLAGE

BY

Mirza Javad Shustary

 

AN ABSTRACT

Submitted to Michigan State University of Agriculture and
Applied Science in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE
Department of Agricultural Engineering

Year 1955

Appreved fV/. 7 M-%%

THENS

 

 

 

 

of 1
tic
olc‘
til

at

(+
,T,

{fit Mirza Javad ohustary

ABSTRACT

Tillage refers to the different mechanical manipulations
of the soil that are used to provide the necessary soil condi-
tions favorable to the growth of crops. It is one of the
oldest of arts associated with farming. The evolution of
tillage implements and machinery has been one of the most
striking features in the growth of the art of farming. Even
though phenomenal advances have been made in the perfection
of tillage tools, tillage operations remain the most costly
of all the various items that are concerned in crop produc-
tion. Thirty per cent of the total power consumption in
agriculture in the United States is expended in tillage.

There has been a tendency among the farmers to over-
till their lands. Midwestern farmers have been in the habit
of working their land several times after plowing. It was
believed that twice with a tandem disk and twice with a
spring tooth harrow constituted an average amount of tillage
for crops such as corn, oats, beans, and sugar beets. With
too much tillage, machinery is worn out, fuel and labor
are wasted and expected yields are never reached. Soils
are being excessively packed. The result is slow, shallow
root penetration, slow water intake, and poor aeration.

The packing is the result of organic matter depletion and

too much tillage (6).-

385284

Mirza Javad Shustary

The truth of these statements has been shown by nine
years of experimental work conducted by the Soil Science
and Agricultural Engineering Departments at Michigan State
University. One of the objectives of the experiments was
to determine the minimum tillage necessary after breaking
the soil with a moldboard plow. Minimum tillage methods
have led to the concept of once—over tillage. The author
accepts the advantages of once-over tillage, and has at-
tempted to adapt certain tillage implements to this method

of seedbed preparation.

 

TESTING AND ANALYZING THE ADAPTABILITY OF
CERTAIN IMPLEMENTS TO ONCE-OVER TILLAGE

By

Mirza Javad Shustary

A THESIS
Submitted to Michigan State University of Agriculture and
Applied Science in partial fulfillment of the
requirements for the degree of

MASTER OF SCILNCE

Department of Agricultural Engineering

Year 1955

C »
ad
CL.
a u n

 

ACKNOWLEDGMENTS

The author wishes to express his gratitude to
Professor H. F. McColly, Agricultural Engineering De-
partment, for his wise guidance and helpful suggestions
that made this thesis possible.

Thanks are also due to Dr. W. M. Carleton, Agricul-
tural Engineering Department, for his timely advice, and
to Mr. James Cawood and the Agricultural Engineering

Research Laboratory staff for their able assistance.

TABLE OF CONTENTS

INTRODUCTION . O C O O O O O O O O O O O O O O O 0
REVIEW OF LITERATURE . . . . . . . . . . . . . . .

Requirements of Seedbed Preparation . . . . .
The Seedbed Profile . . . . . . . . . . . . .
Tillage Tests at MSU . . . . . . . . . . . . .
,Power and Draft Requirements . . . . . . .
Average Yield by Different Tillage Methods

Comparative Results . . . . . . . . . . .

RESEARC H WORK 0 O O O O O O O O O O O O O O O O 0

Objectives . . . . . . . . . . . . . . . . . .
Methods of Procedure . . . . . . . . . . . . .
Experimental Investigation . . . . . . . . . .
Choice of Implements . . . . . . . . . . .
Choice of a Hitch . . . . . . . . . . . .
The Field Tests . . . . . . . . . . . . .
Stress Analysis . . . . . . . . . . . . .
Force Analysis of the Soil Reactions . . . . .
Soil Throw . . . . . . . . . . . . . . . .
Distribution of Pressure . . . . . . . . .
Friction Between Implement and Soil . . . .

FriCtiCnAngle eeeoeeoeeeeee
COhOSiVBSOil eeeeeeeeeoeeee

Total Shearing Strength of Soil . . . . . .

Page

0
o~ 0\ \n \u u: +4

. lO

(REEL:

. 15
. 15

. 38
. h2
. u2
. A3

. A6

TABLE OF CONTENTS (CONT.)

CONCLUSIONS . O O O C O O O O O O O O O
SUGGESTIONS FOR FURTHER STUDY . . . . . .
SELECTED BIBLIOGRAPHY . . . . . . . . .

ii

LIST OF FIGURES

iii

PAGE

17
21

23

25

27

28

28

30
3O
31

31
32

FIGURE
1. The 'Z' hitch and clamp . . . . . . . . . . .
2. The 'L' hitch with hitch bar and direction lever.
3. Various settings of the direction lever of the
'L' hitch . . . . . . . . . . . . . . . .
h. Courey's short-toothed tiller mounted on the
'Z' hitch . . . . . . . . . . . . . . . .
5. Courey's long-toothed tiller mounted on the
'Z' hitch . . . . . . . . . . . . . . . .
6. Courey's long-toothed tiller shown in the elevated
position when lifted with the plow . . . . .
7. Courey's long-toothed tiller shown in Operation
in the field . . . . . . . . . . . . . . . .
8. The cultipacker unit used with the 'L' hitch
shown when on the ground . . . . . . . . . .
9. The cultipacker unit about to be lifted . . . .
10. The cultipacker unit lifted off the ground . .
11. A view of the hitch bar and direction lever of
the 'L' hitch . . . . . . . . . . . . . . . .
12. The cultipacker unit in field operation . . . .
13. A Brookston clay loam field after once-over

tillage with the cultipacker unit . . . . . .

32

 

‘ I

15.

18.

1?. "

20.

21.

'4
A ..
A.

'11

15.

16.

17.

18.

19.

20.

21.

22.
23.

2h.

LIST OF FIGURES (CONT.)

A Hillsdale loam field after once-over tillage
with the cultipacker unit
The plow-packer unit used with 'L' hitch in

tandem with a trail-type plow . . . . . . . .

Plow-packer used with 'L' hitch, showing the

connections .

View showing the plow tipping when the packer
was attempted to be lifted
Another view showing the tipping of the plow
Positions of the gages on the rear plow-bottom
Strain gages placed on the rear plow—bottom
connected to the Brush equipment

Charts showing the strains indicated by the

various gages .

Bulb of pressure or Iso-stress surface
Force diagram of the action of the implement and
the reaction of the soil

Graph of the Coulomb formula for shearing

strength of soil

0

0

iv

Page

33

3h

35

36

37

39

hO

Ln
#5

47

52

 

 

TABLE
I.

II.
III.
IV.
V.
VI.

VII.

VIII.

LIST OF TABLES

PAGE
Power and draft requirements of the various
tillage implements . . . . . . . . . . . . . . 7
Power requirements of various tillage implements
for seedbed preparation . . . . . . . . . . . . 8
Time required for weed control with various
tillage implements . . . . . . . . . . . . . . 9
Average crop yields on Brookston clay loam . . ll
Average crop yields on Hillsdale sandy loam . . 11
The various settings of angle of tillage for
'L' hitch . . . . . . . . . . . . . . . . . . . 22
Specifications of Courey's short and long-
toothed tillers . . . . . . . . . . . . . . . . 26

Specifications of the cultipacker unit . . . . 29

INTRODUCTION

The concept of once-over tillage denotes a minimum
tillage method, whereby a tillage implement is used in
tandem with a plow and the entire tillage work is per-
formed in one operation by going over the field once only.
This method was conceived at Michigan State University
in l9h6 with the joint efforts of the Soil Science and the
Agricultural Engineering departments, and since then con-
siderable field work has been carried on to test the ad-
vantages of this method and to prove its practicability.

The one handicap in this method of tillage has been
the need to pull a heavy and cumbersome implement behind
the plow, which slowed operation and which caused unneces-
sary tearing of vegetation and soil around the ends of the
field and also impeded maneuverability. This phase of
«once-over tillage interested the author and he attempted
'to experiment on various liftable implements that could
be mounted on both "the mounted" type and "the trail" type
Plows, and which would lift off the groundwhen the plow
lifted. This system would eliminate cumbersome pulling,
as the implement would now be one unit with the plow. It
1“Mildalso facilitate maneuverability and simplify turning
at the ends of the field as the implement would lift off

the ground with the plow.

With this goal in mind, several implements were
modified and field tested. The results of those tests
and the practicability of the tested implements are re-
corded in this paper.

REVIEW OF LITERATURE

Requirements of Seedbed Preparation

Tillage operations account for two-thirds of the power
and labor required to produce field crops (1h). On many
farms more than one-half of the tillage time is spent on
seedbed preparation. Therefore, tillage operations which
will prepare satisfactory seedbeds with less power and labor
expenditures are of distinct advantage to the farmer. The
conventional method of preparing a seedbed is, generally,
plowing with a moldboard plow, then pulverizing the soil
with a tandem disk harrow and spring tooth harrow. This
method usually allows the soil to dry out too long after
plowing before the pulverizing operation is performed, so
that the soil becomes too cloddy. In thus fitting a seed-
bed, the farmer travels the newly plowed soil many times,
often until the tractor wheels have excessively packed a
large part of the surface soil.

In order to realize exactly how much tillage is neces-
sary, the objects of tillage should be considered. These
objects are:

1) To turn under and mix stubble, manure, and other
organic matter, thus adding humus-forming material to the

soil in such a manner that it will not interfere with

further tillage and planting operations;

2) To destroy and prevent the growth of weeds.

3) To loosen the soil so that it may take in and
retain the maximum amount of rainfall and allow ready
penetration of roots and air.

h) To loosen soil so seeds may be prOperly planted
and covered.

5) To leave the surface of the soil as smooth as
necessary for a satisfactory seedbed for the type of crop
being planted.

6) To give a soil surface of such character as will
prefent erosion by wind or water in those areas where erosion
is a problem.

It is recognized that not all of these objects of
tillage are obtained at one time, and that they are not
all desirable at any one location. Baver (1) lists the
basic requirements of a seedbed to be: I ‘

1) Permit the rapid infiltration and satisfactory re-
tention of usable rainfall.

2) Afford an adequate air capacity and a ready exchange
of soil air with the atmosphere.

3) Offer little resistance to root penetration.

h) Resist erosion.

5) Facilitate the placement of surface residues.

6) Provide stable traction.

If these are the characteristics of good tilth, the
question arises as to possible means of achieving the de-
sired tilth in the seedbed. This question necessitates a
concept of the seedbed profile, together with the means
of obtaining and maintaining such a profile through tillage

operations.

The Seedbed Profile

In the old type of seedbed, the few surface inches
were reduced to a powdery condition as a result of over-
working with tillage implements. Rollers, drags and other
pulverizing types of tools were used to perfect this fine
condition. Below this thin layer of finely divided soil
there was a little disturbance of the plowed layer. The
whole layer remained somewhat coarse and full of large air
pockets. Removal of these air pockets was attempted by
reaching them from the surface. Consequently, the structure
of the immediate surface was destroyed in trying to establish
better contacts between the surface soil and subsoil. This
dusty surface is the antithesis of good tilth. The finely
divided soil runs together easily under the impact of rain-
drOps which rapidly reduces the rate at which water and air
can enter the seedbed.

The ideal profile should be the old one inverted.

That is, the lower part of the seedbed should contain the

finest granules and possess the firmest degree of settling.
The coarseness of the granules, in most cases, should in-
crease as one approaches the surface. The immediate surface
should consist of distinctly coarse granules to absorb the
shock of the impact of raindrops and thereby preserve an

open structure. It is true that the granules should not be
so coarse in the vicinity of the seed that sufficient mois-
ture cannot be had for the purpose of germination. On the
other hand, the granules should not be so fine that inade-
quate aeration will prove to be the limiting factor. But
what are the limits of coarseness or fineness? This question
cannot be answered satisfactorily in light of existing data.
Yoder (22) found that the emergence of cotton plants from
seedbeds with different degrees of granulation was most rapid
when about half the granules were l/8 to l/h inch in diameter
and the other half were smaller. A mixture of granules of

varying sizes showed the best effects on stand.

Tillage Tests at MSU

Power and Draft Requirements

There are many types of tillage machinery and the
machine selected for any particular operation will depend
upon field characteristics, vegetation, weather conditions,
topography and other factors. Some machines or methods have

been found to be satisfactory under one set of conditions

but quite unsatisfactory in some other locations (9).

i .li. fhl. ill";

TABLE I
POWER AND DRAFT REQUIREMENTS OF THE VARIOUS TILLAGE IMPLEMENTS

 

 

 

Machine Power and Draft Requirements
Plow, moldboard 5-12 lbs/sq. in. furrow section
Vertical disk tiller 150-350 lbs/ft width
Chisel plow 75-200 lbs/ft width
Tandem disk harrow 80-160 lbs/ft width
smoothing harrow 30-60 lbs/ft width
Spring-tooth harrow 75-150 lbs/ft width
Field cultivator 90-160 lbs/ft width
Cultipacker 30-75 lbs/ft width
Rotary hoe 30-60 lbs/ft width
Auger tiller 5-10 H.P./ft width
Rotary tiller 5-15 H.P./ft width

Revolving packing-type tiller 60-85 lbs/ft width
(Clodbuster)

 

 

A horsepower hour is the unit of power consumption
at the rate of one horsepower for one hour (Table II).
Thus, a tractor supplying 1h horsepower to operate a machine
which performs an operation on one acre in one hour yields

1h horsepower hours. If a smaller tractor develops seven

TABLE II
POWER REQUIREMENTS OF VARIOUS TILLAGE IMPLEMENTS
FOR SEEDBED PREPARATION

 

 

Machines Primary Tandem. Harrowing Firming Total

 

Disking

Mbldboard lu.0 9.0* 5.6“ 28.6
plow

Plow with 1h.0 h.5 5.6“ 2h.1
sub-bases

as

Plow and 15.5 15.50
packer

Plow and 17.0** 17.0
mulcher

Plow and ** _
revolv 17.0 17.0
tiller

Disk tiller 8.5 9.0 1.5 19.0

Auger-type 30.0 1.5 31.5
tiller

Rotary 75.0 1.5 76.5
tiller

 

aTwo operations: normal - conventional
**0nce-over tillage: fitting machines in tandem.with plow
«aaPreliminary trials with the clodbuster

horsepower but requires two hours to perform the Operation

on one acre, horsepower hours necessary is still 1h.

To compute the horsepower necessary to pull a machine,

the following formula is useful:

H.P. 8 lbs pull x MPH*
375

*MPH = miles per hour

TABLE III
TIME REQUIRED FOR WEED CONTROL WITH VARIOUS TILLAGE IMPLEMENTS

 

 

 

Machines Time - hours per acre
Moldboard plow 3.56
Plow with sub-bases h.37
Plow and packer 3.08
Plow and mulcher 3.27
Disk tiller 5.00
Auger-type tiller h.59
Rotary tiller 5.5h

 

The power and labor requirements for seedbed prepara-
tion are naturally low for the once-over operations and also
.for those methods employing seedbed fitting immediately
after plowing. The lowest requirements are for the plow

smith a packer in tandem, but for most all around conditions

10

a little soil stirring with the packing is desirable in
order to close up the furrow slice laps to control weed
growth. For this reason the revolving packing-type

tiller following behind the moldboard plow is a good system.

Average Yields By Different Tillage Methods

Tests on the comparison of tillage implements and
their effect on crop yields have been conducted since 19h?
as a cooperative project between the Soil Science and Agri-
cultural Engineering Departments. Points investigated were:

1) Time required to prepare seedbeds

2) Power required by different methods of tillage

3) Weed growth control required

R) General evaluation of quality of tillage, including
deep tillage

5) Crop yield results

6) Adaptation of tillage methods to farm conditions.

Tables IV and V give the five-year average results

(19h7-1951) of crop yields by the different methods.

TABLE IV

11

AVERAGE CROP YIELDS ON BROOKSTON CLAY LOAM

 

 

Tillage Methods

Average Yields, 19h7-1951 (Bu.)

 

 

 

 

Oats Corn Beets Navy Beans

Plow, disk and harrow 76.6 55.1 12.0 23.3
Plow with sub-bases,

disk and harrow 7h.9 5ho3 11.9 22.1
Plow, with plow packer

(once-over) 77.5 56.9 12.1 23.h
Plow, with mulcher

(once-over) 70.1 5h.3 12.h 22.2
Disk tiller, disk

and harrow 7h.8 51.1 11.9 19.3
Auger-tiller, packer 65.7 h3.6 1h.9
Rotary tiller, packer 68.6 hh.8 11.3 1h.3

TABLE V

AVERAGE CROP YIELDS ON HILLSDALE SANDY LOAM

 

 

Tillage Methods

Average Yields, 19h7-1951 (Bu.)

 

Oats Corn Navy Beans
Conventional* 66.6 h5.8 16.0
Plow, with sub-bases 6h.3 h5.0 16.1
Plow, with packer 65.7 h8.5 l6.h
Plow, with mulcher 63.h h6.9 16.0
Vertical disk tiller 63.0 h3.2 1h.h

Rotary tiller

 

 

Roldboard plowing plu? two tandem diskings and two harrowings.

12

Comparative Results

The results led to the following conclusions:

1) In all cases, yields were highest where the tillage
methods employed moldboard plows.

2) The "once-over" soil preparation methods were en-
tirely satisfactory for all crops on all types of soil.
Yields were fully as high as those obtained where conven-
tional tillage was employed, whereas power and labor require-
ments were the lowest.

3) Preliminary trials indicate that any device which
smoothes the soil sufficiently to make accurate planting
possible, accomplishes all the tillage that is necessary
for oats, sugar beets, and corn.~ The soil is usually moist
at the time of plowing and as a result of the firm contact
established between seed and soil, germination is rapid.

From the data presented it is evident that yields
were on the average as high after the "once-over" tillage
methods were employed as they were after the conventional
diskings and harrowings. The horsepower data show that Just
slightly over one-half as much labor was required where the
packer method of "once-over" tillage was used as where the
method employed the old conventional tillage after plowing.
In short, the highest yields were obtained when the least

power and labor were expended in seedbed preparation. In

13

terms of money saved, once-over tillage can result in a
saving of over one dollar per acre, with as high as three

dollars per acre possible.

RESEARCH WORK

Objectives

The objectives of this investigation were to adapt
certain tillage implements for once-over tillage such that
the implement could be mounted on the plow and be lifted
with it, with due consideration to the weight of the imp
plement, the stresses its loading causes in the plow bottom,

and the effectiveness of the implement as a tillage tool.

Methods of Procedure

1) A review of past research work done on minimum
tillage methods and once-over tillage. This study gave in-
formation on the various types of implements that have been
used by the Soil Science and Agricultural Engineering De-
partments of Michigan State University, and paved the way
for experiments to adapt certain of these implements to be
liftable with the plow, as well as to test some new tillers.

2) A study of the available equipment and a choice
of those best adapted for lifting.

3) Field tests of the adapted implements.

h) Stress analysis - to determine the stress caused in

‘the plow due to the weight of the lifted implement.

15

5) Force analysis of the soil reactions on the implements.

6) Suggestions made for further research.

Experimental Investigation

Choice of Implements

Several implements that had been tried by the Soil
Science and the Agricultural Engineering Departments and
some others were considered on the basis of:

a) weight and draft load

b) ease of mounting and dismounting on the plow

c) type of action on soil

d) appearance of soil surface the implement leaves.

Consequently, the following implements were picked for
adaptation to mounting on the plow and liftability, and were
field tested:

1) Courey's* short-toothed tiller

2) Courey's long-toothed tiller

3) The cultipacker unit

h) The plow-packer unit

Choice of a Hitch
Two types of hitches were tried and tested:
1) The 'Z' hitch
2) The iLi hitch.

 

*Named after the inventor of the implement - N. J.
Courey of Saline, Michigan.

16

The 'Z' hitch. A detail sketch of the Z hitch is
given in Figure 1. This type of a hitch proved most prac-
tical and best adapted for maneuverability and lifting.
The clamp is designed to fit any size of plow beam and
can be attached to various parts of the beam.by means of
a system of staggered holes (Fig. 1).

Design of the hitch: bending load in lifting, based
on lifting a plow-packer weighing 350 lbs.

r ’0 "r“— 30——~1p
+8

 

\

 

Checking for load at B:
EMA: 350x15=FBx25

25

A bending stress is caused in the implement shaft, as
‘well as in the diagonal shaft. The two shafts will be con-

sidered separately.

COLLAR7

 

 

 

 

 

H/ TCH SHAFT

 

17

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ADJUST/Mil?

 

 

 

 

 

E a 1:. ©

 

 

 

F/a/ .THE Z H/TCH AND [LAMP
SCALE: /=/0

18

The implement shaft:
Bending moment Mo = 350 x 20 = 7000 in. lbs.

 

Bending stress S = M. c = M = M

’ "T’ 1' 7c" m3

32
c = radius of shaft I = moment of inertia
I/c = section modulus d = diameter of shaft

31 = 0€000 = 13,300 psi.

The shaft being of SAE 1010 material has an allowable
bending stress 3a = 2h,000 psi. (9).

Factor of safety F.S. = §§,000 = 1.8
13.300

To strengthen the Joint 0, a bracing was welded on at the

point. Joint P was also braced.

The diagonal shaft:

L = 15 = 17.3"
sin 00

Bending moment M, 350 x 17.3 = 6050 in. lbs.

Bending stress Sy 60§0 = 11,500 psi.
0. 2

F.S. = 2Q,OOO = 2.1
11, 00

The hitch thus designed would, therefore, be safe for

experimental purposes.

19

Draft considerations:

 

Pulling force P = 100 = 107 lbs.
sin 70°
Tensile stress S = P = 10 3 uh.6 psi.
'7' 'A" 2.

A = cross-sectional'area of the shaft = '7Vd2
This tensile stress is negligible.

The advantages of the'Z'hitch are:

1) Ease of mounting and dismounting

2) Strength - capable of supporting heavy loads

3) Ease of pulling - being fixed at the joints, once
the hitch is set in place, it remains fixed and will not be
thrown out of position

h) Elimination of side support - due to its '2' design,
when lifted the diagonal shaft rests on the hind moldboard,
while the beam shaft is attached to the plow beam. This
menables the hitch to bear the implement without side support.

20

The implement shaft is set at an angle of 10° from the
horizontal (Fig. 1). This inclination is called The Angle
of Tillage. The one disadvantage of this hitch is its in-
elasticity of angle of tillage. Once set for a certain
angle of tillage, it is fixed. Any alteration in this

angle will have to be by means of furnace or torch heating

and reshaping of the joints.

The 'L' hitch. The basis of design of this hitch is
very similar to that of the 'Z' hitch, and therefore will
not be discussed. Figure 2 shows a detail sketch of this
hitch. This type of a hitch has most of the advantages of
the '2' type, plus being adjustable as regards the Angle
of Tillage. The direction lever allows adjustments within
a range of 35°. It consists of a metal bar that connects
the Pull shaft to the Hitch bar (Fig. 2).

The direction lever - adjusting the angle of tillage:

The direction lever support on the pull shaft was
welded in such a way that the triangle formed by the pull
shaft, hitch bar and the lever would be a 30°, 60°, 90°
triangle, with dimensions as shown in Figure 3 when the
angle of tillage is zero.

By a system of holes a, b, c, d, on the lever and the
lxitch bar, spaced as shown in Figure 3, various angles of
'tillage could be obtained from -15° to 20°, giving a range
«of 35°. When the Pull shaft is tilted at a certain angle,

 

 

 

 

 

 

 

 

 

 

Fm. 2 THE L H/TCH W/TH H/TCH BAR
AND DIRECT/0N LEVER
SCALE /- /0

21

22

the same angle is produced on the implement shaft due to the
fixed connection between the two shafts.
With reference to Figure 3 the various settings are

given in the following table.

TABLE VI
THE VARIOUS SETTINGS OF ANGLE OF TILLAGE FOR THE 'L' HITCH

 

 

Settings* Angle of Tillage**
0 on 0 0

A on 0 -10

A on D -15

Bon0 11

B on C 20

0 on C 6

O on D -5

 

 

«*The central hole on both the hitch bar and the lever are

designated as '0'.
«*wAngle toward the furrow is designated by a (- ) sign.

The disadvantages of the'L'hitch are:

1) Slightly longer time (than the'Z' hitch) needed to
mount and dismount on the plow

2) Need for a side support.

The hitch bar consists of two iron bars (1/2" x 3")
with symmetrical holes in them, spaced to fit on the plow

beam. The two bars clamp to the beam by means of a system
of bolts and nuts holding the two pieces together (Fig. 11).

Field tests showed both hitches to be practical and
well adapted to lifting and maneuverability. These hitches
were designed to be versatile. Thus, each has an implement
shaft such that an implement unit can be mounted on the
shaft, removed and replaced by another unit. Both hitches
were used with various implements.

The 'Z' hitch was used with:

1) Courey's short-toothed tiller

2) Courey's long-toothed tiller

3) The cultipacker unit.

The 'L' hitch was used with:

1) The cultipacker unit

2) The plow-packer unit.

The Field Tests
All the field tests on the various implements were

carried out on Brookston Clay Loam and Hillsdale Loam soils.

Courey's short-toothed tiller. The implement consists
of angle-iron spikes welded to a pipe. The unit slides on
and off the implement shaft of the hitch. Figure h shows
the tiller mounted on the 'Z' hitch. '

Field tests on this tiller proved it to be an effective
implement. Its light weight makes lifting easy. The teeth

25

 

Fig. h. Courey's short-toothed tiller
mounted on the 'Z' hitch.

do a good job of tillage. It leaves the soil surface
sufficiently smooth, while leaving the surface granules
comparatively coarse. The soil-stirring action of the
teeth aerates the soil well while causing good coverage
of trash. The tiller teeth mix the soil and the vegetative
cover satisfactorily. Its light weight and draft make
:manipulation.easy. It is economical in operation due to
low power requirements for pull.

Advantages:

1) Good job of stirring, mixing, aerating and trash

cover.

.9.)
O\

2) Economical in operation.

3) Ease of mounting and dismounting on the implement
shaft of the hitch.

Its limitation is that it is an effective tillage tool
only on heavier soils which do not need firming (clayey
soils). 0n sandy soils, its type of action is not essential,
and due to its light weight it does not help in firming.

The following table gives the specifications for the

tiller as well as those for the long-toothed implement.

TABLE VII
SPECIFICATIONS OF COUREX'S SHORT AND LONG-TOOTHED TILLERS

 

 

 

Specification Short-toothed Long-toothed
Tiller Tiller

Weight 20 lbs. 25 lbs.
Draft 60 lbs. 80 lbs.
Overall width 32 in. 30 in.
Number of teeth 6 LL
Width of each tooth 1 1/2 in. 1 1/2 in.
Spacing between teeth n 1/2 in. 7 in.
Diameter of pipe 2 in. 2 in

(on which blades are welded)
ILength of tooth ‘ 6 in. 8 in.

(from pipe to point)
Soil.penetrstion 5 in. 7 in.

Diameter of rotation 111 3/8 in. 18 3/8 in.

T -—J

 

 

 

27

 

Fig. 5. Courey's long-toothed tiller mounted
on the 'Z' hitch.

Courey's long-toothed tiller. This tiller does a suc-
cessful job of tillage and showed itself an effective tool
for once-over tillage. It stirs the soil thoroughly and
covers trash well. Due to its longer teeth it performs
'better for aerating and mixing. Its advantages and limita-

tixnns are the same as for the short-toothed tiller.

The cultipacker unit. This implement consists of a
gain; of cultipacker wheels as shown in Figures 8 and 9. Ten
cnlltipacker notched wheels are mounted on the implement
shaft of the hitch and held in place by means of collars.
Field tests showed the implement to be an effective tillage
tool.

\‘n. V '

I‘m-hit w «T:

I

q-

a
7' ‘3. a. ‘, ‘. “\K

‘3 ‘Wa. ‘5 by"
’1‘." ‘ ‘“ " 4‘4?

 

Fig. 6. Courey's long-toothed tiller shown
in the elevated position when lifted
with the plow.

 

Fig. 7. Courey's long-toothed tiller shown
in operation in the field.

TABLE VIII

SPECIFICATIONS OF THE CULTIPACKLR UNIT

 

Specifications
Weight 300 lbs.
Draft 95 lbs.
Overall width 38 in.
Number of wheels 10
Width of each wheel 3.8 in.
Diameter of axle hole 2 in.
Soil penetration 2 1/2 in.
Diameter of wheel 15 1/2 in.

 

 

Figure 8 shows the cultipacker unit when on the ground.
This implement is best adapted to sandy soils that need
firming. It leaves a smooth surface, covering trash well.
Its limitation is that it does not do sufficient stirring

and as such is not suitable for clay soils.

   

Fig. 8. The cultipacker unit used with the
'L' hitch shown when on the ground.

3 ' .' . .
. '»"‘!‘!.°:‘”')“'»c-

.’ r'
V. . ‘9‘, I,/’

4-;

\,"'./.'
,.‘.r/ . I

 

Fig. 9. The cultipacker unit about to be
lifted. The boom.is for side
support.

 

Fig. 10. The cultipacker unit lifted off
the ground. Note the outer end
of unit is supported by chain
clamped to boom.

 

Fig. 11. A view of the hitch bar and direction
lever of the 'L' hitch, and the boom
support on the plow beam.

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’2—mflfi-__ ’3 _

Fig. 12. The cultipacker unit in field
operation.

‘1.-

 

Fig. 13. Brookston clay loam field after
once-over tillage with the culti-
packer unit.

 

 

 

 

Fig. 1h. A Hillsdale loam field after once-over
tillage with the cultipacker unit.

The plow-packer unit. Several tests have been conducted

by the Soil Science and the Agricultural Engineering Depart-

ments to show the practicability of this implement for once-

over tillage. The author was mostly interested with the

weight problem involved in lifting this unit.
Analysis of the maximum weight that can be lifted behind

a plow is as follows: _
Wr 24/0 #

 

 

. ‘ l
. ‘ .v ‘ , O ' °
I. “9* - _ p -~..«- ~- -
e ,, l\.

J g . ,.,\_ - .9. x_ ,"._~.-;-

Fig. 15. The plow-packer unit used with the 'L'
hitch in tandem with a trail—type plow.
Note the boom and hydraulic cylinder
used for lifting.

Basing computations on a mounted plow:
Tractor data: (Ferguson, model 35)
Wheel base: 70"; tread: h8 " '
Shipping weight: 2&10 lbs.
Center of gravity: approximately one-third the distance
between axles, in front of the rear
axle. (1/3 x 70 = 23.3")
With reference to the diagram on page 33:
Moments at A: 2h10 x 23.3 = W'x 70
WI = 80h 1bs.; wz = 2h10 - 80h = 1606 lbs.
Using a Dearborn 2-bottom 1h" plow: weight = M20 lbs.

 

Fig. 16. Plow-packer used with 'L' hitch,

showing connections.

 

 

 

 

 

 

 

Iiaéav
204#
[00 II at n
i ‘i 7”
IJPLE'm-év? ----- PEAK/"- ——A I .- ------- I_ _

ZMA: 801; x 70 = (uzo x to) + 100 x
56,300 - 19,320 100 x
x 369.8 lbs. ‘9? 370 lbs.

The plow-packer weighs 350 lbs. Thus, as far as the tractor
stability is Concerned, it would be safe to lift the packer

behind the plow.

 

36

 

Fig. 17. View showing the plow tipping when
the packer was attempted to be lifted.

Basing computations on a trail-type plow:

Lifting tests were carried out on the plow-packer with
the 'L' hitch in tandem with a trail-type McCormick two-bottom
plow. To lift the packer a one-way hydraulic cylinder was
mounted on the plow-beam.

As expected, an overturning moment was caused tipping
the plow. Taking the plow to weigh 500 lbs, and the packer
to weigh 350 lbs, the analysis is the following in reference
to the diagram on page 37:

2MA : 350 x 60

Mx

(to x 250) + M"

21,000 - 10,000 = 11,000 in. lb.

 

37

 

Fig. 18. Another view showing the tipping

of the plow.

 

 

 

 

 

 

 

 

 

 

 

 

40”
J.
.H
350 # Ir: 60———- *4
2517;?
1 T
um... 60 ,, ...__. 24.--... 40'... s;

 

I
o
,
3 .
) l
h....,
F

ll.

 

38

An overturning moment of 11,000 in. lbs. is caused.
Hence, the tipping of the plow. For a trail-type plow,
therefore, with a load acting 60 inches behind the wheels
of the plow, the weight of the implement should not exceed

the value computed below.
60 X Fx 3 14.0 X 250 "L.-

F . 10 000 = 166_lbs.
x " "80'

Allowing a safety margin of h6 pounds, the load should not

1‘”AKUD.A_—t. ‘ ' . ._.

r.“ ..-..,_

exceed 120 pounds.

Stress Analysis

In order to check for stresses caused in the rear
plow-bottom.due to the weight of the implement resting on
it, a stress analysis test was conducted. The Brush equip-

ment was used, together with electric resistance wire SR-h

strain gages, type A-l.

Attachment of the gagg to the test structure. The sur-
face was made free of any coating, such as paint or mill
scale, and then made smooth by using a medium-fine-grain

The surface was cleaned thoroughly with a sol-

 

emery cloth.

vent (carbon tetrachloride). The test surface and the under-

side of the gage were coated with a suitable cement (Duco

cement) and the gage was applied to the test surface. .A
‘unifbrm.pressure was applied over the top of the gage to

assure uniform contact and to eliminate all excess cement

   

39

 

Fig. 19. Positions of the gages on the
rear plow-bottom.

between the gage and the surface. This pressure was main-
tained until the cement was thoroughly dry (about 2h hours).
The Brush equipment was set up in the laboratory and

the leads connected to the gages.

Checking for maximum strggg. Figure 19 shows the posi-
tions in which the four gages were placed to check the strains
caused at those points. The charts obtained for the differ-
ent points are shown in Figure 21.

Recorder speed: 5 mm./sec.

Attenuation: 10 f! in./in. per line.

With reference to Figure 21, the unit strains obtained are:

1) Point 1, e == 28,) in./in.

2) Point 2, e = 20)» in./in. (shock)

3) Point 3, e = 30 ,u in./in.

h) Point h, e = 70 ftin./in. (steady)

e = 120,01n./in. (shock-loading)

   

 

Fig. 20. Strain gages placed on the rear plow-
bottom connected to the Brush equip-
ment. Loading by the cultipacker unit
mounted on the 'Z' hitch.

Material of the plow - S.A.E. 1010
Modulus of elasticity E = 30 x 106 psi.
Elastic limit = 31,000 psi.

Unit stress S = E e.

Unit stresses at the various points are:

6 8h0 psi.

1) s = 30 x 106 x 28 x 10'

2) s = 30 x 106 x 20 x 10'"6

3) S = 30 x 106 x 30 x 10-6 = 900 psi.

600 psi.

 

ill

 

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L , 5‘ . A‘ . 5 ._ . I _ V . . , \ . I. ‘9 ‘ .

I I ' - . I V
r“.-.— _W-,__ —-—~—¢~-- --—4 _x..— ~§ -.— .-— .- ——.§ -_ ._- _, .-, .__-- - .. —'—~-‘——. __.—._. .4 4. -_. -_. —--- L \—-.—.4 - 4.—<— .— -——- 4-
l , It . L e . I v x‘ I Q a I . A O

x i ' ‘ ' \ ‘ ‘ \ - ‘ ‘\ » ‘ ‘ v v ‘ ~ ‘. ‘

.b . l l - - 3 a e ‘ . . . ‘ 1 u ‘ \ -.
- I _ - g, ‘ . - ..\ . . _‘ . . ‘ . ‘ l . , I . . ,

—'5_-. M.---- L ._...- ~_.-‘ ._ -__.---. —._e_ . . . __.—.__.... .1 —- -—~‘. J- —L Q—— t ‘

 

 

 

 

“RT Nf‘ EL 905? BRUSH E1 EC’i'RUNlCS (:0. «Ir-ANY comm)... of...

Fig. 21. Charts showing the strains indicated
by the various gages.

 

 

h2

 

h) S = 30 x 106 x 70 x 10'6 = 2100 psi. (steady-
loading)
S = 30 x 106 x 120 x 10'6 = 3600 psi. (shock-i
loading)
Maximum stress is seen to occur at point (h).
Checking for safety factor:
Safety Factor F.S. = Allowable Stress {41“-
Actual Stress Q
= 31,000 = 8.6 2
3. 00 i
Say a Safety Factor of 8:1. g
E

Shock loading takes place when the plow is being
lifted. In field Operation, the undulations in the field
will cause the implement to rock, which results in shock-
loading. ‘

The stress analysis test shows that stress caused in
the rear plow-bottom due to loading of the implement is within
the safe limits and, therefore, no damage is done by raising

and lowering the implement with the plow.

Force Analysis of the Soil Reactions

Soil Throw
The following diagram.shows the forces determining the

direction in which the soil is thrown.

 

b3

 

 

 

FR = Resultant force

FP = Force in direction of pull

FB = Force in direction of rotation of implement
FC = Resultant of Fp and PB.

S = Side force

Distribution of Pressure

The distribution of the vertical pressure on any hori-
zontal plane in the soil beneath a concentrated load is
represented by a bell-shaped surface (19). The maximum
ordinate of this stress surface is at the vertical axis.
Theoretically, the stress approaches zero at infinity; but
for practical purposes it may be considered to reach the

zero value at a relatively small finite distance. The

tn. 1. _ in. ,
i

 

3+4

maximum.pressure ordinate is relatively high at shallow
depth, and it decreases as the depth increases. In other
words, the bell-shaped surface flattens out with increasing
depth.

If the stress surface is plotted for each of a series
of horizontal planes at various depths and if points of
equal stress on the various planes are connected, a surface

of revolution having a bulb shape is developed. Such a sur-

'- v."§f.l 3‘ '

face, which is often called the bulb of pressure, is illus—

trated in Figure 22. The pressure at each point on the

 

pressure bulb is the same. Pressures at points inside the
bulb are greater than that at a point on the bulb surface;
and pressures at points outside the bulb are smaller than
the pressure at points through which the bulb surface passes.
Any number of bulbs of pressure may be drawn for any applied
load, since a different one corresponds to each arbitrarily

chosen value of pressure.

Friction Between Implement and Soil

When the implement is at rest, it is in equilibrium
under its own weight w and the equal and Opposite reaction
N provided by the soil (Fig. 23a). When a horizontal force
S is applied to the implement, it will be balanced by an
equal.and opposite force S in the plane of contact, and
the implement will remain at rest if the force is relatively

small. If the applied horizontal force is gradually

I4;- .. L. n

 

1L5

 

Ground surface

 

 

 

 

l I . }
.__ijLflijL} ‘ ‘ if) J___L_L__.

———- Bulb of pressure

 
 

 

 

 

 

Fig. 22. Bulb of pressure or Iso-stress
surface.

 

 

. 1' -
“'1'

 

1+6

increased, the resisting force will likewise increase, always
being equal in magnitude and opposite in direction to the
applied force. There is a limit, however, to the amount of
resistance which can be developed at the plane of contact;
and, when the applied force equals or exceeds the maximum
possible resistance, equilibrium will be destroyed and the
implement will move along the soil. This movement is a ;
shear failure. The applied horizontal force is a shearing
force and the developed force is friction or shearing resis-

tance. The maximum shearing resistance which a soil is f

 

capable of developing is called the shearing strength.

Friction Angle
The resultant R of the shearing force and the weight

acts at an angle with the line of action of the force repre-
senting the weight. This angle, designated as cz'in Figure
23b,is called the obliquity of the resultant or simply the
obliquity angle. When the shearing force is increased to a
value Just equal to the shearing strength, that is, when
sliding or failure is impending, the obliquity angle reaches
its maximum value and is designated (xi. The forces that are
applied normal and tangential to the shear plane are related

to each other in accordance with the following equations:

tan 0‘ = SQ

 

M7

 

 

 

 

_
_ .3 - - .x.
. f I \
_ fl. QwJ\ _
M» n N W _. \«Mva L
\ ,K d 11.414?" - v
I.\ _ d\\x\ __ I.
_\\m s:

 

 

 

 

Force diagram of the action of the

23.

Fig.

of the

implement and the reaction

soil.

In a similar manner, the reaction N to the weight of
the implement, which also acts normal to the shear plane,
may be combined with the shearing resistance to obtain a
resultant R, which makes an angle ’00, with the normal. This
angle fl; is called the developed friction angle; and it is
equal to the ooliquity angle since the reaction is equal to
the weight and the shearing resistance is equal to the ap-
plied shearing force. The angle 4 depends on the magnitude
of the applied shearing force, as long as this force is not
sufficient to cause shear failure. The angle Q2,reaches its
maximum value at failure and this maximum value is designated
as g? , as shown in Figure 230. This limiting angle Q? is
called the friction angle and constitutes a physical property
of the soil.

If shear on an interior plane in a mass of soil is con-
sidered, the angle Q? is a property of the soil, and the
value of tan ¢ is called the Coefficient of friction of the
soil. This Coefficient is here denoted by [I . The value
of tan ¢ is equal to the shearing strength of the soil
divided by the reaction normal to the shear plane. Also it
is equal to the shearing stress at failure divided by the
aPplied weight force normal to the shear plane.

Thus,

tan = = Sr = Sm = tan 6K
¢ /* N w m

 

 

. ‘ -.'-../-flt- . .. .

 

For example, if the friction angle ‘1 of a cohesion-
less soil is given as 20°, it means that the soil is capable
of providing sufficient shearing resistance to maintain
equilibrium as long as the applied shearing force produces
an angle @less than 20°. When the applied shearing force

causes fiavto become equal to or greater than 20°, shear

failure will result.

Cohesive Soil

Some soils have a finite shearing strength even when
they are not subjected to external forces normal to a shear
plane. Furthermore, when soils of this kind are subjected

to normal forces, the shearing strength is not increased.

These are called cohesive soils; and their shearing strength,

which is independent of normal pressure, is called cohesion
or no-load shearing strength. Cohesion may be illustrated
by considering two sheets of fly-paper with their sticky
sides in contact. Considerable force is required to slide
one sheet over the other, even though no normal pressure is
applied. The shearing resistance in this case is due to
cohesion between the sticky surfaces. In contrast to this,
Shearing resistance due to friction may be illustrated by
ccnasidering two sheets of sandpaper with their sanded sur-
LEaces in contact. These may be very easily caused to slide
cyver'each other when no normal force is applied. When a

normal force is applied, the resistance to sliding or the

-J‘M‘th

; l-v -r

So

shearing strength increases in direct prOportion to the

normal force.

Total Shearing Strength of Soil
Most natural soils exhibit shearing resistance due to
both cohesion and friction. These components of strength

are found to exist in widely varying relationships, ranging g

th.-+1-

from zero cohesion in the case of clean dry sand to practic-

ally zero friction in the case of fine-grained, highly plastic

mil-lava 'm r' ‘

clay. The cohesion and friction components are added to-

u‘l‘

gether to give the total shearing strength properties of
soil. The shearing strength is expressed by an empirical
formula proposed by Coulomb (19). This formula is:

s = c_+N£an¢'

S = Shearing strength, in pounds per square foot

C = Cohesion, in pounds per square foot

N = Pressure normal to shear plane, in pounds per square

foot

¢= Friction angle of soil

tan g: ,a = Coefficient of friction.

The Coulomb formula is an equation for a straight line
having an intercept on one coordinate axis. A typical graph
of the equation is shown in Figure 2h, in which unit pressures
:normal to a shear plane are plotted as abscissae and unit
shearing stresses are plotted as ordinates. The intercept

.at zero pressure represents the cohesion of the soil, and

the angle which the graph makes with the horizontal is the
friction angle g6 .

A graph of this kind is called a shear diagram. If
the diagram is extended to the left of the origin and the
graph is prolonged to intersect the horizontal axis, the
distance from this point of intersection to the origin may
be thought of as an internal initial stress which is in-
herent in the material and is associated with the cohesion
property. It is analogous to molecular attraction in solid
materials. If the origin is transferred to this point of
intersection, a new shear diagram representing total stresses,
both initial and applied, is obtained; whereas the diagram

as first drawn represents applied stresses only.

' ‘Dsu at 2" out:

if n 1‘:

S2

 

S =.&H£7LRHV6:S7VHFSS

 

 

\
\

\
\
‘—

 

o N... NORMAL UNIT PRESSURE
shew—17a.T
.STWETS

 

Fig. 2h. Graph of Coulomb Formula for
shearing strength of soil.

CONCLUSIONS

As a result of the tests on the various implements
and a study of their applications, the following conclu-
sions can be derived:

The once-over method of tillage is very practical and
a time, labor and money-saving system. For the conditions
and the crops to which it is applicable, it provides all
the tillage that is necessary in preparing the seedbed.

It avoids excessive packing of the soil and preserves the
soil structure.

. Liftable once-over implements are an efficient means
of tillage as they are simpler to operate than the trail-
type implements, and eliminate dragging and tearing of
soil at the ends of the field.

Courey's long-toothed and short-toothed tillers are
well adapted to clayey soils. The cultipacker unit is
most effective on sandy soils which need packing.

The weight of the implement lifted causes stresses in
the moldboard of the rear plow, the maximum stress being
caused around a point designated by gage number four in
jFigure 19. By keeping the weight of the implement within

safe limits, the stress caused in the moldboard will be
negligible and lifting the implement will cause no damage

to the moldboard.

:11
+-

SUGGESTIONS FOR FURTHER STUDY

The advantages of a once-over tillage method using
liftable implements are manifold. It offers great possi-
bilities as a time and labor-saving device, which does an
effective job of seedbed preparation. Various aspects of
this system offer a challenge to ingenuity of design and
ability of analysis.

Research in design work for various shapes of a lift-
able tillage implement would hold great promise. This work
should be done while considering the type of action of the
implement on the soil, whether it would produce the ideal
seedbed profile - the lower part of the seedbed should con-
tain the finest granules and possess the firmest degree of
settling, with the coarseness of the granules increaseing as
the surface is approached.

Another interesting study would be a weight analysis of
the different types of metals that could efficiently (and
economically) be used in the design of such an implement.
In.lifting, weight of the implement is a definite problem;

ihence, the importance of this study.

_ZflflA- 0

19-1-

1.

2.

3.

10.

SELECTED BIBLIOGRAPHY

Baver, L. De
Soil Physics. John Wiley and Sons, New York. l9h8.

Baver, L. D.

The physical properties of soil of interest to
agricultural engineers. A. E. Jfi3Vol. 13: 32h,
Dec. 1932. .

BlaCk, P c He
Machine Design. McGraw-Hill Book Co., New York.

19MB.

Clyde, A. w.
Measurement of forces on soil tillage tools. A. E. J.
Vol. 17: 5, Jan. 1936.

Clyde, A. We
Load studies on tillage tools. A. E. J. Vol. 18: 117,

1937.

0001‘, R. L.
Are your tillage methods up to date? Hoard's Dairyman.
March 25, 1953. -

Cook, R. L.
A comparison of tillage implements. A. E. J. Vol. 31:
211, 1950.

Cook, R. L., and Peikert, F. W.
A comparison of tillage implements and their effect
on crOp yields. Michigan Agricultural Experiment
Station Quarterly Bulletin, Vol. 32, No. 1: th-llB,
August l9h9.

Cook, R. L., Turk, L. M., and McColly, H. F.
Tillage methods influence crop yields. Soil Science
Society of America Proceedings (SSSAP), Vol. 17, No. A,

- October 1953.

Gordon, E. D.
Physical reaction of soil on plow disks. A. E. J.
Vol. 22: 205, l9hl.

*A.E.J. = Agricultural Engineering Journal.

 

11.

12.

13.

1h.

15.

16.

17.

18.

19.

20.

214

HOitBhu, D. C.
Kinematics of tractor hitches. A. E. J. Vol. 33:

3&3, 1952.

Kummer, F. A., and C00per, A. W.
The dynamic properties of soil. A. E. J. Vol. 26:

21, 19MB.

LOO, G. H.
An Introduction to Experimental Stress Analysis.
John Wiley and_Sons, New York. 1950.

”I

McColly, H. F., and Cook, R. L.
Power and labor requirements of seedbed preparation.
Agr. Eng. Dept. Mimeo. Mich. State Univ., March 1952.

McColly, H. F., and Cook, R. L.
Good yields with less work (Once-over tillage gives).
Crops and Soils, What's new in. Vol. 7, 18, April-May,

1955.

McKibben, E. G.
A study of the dynamics of the disk harrow. A. E. J.
Vol. 7: 92, March 1926.

mam-”i can _n. u... s. .m-

- céT'lr‘ 7

'WT‘"

N1Ch018, M. Le

Methods of research in soil dynamics as applied to
implement design. Alabama Experiment Station Bulletin,
May 1929. Also, A. E. J. Vol. 13: 279, 1932.

RfifldOlph, J. W.
A method of studying soil stresses. A. E. J. Vol. 26:

13h, June 1925.

Spengler, M. G.
Soil Engineering. International Textbook Co. Scranton.

1951.

Standard Dimensions and Specificiations (ASAE - SAE).
Application of hydraulic remote control to farm tractors
and trailing-type farm implements. A. E. J. Vol. 32:
328, 1951.

Worthington, W. H., Seiple, J. W.
Hydraulic capacity requirements for control of farm
implements. A. E. J. Vol. 33: 273, 1952.

22. Yoder, R. E.
The significance of soil structure in relation to the
tilth problem. Soil Science Society of America Pro-
ceedings (SSSAP). V01. 2: 21-33, 19370

 

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