WERAYEONAL AND TECHNICAL REQUIREMENTS
BNFLUENCING THE $HAPE OF AGRICULTURAL YRACTORS

Thanh: for flu- Dagmo of Ph. D.

MUCWGAN STA-VI UNWERSlW

Per Eb!” Swarm Damon
1960

TH ESlS

09* LIBRARY

Michigan State
University

 

This is to certify that the

thesis entitled

OPERATIONAL AND TECHNICAL REQUIREMENTS INFLUENCING
THE SHAPE OF AGRICULTURAL TRACTORS

presented by

Sverker Per Ebbe Persson

has been accepted towards fulfillment
of the requirements for

Ph.D, degree in Agricultural
Engineering

X/ZM%

Major professor
13mm

0-169

OPERATIONAL AND TECHNICAL REQUIREMENTS INFLUENCING
THE SHAPE OF AGRICULTURAL TRACTORS

by

LSverker Per Ebbe Persson

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1960

.Approved: 27<;{’;2?;>7§732éar{:§;9’

ABSTRACT

All implements for farming operations need power in some
form. For field operations this power is now generally supplied
by an automotive power unit consisting of engine, transmission,
wheels and means for control and for attaching implements, all
mounted in a suitable frame. It seems likely that an automo-
tive power unit containing the same basic parts and interchange-
able between different implements, will be used for field opera-
tions in the future also. For farmstead operations other types
of power units seem preferable.

The implements and the power unit are now both mechanical
devices which could be integrated into one operational unit.

In order to increase the operational efficiency this integra-
tion should be carried as far as possible. When judging exist-
ing designs and developing improved designs implement and power
unit should therefore be treated together as one unit.

The implements are the most important parts of the combin-
ation implement -- power unit, because they perform the direct
operation on the soil, the product, etc. The requirements of
the implements should therefore be given the primary considera-
tion. Some of these requirements are operational, being dic-
tated by the product and the method for handling the product;
others might be called teChnical, being connected to a certain
design of the implement. The operational requirements refer

to such factors as supervision, height control, steering and.

other adjustments, position within operational unit, field
conditions, quantities of product involved, etc. Requirements
from the implements on horizontal pull, vertical and lateral
supporting forces, power for rotating parts, speed and speed
adjustment, room needed for implement, etc., may be classified
as technical requirements.

Also the functional requirements of the elements of the
power unit must be satisfied if an efficient combination imple-
ment -- power unit shall result. Because this study is limited
to requirements affecting the general shape of the power unit,
the only thoroughly discussed requirements from the power unit
are the requirements on good drive and steering effectiveness,
sufficient stability and suitable driver position. Some tractor
mechanics needed for the discussion of these requirements are
given in Appendices A and B.

Many implements are now combinations of elements perform-
ing different functions. In this study such implements have
been broken apart in their elements and the requirements re-
ferred to the elements instead of to the whole implement. In
this way it is possible to arrange each element in its best
position and to determine the effectiveness of other arrange-
ments and other combinations than are presently used.

The operational and technical requirements of the imple-
ments are briefly listed in tables 201-215 and the functional
requirements of the parts of the power unit discussed in sec-
tion III. Especially the tables 210-215 are incomplete because

the information needed is not available.

Starting from the requirements power units can be devel-
oped. The procedure suggested in section IV is to start making
power units for a single implement. In this way the require-
ments of that implement can be satisfied as far as possible.
The most efficient operational unit should be found in this way.
Factors to be determined at this stage are wheel, drive and
steering arrangement, weight distribution and engine power.

There are, however, only very few cases where a power
unit for economical reasons can be used for only one implement.
In some cases the individual power units for different imple-
ments might be similar enough to permit the use of the same
power unit for these implements without any important change,
but in most cases compromises in the design must be made. Most
consideration must thereby be given to the requirements of the
most important implements. The importance of an implement may
be measured by the area for which it is used, by the number of
"times it is used, by the value of the product processed, etc.

It is probably not possible to make a single, general
purpose power unit for all types of implements without a great
loss of effectiveness for at least some of the implements.
Differentiated power unit types, for instance tillage tractors,
harvest tractors, etc., will, however, presumably be needed as

the demand for more efficient power increases.

OPERATIONAL AND TECHNICAL REQUIREMENTS INFLUENCING
THE SHAPE OF AGRICULTURAL TRACTORS

by

Sverker Per Ebbe Persson

A THESIS

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1960

 

ACKNOWLEDGMENTS

In the long time since I first started studying the fac-
tors affecting the shape of the agricultural tractor, I have
received inspiring impulses from many persons. Among those
who have in a valuable way contributed to this doctoral thesis

I would like to give special thanks to the following:

to my major professor Howard E. McColly, who has greatly en-
couraged me and in numerous discussions has helped to
bring my disorderly ideas together and also has corrected
linguistic mistakes,

to professor ngig L. Qgtg, whose teaching on similar problems
concerning automobiles has greatly inspired me and among
other things has given the impulse to my way of treating
the drive effectiveness,

to Dr. Wesley E. Buchele and Dr. William Dowell Eaten for their
help as members of my guidance committee,

to the E. 5. Kellogg Foundation, for the generous fellowship
which made my studies possible,

to professor Nils gerglund and the figygl Agricultural College,
Uppsala, for giving me leave of absence for the time when
this thesis was prepared,

to Dr. Arthur E. Farrall and the ggricultural Engineering De-

partment, Michigan State University, for providing facili-

 

ties for my studies,

iii
to my wife, Anne Marie, for checking equations and typing manu-
script,

to Mrs. Joann Piermattei for typing and assembling the thesis,

 

to engineers in tractor manufacturing industries and agricul-
tural engineering departments, and to farmers, who all
have given their opinions and suggestions on the subject.
Uppsala in February 1960

Sverker Persson

TABLE OF CONTENTS

InLI‘OdUCtIOn. o o o o o o o o o o o o o o o ‘o o o o o 0
Limitations and general assumptions of this study.

Section I. Farming operations in which agpower unit
is needed 0 O O O O O O O O O O I O O O O O O O O 0

Chapter 1. A general review of farm operations
and their power sources . . . . . . . . . . .

Field operations . . . . . . . . . . . . . . .
Farmstead operations . . . . . . . . . . .
Loading and transport operations . . . . . . . .

Chapter 2. Basic parts of field operations, where
an automotive power unit is used. . . . . . .

Chapter 3. Combinations of operations . . . . . .

Chapter h. The relative importance of the dif-
ferent field operations . . . . . . . . . .

An analytical determination of the duration and
frequency of farming operations with an
automotive power unit involved. . . . . . . .

Section II. Characteristics of implements and their
operation of importance for the_ppwer unit . . . .

Chapter 5. The requirements of the implements are
the most important factors, determining the
power unit design . . . . . . . . . . . . . .
Chapter 6. The requirements of the implements . .
Section III. Thegparts of thegpower unit . . . . . . .

Chapter 7. The functional requirements of the
parts of the power unit . . . . . . . . . . .

The engine . . . . . . . . . . . . . . .
The transmission . . . . . . . . . . .
Connecting power unit and implement. . . .

The driver and the driver' 3 platform (cab) .
The power take-’Off o o o o o o o o o o o o o

10
10

15
29

32

33

hi

bl

1&3
60

62
62

64
68

73

Chapter 8. The drive effectiveness of a power
unit. 0 O O O O O O I O O 0 O O O O O O O O

Drivewheel loading effectiveness . . . . . .

Level ground. . . . . . . . . . . . . . .

On a slope. . . .

The effect on the drivewheel loading effec-
tiveness of a change from rear-wheel
drive to front-wheel drive . . . .

The stall limit . . . .

Effect of nonsymmetric weight distribution.

Ground grip effectiveness. . . . . . . . . .
The maximum load on a wheel . . . . . . .
Influence of the wheels on each other . .
Other factors influencing fopt' . . . . .

Chapter 9. The stability of the power unit. . .

Longitudinal stability . . . . . . . . . .
Static stability. . . . .
Instability due to rolling resistance . .
Instability due to pull . . . . . . . . .
Inertia instability . . . . . . . . . . .

Lateral stability. . . . . . . . . . .
The basic lateral stability . . . . . . . .
The stability of front and suspension y”. .
Side pull influence . . . . .
Influence of the height of the center of

gravity of the power unit. . . . . .
Influence of the height of the implement. .
Influence of implement position sidewise. .
The angle of lateral stability. . . . . . .

Chapter 10. Steering effectiveness of an agri-
cultural power unit . . . . . . . . . . . .

What causes a vehicle to turn? . . . . . . . .

Steering systems . . . . . . . . . . . . . . .

What opposes turning? . . . .

Influence of rolling resistance on steering
effectiveness . . . . . . . . . . . . .

Lead on the steering wheels. . . . . . . . . .

Section IV. Thepower unit . . . . . . . . . . . . .
Chapter 11. Wheel arrangements. . . . . . . .
Chapter 12. Individual power units. . . . . .

Power unit for moldboard plow. . .

Power unit for a grain drill . . . . . . . . .
Power units for other implements . . . . . .

gage

101
101
102
102

105
107

108
109
116
117

121
125

vi

Chapter 13. Power unit for more than one
implement O O O O O I O O O O O O O O O O 0

Is it absolutely needed that the power unit
can perform every operation on the farm? .

Summary and further investigations. . . . . . . . . .
Summary. . . .‘. . . . . . . . . . . . . . . .
Further investigations on this subject . . . . .

References. 0 O O O O O O O O O O O O O O O O O O O 0

Appendix A. $93 forces between a wheel and the ground.

Resultant forces in the wheel plane. . . . . . .

The coefficient of net traction. . . . . . .
DISCUSSIOH 0f X1 0 o o o o o o o o o o c o o

Stresses in the wheel-ground contact area. . . .

Pressures and sinkage. . . . . . . . .
Traction as a function of soil values. . . .

Steering forces on a wheel . . . . . . . . . . .
Resistive moment on a steered wheel. . . . . .

Appendix B. Basic equations of mechanics for a power
unit 0 I I O O O O O O O I O O O O O O O O O O 0

System of notations for forces, distances, etc..

Forces . . . . . . . . . . . . . . . . . . . .
Some ratios. . . . . . . . . . . . . . . . . .

Basic equilibrium equations for a power unit and
its implement . . . . . . . . . . . . . . .

Forces in the longitudinal plane on a two-axle
power unit with implement . . . . . . . . .
The air resistance . . . . . . . . . .

Forces in planes, perpendicular to the direction

of travel . . . . . . . . . . . . . . .
The ”centrifugal force". . . . . . . . . . .

O

125

128
130
130
135
138

A1
A1

At
An

A12

A12
A13

A15
A17

Bl
Bi
132
Ba
Ba
BS
BIO

B11
BZO

101
102
103

LIST OF TABLES

Field operations and suitable power units. . .
Farmstead operations and suitable power units.

Loading and transport operations and suitable
power units. . . . . . . . . . . . . . . . . .

105-114 Basic operations and combinations of

Operations . . . . . . . . . . . . . . . .
105 Tillage, seed-bed preparations and planting. .
106 Field work during the growing season . . . .
107 Harvest of green matter (grass, legumes, corn,
etc., for silage or direct feeding). . . . . .
108 Hay harvest (straw harvest). . . . . . . . . .
109 Small grain harvest. . . . . . . . . . . . . .
110 Corn harvest for grain . . . . . . . . . . .
111 Potato harvest . . . . . . . . . . . . . . . .
112 Beet harvest . . . . . . . . . . . . . . . . .
113 Transportation . . . . . . . . . . . . . . . .
11h Loading. . . . . . . . . . . . . . . . . . . .
120 Actual use of power units and implements .
121 Major craps for different types of farms,
examples . . . . . . . . . . . . . . . . . . .
122 Size and frequency of the operations for some
major crops. . . . . . . . . . . . . . . . . .
123 Acreages covered yearly in operations on farms
of different types . . . . . . . . . . . .
201-206 Operational requirements . . . . . . . .

201 Tillage, seed- bed preparation and planting

Operations . . . . . . . . . . .

12

17
19
20

21
22

23
24

25
26

27
28

3A

36

37

39
an

#6

viii

202 Field operations during the growing season . . . . 47
203 Harvesting of green matter, hay and silage . . . . 47
204 Grain harvest. . . . . . . . . . . . . . . . . . . 48
205 Harvesting of root crops . . . . . . . . . . . . . .49

206 Transport and loading Operations . . . . . . . . . 50

210-215 Technical requirements . . . . . . . . . . . . 51
210 Tillage, seed-bed preparation and planting . . . . 54
211 Operations during the growing season . . . .1. . . 55
212 Harvesting of grass, hay and silage. . . . . . . . 56
213 Grain harvest. . . . . . . . . . . . . . . . . . . 57
214 Root harvest . . . . . . . . . . . . . . . . . . . 58

215 Transportation and loading . . . . . . . . . . . . 59
301 Basic types of steering. . . . . . . . . . . . . . 103
401 Variables in wheel arrangements for a power unit . 111

402 Basic wheel arrangements for power units . . . . . 112

A1 Examples of distance of rolling resistance, x1 . . A9

A2 Calculated distance x1 for special cases of
wheel-ground contact . . . . . . . . . . . . . . . A10

INTRODUCTION

 

The aim Of man always has been to employ power as extensively
as possible to his services, thereby making it possible for him
to produce more and secure a more comfortable living, the word
comfortable taken in a broad sense. This has been true in
agriculture, too. The earlier steps have been the replacement
of human energy by animal energy. Today, this evolution means
using larger and larger mechanical power units (electric,
atomic, solar included). We are, however, in agriculture far
from using the largest power units available in other fields.

The limit for the size of the power unit usually is set by
economic factors, but sometimes technical difficulties--both on
the power-unit side and on the implement side-~make the applica-
tion of large power useless. The economic limit is determined
by the size and type Of farm, the labor Situation, et a1.; and
it changes from time to time. The technical limit can be pushed
further away through new methods of converting the power in
efficient work, through combination of Operations, through
develOping entirely new methods for a certain basic Operation,
and so forth. This study will be limited to the efficiency in
converting power into desired work of the kind normally used
‘today and will leave Open the possibilities of using entirely
new methods of treating the soil, the crOp, etc. The economic
limit cannot be discussed at any length, but will be mentioned

briefly.

2

Connected to and of the same importance as the tendency of
using bigger sources Of power for a certain Operation is the
tendency Of reducing the human effort needed for the same
Operation. Though far from completed, great progress has been
made in the efforts to reduce human physical work. The psychical
strain (inconvenience) has not been reduced to the same extent
and actually has been more accentuated in some cases. This
study will, as far as possible, take these aSpects in consider-
ation, too.

The two tendencies mentioned always have existed more or
less pronouncedly. The reason why a study Of the basic design
of the power units seems justified just now is that the
possibilities Of further improvements of existing power units
by only slight changes in their design seem limited. Many
power units still Operate on the same principle as their
predecessor the horse, i.e., by merely pulling the implement.

A mechanical power unit can be capable of doing much more than
this; these additional possibilities could be advantageously
utilized for many Operations. The possibility Of mounting the
implement directly on the tractor has been used to some extent
and has meant a great improvement in some cases. The general
shape of the tractor, however, usually has not been changed in
such a way that we can take full advantage of the possibilities
Of mounting implements. The number of implements that can be
mounted is limited.

There is an increasing tendency to use self-prOpelled

implements for certain Operations. In this case, the power unit

3

is used for only one implement and can therefore be tailor-made
for its requirements. In this way, an Operational unit with the
highest possible efficiency ought to be found. From an economic
standpoint, however, it seems impossible to make all implements
selffprOpelled. Before accepting this as the goal Of the
evolution, all other ways should therefore be investigated to
see if it is possible to reach, or at least approach, the
indisputably superior Operational performance Of the self-
prOpelled implement using the same power unit for several

implements.

Limitations and General Assumptions of this Stugl

As mentioned previously, the study will be limited to
farming Operations as we know them today, either that they have
been used for a long time or that they have been develOped lately
but show such promise that they can be supposed to be in practical
use in a near future. Beside this, further assumptions must be
made according to the conditions on the farm for which the power
unit and its implements has to be selected and where they have
to work. I assume that some of the more important ones in this
connection must be:

1. The only source of power Egg §$e1g_pp§k_will be a
power unit with an internal combustion engine of
any type. £23 3933 Ag, pp_;p the neighborhood
22, £22 farm buildings, either electric motors or
internal combustion engines would be used, with a
preference for the former. NO animal power will
be used.

2. Normally there will not be more than one Operator
on each machine. The possibility of one Operator
handling two or more machines will be discussed
in the study.

3. The farm always will consist of several fields.

.There usually will be more than one product
produced (different animal products included)

with the Objective of minimizing the risks if one

5
product should fail. The number of products on
each farm, however, will be smaller than today.

4. I will disregard, from a functional standpoint,

such irrelevant reasons as styling and convention.

The study is intended to give some aSpects on the future
develOpment of the power unit. Types which do not exist today
therefore will be discussed together with existing construction.
This extension of the field of discussion will be indicated by
the use of the words "power unit" instead of the word "tractor,"
with the purpose not to lead the thought to the shape of the
tractor of today. The expression ”power unit" will include all
types. e.g., those of self-prepelled machines, and will be more
strictly defined later on.

As mentioned above, the self-prepelled implement, Specially
designed for a single Operation, ought to be the most efficient
unit for this Operation. A logical first step seems, therefore,
to be to study the basic Operations and the implements used to
perform them and to determine which requirements these implements
have on their power units. The next step is to try to find the
best power unit for two or more Operations or implements. This
usually will involve a compromise; consequently, some measure of
the relative importance Of the Operations is needed. These
factors might be called Operational and are treated in Sections I
and II.

Of course, there are technical factors determining the basic

shape of the power unit. As such can be mentioned traction,
steering, and stability Of the power unit. The equations governing
these factors are given in Section III.

6

The different tractor types are described and compared
in Sectionlv, using the earlier discussion of the factors which

ought to determine their shape.

SECTION I; EARNING OPERATIONS IN WHICH
A POWER UNIT IS NEEDED

 

Chapter 1. A General Review of Farm Qperations

and their Power Sources

 

This study later on will discuss only the automotive
agricultural power unit, i.e., a power unit with similar tasks
as the present agricultural tractor. It may, however, be '
worthwhile to start with a more complete list of farm
operations and implements and to indicate what other power
sources might be used besides the mobile power unit. In some
cases,depending on the conditions, alternative power sources
might be used.

A first division of the Operations may be made into:

1. field Operations, i.e., Operations dealing with the
plants;

2. farmstead Operations, i.e., Operations dealing mainly

with the animals and the processing of agricultural
products.
3. transportation of farm products;

4. forestry Operations (will not be treated here).

Some Operations could be carried to more than one of the groups.

Field Qperations
These Operations include preparation pf the soil before
planting, plantipg and caring for the plant when it is growing,

and harvesting.

TABLE 101. FIELD OPERATIONS AND SUITABLE POWER UNITS.

 

Operation Type of power source
Beet Egpally_good Unusual

 

alternative alternative alternative

Field improvement:
Land clearing

Drainage contr apu
Terracing, pond
building
Land smoothing apu contr
Soil preparation:
Plowing
Moldboard plow
Disc plow apu
Rotary plow
Shallow plowing apu
Harrowing, cultivating
Heavy cultivator apu
Rotary cultivator
Light barrow
Rolling apu
Spreading lime contr apu
manure apu
solid fertil. apu contr
liquid " apu contr
Planting and care of the plant:
Planting
Small grain and grass
seed
Corn and beans
Beet seed apu
Potatoes
Seedlings
Thinning apu
Spraying apu contr
Dusting contr apu
(Cultivating)
(Topping)
Harvesting

Grass and legumes
Mower (cutting the crop)
Tedder
Rake apu
Grass loader

 

Abbreviations, see page 11

may; 1014 cont .

 

 

 

Qperation Type of power source
Best Eguallyigood Unusual
alternative alteppgtive alternative

Hay loader apu
Baler apu contr
Chopper apu
Small grain and grass seed
Windrower apu
Binder
Combine apu contr
Corn _
Corn picker apu
Corn sheller}
Potatoes
Potato stalk cutter
Non-collecting potato apu
harvester
Collecting or direct load—
ing potato harvester apu contr
Root crops
Root lifter} apu
Tapper
Collecting root-harvester apu contr
Tick-up ro'at loader }
Special crops (vegetables etc.) apu contr
Preparing the harvested crop
for the market (stationary
or semistationary equipment)
Dryer for grain (hay) elmo apu
Cleaner for'grain elmo contr
Grader, dryer, etc. for
various crops elmo

 

Abbreviations, see page 11

 

 

10

Farmsteadfigperations

The basic Operations are, to a great extent, the same for
all common kinds Of animals; cattle, (horses), swine, and
poultry. They include preparation and distribution of the
feed, cleaning of the buildings, and milking. A great part of
the Operations connected with the animals may be classified as
loading and transportation and is placed accordingly in that
group. Some other Operations often are included in the daily
process of feeding cattle, e.g., cutting and chOpping grass or
corn for feed, but these Operations are in themselves field
operations and as such are included in the group Operations
connected to the plant. Manure spreading is another such daily

operation on some farms..

Leadingand Traneport Operations

Certain of the Operations mentioned earlier include a
loading or transportation part, but this is only a minor part
of the whole Operation carried out by the machine. Loading is,
in itself, a sort of tranSportation and sometimes can be
carried out by the same implement as performs the tranSport in
a more restricted, common notation.

In tables 101 - 103, some possible power sources for the
different implements (Operations) have been given in order of
importance. The "best“ alternative does not always reflect
what is presently most common, but what could be considered good
practice under most conditions. In quite a number of cases,

however, the ”equal” alternative may be the best, and in a few;

p.»
9"

TABLE 102. FARMSTEAD OPERATIONS AND SUITABLE POWER UNITS.

 

 

Operation Type of powep soupce
Best Equally good Unusual

 

alternative alternative alternative

Feed preparation:
Grass and legume crops
Stationary chopper elmo apu
Silo distributor}

Silo unloader elmo
Grain
Mills - elmo apu
Mixers elmo
Feed distribution elmo pneum., hydr.
Barn cleaner: conveyor
type elmo
washing type elmo
Milking machine elmo stat
Water supply elmo stat
WorkshOp: power tools elmo pneum.
welding line elmo apu or stat
Emergency electric power
supply apu stat

 

Type of power source:

‘epp_= agricultural power unit, automotive, 'farm tractor'

ceptr. - contractor's (seller's, buyer's) unit, tractor, vehicle
elmo a agricultural electric motor

gtat a stationary engine, movable, not connected to a power supply
farm a farmer's own

hand : hand Operated

pneum. a pneumatically (hydraulically) Operated

£293:-

12

TABEE 103. LOADING AND TRANSPORT OPERATIONS AND SUITABLE POWER UNITS.

 

Operation Type of_power source
Beg Egually good Unusugl

 

t
alternative alternative alternative

Loading:

front loader and other loaders
attached to the tractor and

taking one piece at a time apu
continous loader apu and elmo stat
heavy loader contr apu
excavator and crane}
stationary manure loader elmo
unloading device elmo apu stat
hoist, stationary elmo pneum hydr stat
small crane
loading platform pneum hydr
Transportation
truck I farm contr
tractor trailer apu
tractor load platform apu
fan . elmo apu stat
conveyor }, elmo stat apu
pump ,
rail conveyor elmo hand
fork truck special apu
Snow plowing apu contr

Road scraping

 

Abbreviations, see page 11

13
Nthe ”unusual" alternative. The table has been used as a basis
for further discussions.

Some of the reasons that have influenced the choice of
power source for the different Operations may be givén as
follows:

Contractor units may be preferred for such Operations
which will be best performed by heavy, expensive, Specialized
implements, requiring considerable skill of the driver and an
eXperienced crew, or if the Operation is rare, e.g., drainage
and earth moving. Contractors' units also may be used when
the contractor can furnish the material involved, e.g., lime or
fertilizer, spraying chemicals; or can take care of the material
collected, e.g., potatoes, sugar beets, and grain. He then can
have highly specialized equipment which can be used on many
farms and, therefore, he can pay the high, initial costs of such
implements. A condition also is that the distribution of lime,
etc., or the harvest can be performed only once or twice a year
and in a relatively short time on each farm. Contractors' units
today often are built up around farm tractors. Their future
develOpment probably will carry them further away from the
agricultural power unit as they become more specialized. They
will not be included in this study in their most specialized
form.

The farmers own implements are supposed to be used in all
other cases. (Sometimes two or three neighbors may use one
implement, but the implement still retains its character of a

farmer's implement.)

14

For all Operations where the implement is moving ig_thg
figlg’when working, an independent, automotive, agricultural
power unit (tractor) must be used. Electric tractors, connected
by a cable to a power line, have been tried, e.g., in England,
Russia, and Sweden, but have not yet proven practical for field
work.

For all stationary operations, permanent or temporary, the
electric motor should be considered as the first choice. It is
very convenient to Operate, takes up little space, gives no
exhaust, and does not cause fires if prOperly maintained. It
is easily started and stepped and is the most suitable type
power (together with pneumatic or hydraulic motors) for
automatic Operations. When the power requirements are low, the
electric motor always should be chosen. Large, electric motors
require a high-voltage, three-phase supply system, which is not
always available.

For a stationary Operation where an electric motor, for
some reason, cannot be used, an internal combustion engine or
hand power must be used. When the operation shall not be made
too Often and does not have too long a duration and if the
power requirement is high, the mobile power unit (tractor) may
be used. Sometimes an old, outranged tractor--one that cannot
be used for field work any longer-~can be used. In most cases,
however, a separate, internal combustion engine should be
preferred as the best substitute for an electric motor.

In industry, pneumatic and hydraulic power has been used

for a long time as a substitute for hand labor. It is used

15
advantageously when power shall be applied on many places,
e.g., for materials handling. The Speed and the force of the
action can be regulated easily and the components can be made
very rugged. This possibility should not be forgotten when
choosing a power system.
Chapter 2. Basic Parts of Field Operations where
an Automotive Power Unit Is Used

From now on, only Operations where an automotive power
unit is used are discussed. Operations for special farms, for
instance vegetable or fruit farms, are not included. These
farms are Often of another size than "ordinary" farms and they
select their equipment from a different standplint.

Many of the Operations listed in Chapter 1 contain two or
more basic parts, each performed by a distinguishable element
of the implement. A field forage harvester contains, for
instance, a pick-up element, a conveyor-feeder, a chOpping
element, and an elevating blower.

Often new machines have been designed by combining existing
basic elements in a new way. Such new combinations appear much
more often than entirely new basic elements do. When discussing
the interference between implement and power unit, it therefore
seems favorable to first study the elements and not the complete
machine. Later, the combinations also should be considered.

The breakdown into elements can be made into smaller or
larger units. I have tried to keep the elements as large as is

possible with regard to the analysis.

16

Sometimes a basic part of a machine has had to be given the
same name as the complete machine. For instance, in this
connection "chOpping" means Just chOpping and not the other
functions a chOpper usually also performs.

For each group of Operations in the following tables,

105 - 11“, it is first indicated how many Operations could
theoretically be performed by the same machine or unit. The
criterion here is that the Operations can theoretically be
perfOrmed at the same time. Hay baling can be combined with
raking, but not with tedding or cutting. Then are indicated

the Operations which are combined using our present machines and
methods. A further discussion of the rules for combining
Operations is given in Chapter 3.

One earlier mentioned limitation of the study must be
remembered here: only elements of machines commonly known today
are considered. Also, operations which the author finds
possible or impossible to combine might be considered otherwise
by others.

Summing up the tables 101 - 103, we get the following list
of separate groups of farming operations in which the automotive
agricultural power unit is normally employed and for which a
suitable power unit should be provided:

seed-bed preparation and planting (including all soil
treatment up to the time of planting);

field work during the growing period;
harvesting;
loading;
transportation.
An analysis of these Operations is given in Tables 105 - 113.

17
Occasionally the power unit will be used also for field
improvement work and for some miscellaneous work, but these uses
are not of such importance that they should influence the shape
of the power unit. It might, however, be of interest to check
how many Of them could be performed by a power unit designed

for normal Operations. They are, therefore, listed in Table 11h.

Tables 105 - 11h. gasic Operations and Combinations of
Operations.

In each table are listed all operations that can be performed
simultaneously and, therefore, theoretically could be performed
by a single (combined) unit. As a consequence, some Operations
are listed in connection with several main operations. Such
duplication is indicated by a parenthesis around the name of the
duplicate operation.

An operational unit is a combination of implements and one
power unit such that all the implements can operate as they are
mounted in the Operational unit. In most cases, all implements
operate simultaneously, but it also might happen that when some
of the implements Operate the others are idle but still connected
to the unit; example: a self-prOpelled combine is an Operational
unit, the unloading auger is permanently mounted on the combine
but is for most of the time idle.

A given set of Operations usually can be performed by
different sets of Operational units. In the following tables,
all Operations in one table could theoretically be performed by
a single operational unit. This alternative is indicated by a

3 (t1, t2, etc.).. Other alternatives are called g, p, 3,. . .

18

Some operations might not be included in all alternatives be-
cause they might not be needed at the same time as the other
operations or in every case. The different operational units
in an alternative are numbered 1, 2, ... The operations, per-

formed by each unit, are indicated by a full, vertical line.

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27

TABLE 111. TBfilSFORTATION

 

Loads Carriers
Heavy (2-6 tons) or Wagons, trucks, (ev. tanks or
voluminous (hay, straw)' bins on implement)
Light, not voluminous Tanks or bins on implement,

loading platform on power unit,
hand carts, wagons, trucks

Stationary or portable, horizontal conveyors or pipelines are
not used very much for field work. They usually do not use a
power unit of the kind discussed here; therefore, they are not
included in the study.

It should be remembered that considerable tranSportation is
included in many of the Operations listed earlier.

 

 

 

 

Parts or Operation Combinations in One Unit
Practically
Theoretical Possible

t a b

Hitching carrier to power l W i

unit

Placing carrier in position
for loading 1

 

 

(Loading, see 114 Loading)
Hauling
Parking carrier

Adjusting position of carrier

 

 

P
(Unloading, see 114 Loading) f J

TABLE

Material Loaded or Unloaded

Bulk material, light,

fibreous: hay, straw, grass,

Bulk material, light,
granular: grain, feed

Bulk material, heavy: sand,
gravel, dirt

Small sized or light pieces:
potatoes, beets, haybales,
strawbales

sacks, boxes,
stones

Heavy pieces:
barrels, logs,

28

11H. LOADING

__Loaders

Continuous loaders, grass loaders,
front loaders, by hand

Continuous loaders, augers, by
hand

Front loaders, loading machines,
excavators

Continuous elevators, front loaders,
by hand

Front loaders, loading machines,

cranes

W

Dumping devices

Elevators
Front‘loaders

Wagon bottoms
False ends
Cranes

gagts of Qperation

Gathering
Elevating
Carrying

Picking up
(Storing)
Dumping

Chapter 3. Combinations Of Operations

As a general rule, it is most efficient tO perform as many
Operations as possible at the same time, instead of performing
them one at a time in a sequence. The energy to prOpel the
power unit over the field is needed every time the Operating unit
passes the field, independent Of the number Of Operations
performed. The total energy needed therefore is higher for a
Split Operation than for a combined Operation. The same holds
. true for the compaction caused by the wheels and for the
Operator's time. Consequently, the total cost and the total
time for a Split Operation is higher than for a combined. (In
a few cases, the truth Of this statement is not.immediately
obvious, but the contrary is never true.) The trend therefore
should be to combine as many Operations as possible. The
theoretical limit for such combinations in indicated in
Tables 105 - 115.

This limit, however, in many cases, can be neither reached
run~ approached for practical reasons. Some of the reasons are:

1. A combination Of tOO many functions makes the unit

very clumsy, difficult to handle, and difficult to
support on soft ground. Nor might the work force on
the farm be large enough to Operate it.

2. The reliability becomes lower, or in other words, the

time lost for repair and adjustment becomes greater
when many functions are combined. If the reliability

of a single function is p (a number between 0 and 1),

30

the reliability of a combination of n such functions
is only p“, which always is lower than p. (Ref. 1).
This multiplication of reliabilities is especially
serious when a function with low reliability is added
to a machine, e.g. a straw baler to a grain combine.
The relatively unimportant straw baling slows down the
more important grain harvest.

The timeliness factor. A certain Operation A_might

be most efficiently performed during a given short
period of time. A given power unit can handle a
correSponding implement A with the capacity of a
acres/hour. If another Operation g is added, and g
demands more power so that the capacity for §_+ 5,18
only b acres/hour, b being less than a; the time for
completing Operation A,(and §)is b 5 times the time
for A alone, 1.9. longer than this time. If this time
is longer than the favorable period, the combination
has resulted in a poorer final result Of Operation 5,
which should not be tolerated. Examples of such
time-sensitive OperatiOns, A, are planting and
harvesting. They should not be combined with ”slow"
and power-consuming Operations unless the machine
capacity is large enough and the acreage small enough
to ensure that the work is finished in proper time.
Knowledge about the timeliness factor is necessary,
therefore, when calculating the merits of combinations

Of Operations (and also when determining the Optimum

31

size of a single implement). More research in this
area should be done. For some values, see Barnes-
Link. (Ref. 3). An indication Ofthe time available
for each Operation is given in Tables 201 - 205.

4. The field efficiency (defined by e.g. Bainer, (Ref. 1),
p. 25) is usually lower for a combination than for the
same implements used alone. Nothing is, however, known
about the size of the reduction.

In Tables 105 - 11h, some combinations of Operations are
indicated as "practically possible” with due regard taken tO.the
factors mentioned here. For lack of numerical values, no
analytical test of how "practical" they are has been made, but

only subjective appraisals.

Chapter 4. The Relative Importance of the
Different Field Operations

 

As long as the aim is to design a separate power unit for
each implement or, in other words, to make self-propelled
implements, the only reason to consider the importance of the
implement in question is to estimate the future demand for it.
When, on the other side, the power unit shall be used for
several Operations, their relative importance ought to be known
because, thereby, it will be possible to decide how much
consideration should be given to the different--probably conflict-
ing-~requirements from the Operations. If the power unit shall
be used for all Operations, this is really important and might
be the hardest problem Of all to solve.

There are many ways Of defining importance in this case.
One of the most apparent is the duration Of the Operation, which
gives the size of the Operation, e.g. in hours/year or better
in acres/year. A frequency measure is how Often the operation
is performed, e.g. in times per year or times per week. More
difficult to express in figures are such measures as the value
of the product involved in the Operation, or the importance of
the Operation from the standpoint Of it having to be performed
at a fixed time or if it can be postponed or excluded without any
great disadvantage.

There are two ways of finding these measures Of importance.
One is to analytically study the work schedule of theoretical

farms with assumed acreages Of different crops. The acreagss to

33

be covered can then be calculated and from there the duration of
the Operation by assuming a given capacity Of the outfit. This
procedure makes it possible to investigate future, improved
types of farming. An attempt in this direction is made on

pages 33 - no.

The other method is to statistically study the Operations
on existing farms. Correctly made, such a study should be able
to give information that can be used in the future. The main
advantage with this method is that it gives more accurate values
for the waste time (field efficiency) than the analytical method.
The extent Of such Operations as transportation also is very
difficult to estimate analytically.

A summary Of statistical investigations on the time used

by the tractor(s) for different Operations is given in Table 120.

An Apalytical Determination Of the Qpration and Frequency Of
Farming Operations with an Automotivefigower Unit Involved

There is an almost innumerable number of types of farms,

 

but the analysis must be limited to a few which might be called
type farms. In reality, there might not be many farms exactly
like the type farms, but for this purpose, the type farms could
probably be made to agree close enough to a great number of
real farms. In describing the type farms, more consideration is
given here to conditions as they are on advanced or even future
farms in the group than as they are as an average.

Six type farms are described in Table 121 and the Operations
involved for each crOp are described in Table 122. The final
result as to duration and frequency of the different Operations

on these six type farms is given in Table 123.

34

TABLE 120. ACTUAL USE OF POWER UNITS AND IMPLEMENTS.

1. USA. According to Brodell (ref. 8). 1941. Only tractor-driven

implements.
Hourszyear
Avergge Limits Quantities
Manure spreading 142 25-1000 177 tons/year
Row-crop planter, 2-row 76 20-250 131 acres/year
- " b , 4-row 80 20-250 262 —"-
Grain drill 79 20-500 201 -"-
Mower 78 20-500 154 -"-
Binder 55 20-350 100 -"-
Combine, less or equal to 6 ft 110 25-400 126 -"-
-"- , wider than 6 ft, less
than 10 ft 126 25-400 207 -"-
~"- , 10 ft or wider 143 25-400 400 -"-

2. Sweden. According to Jeppsson (ref. 16). Tractor size around 30
belt hp. One horse used for some light work. Calculated use for

a given farm.

Plowing 26 % of total tractor time
Cultivating 10 % - " -
Fertilizer spreading 7 % - H -
Planting 6 % - fl -
Binder 7 % - H -
Forage harvesting 5 fl - fl -
Transportation 35 fl - N -

3. Sweden. According to Berglund-Karlson (ref. 6}. 1953. General
type Of farm. Average Limits

Farm size, acres 53 32-80
Tractor size, belt horsepower 25 16—40
Other field power (x) 1 horse, used for rolling, fort. distr.,

planting, transportation.

35

 

(TABLE 120. Cont. 512.2269. £29.12;
Field work, total, Hours/acre 5.2 2.8-7.5
pIOWim ’"" 1 08 00 6-3 .4
cultivating -"- 1.7 0.8-3.4
rolling (x) -"- 0.2
fertilizer distr. .
(X)! """' 002
Planting (x)
”0131‘ """' 005 001-103
Binder _N. 006 001-104
Other field work -"- 0.2
Transportation (x) -"- 2.8 0.4-6.9
Belt work -"- 0.2 O—l.4
Miscellaneous -"- 0.3 O-l.9

Basis for area indication is total farmland acreage.

(x) indicates use of other power source than tractor.

4. west Germay. According to Schilling (ref. 28). (Figures taken from

 

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£33m sizelacres
25 - 250
Tillage 7-26 % of total tractor time
Planting and care of plant 18-16 9% - u ..
Harvesting . 20-20 % .. " ..
Transportation 51-37 % - fl -

Belt work 4-1 % - " -

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.NNH Ends

 

38

Explanations to table 1&2

Figures estimated after discussion with Mr. Clarence Hansen, Michigan
State University.

1/ An Operation interrupted before finishing for such reasons as
shortage of labor or power units, which are not inherent in the
operation as such, is considered performed only once. An Operation
is consider performed more times if it has to be repeated at another
season or time, e.g. early or late fall plowing and early or late
spring plowing.

2/ This area limited by the amount of manure available.

3/ In other cases than the one, indicated in brackets, the operation
is performed only once a year.

39

TABLE 123. ACREAGES COVERED YEARLY IN OPERATIONS ON FARMS OF DIFFERENT
TYPES. '

Based upon tables 121 and 122 and consequently referring to small to
medium sized farms. The acreages are calculated for the major crops,
which use 80-95 % of the total cropland, and then extrapolated for the
total cropland acreage. The figures are rounded.

The figures for small grain, cash or0p farmscare adjusted downwards
slightly on account of the special conditions for this type of farms.
For the other farms part-time fallow is included, = 10 % of cropland
acreage.

 

[ Type of farm and acres cropland

General, Dairy, Dairy, Cash, Cash, Livestock
Michigan Wisconsin New York small corn, hogs,

 

 

 

 

 

( Operation grain, Ill. Iowa
‘ N. Da-
kota
9O 75 80 400 100 100
Acres covered_yearL1
Plowing 6O 45 20 330 100 so
Cultivating 200 130 85 1000 225 225
Rolling 10 10 10 100 40 30
Planting, drill ' 45 25 15 300 30 25
(y " , planter 20 20 10' o 70 60
Fort. after planting 7o 60 70 180 50 6O
Row—crap cultiv. i 70 35 15 o 120 100
Spraying 70 6O 50 300 75 65
Mowing 45 55 110 O O 30
”Forage harvesting O 10 10 O O 5
iCombining E 35 25 15 300 60 45
Corn harvesting § 20 15 O O 40 3O
‘Baling, hay, straw i 55 so 125 o 0 40

l

 

 

NO

The result is given as 81%fil covered per year. In order
to get a figure for hours per year, we have to divide by the
field capacity of the implement. This is given for some machines
in Tables 210 - 215, and also can be found by multiplying Speed,
working width, and field efficiency. Field efficiencies are
given in Tables 210 - 215.

A more thorough study of type farms and their relative
importance would be desirable, but the figures given here might
he sufficient for the calculations in following sections.

In the future, farm size will increase and the number of
crops on each farm will decrease, but these changes will take
place slowly only. The figures for the crOp acreages on a farm

can, therefore, be used possibly for a long time.

SECTION II. CHARACTERISTICS OF IMPLEMENTS AND THEIR
OPERATION OF IMPORTANCE FOR TH; POWER ONE

Chapter 5. The Requirements of the Implements Are
the Mostgmportant Factors Determining
the Power Unit Design

With a few early exceptions of almost experimental
character, the develOpment of the mechanical power unit has
gone along the lines of making a machine which could be a
substitute for the horse and, therefore, which could use
implements of the same design as when the horse was the sole
power source. This mainly was due to the fact that the transi-
tion to the new power unit had to proceed gradually with the
Old and the new power unit being used alternately. Because the
horse could not be adjusted to the implement, the implements had
to be designed for the horse.

This transition period now, however, should be considered
past in the highly mechanized countries, the mechanical power
unit there being the only one. The implements now can be
redesigned to make full use Of the possibilities a mechanical
power unit can give. At the same time, the power unit can be
transformed from being a mechanized horse to better complying
with the requirements of the new implements.

Logically, the best-working outfit should be found when the
design is based upon the requirements of the implement; the
implement is the productive, primary part of the combination and

the power unit the secondary, essential, but unproductive part.

42

Therefore, the requirements Of the implement must be of primary
interest and the design of the power unit, as far as possible,
adjusted to them.

The self-prOpelled implement can be built to satisfy the
functional demands of the working parts as closely as possible
and should, therefore, be the best design. Lately, we also
have seen an increasing pOpularity of some self-prOpelled
implements--when the farmers want a machine with high capacity

and good Operational efficiency.

Chapter 6. The Requirements of the_;mplements

The requirements of the implements can be classified as
Operational and technical. Operational requirements may be
considered requirements on working speed and speed adjustment,
on height adjustment, accuracy of steering, supervision needed,
position of implement relative to the wheels of the power unit,
quantities to be handled, field conditions, etc. Operational
requirements usually are determined by other factors than the
implement itself and do not change with the design of the
implement. They will be different for different farms, areas,
or countries, but they will not change at all, or at the most
very slowly, with time.

Technical requirements or descriptions may be classified
as draft and power requirements, weight, center of gravity,
outer dimensions, etc. The technical requirements may differ
considerably between different existing designs and also will
change as new designs are developed. Because speed is.very
often limited by the design of the machine instead of by factors
in the Operation, it will be considered together with technical
requirements.

Many of the figures in the following tables on requirements
will be given relative to a certain capacity. The capacity_may
be considered the independent variable in the case. When
several elements work together, their capacity should, of course,
be the same. However, capacity also plays an important role in

the decision of which elements or implements should be combined

as

for simultaneous work. Furthermore, there ought to be some
matching between the capacities of implements used at differ-
ent times but in the same enterprise, especially for economic.
reasons. These two questions about matching and combining
implements which both influence the power unit design have
been discussed in Chapter 3 and will appear again in Section
IV.

In Chapter 2 there was introduced the concept of elemen-
tary parts of operations and implements. This breakdown is
also useful when listing the requirements Of the implements
because different elements have different requirements. To
refer to all these as requirements of the complete machine
would be to introduce them also for elements, for which they
do not apply and would make it more difficult to find a good

solution.

Comments On Tables 201 - 206 Operational Requirements

Field conditions have to be described by words. It would have

 

been much better to give soil values but such are not yet
available.

Time available for operation gives an indication of the impor-
tance of the Operation as discussed in Chapter 3. The follow-
ing scale has been used: plenty, enough, limited, short, very
short.

Supervision of function given by the driver when the implement
is working, is classified according to the'scale: continuously,
often, occasionally, none. When continuous supervision is deemed

needed, the part of the implement which needs particular atten-

tion is sometimes mentioned.

145

Adjustments of implements in work: Adjustments besides height
control and steering.
Height control of implements in work

none = implement working at fixed height

preset = height determined by gauge wheel, shoe, etc.,
adjusted beforehand in fixed position relative
to the implement.

manual = manual change of working height

automatic = change of height is or could be performed
automatically by devices in implement or
power unit.

Height control of implements on headlands

 

none 2 no change in height needed
mech. lift = implement must be lifted
automatic = implement is or could favorably be raised
by devices which sensed the end of the land
and automatically lifted.
Accuracy of steering_of implement in work. Scale: none,
fair, good, high, very high.
Steering of_power unit in work as imposed by the implement in
question:
none = implement works or could work stationary
manual
automatic = power unit is or could favorably be steered
automatically in this operation. ( ) indi-

cate alternative might be questionable.

automatic and manual = additional manual fine steering
needed.

Type of container for (loading and) transportation (table 206)
platform: only a bottom
closed: bottom and sides

tight: bottom and sides tight

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51

Comments on Tables 210 - 215. Technical Reguirements

 

Speed limited by:

Pull

function = the limit is inherent in the soil or the crop,
mostly being caused by the sensitivity or the
inertia of the particles.

field = the evenness of the field or road

machine a a redesign of the machine would permit higher
speeds

power = enough pull or power not available for higher
Speeds

and_power: Power means here other power than the pulling
force or draft. Implements with no power-driven parts
will therefore be indicated as requiring only pull, no
power.

Pull caused by rolling or sliding resistance to wheels,
shoes, etc. carrying the weight of the implement and of
the product on it is included in the pull when there is
a useful pull, also, caused by the action of the imple-
ment on the soil, etc. When the pull is only parasitic,
being caused only by the weight-carrying wheels, it is
not indicated because the weight can perhaps be partly
transferred to the power unit and utilized. Further
studies are needed to show what part of the pull is use-
ful and what is parasitic. For examples, see Chapter 8.
The pull, caused by grade is not included, but should be
remembered. Power for groundewheel-driven mechanisms is
counted as power, not as pull. The figures given refer
to horizontal pull. The vertical pull that can or must

be exerted on the implement is also important. With some

52

exceptions, as e.g. disc plows and harrows, grain drill
openers and cultipacker, the maximum allowable vertical
pull is of the same size as the weight of implement.
Knowledge about the vertical forces would be of great
value when designing the power unit, but very few invest-
igations give any information about these. The figures
given for pull and power in the tables should be con-
sidered only as rough information about their order of
magnitude. They should not be used directly when making
a design. Instead a survey of original investigations
should be made in order to find out their real nature.
The pull and power needed can sometimes be changed con-
siderably by changing the design. For natural reasons
these variations cannot be described here, but a list
of references is given in the tables. References, listed
in (ref. 1) are not listed again here. Bainer (ref. 1)
has on pages 116-138 and 548-5h9 given a general discus-
sion, some figures and general references. The power and
pull figures should be related to some basic quality of
the material, e.g. soil values, moisture content, etc.
Thereby, it would be possible to reduce the variations
in the figures for each individual case.

Power type: Way of transmitting power from the pgwer unit to
the rotating parts of the implement. "None é" means that
power driven parts are not used now, but might be used in

the future.

53

Weight and dimensions: Weight and dimensions are given for

the whole part of the implement, including transmissions
and adjustment devices for this part. The dimensions of
the working parts inside it are smaller. Carrying wheels,
outside frames, engines or driver's platforms are as far

as possible excluded.

Minus-sign after weight means that weight of wheels, etc. is

 

U)

 

included in the figure. Two minus-signs indicate that
weight of heavy parts such as an auxiliary engine is also
included. Minus-sign after length indicates that length
of the drawbar, etc. is included. When possible, the
weight is given per foot working width. This is indi-
cated by a "1” in the size column. The width is then
sometimes given as w + 00 which indicates how much wider
the implement is than the working width.

Size has as far as possible been given as feet nominal
working width. For implements with optional working
widths, as e.g. combines, the smallest width has been
chosen as representative, because it is the width for the

highest producing fields.

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57

man 213. mmxw. momma. 0mm must.
run ottioionoy: 55 - 15 S 5/.

t. i Pro-oat. m $1.7 Mien Ho ht. and dim-ion-
or 1 m o d routioml o t.
no 1/ 9—!” E lap/rt. spent :1- 3/ It “'55
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cutter hood 0.25-0.30 18 n l-h.5(6)runct.ion hoo - 1150 1 ho a: + 10 3311-001
“chino
Hindu-or 16 ft. 3- hmotion 10 2800- n+1}
homo 16 3100-
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dovioo ass-chino
contain. 0.22 18 It. 1-h.5( 6) 1.5 pm
.opo
uu-uhin cloning 200 -1500 7 32 £9 3)
10 36 6 3h
12 36 51 3h
16 36 Sh is
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10 13h 116 28
12 139 51 23
16 11.3 511 28
cleaning noun.
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rain 10mm; nohino
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Machine
Strut om nohino
(int-3rd)
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(intuit).
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O. .
lit-hr piclcor 250-700
Sholhr picknr 1700 90 62
Cloning shoe pick-r
Stolk throat:- 2 - 3 uchine
1/ Raf. 11), 1h). 3/ not. 1) p 388, 399.
2/ Hot. 1), 7), 22), 29). 13) h/ Bar. 9), 26).

Figaro: max-dug) m ginnin 0.
5/ Ref. 1) p 25, 19) p 203.

58

IAELE Eli, IEQHNICAL REQUIREMENI§L ROOT HARVEST.

Part of Ca acit
implement acres hr&£§_

 

Potato harvest

Digger

Separator

Hopper

Loading from
machine

Loading from
ground

Grader,
washer

Spgar‘beet harvest

Top cutter

Top hopper

Beet lifter

Beet cleaner
Beet hopper

Sampling
device

1) Ref. 1) p 453, 7), 22),

Present

max.
ft

29).

size

Speed
rangg
mph. 1)

2-3.5

2.5—3.5

1—3.5

Speed

limited

2!.

separator

machine &
function

separator

machine &
function

machine,
function &
driver

function &
driver

machine

59

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.mezwzmmeomm H<0Hamoma .WHN QHNqH

SECTION III. THE PARTS OF A POWER UNIT.

 

 

We have in preceeding sections considered the different
operations we want performed on a farm, and we are now going
to try to find a suitable power unit or units for these opera-
tions. Suitable means primarily that the power unit shall
fulfill the requirements of the operations, but also of equal
importance is that it shall be technically efficient. Tech-
nical efficiency may be measured by e.g. the amount of work
a power unit of given size can perform and at what cost the
operation is performed.

The amount of work done as well as the cost of operation,
is determined by how efficiently the power from the engine is
transformed into useful work. For power transmissions through
rotating shafts the transmission efficiency is fairly high,
but when the power is delivered in form of pull, it can be
very low. In order to determine the suitability of different
power units we therefore must study their drive efficiency or
effectiveness. This will be done in Chapter 8.

Related to the drive effectiveness is the steering effective-
ness, which will be discussed in Chapter 10.

All parts of a power unit have an influence on how good
it is. The influence of the design of individual parts them-
selves on the overall efficiency will not be discussed here,
but only the effect of different layouts, i.e. of how the parts
are arranged relative to each other and'relative to the im-
plements. Consideration must, of course, be given to the

Special requirements on position which the power unit parts

might have. These requirements are therefore described in the
first part of this section.

A further and important limitation of the ways to arrange
the implement and the parts in the power unit is that the com-
bination must have enough stability under all but not too ab-
normal conditions. Chapter 9 describes how the stability is

influenced by the layout.

Chapter 7. The Functional Requirements of the Parts of the
Power Unit

As the name implies, the power unit contains the source
of power for the implement whether the power be delivered as
pull, power in a rotating shaft, oil under pressure, etc. The
power unit is always considered automotive and also carries
the implement when this has no means of support. Thirdly, the'
implement is maneuvered from the power unit, the driver's plat-
form generally being a part of the power unit.

The elements of a power unit are engine (engines), trans-
mission, driving wheel (wheels), steering wheel (wheels), dri-
ver's platform with controls for the power unit and the imple-
ment, and means for connecting the implement to the power unit.
All this is built into a suitable frame. From some of these
elements there usually are power outlets to the implements for
rotational, hydraulic, pneumatic or electric energy. Steering
wheels might be driving wheels also. Tracks might be used in-
stead of wheels, and other substitutes for wheels might also
be seen. '
The Engine

The type of engine is not of major importance for the
general layout of the power unit, but I will assume that it is
some sort of internal combustion engine. There might be more
than one. For the internal combustion engine the most impor-
tant accessories from the layout point of view are the air
intake and the air cleaner, the exhaust pipe and the spark

arrester, the fuel tank, the battery, and the engine‘cooling

63

elements. The remaining parts can be placed on or in the motor
block and considered a part of the engine unit.

The engine can function as well lengthwise as crosswise
in the vehicle and as well horizontally as vertically. No
special consideration need therefore be given from the engine's
own standpoint how it is placed in the vehicle. The main view-
points are in what direction the main power outlet is, avail-
able space, the influence of the engine weight on the vehicle
and how to service the engine. These are the only considera-
tions given the engine in the further discussion.

The Transmission

 

The transmission transmits the power to the driving wheels.
Its purpose is (1) to give the power unit the desired speed,
and (2) at the same time allow the engine to run at a speed
where it can deliver the power needed in the most efficient
way.

There are today mechanical transmissions,in some cases in
connection with hydrodynamic parts, hydrostatic transmissions
and electric transmissions. The evolution is making rapid pro-
gress in this field.

The transmission plays an important role in tractor layout
because it limits the possibilities to arrange the drive. Some
new transmissions, e.g. hydrostatic and electric, permit more
freedom in this aspect, but have other disadvantages. The
technical possibility to get the drive to the wheels and the
space needed for the transmission are the only concern that

will be given the transmission in this study. A few cases

6a

where the transmission is used for steering will also be men-
tioned.

Different 3322; arrangements will be discussed in Chapter
11.
Connecting Power Unit and Implement

There are three principally different ways to connect
power unit and implement. A pplled implement (trailing imple-
ment) is fully carried by its wheels, etc. and is coupled to a
hitch point in the tractor rear end. The weight of a ppm;-
mounted implement is partially carried by the power unit and
partially by the wheels of the implement. A semi-mounted im-
plement can be placed on any side of the power unit, not only
behind it. A mounted implement is at least in transport car-
ried entirely by the power unit. When working it may run en-
tirely or partly on its own wheels, working surfaces, shoes,
etc. A mounted implement may be placed in any position rela-
tive to the power unit and is accordingly called rear-mounted,
mid-mounted or front-mounted. Front and rear-mounted imple-
ments are often centrally mounted, but mid-mounted implements
might be centrally mounted or side-mounted.

As a general rule the following demands on the mounting
system ought to be satisfied:

1. One man must be able to attach the implement without
help and with normal physical effort. It must be born in mind
that on all sizes of farms, the power unit and its implements

are a one-man tool.

65

2. The time needed for mounting must be in a reasonable
proportion to the effective working time of the implement. The
time needed for mounting and dismounting is a waste time during
which no productive work is performed. If the productive work-
ing time is short compared to the time for mounting, the aver-
age efficiency will be low and in some cases so low that the
use of a tractor implement does not give any gain compared to
doing the work by hand. Short working periods appear on farms
of all sizes, but to the greatest extent on the small farm
where the same tractor has to be used for many tasks often on
the same day. A short mounting time is therefore especially
important for such tractors. On larger farms it is not of the
same importance because the tractor is used for a longer time
in the same work. Furthermore, larger farms often have more
than one power unit and can afford to designate one of them
for certain work, where the implement consequently might be
mounted for a long time uninterruptedly. It is in some cases
possible to have a power unit always designated to one imple-
ment only and thereby, in fact, to create a self-propelled
implement. This procedure may, in some cases, be justified
but cannot for economical reasons be applied for most imple-
ments.

3. The attachment should preferably be made without
loose bolts, pins, etc. and, if possible, also without tools
such as wrenches, screwdrivers, etc. Such small parts are

apt to disappear or be damaged in the field.

66

4. If possible, the same system for attachment should
be used for all implements that are supposed to go with the
power unit.' This standardization of the mounting system will
become an increasingly difficult problem as better types of
mounting for individual implements are designed. Individual
perfection and generality can very seldom be achieved at the
same time. The problem will be less difficult if the number
of implements for each power unit is reduced.

5. The easiest exchange of implements is made possible
if all individual adjustments on the implements are performed
inside the implement and not on the power unit, i.e. if the
hitch points are fixed on the tractor (ref. 17). Then all
implements would be ready to work immediately, being adjusted
in the same way as they were last time they were used. This
system, however, necessitates some duplication of adjustment

devices and is therefore slightly more expensive.

Mounting of the implements has a decided influence on
the drive effectiveness of the power unit because the weight
of the implement and eventual downward pull exerted on it can
be used to increase the load on the driving wheels of the
tractor and thereby its pulling ability. This is the natural
way to increase the drawbar pull and should be used before
other methods. This influence of mounting will be thoroughly
discussed in Chapter 8. Furthermore, mounting makes it easier
to maneuver the implement and to transmit power to it. The

implement design becomes simpler and the implement thus cheap-

67

er. Therefore, the implement should be mounted on the tractor
whenever this is possible.

Mounting also has a decided effect on the steering effect-
iveness, and the stability of the combination, as will be dis-
cussed in Chapters 9 and 10.

Some implements require to be mounted in a certain posi-
tion within the combination implement-power unit. This is
indicated in Tables 201 - 206.

A brief summary of the characteristics of different ways
of mounting and hitching may be given thus:

If a mounted implement, requiring a large pulling force,
is rear-mounted the result is an advantageous transfer of load
to the rear wheels, even if there is a risk that the transfér
becomes too large, causing poor steering and overturning of
the tractor. The implement tends to keep the tractor on a
straight course. It is easily mounted. The wheeltracks of
the tractor can easily be erased.

Light implements can be side or front-mounted. In these
positions the implements are easy to watch and easy to mount,
at least if the power unit is suitably designed for it. Front-
mounted implements can open a road into a field. With a front
or side-mounted implement another implement can be rear-mounted
making two or more simultaneous operations possible.

Some implements are favorably mounted between the front
and rear axles. There they are easy to watch and to steer and
they put an even lead on both front and rear wheels. They

might, however, be difficult to mount in this position.

68

Heavy and bulky implements ought to be made semi-mounted,
i.e. some of their weight ought to be carried by their own
wheels. How rigid the connection between tractor and imple-
ment shall be made, is determined by how often the implement
must be disconnected and how complicated the power transmis-
sion to the implement and the maneuvering of it is. Semi-
mounting increases the drive effectiveness of the tractor and
makes the aggregate easier to handle, compared to pure trail-
ing implements.

Pulled (trailing) implements can be very easily connected
to the tractor and disconnected from it. They can be moved
without a tractor which can be an advantage for e.g. a wagon.
This reason is especially important for implements that are
used together with the tractor only for a short time on every

occasion.

The Driver and The Driver's Platform (Cab)

It is possible that in the future no driver will be needed
on the power unit, the unit being governed and steered by a
mechanical device, following a predetermined program. It will,
however, take a long time before this can be common practice
and up till then a driver will be needed.

When there has to be a driver watching the power unit and
its attached implements, there seems to be very little to be
gained by using such remote control where the driver is placed
at some fixed point in the field and controls the power unit
by telecommunication. He then gets a poorer view of what hap-

pens around the implement and less control of the different

69

factors. Demonstrations of radio-controlled tractors are
therefore more a way of arousing public interest than of gen-
eral practical value. In the case, however, where implement
and power unit are far apart, as e.g. in winch-hauling of
timber, radio control might be useful.

In order to utilize the driver's time more efficiently,
it might sometimes be desirable to hitch two or more operation-
al units together and to govern them all by a driver on one
of them. This type of remote control seems a more profitable
and practical prospect than radio control. The system is in
wide use on e.g. railroads and has also been tried in agricul-
ture in the form of tandem tractors or in prior days, when
large teams of horses or mules were used.

The power unit and the implements ought to be handled
by the same man as far as possible. When the horse was the
power unit, the driver usually walked behind both horse and
implement and could therefore both rein the horse and watch
the implement, both of them being in his field of view. When
the tractor was substituted for the horse, the driver moved
to the tractor where he was placed in front of the implement
and often far away from it. This made it sometimes necessary
to use another man on the implement. This could for some time
be justified because the output per man hour was still in-
creased by the increased speed and working width of the tractor
drawn implement. On a small farm, however, with just one or
two workers, it is often difficult to get two men for one

operation and the mechanization could therefore not proceed

70

very far, until both the tractor and the implement could be
managed by one man. Even on a larger farm a one-man unit is
usually desirable.

It is, however, not enough that the tractor and the im-
plement can be driven by a single operator. It is also essen-
tial that they can be driven with as little stress and fatigue
on the driver as possible. If the driving is in any way in-
convenient, this will result in a lower accuracy, a lower
speed and more pauses for rest and "repair”.‘

The following conditions ought to be fulfilled in order
to give a convenient driving of the power unit:

1. The driver and the implement ought to be placed in
the right position to each other. This means that all parts
where something happens can be seen from the driver's posi-
tion. It is further important that parts that need a contin-
uous supervision are inside the driver's normal field of
view, i.e., in a certain direction and at a certain distance
from him. This is especially important e.g. for row culti-
vators. An investigation by NIAE (ref. 2h) shows that such
vital parts should not be more than “0° off the direction of
travel and not less than 6 feet from the driver's eyes. An-
other investigation shows that even a single beam in the line
of sight is very disturbing (ref. 22). Further investiga-
tions are needed in this field, however. Not all implements
need such continuous supervision and can therefore be placed
away from this ideal position, but the condition of visibility

must always be considered. The requirements on supervision

are indicated in Tables 201 - 206.

71

2. Servopower ought to be used for all heavy adjust-
ments of the implement. Most common is at present the hy-
draulically actuated three—point hitch which can be used for
all implements mounted there. The free hydraulic cylinder
(remote control cylinder) gives a greater freedom in applying
the hydraulic power. Electric and vacuum servopower can some—
times be used, e.g. for applying the brakes on a trailer. The
servopower ought always to be available, or at least as soon
as the engine runs. The servopower for lifting and adjusting
implements could in some cases be automatically released.

This is further discussed below. Examples of prospective
cases are given in Tables 201 - 206.

3. The driving is made easier if the implement is to
some extent self-steering, i.e. if it tends to return by it-
self to the wanted position when it has deviated from it.
Otherwise all deviations, even small ones, have to be counter-
acted by the driver.

In many field operations the operational unit is
driven along a furrow, row, swath, etc., made in a preceeding
cycle. In such cases the steering could easily be made auto-
matic. The driver could thereby be released from continuous
steering and watching direction and could devote more time to
watch the operation of the implements. He would probably oc-
casionally have to watch the automatic steering also, but
this would be much easier than to do the actual steering. In
as few cases where very high accuracy in steering is needed, he

Inight have to do additional fine steering.

72

Another group of functions which could be automized
are the operations at the headland, e.g. raising and lowering
the implement and shutting it off and on. If the responsi-
bility for these functions could be taken away from the driver
he could devote all his attention to steering the unit and
would probably not drive into the ditch as often happens now.

b. An important part of a convenient driving is an easy
way of transporting power unit and implement to and from the
field.

5. The points given above refer to the influence of the
implements on the driver's position and on the ways of maneu-
vering the power unit. The driver himself must also be given
due consideration. This means e.g. that all controls should
be conveniently located relative to the driver, that they
should move in the best direction, and that they require the
least physical effort from the driver. These points have been
studied by e.g. Dupuis (ref. 12). From the driver's platform
can furthermore be required that it shall protect the driver
from dirt, vibrations, rain, heat, cold, gases, etc. It must
be easy for the driver to get on and off the platform. If
possible, it shall protect the driver from severe injury, if

the power unit overturns.

The point, which must be especially taken care of, when
making the layout of the power unit, is the first one about
supervision of the implement. The fifth point will be con-
sidered by assuming that the power unit will be equipped with

a cab containing all necessary controls neatly arranged. The

73

other points enter the problem mainly at a later stage than

the layout stage.

The Power Take-Off

The mechanical power take-off in the form of a shaft or
a belt is the most efficient. It can, however, not be used
in more than a few directions from the tractor body. It is
also often difficult to connect it to implements that move
relative to the power unit.

Hydraulic power take-off in form of oil under pressure
is now used for certain functions, e.g. power cylinders for
loaders, etc. Hydraulic power take-off could, however, also
be used for faster, rotating or reciprocating parts. Experi-
ments with hydraulically driven cutter bars have been made in
several places. Hydraulic power transmission has the advan-
tage of greater flexibility and can be carried to any point
around the power unit.

Electric power take-off seems still to be too expensive
for most purposes. It is characterized by great flexibility
and easy control.

The method for power transmission must be given some
consideration when deciding where to place an implement in
the operational unit, and it might exclude some otherwise

good possibility.

CHAPTER 8. The Drive Effectiveness of a Power Unit

The drive effectiveness is intended to give a measure of
how effectively the torque from the engine is transformed in-
to useful pull at the implement. (The word effectiveness is
used instead of efficiency because the word efficiency has
often been given the specific meaning of ratio between output
and input energy, i.e. not forces and torques as in this case.)

As a first step we need to define "useful pull“. Take
as an example the moldboard plow. The useful forces in a re-
stricted sense are the forces which break the soil apart and
turn it. To this is added unproductive forces to overcome
friction, made necessary by the working principle itself;
e.g., the friction between the soil and the moldboard. These
two types of forces cannot be changed without changing the
basic working principles of the implement.

Then there is resistance caused by the devices which
take the reaction forces from the implement. Examples are
friction against the landside of the plow bottom and rolling
resistance of the plow wheels. These forces can be influenced
by proper mounting of the implement where the reaction forces
are taken by wheels instead of by sliding surfaces and by
large wheels instead of small wheels. Sometimes the reaction
forces can be used to increase the drive effectiveness as for
instance when the weight of the implement is used to put load

on the driving wheels of the power unit. In general these

75

resistance forces, caused by supporting devices, will also

be included in what we call useful pull from the power unit.
For some mounted implements it will, however, not always be
possible to completely distinguish them from interior forces
in the power unit, and an explanation about these forces must
therefore be given for each individual case.

Of course, the rolling resistance of the power unit it-
self should not be considered useful, even if it is unavoid-
able (for automotive units). Nor should the force caused by
gravity on the power unit on a slope be counted as useful.

Useful pull could therefore be defined as the horizontal
force delivered by the power unit in order to overcome work-
ing forces on the implement and resistances to its motion.

The word effectiveness implies a comparison between what
we really get, in this case useful pull, and what we should
have obtained under most effective arrangements. What, then,
determines this maximum?

The pull is limited mainly by two factors; the torque
available at the drive wheels and the slip in the wheel-ground
contact. If the pull is exerted above a certain height above
the ground, the stability of the power unit may also become
critical.

From operational reasons most tractors have a low gear
which gives a much higher torque in the drivewheels than the
other limits will permit. Torque is therefore very seldom a
limiting factor for the pull if not a certain speed is also
required. 'This limit is also'easily increased by using a

larger engine.

76

The stability limit for the pull will be discussed in
connection with overall stability in Chapter 9. There usually
is no difficulty to stay within the stability limit if one is
aware of the risk in exceeding it.

The slip limit remains the most serious limit. As ex-
plained in Appendix A, the maximum net tractive effort of a
wheel is expressed as

F2 = roptFi

where F1 is the vertical load on the wheel and f t is a co-

Op
efficient determined by the soil, by how much slip we can
allow and by many other less important factors.

We therefore can write:

Drive effectiveness =

q useful pull _ useful pull (ppt =

“ maximum value of (foptF1) - fopt(F1)mai x (fgpt)max

=¢drivewheel loading effectiveness x ground grip effective-
ness

Drivewheel LoadingiEffectiveness
For the following study of the mechanics of the power
unit a system of coordinates, forces and notations has been
used, which is thoroughly explained in Appendix B. Here
shall only be pointed out, that all dimensions are given as
dimensionless quantities, in fact as ratios between the actual
dimension and the wheelbase. In other words, they apply for
a power unit with the wheelbase equal to 1 length unit.
Excluding the rare occasion, when the usable reaction
force 351 from the soil on the implement is directed down-

wards (negative) the maximum available load on level ground

77

is the sum of all weights, W0 + W50. The maximum net trac-

tive force is then

(‘J

“6

 

 

e01

é’——I
R5, R52

The tractive force is utilized as the force by which the

 

 

implement works on the soil, which has the same magnitude as

the reaction force R52. This is our useful pull. If R52 is

determined for f = fopt' the drivewheel loading effectiveness

7! given below indicates how effectively the available weight
is distributed on the drivewheels in order to produc traction.

R
.. :2
7! " foptwo + ”SOT (303)

 

 

78

On a slope the available load, perpendicular to the
ground, is only (wo + w50)cos/@. Useful work is produced also
in moving the implement up or down the slope which requires

the force W5osin/9. 7‘ might be defined as

R52 + w50511153
71 3 rcptwo + W5o)cos/a (30b)

 

Lgvel Ground
Using the basic equations B3-5a, 6, 7 and 8 in Appendix

B, we get for a power unit on horizontal ground:

X11 ‘ x21 - V52 (fg-f17

 

[(fZ-le-xo - 1 x50 +11 x51)+ (1 + i -fii) (fzxu - f1x21)]

1 1 1
’71. -1+1 fopt.X11-X21-y52(f2'ffi.

[(fz - f1)(-XO - i X50 +11 X51) +
+ (1 + 1 ”(1)“sz - f1x21)] (31a)

where 1 indicates the ratio of implement weight to power unit

 

weight and [indicates how much of the implement weight is.
carried by its own wheels, etc.

This is the shortest, complete expression for '21 , but
the parenthesis can also be written as

-. (f2 - f1) [(xo - x21) + 1(x50 - x21) .

...! 1(x51 - 3:21)] + f2(1 + i - [ i)(x11 - x21)

which shows, as expected, that if the rear point of suspen-
sion (x = x21) had been chosen as origin, the equations would
have become much simpler. However, x21 is not constant, where-

fore this point is not well suited as a reference point.

79

For an all-wheel driven power unit we can in the ideal

case assume f1 = f2.= rcpt which gives

, _ 1 + i - 12? 1‘2

.3 "“"I‘I‘I“' = 1 - I‘I‘I (31b)

This shows, that the drivewheel loading effectiveness of such
a unit depends only on the magnitude of 12, i.e. to what ex-
tent the implement is self-supporting. An all-wheel driven
power unit must consequently use fully mounted implements to
achieve a drivewheel loading effectiveness equal to 1.

Making the approximation, that x11 - x21 is equal to the

wheelbase = 1, we get for all types of power units:
f2-f1

iopt

(ZQ.= (1 + 1) 1 - y52(r2 - r1)

. 1‘2
.L- x0 - ixjO +Qi x51 + (1 + i -21“??? 4- 1:21)]

(310)

80

On a Slope

 

The basic equations in this case are given in Appendix B

as equations B 3-5b. With )7! slope defined as

_ 352 + Wpo sinfi

[5,“- fopt(W0 + W50) 005p

and using the approximation Z/cosfl = I, we get

 

 

= 1 tan 3 +
7,2 slope ’21 level + 1 + 1 {Opt
(ye + i y ) tan
* 1 i 1 ' x V 50 (r If) "1““ (32)
11 ' x21 ' y52 2' 1 opt m

This expression gives the change of the drivewheel load-
ing effectiveness, caused by the slope. The equation shows
that the slope causes the same change in effectiveness whether
the implement is mounted or not, as zzedoes not enter the ex-
presSion.

Equations 31 and 32 are very clumsy to handle analytically
but could favorably be set up on an analog computer which would
make it easy to study the influence of changes in all the dif-
ferent factors and to find the best combination of them.

Another use for the drivewheel loading effectiveness may

 

 

also be mentioned. Equation 30a can be written:

R

jg
W = - W a
0 rcpt ”7K 50 (33 )

and H w
jZ + 50 sing

W = r - w ( b)
0 tom '71 cos 6‘ 50 33

For a given implement 352 and W50 are known, as well as the

81

condition of the field where it works, i.e. fopt- It is then
possible to approximately calculate the absolute minimum weight
of the power unit (for '22 = 1) or the minimum weight for any

other IZl-value, chosen from experience.

The Effect on the Drivewheel Loading Effectiveness of a Change
From Bear-Wheel-Drive to Front-Wheel-Drive

For rear-wheel drive, f2 is positive and fl is negative
and usually numerically smaller than f2. For front-wheel
drive the opposite is true. Therefore f2 — f1 can be written
= i fopt (1 + n) = 3 k1 where 0<n<1 and the plus-sign applies
for rear-wheel drive and minus sign for front-wheel drive. If
we substitute positive constants k for all factors, which are

not influenced by this discussion and assume x - x21 = 1, we

11
get

 

+

71 - 1 "‘ [(1)152 [I k2 {(XO - 005) + 1(150 - 005) -

'
O
O
‘J
Lw
+

1 +
Wherekz 1+?;k3=i:?(1+1-11);

 

 

1 - n i + i -.Zi
2 1 + i

“a
and the upper sign applies for rear-wheel drive.

This expression shows:

1. the effectiveness has one factor, k4, independent
of rear or front—wheel drive. The magnitude of this factor
is close to but less than a.

2. the rolling resistance, represented by x21, de-
creases Q! for a front-wheel drive, increases it for a rear-

wheel drive.

82

3. If the center of gravity and the implements are
placed at the same distance from the middle of the tractor
in both cases, but in front of it on a front-wheel drive and
behind it on a rear-wheel drive, there is no difference caused
by the gravity.

b. Increasing the height of the pull, y52, increases
the effectiveness for a rear-wheel drive, decreases it for a
front-wheel drive.

A study of the formula for.7£;on a slope shows that 7
increases with increasing slope for rear-wheel drive and
decreases for front-wheel drive.

Most of these reasons speak against front—wheel drive.
In some cases, however, front-wheel drive can give better

drive-wheel loading effectiveness than rear-wheel drive.

The Stall Limit

The stall limit is one of the limits for where an imple-
ment can be mounted on a power unit. When the implement is
placed too far ahead on a rear-wheel driven unit or too far
behind on a front-wheel driven unit, the load on the drive-

wheels is no longer enough to give any useful force. (R52 +

+Wsosinp), i.e. '71 becomes 0. At this point the unit is
stalled. The condition $1.: 0 inserted in equation 31a for

level ground gives the following limit for x50 and x51.

_ 1 f2X11 - f1x21 X0
XSO'flx51’(1'Z+I)~ £2-13 - 1

 

(Baa)
or if x51 = x50 (i.e., the implement is supported under its

center of gravity):

83

 

1 A f2X11 - f1X21 xo

x50 =[1 + H1 ~17] f2 _ f1 - 177-7-5- (Bub)
Effect of Non-Symmetric Weight Distribution

Earlier equations for the drive-wheel loading effective-
ness can be directly applied for all symmetrical cases; i.e.,
where the individual resultants of the forces lie in the center
plane, the xy-plane. I

If the drive-wheels are unequally loaded, the maximum pull
is decreased by an amount determined by the inequality and by
the differential (differentials).,

To illustrate the effect on a two-wheel axle, we assume
the wheel loads are

F F
Flh = (1 +A)E—}- and F1£= (1 -A)§—1-

The differential gives the torque
Tue = (1 - d) g to the wheel which slips most
and Th = (1 + d) % to the least slipping wheel.
Because we want to see the effect of uneven load only, we

assume the same coefficients f and f on both sides.
opt res -

In addition we use the equations

F2 =.T-L-

l 9'0 F11 {res = F1z topt ;

Th
F2 =--F|2f . F

h yo h res I 2 = F2 + F

1 2h

The pull F2 from the axle can be calculated to

 

i -A A - d fres] <
Opt)1 _ d — TL:“E ‘FEEE valid for d«» 43

-.

Flf

which should be compared to the pull with even load which is

F f We therefore see that the effectiveness which we may

1 opt‘

84

call ’Zsideload is

 

rZsideload ’ 1 - d 1 - d fopt (35)
This is = 1 as long as d is =4 (or greater).
For an ideal differential d = O and our effectiveness is

f
:1_A_Afres
opt
This shows that both the diminished torque and the rolling

 

resistance of the "unused" part of the load on the high-loaded
wheel decrease our effectiveness.
Similarly the effect of uneven load on a four-wheel drive

power unit can be calculated.

Ground Grip Effectiveness
The other possibility to increase the pull of a wheel is

to increase the coefficient of net traction f which is de-

cpt’
fined f = F2 0 t
Opt F1

There are numerous ways to increase fo This study is

t'
limited to the influence of different powerpunit designs and,
therefore, only the following subjects will be taken up for
discussion as they are determining for the layout. These two
factors are the maximum carrying and tractive load on the

wheels of a farm power unit and the influence of the wheels

on each other.

The Maximum Lead on a Wheel

The equations for drive-wheel loading efficiency will
give the same result if all the weight is put on two wheels
as if the load is distributed on four or six wheels. This

85

might in many cases be true, but when the load on a single
wheel is increased, a state will soon be reached where an in-
crease in load does not give a corresponding increase in net
traction. For still higher loads the result might even be
negative. The factor maximum load therefore deserves study.

The maximum load is mainly determined by the qualities of
the soil and by how the load is applied to the soil. Unfortu-
nately, not enough is yet known about the mechanical properties
of the soil in contact with a wheel. Bekker (ref. 4) has
assumed the following relationship between normal pressure, p,
tangential stress,17, and the sinkage, z.

P=('li:£+k?)zn T=c+ptanfl

where b is the width of the carrying surface and k , kc, n,
c and O are soil constants. It has not yet been shown that
these expressions are correct for agricultural soil but an
attempt has been made in Appendix A to develop formulas for
fopt where the influence of the load W and other factors can

be seen. One Of the expressions is
1 2

a . _, 1
f0” ... tan” + '3 " (5)11 ((1.1. 1) ' (and t)“ €32

where p = ¥b’ W is the load on the wheel,.( and b length and

 

width of contact area and A1 and A2 further soil constants.
This formula indicates that fopt decreases as p increases.

In the first place, p is determined by the size of the tire.

The relationships can be written as p = Pi + pC

1

n n n
_ 2
w - A3 D B (p1 + A“) 3

where p1 is inflation pressure. B and D are tire dimensions

86

and A3, A“, p0, n1, n2, and n3 are tire constants (at present
unknown).

This gives us reason to expect higher fOpt for a given
load if tire dimensions are increased and inflation corres-
pondingly decreased. This has also been found to be true in
many cases, even if not in all. There seems to be specially
favorable values with less favorable values on both sides.
These are sometimes, however, at so low inflation pressures
that they cannot be used with regard to buckling of the side-
walls, slip on the rim, etc.

These relationships have been partly studied, especially
for very special purposes such as off-the-road military vehi-
cles, but they should also be studied for ordinary agricultural
conditions and extended to extreme values in order to give an
idea about where the real limits are.

The size of the tire cannot be increased indefinitely,
both with regard to cost and design. The limit seems to lie
around 13 or it inch wide tires for ordinary inflation pres-
sures up to around 20 psi and at about 18 inch for slightly
higher pressures. The limit for outer diameter seems to be
around 65 inches.

There consequently is a limit for the pull that can be
taken from one wheel. One tractor manufacturer reports that
this limit seems to lie at around 50 hp per wheel, developed
at 5 to 7 mph. The inflation pressure used in this case in-
dicates, however, that the highest fOpt would certainly be

found at much lower load for ordinary agricultural conditions.

87

An investigation in the practically highest output per wheel
seems to be of great value.

When the limit for the output from existing drive wheels
on a power unit is reached, there is no other way than to dis-
tribute the power to more wheels. The evolution in the tractor
field seems to have reached this state now.

Another conclusion can also be drawn from this discussion.

The most favorable fo is found for a given combination of

pt
tire, load and inflation.~ If the load is changed considerably
without changing the inflation, a less favorable value should

be eXpected. Because change of inflation is usually not easily

done, great fluctuations in the wheel load can mean poorer per-

formance. Here again more information is needed.

Ipfluence of the Wheels on Each Other

 

As mentioned in Appendix A, the gross tractive force be-
tween the soil and the tire must be reduced by the rolling re-
sistance in order to get the net traction. If this rolling
resistance could be decreased, the net traction would become
larger. Traction could also be increased if the shear proper-
ties of the soil were improved.

Both these improvements probably take place when a wheel
runs in the track made by another wheel. Such improvement was
obvious from Ford's test of a tandem tractor and has also been
shown by Reed-Cooper-Reaves (ref. 27). Bekker (ref. h) dis-
cussed the problem but has later mentioned that this discussion

is perhaps not quite correct. More research is needed here

88

also. Some of the questions are: What is the best relation
between the front and the rear wheel with respect to load,
dimensions, and slip?

As much seems already very probable that the wheels

should run in the same track when possible.

Other Factors Influencing fopt

 

A third possibility to increase fopt should also be men-
tioned. In many operations there are field surfaces around the

power unit which would give different f At plowing for

opt‘
instance, the bottom of the furrow would give a different and
usually better value than the unplowed land. Consequently,

the drive wheels should, as far as possible, be placed where

the highest fO could be expected. Sometimes, however, soil

pt
compaction or other reasons might make such an arrangement

objectionable.

CHAPTER 9. The Stability of the Power Unit

The requirements for good stability and for high drive
effectiveness on a power unit very often work in opposite di-
rections. The trend has, therefore, been to decrease the sta-
bility down to a limit which was considered safe, thereby in-
creasing the drive effectiveness. Unfortunately, it has not
been possible to predict the stability exactly enough, and
accidents where the stability has not been enough have there-
fore occurred. The evolution towards lighter tractors with
stronger engines as well as the introduction of some mounted
implements has made the problem increasingly important.

When discussing stability it must first be said that it
is practically impossible to make a power unit one hundred
percent stable under all conditions. A limit must be chosen
for how much should be required and other safety measures be
introduced to reduce the damage when this limit on rare occa-
sions is trespassed. As such an emergency device may be men-
tioned the protective cab.

There are at least two principally different ways to
prevent stability accidents. One is to increase the stability
of the power unit, and this is the way that will be mainly
discussed here. The other way is to make it impossible for
the power unit to get into situations where the stability
would be endangered. Such a way is to limit the forces which
are involved to safe values. In most cases the wheel slip

limits the torque that can be absorbed by the drivewheels.

90

Many vehicles slide sidewise on a slope instead of tipping
over. Unfortunately, this way to safety is a very unreliable
one because situations may occur where, for instance, the
wheels do not slip.

Stability accidents occur as a rule when the power unit
is started or turns. They seldom occur when the power unit
is in steady motion, with or without implement, even if a few
ssuch accidents are known also. The equations must therefore

contain all acceleration and similar forces as do equations

B3, it, So in Appendix B.

L ongitud inal Stabil ity

In some cases it is possible to run a tractor with the
front wheels above the ground, i.e. with R11 = 0, because the
instability due to pull may at first decrease faster than the
basic longitudinal stability. In such a case, however, steer-
ing cannot be performed in the ordinary way and it is further-
more a dangerous way of driving if no special hitching device
has been used. This exceptional case is therefore considered
unstable in this study.

Equation Bjc solved for R11 gives:

311x11 = Woxocos’; - Woyosinfl+ W50x50cosfl-

' "soysosmfl ' B51"51 ' R2:1"21 ' R525'52 * w1"o "
- W2y0 + W51x50 - W52y50 + To + T10 + T20 + T50 (36a)

Because x11 and W0 always are positive quantities, # 0,

the condition for stability R11; 0 can be written:

91

xocos’g - yo sin/5 + i xjocosfl - i ysosinfl -

__ 21 R 2 81 a2
11sz - wa- a a? “ ”a;
a§1 852 _9_ 10 T20 + 0
+ i X50 - i 5'50 g 4’ W0 4- 0 + 0 wo
,>,o (36b)

( Equations 87-10 were also used.)

I write this equation thus:
(static stability) 2 (instability due to rolling re-

sistance) + (instability due to pull) + (inertia

instability).
In consequence with earlier work, the expressions above

are partly dimensionless. If equation 36a is multiplied by

L and equation 36b by WOL, they would be expressed in foot-

pounds. (L = wheelbase)

Static Stabilipy
Static stability = xocosp -'yosin/5 + i x5ocos/g -

- i y5osin/5 -,[i x51 (37a)

Here should first be noted that x50 and x51 often are
negative quantities and that consequently xocos/S is the
only quantity in this expression which is always positive.

It is called static stability because for a static power unit

eOluation 37a is all that remains of the stability equation
36b. The static stability does not change when the

Power unit starts moving, with exception for some eventual

change in the Z-value.
The static stability could also be written:

(x0 + 1 x50 - i Z x51) - (37b)
- [(1 - cosp) (x0 + 1 x50) + sinfl, (yo + i 530)]

\O
h.)

where the first part is the static stability on level ground
and the second part is the instability due to slope.
The static stability could be characterized by the angle

fls at which it is equal to zero.

 

[1
X - —— X
tan 165 = o + 1 x50. C03!“ 51 (38)
yo + 1 3’50

This is an extension of the meaning of the angle of static

L ongitudinal stability used by Worthington (ref..31).

Instability Due to Rolling Resistance
The instability due to rolling resistance

= 3(2); x21 (39)
can take values up to the neighborhood of (1 + i - [1) x21.
Even if x21 is relatively small, 1 + i - [,1 is larger than
any other factor in equation 36b and the importance of the insta-
bility due to rolling resistance is not negligible.

If not only stability but also weight transfer (811#0)
is studied, regard must be given also to the rolling resist-
ance of the front wheels (xll-l).

According to our system of notations x21 for the rear
Wheels is the same as x1 for a single wheel. This quantity
is discussed in Appendix A. It seems as if x1 should be rela-
tively little influenced by the wheel diameter on a flat sur-
f.aCBe. Under exceptional circumstances, ditches, etc., where
7 x1 is relatively large, it is, however, also proportional to

the wheel diameter as shown in Table A 2. In order to keep

the instability due to exceptional rolling resistance con-

93

. wheel diameter '
:Btant, the ratio wheel base ought to be kept constant,

Iprovided the weight distribution between the axles is left
unchanged.
Table A2 also shows that the pull F2 has an influence 4
can x1. This will, however, be discussed in the next paragraph.
The neglecting of x21 (and x11) seems to be one of the
x1nost important reasons for the discrepancy between calculated

.aand measured values for weight transfer and longitudinal sta-

‘t3ility, which has been pointed out by Buchele and others.

Instability Due to Pull
The instability due to pull

(#0)

I
EFF
o
m

3’52
. 322
'Ifkfie max1mum value of ”O is in the neighborhood of

rcpt (1 + 1 J11)

Ufluis is usually less than 1.
The fact that the front end of a tractor became lighter

6111(1 could rise when the tractor pulled has long been known

£11113. also that this happened earlier when the drawbar was high

Eit>c3\1e the ground rather than low. There has, however, been

Ei :rllamber of accidents where the tractor did not overturn until
tPlEB load was disconnected which spoke against this concept of
tklée effect of the pull on the stability, and the opinion has
been expressed that the pull helped to keep the front end of

‘b*1€3 'tractor down, as long as it was not applied above the

Center of the drivewheels.

9h

The main explanation to the accidents seems to be that
the pull has a considerable influence on the value of x1.
Take as an example a tractor which has dug down (Table A2).

As long as the load R52 = 0.6 321 is attached, the instability

95

R 1
caused by the pull is 0.6 y52 W0—
D/u
or if we assume y52 = _f— = 0.15
D R21
the instability is = 0.15 — .-———
L NO
R
The instability due to rolling resistance is 0.1 2%; wgl

and the total instability from these two sources

, 9 R21
- 0.20 L'Wa'

If the load is unhitched the first type of instability dis-

appears, but the second increases making the total increase

‘0 942 R21 D R 1
0.6 L WE‘=0.30E WE)—

i.e., an increase of fifty percent. Furthermore, the hitched
implement had probably partly supported the tractor and this

support was removed when the implement was unhitched.

Inertia Instability
The inertia instability =

a1 a2 8:1 352
-x __ + —— — 1 x +.1 -
0 3 yo 8 50 g y50 s
T T T T

The following quantities are often negative (accelerating

tractor assumed): T T , a and x50. For a rear-wheel

10' 20 51

driven tractor, T10 is usually small, eSpecially when 311 is
.mmnll as it is when the stability is low. a1, a51, To and
T50 are zero as long as the tractor is stable. A good appro-

ximation for most conditions is therefore:

96

Inertia instability = y 3.2. + 1 y 32. - .1120
k 0 g 50 g (hit)

0
where T20 is negative.

It is seen here that all important inertia forces increase
the instability of the power unit. Accelerations should there-
fore be kept low.

The inertia torque T can be written T = é-d . A relation
between angular accelerationcx and linear acceleration 3 can
be found. It should again be pointed out that our force and
length system is dimensionless. ‘g must therefore be given in
the same dimension as g and for %6 must be used Eéfig
which must be dimensionally correct (foot and poung? i.e., in

both numerator and denominator).

Lateral Stability

Actually more accidents happen at present where the
lateral stability has not been enough than where the longi-
tudinal stability was insufficient. One of the most common
accidents of this type is when one of the tractor wheels goes
over the edge of a ditch along the field or the road; but
accidents also occur when one wheel passes a hindrance or on
a sideslope when a heavy load is lifted or carried high above
the ground in a front-loader.

As was the case for longitudinal stability, inertia or
dynamic forces should also be considered for the lateral sta-
bility. In order not to complicate the equations unnecessar-
ily, the only inertia force that will be included is the cen-

trifugal force. For the power unit, the centrifugal force

97

acts through the center of gravity of the power unit. Its

. W
lateral component is called W3 and has the magnitude gg'zfa@

where aiis the angular velocity of the e.g. and zf is the z-
coordinate for the center of rotation (same length dimension
as g). Because it acts through the center of gravity in the
same manner as the side component of the gravity on a slope,
W0 sin I" it can simply be added to W0 sin, in the equations
and the resulting side force =

W0 (sin/+ zfé’g—a (42)
See further discussion in Appendix B.

We are first going to study the four-wheel tractor for

which equations 812-18a, 19-21 apply, and we
assume that the limiting device on the front axle movement
is not brought into action. The condition for lateral sta-
bility can then be written:

B211...? 03

We further assume a symmetrical power unit:

2” = 0 210 = 0 -ZI¥L = 211!. = 211

’zzil = zZir = 221
Then equation BiBb can be written, also using B13a and 88:

0‘ ZR21,. 221 = R21221 + m [3131f B13,."

" ”10(Sinc)” Zr ‘7] - “20(31113/+ 2 f-) yg

- w50L1n1+ (z? - 250) ‘g"-'] 3’50 4’ ”50(COSI:SO “K 251) +
+353y53 (“3)

We can here recognize three stabilizing factors: R21 221,

2 .
a) .
yM [313 + . . . 5-] and 353y53 and three instability

98

factors connected to the height of the c.g. of the power unit
Y20v to the height of the implement y50' and to the position
of the implement sidewise 250 and 251.

The Basic Lateral Stability

821221 (4h)

That the lateral stability increases with the tread, 2221
is well known and needs no further comment. It should, how-
ever, be noted that the other factor here is R21, i.e., the ..
load on the rear axle. If the load on the rear axle is small
compared to the overall weight, as can be the case with heavy
front-mounted implements, the basic lateral stability is also
small. 821 can be calculated from equations 83-5 which show

the different means to influence R21.

The Stability of Front End Suspension, yM

 

The coefficient for y” in
in [8132 + R13r - W10(sinJ/+ zf‘gLZU (145)
is in fact the force in the z-direction at the Joint. It is
almost always positive and this is therefore a stabilizing
moment. It increases when yM increases, i.e., when the pivot
between the front axle (front part) and the rest of the power
unit is placed higher up. For a tricycle tractor, where we
can consider yM = 0, this stabilizing moment does not exist.
There is a limit, however, for how large y” can be. If
y“ is made too large, the front axle becomes unstable and the front

right wheel leaves the ground. This value is:

99

2

60
51121.1 ' wio ($111+ 2; —) 3’10
1213 - W10(sin(y+ 2).?)

As 811 almost always is larger than R13, this means that y”

yna (46)

could be equal to or slightly larger than 211, i.e., half the

front tread.

Side Pull Influence

 

The side pull R53 has a stabilizing moment Bj3y53. As
y53 usually is small, this influence is small. Furthermore,
R53 can be negative. This moment is included in the equation
mainly to show its importance compared to other lateral forces.

R53 also usually increases 813 and therefore has another
slight beneficial influence.

A Special side pull is the wind force on the implement
and its load, which according to Appendix B, p. B10, can
amount to 5 lb/sq.ft. net area. Even if this is a small
force, it can be applied high up. Because it should always
be considered negative, its influence ought to be checked

for, e.g., frontloaders with hay, cotton bins, etc.

Influence of the Height of the Center of Gravity of the
nger Unit

The expression

”20 (5111)” 2f :3) yzo ‘ (a?)
shows that it is the weight of the rear part only (20) and
the height of its e.g. that are involved in this instability.

Wzoyzo is usually, however, not far from Woyo.

100

The consequence of the influence of this factor is, of
course, that the center of gravity of the power unit should

be kept low in order to give high lateral stability.

Influence of the Height of the Implement
The instability caused by the height of the center of
gravity of the implement is of the same type as that connected

to the power unit itself.

2
0)...

W50 [Skid/4' (2)9- 250) 81 5'50 ((+8)
Even if W50 usually is smaller than W20, y5O often can be
much greater, as for example for a front-loader. This might
therefore be a much more serious cause of instability than

the height of the power unit itself.

Influence of Implement Position Sidewise

The moment W50 (250 cosy -Z 251) should always be con-
sidered negative for a symmetrical power unit because tipping
could occur to either side and all other factors are symmetri-
cal. The instability caused by mounting an implement to one

side is therefore:

\WSO (250 cosy -(z51)\ ((+9)

The Angle of Lateral Stability
An angledn_could be found for which the lateral stabil-
ity is = 0 if a)2 is 0.

CHAPTER 10. Steering Effectiveness of an Agricultural Power

Unit

It is commonly known that the agricultural tractor can
have steering difficulties, especially on soft and uneven
ground and with heavy, rear-mounted implements. These diffi-
culties have promoted the introduction of steering brakes, an
effective if not efficient or desirable solution.

Some unorthodox tractors, e.g. the Unitractor, have en-
countered still greater steering difficulties than the ordi-
nary tractors. It seems necessary to calculate and predict
the steering properties of the tractor, which could otherwise
seriously reduce its usefulness.

.The basic elements in the steering are the steering forces
between the wheel and the soil. These are discussed in Appen-

dix A.

What Causes a Vehicle to Turn?

Except for the purely theoretical case that there is no
resistance at all to the movement, the turning of a vehicle
must be propagated by a moment on the vehicle working around
a vertical axis. This means that the steering force, caused
by one wheel at an angle to its direction of motion, is not
enough, but there must also be another steering force at an-
other element of the vehicle and these forces must constitute
a couple. This means that the steering effectiveness can be
increased both by increasing the steering forces and by in-

creasing the distance between them.

102

Steering Systems

There are two different ways to initiate a turn, namely
to put some wheels at an angle to the original direction of
travel and to introduce a difference in speed between the
driving members. In the first case, the wheels can be turned
individually around their center, automobile steering, or
pairwise together with their common axle, pivot steering.
Steering with different speed on the drive wheels might be
called brake steering, even if this notation is in some cases
misleading. (”Differential steering" would have been better.)
These systems are exemplified in Table 301.

Automobile steering is controlled by a torque around the
king pins. Brake steering is maneuvered via the transmission.
Pivot steering is usually performed through a torque around
the Joint. Both automobile and pivot steering can be assisted
by brake steering. Pivot steering should probably be given

more attention than it has had up till now.

What Opposes Turning?

The need for a steering moment arises from the existence
of forces and moments, which oppose the turning of the vehicle
or which try to make the vehicle turn in an undesired direc-
tion. Some of the opposing forces are as follows:

1. The rolling resistance of steered wheels give a re-
sultant which does not pass through the point of action of
the resultant of the forces on the drivewheels. A steering

force must therefore be introduced.

103

TABLE 01. BASIC TYPES OF STEERING.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Automobile

 

 

 

gteerigg

 

Pivot

 

 

 

 

 

Brake.

 

 

  

steerigg

 

 

 

 

 

10h

steering
force .‘ /\ rolling resistance
IA / of front wheels

0 n

 

 

7

 

 

 

 

u u

\drive force from rear wheels

2. When a wheel is forced to roll in a circle, there
arises in the contact area resisting moments (See Appendix A).
These are greater the greater the length of the contact area
is and the smaller the radius of the circle. These moments
are negligible for automobiles (except when parking) but can
be important for tractors.

For tracklaying and other brake-steered tractors
this is the most important opposing moment but it has pro-
bably influence also on ordinary wheel tractors.

3. The resultant of outer forces on the tractor from
implement, etc. does not always pass through the point of
action of the resultant of the forces on the drivewheels and
gives thereby a turning tendency which must be counteracted
by steering forces.

It ought to be observed in this connection that an

attempt to make the implement move sidewise in a turn often

105

causes the resultant draft to move far out to one side and at
the same time to increase. Such turns should therefore be
avoided because very large steering moments are needed to
carry them through. The center of rotation for the whole unit
must consequently be given attention.

4. The rolling resistance on the left and the right
side of the vehicle might be unequal.

5. When there is a side force on the vehicle, as on a
side slope, or in a curve with high velocity and centrifugal
force, no steering moment is needed, but still a steering of

must be made

the wheels/in order to give them sufficient slip angle to

create the reactive side forces on the wheels.

Influence of Rollingyfiesistance on Steerinngffectiveness

As mentioned in Appendix A the steering wheel stops roll-
ing and thereby stops working as a steering wheel at a lower
steering force, the higher the rolling resistance is. Even
before that, however, the rolling resistance diminishes the
steering effectiveness by decreasing the lever arm of the
steering force on the steering wheels as shown in following

picture.

106

    
     
 
 
 
 

rolling
resistance

steering
force

lever arm with no
resistance

lever arm\with resistance

 

 

 

 

 

 

U U

If on the contrary the steering wheels were driven, the
steering effectiveness would increase, as shown by the follow-
ing figure. This explains one of the big advantages of all-
wheel drive for vehicles working in the forest, in swamps or

in snow.
steering

drive force from ‘H/
front wheels

lever arm with driven’““‘\
front IbBOl 8 h
r

 

 

 

 

 

Q U

107

Load on the Steering Wheels

Steering forces as well as driving forces originate in
the contact between the wheel and the soil. These forces are
in general proportional to the vertical load on the wheel.

It would therefore seem to be most effective to put all or
almost all weight on wheels, which were both driving and
steering, or otherwise expressed to use the drivewheels for
steering also.

One objection against such a method is that a steering
force might reduce the driving force available from the same
wheel. This is to a certain extent true, but of less import-
ance, because steering and driving forces add as vectors, not
numerically. Other reasons make this objection of still less
importance for tractors.

Another more serious objection against steered drive-
wheels is that this makes a complicated drive mechanism neces-
sary, especially if automobile steering is used as is at pre-
sent most common. The steering radius is usually also in-
creased. Therefore unpowered steering wheels are common on
present tractors. In order not to make the drive effective-
ness of the tractor too poor, the load on the steering wheels
is kept relatively low. If other systems for steering are
used, it is easier to combine steering and driving in the

same wheels.

SECTION IV THE POWER UNIT

 

Preceeding sections have given the necessary information
about the parts of the operational unit, the implement being
described in Section II and the parts of the power unit in
Section III. In this section this information will be inte-
grated into the lay-out of a power unit with the aim to get
the best possible Operational effectiveness for a given opera-
tion or group of operations.

There are in the literature many discussions of different
tractor types. A general discussion and comparison is made
by Meyer (ref. 21). Discussions of the merits of certain types
of power units are numerous.

Among historical reviews of the types of tractors which
have been used, those made by Gray (ref. 15) and McColly
(ref. 19) may be mentioned and an article by Moberg (ref. 23).

When making the lay-out the following steps may be in-
cluded:

1. Determine the relative position of implement and wheels.
2. Determine which wheels should be driven and steered.

3. Determine place for operator.

N. Determine place for engine.

5. Check that the stability is within reasonable limits.

6. Evaluate the operational effectiveness of the combination.
7. Evaluate drive and steering effectiveness.

8. Further evaluations.

109

Before starting this it might, however, be desirable to
study which wheel arrangements are possible and which have

been used.

Chapter 11. Wheel Arrangements

It is possible to make power units with 1, 2, 3, h and
more wheels and tractors with these numbers of wheels have
also actually been made. Tractors with only one or two wheels
need, however, with a few, theoretical exceptions some addi-
tional support to become stable. For fractional horsepower
tractors this support can be supplied by the operator, who
walks behind the tractor, but for all larger tractors it is
not in line with the requirement on driver convenience to let
him take the thrust of the engine. Such tractors should there-
fore not be made. In some cases two-wheel ”tractors“ are
attached to their implement in such a way that the implement
takes the thrust, but then they are not any more true two-
wheel tractors, because the wheels or other supporting de-
vices on the implement could be counted as wheels of the en-
tire unit. In the future I will count such implement wheels
as belonging to the power unit if the connection between the
basic power unit and the implement is designed to take the
thrust and the implement wheels are necessary to make the
outfit stable. Examples of such combinations are found among
heavy earth-moving equipment.

A summary of the variables in the wheel arrangements and

0f the possible values of each variable may look as in table

110

401. When combining these in all possible ways and only re-
moving duplicates there seems to be more than 100 three-wheel
solutions, and more than 300 four-wheel solutions when only
wheel arrangement alternatives are counted. Only very few of
these possibilities are really utilized.

Table 402 gives examples on some basic wheel arrangements.
These examples can be carried further

by combining different drive and steering arrangements with
the basic lay-outs.

The best wheel arrangement should be sought for every
special use. Some general rules apply, however, for many
cases. General rules concerning drive and steering effective-
ness have been discussed earlier as has stability and these
will therefore not be mentioned again here.

elf the implement requires any considerable pull, this
pull should be in the same longitudinal plane as the resultant
force from the drivewheels. In tractors with an ordinary dif-
ferential no wheel can usually give any appreciably higher
pull than the others. The pull of the implement must there-
fore work on or close to the centerline of the drivewheels.
This means that a plow, at least a multi-bottom plow, cannot
be placed in front of the driving wheels, if one driving
wheel is not to run on top of the plowed land, which is usu-
ally avoided.

Even if the implement is centrally attached, but mounted
in front of the main drivewheels, this is not a good solution,

because the force system is unstable. Any deviation from the

111

 

TABLE #01. VARIABLES IN WHEEL ARRANGEMENTS FOR A POWER UNIT.
Variable Possible alternatives

Type of 'wheel'
Number of wheels
Front wheels

Axles

Sidewise symmetry
Drivewheels, number
Drivewheels, position

Steering type

Steering wheels
Steering wheels

Direction of travel in work

 

Wheel, track, sled (ski)
(1). (2). 3’ “D

1, 2, 3, u, or more

(5), 6 or more

(1). 2, 3, or more
Symmetric, not symmetric
1, 2, 3, 4, (5), 6 or more
Front, rear, combinations

Automobile ty e, pivot, brake
(differential

i, 2, 3, h, (5), 6 or more
Front, rear, combinations

One, both.

112

TABLEyhOZ. BASIC WHEEL ARRANGEMENTS FOR POWER UNITS.

Only alternatives, which at least theoretically are
stable, are shown. Only one of left-hand and right-hand
alternatives is shown.

1-wheel unit.

 

 

(.9.

 

 

 

 

 

 

 

 

 

 

 

 

 

O C

 

113

TABLE h02(cont.) BASIC WHEEL ARRANGEMENTS FOR POWER UNITS.
l-Ehsel units.-

0 F“ p fl (0

U Q ”‘

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h-wheel units.

 

 

 

 

 

 

 

 

 

 

 

DC

 

 

 

 

 

 

 

 

 

 

11’»;

ggpts h02(cont.) BASIC WHEEL ARRANGEMENTS FOR POWER UNITS.

11.-E11281 units .-cent-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

115

TABLE 0,02 Leona; BASIC WHEEL ARRANGEMENTS FOR POWER UNITS.

6-wheel units.

""1. 7T,

 

 

 

 

 

 

 

D C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A
U p u
T ”W

ill
U U

 

 

 

 

 

 

 

 

 

 

 

 

 

 

116

straight course causes a moment that tries to make the devia-
tion still larger. When the load is attached behind the driv-
ing axle the draft tends to stabilize the power unit on a
straight course.

The most important group of implements, requiring high
pull, are the tillage implements. Their object is mainly to
loosen the soil. It is then inconsequential to let the drive-
wheels follow behind the implement, because the drivewheels
are heavily loaded and will compact the soil again. The till-
age implements are therefore sometimes divided in two parts,
one in front of the drivewheels and the other behind them, but
this arrangement should be avoided if possible.

Most tractor wheels are chosen with regard to the part of
the tractor weight they normally carry. The weight acts in
the center of gravity of the tractor. The load distribution
on the wheels is least changed when the implement load also
acts in the center of gravity of the tractor. The further
away from the center of gravity the extra load is applied, the
greater will the changes in balance be, with corresponding
poorer steerability, traction and roadability of the tractor.
Therefore from the viewpoint of tractor stability and load
carrying capacity centrally mid-mounted implements are the

best and front and side-mounted implements the poorest.

Chapter 12. Individual Power Units
As mentioned earlier, the requirements of the implement

has to be satisfied first of all if a good operational unit

117

shall be found. These requirements can most easily be satis-
fied if individual power units are designed for each implement.
This is consequently the first step of the evolution.

The implements are listed in tables 105-114 and the re-
quirements and characteristics of the implements in tables
201-215. One way to use this information will be illustrated

by a couple of examples.

Power Unit for Moldboard Plow
From table 210: (notations according to App. B)
implement weight W50: 250 lb/ft
implement pull R52 = 1000 lb/ft
From table 201:
Field conditions: firm but sometimes slippery
Assume fopt = 0.6 (anti-slip devices used when needed)
Assume 15% grade, i.e. sinlbm 0.15
The weight W0 + W50 can now be calculated as a function

of 71 from equation 33b.

 

w = — - 250
0 0.67 oz
= iézg - 25o lb/ft
’71

Assume tentatively a drivewheel loading effectiveness of
0.85
”o = 1720 lb/ft
We intend to make a power unit for a 3 x 16 inch plow =
4 ft. working width.

NO + W50 = 7900 lb.

118

This load may be carried by two 12 x 38 tires and one 7.50 x
20.
The drivewheels have to be in front of the plow in order
to get even pull on both of them without any of them on plowed
ground and to insure travel direction stability as discussed
earlier.
The third wheel has to be placed behind the plow in order
to insure constant plowing depth. (It should be remembered
that the plow is supposed to be fully mounted with almost all
of the reaction forces taken by wheels. The load on the land-
sides and other sliding surfaces should be kept at a minimum.)
Steering the rear wheel only is not effective enough.
The simplest way of steering drive-wheels, pivot steering,
can be used.

The wheel arrangement will then be as in the picture
below. The dimensions of the plow are taken from table 210.

The figure gives a wheelbase L = 123 in., tread 62 in. and

£16.
123

The position of the center of gravity of the power unit

implement position x50 = 66 in. = = 0.54

is determined by the stability. This being a front-wheel-
driven power unit the longitudinal stability is least when
the unit is backing. Assume distance of rolling resistance =
'15 in. (hindrance, e.g. furrow wall).

x11 = 123 - 15 = 108 in. = 0.88

X21 = -2 in. = -0002

1 = 0;
- Z50 -
1 "' 17m - 0.1“

 

 

 

 

 

 

119

 

 

 

 

 

 

 

 

 

 

EXAMPLE OF POWER UNIT FOR
MOLDBOABD PLOW.
Scale 1:25

120

352 = 0;

y52 = 0;
This inserted in equation 36a gives for ’8: 0.

xos 0.93; Take x0 = 0.90 =‘111 in.
We can now calculate the actual drivewheel loading ef-
fectiveness for

x11 = 123 + 3 = 126 in. = 1.02

le = 2 in. = 0.02

y52 = 3 in. = 0.02 (height of the center of re-
sistance of the implement)

y: = 0.1 (10% of implement weight carried

by landsides, shares, etc.)

X51 = X50 = 0.5“

fl = 006
f2 3 -0.1
)2! = 81%

This is less than assumed at the beginning of the calcu-
lations. The weight of the power unit therefore has to be
increased to 7300 lb.

It should be mentioned that this weight 7300 lb. does
not need to be all in the power unit proper but could partly
consist of ballast placed elsewhere, e.g. advantageously on
the plow. All that is required is that the power unit and
the ballast together weigh 7300 lb. and that their common
center of gravity is 12 inches behind the drive axle.

For a rough calculation the rolling resistance can be
put equal to

0.1 (1000 + 7300) = 830 lb.

Total force on drive-wheel periphery is then
4000 + 83’, #5000 lb.
According to table 210 the maximum speed of plowing is around
5 mph. Corresponding engine power with a transmission effi-
ciency of 0.9 is then 56 hp., which therefore is the maximum
horsepower that can be utilized in this operational unit.

The figure below shows a power unit for a 6 x 16 inch
plow. This has to have four-wheel drive.‘

A corresponding calculation for an ordinary tractor and
three-bottom plow, using Z = 0.5 gives I21 = 64%.

The calculations for the plow power unit are probably
made with unnecessary wide safety margins, because e.g. the
values for draft are taken from plows with less favorable
mounting system. The calculations show, however, how the
basic data can be used. For better reliability the basic
values must be better specified, giving corresponding values
for plowing resistance, fOpt and x1. Such a specification
can be much easier done if a reliable soil value system can

be found.

Power Unit for g Grain Drill
From table 210:
150 lb/ft

W50
75 lb/ft

R52
The grain drill consists of two main parts, the openers

and the seed-metering devices being one and the hopper the

other. Assume the weight of the openers and seed-meters being

 

 

 

 

 

 

 

 

122

 

 

 

Exam 1e of ower unit
for E-bottom moIdboard
plow.

Scale 1:50

123

110 lb/ft and of the hopper 40 lb/ft. If the pull was calcu-
lated for 50 lb/ft grain in the hopper and the coefficient of
rolling resistance 0.2, the pull of the openers should be 75
- 0.2 . 90 a 55 lb/ft. The data are consequently: ‘

 

 

Openers and seed-meters ngper andgrain_
Weight W50 = 110 lb/ft W5O = 40 + 100 lb/ft
Draft R52 = 55 lb/ft D52 = rolling resistance
Self-support Z = 0.9 ,( = 0 I

(no slippage wanted) a power unit for a 15 ft. drill would

have (equation 33b)

15 g?3+ §?25x 8:93 - 250 = 15 . 230 = 3500 lb.

The arrangement is shown in the sketch below.

WC:

124

EXAMPLE OF POWER UN;3_F0R GRAIN DRILL
Scale 1:50

 

Grain
(fert.)
hopper

 

 

 

 

 

 

 

Driver ~‘n
DEX L1

 

 

 

i..J

 

Openers and seed-meters

125

Power Units for Other Implements

Using the same basic procedure as in the two examples
given, the most suitable power unit can be found for other
implements.

Different possible arrangements can easily be compared
by using cardboard templates Of the parts involved as have
been used in the examples here. The templates were made to
scale 1:25 and showed the contours of the part in the horizon-
tal plane. They could easily be moved around on a paper with
a coordinate system, drawn to the same scale. In that way
the actual coordinates could be read directly when the parts

(templates) had been located in the right place.

Chapter 13. Power Unit for More Than One Implement.

From a study of individual power units it can be seen
that the same type of power unit can be used for more than
one implement, even if the dimensions Of the power unit might
not be the same. This is, for instance, the case for ferti-
lizer distributor, grain drill and sprayer, where the imple-
ment consists of a ramp for distributing, placed behind the
power unit and a container for the material being distributed,
placed at the center of the power unit.

These power units for two or more implements are closer
to reality and should therefore be more carefully checked for
the practical possibility Of the arrangement. A way to do
this is to make wooden blocks Of the important parts of im-

plement and power unit to some scale, e.g. 1:10. The blocks

126

should indicate the space needed for each part including all
transmissions, etc. belonging to it. The figure below shows
some such blocks and an arrangement Of them.

Even if the number of power units can be reduced in this
way there are still more types than can be economically used.
A further reduction Of types is therefore necessary, even if
the reduction probably does not need to be reduced down to a
single, general-purpose type. This is discussed in the next
paragraph.

When reducing the number of types, this means that a com-
promise must be made between the requirements Of the different
implements which the power unit shall serve. Most considera-
tion must then be given to the most important implement. Dif-
ferent measures of the importance Of the implements were dis-
cussed in chapter 4 and can be used at this time.

One detail may be mentioned here. One of the implements
in a group might require a heavier power unit than the others.
It is then logical to place as much as possible Of this extra
weight in the implement and not in the power unit. Savings
in fuel economy and less soil compaction will be the result
Of such a proper adjustment Of the weight.

This section has shown some definite proposals Of power
unit design, to which many Objections might be raised. They
are, however, not given as final answers to the question,
Which would have been very pretentious, but as examples of a
way to attack the problem, and in the author's Opinion, the

best way to attack it. Using this method, somebody else with

127

 

1‘

side delivery pick-up baling wagon (should
rake device chamber have sides)

Elam! NOBEL 01‘ POIER UNIT WITH PICK-UP OUTFIT.

 

driver' 3 cab I Idriveeheel Ietoering
(supporting legs Tongue wheels
only in model) drivewheel

POWER UNIT FOR THE BALER.

 

128

better knowledge Of all facts, could certainly find better

solutions.

;s It Absolutely Needed That the Power Unit Can Perform Every
Qperation on the Farm?

The OpiniOn is sometimes expressed that the farm cannot
afford to buy machines, made especially for a certain opera-
tion, at least not more expensive machines. Some Of the new
types of power units that are available today cannot be used
for more than a limited number of Operations, and this has
been given as the most important reason for their relatively
small popularity.

There is, however, an increasing demand for self-propelled
combines, in spite Of the fact that these are both expensive
and specialized. A certain demand for other self-propelled
harvesting machines has also been felt. This indicates that
there might be a market for a power unit that could make more
than one harvesting machine self-propelled, even if the power
unit could not be used for other farming operations.

Furthermore, the farm Of today usually has more than one
tractor. The farmer therefore does not have any more the same
need for a tractor that can perform all operations, i.e. that
all tractors should be Of the same general, all-purpose type.
0n the contrary, there seems to be a good reason, that differ-
ent types of power units be used, each specially fitted for a
certain group of operations. A better efficiency could be ex-
pected with such a solution, because the all-purpose tractor

must be a compromise between very differing demands.

129

A reason against differentiated tractor types, though Of
minor importance, could be that the different power units on
a farm could not be used as spares for each other to the same
extent as now. Neither would it be possible to use the new
tractor for some Operations, even if it was not busy, because

the Old tractor was the only one, made for that type Of im-

plement.

SUMNARY ANL FURTHER INVESTIGATIONS

Summary

All farming operations are performed by implements, which
require power of some kind. For a long time this power was
supplied by man but it was not until man could employ other
power sources for his implements that he could increase his
productivity and thereby his standard of living by any appre-
ciable amount.

The most important, early power source was the horse or
other animals; and implements were made which would fit this
power source. When mechanical power began being used besides
animal power, the implements were basically the same as used
earlier for the reason, among others, that the implements
Often had to be used alternately with mechanical and animal
power and also because special tractor implements had not been
developed. The function of the mechanical power unit, there-
fore simulated the function of the horse to a very high degree.

When now the horse in many countries is without importance
as a power source, pure tractor implements could be developed.
A basic difference between the horse and the mechanical power
unit should thereby be Observed. Contrary to the horse, the
mechanical power unit can be adjusted to fit the implement as
well as the implement can be adjusted to utilize the mechanical
power unit in the best way. Implements and power unit should,
therefore, not be develOped separately but at the same time and

as one operational unit.

131

One of the fundamental preparations for the design of a
power unit should consequently be a study of what the imple-
ments require of their power unit. These requirements are of
two kinds; namely, those which are dictated by the Operation
itself andvthe product involved and those which mainly origin-
ate from the design of the implement. The first kind Of re-
quirements is called the operational requirements of the im-
plement; the second is called the technical requirements.

Some existing implements perform several operations at
one time. Each such operation should be studied separately
when determining the requirements of the implements in order
to connect the requirement only to the part where it belongs.
This makes it easier also to discuss other combinations of
Operations than is common at present.

Requirements which could be listed as operational are
those related to field conditions, quantities of product in-
volved, time available for pperation, supervision of function
needed, adjustment of implement in work, height control of
implement in work and on headlands, accuracy of steering of
implement and power unit in work, and special factors affect-
ing the position of the implement -- for instance, if it should
be in front of or behind the wheels. Operational requirements
are briefly listed in tables 201-206.

The technical requirements of the implements are connected
to such factors as size, weight and outer dimensions, draft,
power type and amount of power, if rotational power or pull is

needed, vertical forces (weight transfer), speed and speed ad-

132

justment and capacity. Technical requirements are listed in
tables 210-215. These tables are very imcomplete because
values are not available.

The Operational requirements will usually not change very
fast because they are connected to the crop and the methods
used in producing the crop. Most technical requirements, being
connected to the implement design, will change must faster.

Requirements mentioned earlier are all connected to the
implements and their Operation. In order to make the unit
implement and tractor an effective unit, certain functional
requirements connected to the tractor parts have to be ful-
filled also. There are many such requirements but the most
important ones, affecting the general shape of the power unit,
are the requirements on good drive effectiveness, good steer-
ing effectiveness and sufficient stability. Driver position
and method for connecting the implements to the power unit
should also be considered.

The drive effectiveness is defined as the ratio between
the actual useful pull and the highest possible pull that
could be exerted by an operational unit (implement + tractor)
of the same weight on the same type of ground and when the
implement works in the same manner. The drive effectiveness
has two components -- the drivewheel loading effectiveness
and the ground grip effectiveness. The drivewheel loading
effectiveness indicates how effectively the available vertical
forces are utilized for loading the drivewheels and thereby
producing pull. Equations for the drivewheel loading effec-

133

tiveness are given in chapter 9. The drivewheel loading effec-
tiveness for a rear-wheel driven power unit is favorably in-
fluenced if the weight of power unit and implement is placed
far back, by a pull high above the ground, by a long distance
of rolling resistance, by fully-mounted implements, etc. The
limit for increasing the drivewheel loading effectiveness for
a two-wheel-drive power unit is usually set by the stability

of the unit.

The ground grip effectiveness is intended to indicate
the effectiveness of producing pull, i.e., the effectiveness
Of the force transmission between the wheel and the soil,
when the size of the wheel load is fixed. It is usually fa-
vorably influenced by relatively low total load on a given
wheel, by low inflation pressure, and by running the wheel
in an earlier wheeltrack, where the rolling resistance usually
is smaller and the strength of the soil increased through com-
paction. Increasing the load on a given wheel generally de-
creases the ground grip effectiveness. This fact limits the
pull that can be produced by an individual wheel because the
size of tires is limited for design reasons. The ground grip
effectiveness has not been observed enough in present research
and design work.

Both longitudinal and lateral stability are based on a
suitable positioning of the centers of gravity of the power
unit and the implement relative to the wheels or other support-
ing media. Both stabilities are adversely affected on a slope
and in a curve by high positions of the centers of gravity.

134

The longitudinal stability is further decreased by the height
of the pull above the ground, by increasing distance of roll-
ing resistance and by inertia forces, especially the horizontal
acceleration force on the Operational unit and the rotational
inertia moments on the drivewheel. The lateral stability is
higher for a four-wheel power unit than for a three-wheel unit,
and this superiority is better the higher the joint between
the front axle and the rest Of the power unit is placed.

The steering effectiveness is influenced by the system
for steering but the relative merits of different systems have
not been investigated. The steering effectiveness is higher
for a driven wheel than for an unpowered wheel and higher for
a steering wheel with high load than for a lightly loaded
wheel. The movement Of the implement in a turn must be Ob-
served because it could have an important influence on the
steering.

The Operational and technical requirements mentioned
above give the basis for the design Of the power unit. One
procedure for making the design has been outlined in section
IV. It starts from the concept that the self-propelled im-
plement is or can be made the most effective Operational unit.
The first step in the procedure is therefore to design indi-
vidual power units for each implement, where the requirements
of only one implement are satisfied, as far as possible. The
factors to be determined for this initial design are, for in-
stance, wheel arrangement, driver position, weight, positions
of center Of gravity, steering system and engine horsepower.

A detailed design is not needed at this stage.

135

The second step is to find power units for more than one
implement and for combinations of implements. Combinations,
which are Of value, are indicatedoin tables 105-114. In some
cases a power unit found in the first step can be used as it
is for more than one implement; in other cases, the new power
unit can be found by combining common features of the indivi-
dual power units. When making combinations, the capacities of
the implements and the power unit in the combination must be
matched. It is not always possible to fully satisfy all re-
quirements Of the implements in a combination. For the deci-
sion on which requirements could be neglected, knowledge about
the importance of the implements is essential. The importance
Of an implement can be measured by the area covered, the fre-
quency of the use Of the implement, the value of the product
involved, etc. This is discussed in chapter 4.

It is unlikely that a power unit can be found which can
be used for all implements without severe sacrifices on the
Operational effectiveness Of at least some Of the implements.
Such a general purpose tractor is, however, not absolutely
needed because a future farm could very well have special
tillage tractors, harvest tractors, etc. Higher Operational
effectiveness would likely be the result of such a diversi-
fication Of the power unit design.

' Furtherplnvestigations on This Subject

This study is mainly a framework, intended to show what

basic information is needed to make a power unit layout and

also to show a method Of finding a suitable power unit. Each

136

Of the parts of the study could probably favorably be made
Objects for further study. Among the subjects I would like
to mention are the following:

1. The listed requirements Of the operations and the
implements are only incompletely described. The technical
requirements should be especially checked because the values
now given contain factors which are not inherent in the basic
Operation or implement. Parasitic pull is included in some
draft figures, carrying wheels, etc., in the weight figures,
etc. A more thorough study of the literature would probably
give more information here but more new research must also
be made. It is thereby important that the basic functions
are studied without irrelevant factors being included.

2. Among the technical requirements more attention than
now should be given to the vertical forces that can or must be
applied to an implement. For good drivewheel loading effec-
tiveness these forces are essential. It is now possible to
utilize them when the implements are mounted.

3. The values for draft and power consumption as well
as for traction and rolling resistance should, as far as pos-
sible, be related to properties in the product or the ground,
not to the implements. A reliable soil value system is one
Of the necéssary ingredients in this. If possible, soil values
should be given for the separate operations.

4. Among mechanical relationships which should be stu-
died further in order to make this method Of design more re-

liable, should be mentioned:

137

a. ground grip effectiveness
b. Optimum load and power on a tire
c. the distance of rolling resistance, x1, for both
ordinary and exceptional conditions
d. the behavior of a tire under lateral load
e. the mechanics Of stability for both the power
unit alone and for the combination of power unit
and implement
f. the mechanics Of steering for both power unit
and combination
5. A thorough investigation should be made to find the
best individual power unit for each implement. Then power
units for combinations Of implements should also be found.
This would indicate the direction for the evolution Of the
present tractors. Such investigations would have to be re-
peated with regular intervals as more information becomes
available and the outer conditions are changed.
6. This study has been limited to existing implements.
Some of these implements do not utilize the power unit very
well. Better substitutes for them should be sought with due
regard taken to the possibilities of the mechanical power unit.
When such implements are found, however, the method shown here
can be used to find out what type of power unit the new imple-
ment requires.
7. Consideration should be given now and then to en-
tirely different types of powered farming (circular fields,

permanent 'tracks", cable-operated implements, etc.).

9.
10.

11.

12.

13.

14.

REFERENCES

Bainer, Roy, R. A. Kepner, E. L. Barger (1955). Princi-
ples of farm machinery. John Wiley & Sons, Inc., New
York. 571 p..

Barger, E. L., W. M. Carleton, E. G. McKibben, Roy Bainer
(1952). Tractors and their power units. John Wiley &
Sons, Inc., New York.'496p.

Barnes, K. K., T. W. Casselman, D. A. Link (1959). Field
efficiencies Of 4-row and 6-row equipment. Ag. E g. 40:
148-150, March 1959.

Bekker, M. G. (1956). Theory of land locomotion. Univ.
Of Mich. Press, Ann Arbor. 520 p.

- " - (1959. Private communication.

Berglund, Nils, B. Karlsson (19 5). En undersbkning

Over traktordriften p8 mindre g rdar (A Study on Tractor
Work on Small Farms). Swed. Inst. of Agr. Eng., Uppsala,
Sweden. Bull. 260. 79 P.

Brenner, W. 0., H. Luckner (1950). Die Arbeitsgeschwin-
digkeiten von Schleppern und Landmaschinen. Die Land-
technik, no. 17. Munich.

Brodell, A. P., G. W. Birkhead (1943). Work performed
with rincipal farm machines. USDA Bureau of Agr. Econ.
F.M. 2, May 1943. (Excerpts in ref. 11)

Case, 0. A., Machine specifications, 1959.

Census Ongriculture (1954). Special reports, Vol. III,
part 8.

Cooper, M. R., G. T. Barbon, A. P. Brodell (1947). Pro-
grfiss of farm mechanization. USDA Misc. Publ. 630. Oct.
19 7.

Dupuis, H., R. Preuschen, B. Schulte (1955). Zweckmdssige
Gestaltung des Schlepperffihrerstandes. Schriftenreihe
Landarb. u. Techn. Heft 20. Bad Kreuznach, Germany.

Eaton (1957). Torque converting the farm tractor. SAE
reprint #188. 'Milwaukee. Sept. 9 - 12, 1957.

Eklund, B. (1946). Arbetsledaren (The Foreman). Lant-
brukstrbundets Tidskrifts AB, Stockholm. 387 p.

15.

16.

17o

18.

19.

20.

21.

22.

23.

24.

25.

26.
27.

28.‘

29.

139

Gray, R. B. (1958). Development of the agricultural
tractor in the United States. Am. Soc. Of Agr. Engr.,
St. Joseph, Mich. Parts I & II, 46 + 55 p.

Jeppson, Gunner (1955). Brdnslefbrbrukning och uttagen
motoreffekt under Olika slagav traktorarbeten (Fuel
consumption and average engine load for different tractor
Operations). Swed. Inst. Of Agr. Eng. Uppsala, Sweden.
Bull. 259. 80 p.

Johannsen, B. B. (1954). Tractor hitches and hydraulic
systems. SAE Trans. 62:173.

Larsen. H. (1946). VAxtodlingsldra (Plant husbandry).
Hermods Korrespondensinstitut, MalmO, Sweden. 398 p.

McCOlly, H. F., J. W. Martin (1955). Introduction to
agricultural engineering. McGraw-Hill, New York. 553 p.

McKibben, E. G. (1927). The Kinematics and Dynamics Of
the Wheel Type Farm Tractor. Agr. Engr. Journal, Jan.-
July. 1927.

Meyer, H. (1951). Der Schlepper und sein Gerdt im bduer-
lichen Betrieb. Die Landtechnik, p. 785, no. 23/24, 1951.

- " - (1957). Probleme der Schlepperentwicklung. Grundl.
d. Landtechnik. Heft 9. page 10, 1957.

Moberg, H. A. (1955). Traktorn och dess utveckling (The
tractor and its development). Maskinteknik i jord och

skog, p. 14, no. 1, 1955.

National Inst. of Agr. Engg. (1956). Rep. NO. 41, The
influence Of the Operator's position on steering perfor-
mance in tractor rowcrop hoeing. Silsoe, England.

Persson, S. (1959). Economic factors in agricultural
mechanization. Unpublished report. Mich. State Univ.

The Red Book (1959). Implement and Tractor.

Reed, I. F., A. W. Cooper, C. A. Reaves (1957). Effects
Of two-wheel and tandem drives on traction and soil
compacting stresses. Trans. of the ASAE, 2:22-25. 1959.

Schilling, E. (1955). Landmaschingp. Band I: Acker-
fighlepper. p. 130-132. Verlag Dr. Schilling, Cologne.
O p.

The Tractor Field Book (1948/1949). England.

”‘91

140

30. Walters, , W. H. Worthington (1956). Farm tractors and
their tires. SAE Trans. 64:395-407. 1956-

31. Worthington, W. H. (1949). Evaluation of Factors Affect-

ing the Operating Stability of Wheel Tractors. Agr. Eng.
30:119-123, 179-183. 1949.

APPENDIX A. THE FORCES BETWEEN A WHEELgAND THE GROUND.

 

The discussion of the drive and the steering effective-
ness and of the stability of the power unit is based on the
laws of mechanics, regarding forces, etc. on the unit. The
most important of the forces are the forces between the wheels
and the ground because they enter into all equations. A de-

tailed study Of these forces is therefore justified.

figsultant Forcesln the Wheel Plane
The forces on the wheel in the contact between the wheel
and the ground are sometimes (ref. 2, p. 284) represented by
the four forces R3, R4’ R5 and R6 as indicated in the figure

below.
*5’

6'

 

 

 

 

 

 

A2

R3 is "pure rolling resistance"
R4 is reaction against driving torque

R5 is downward reaction on the wheel, especially its
lugs. It is Often = 0.

R6 is supporting reaction on the wheel

Even if these forces are helpful in explaining the forces
at the contact between soil and wheel, they are difficult to
determine separately and they are not needed to represent the
contact forces. The four forces can in fact always be re-
placed by one single force or by one vertical and one hori-
zontal force, working in the same point. The latter system

is shown in the picture below, where

(by

I
82 = Ru - 83 (A2) Y

 

 

 

.1 1*,7 II fig: ‘>

 

 

 

When we compare the two-force system and the four-force
system, we find that they give the same resultant force on
the wheel, but that there is a difference in the moment Of

size.

A3

86x6 + R3y3 - Ray“ - 35x5 - Rlx1 + R2y2 =

R6(X6-X1) - 85(x5-x1) - R4(Y4-y2) + 33(Y3'y2)

It is, however, possible to simplify this system further
as shown in the picture below. Here y2 is given a fixed value
= O, and we want to find the value of x1 which makes the dif-
ference in moment = 0, i.e. which makes this system entirely

equivalent to the original four-force system. This value of

 

 

X1 is 1 _ $2 $2 R R
6 3’ -
xi = X6 {621 + 332 _ Rum (A3)
1 - 36 5

In most cases x5 is negative but R5 close to 0. R6 is
larger than any other force, y3 is equal to or smaller than

x6 and yg is small. Then x1 is slightly larger than x6.

Al?

 

 

 

 

A method Of determining x experimentally will be des-

1

cribed later.
In the future treatment I will, where nothing else is

said, use the two forces R1 and R working at the same point

2

A4

x = x1 and y = 0. This will always be a true representation

Of the forces, provided the right value for x1 is used.

The coefficient Of net traction.

The ratio FZ/F1 is given the symbol f, where f is the
coefficient of net traction. Two special values Of f are
fopt and fres'

fopt is the highest practical value of the coefficient
Of net traction for a given combination of wheel and soil.
'Practical' means in this case giving the highest power effi-
ciency or giving a fixed slip for a certain load. Higher f-

values than fo t can usually be found, but with sacrifice of

P
power efficiency.
frés is usually called coefficient of rolling resistance.

It is a negative f-value, -f = fres = 7;? where F2 and F1 are
measured on level ground, when no torque-is applied to the
wheel. A relation between fres and x1 can be found as shown
on page A5.

f-values should always be given together with information

about the tire, the soil, the slip and the inflation, for

which they apply.

Discussion Of x1

 

From the preceeding chapter it might be remembered, that
x1 as it is used here, is defined as the x-coordinate of the
intersection of the x-axis and the resultant Of the soil forces
on the wheel. The x-axis lies in the ground plane only for a

wheel with rated load and rated inflation on hard ground. This

A5

means that the point (x130) is not necessarily a pOint on the
wheel. It also means that it has nothing to do with the roll-
ing radius of the wheel (except on hard ground).

We first try to find a relation between it and the coeffi-
cient of rolling resistance. The rolling resistance is usually
defined as the force needed to pull the loaded wheel, when no
torque is applied. The coefficient Of rolling resistance,

f is defined as the ratio between the rolling resistance

res’
and the vertical load carried by the soil or the vertical load
on the wheel, including the weight of the wheel itself. This

is shown in the picture below.

 

 

 

 

The equilibrium equations for this special case are:

F1 3 R]. F2 3 32 X1. B]. = Fzyo
F2
and fre = -—
5 F1
This gives:
...-5?- -,~ (4)
1 F1 y0 ‘ resyo . A

The Special value of x1 discussed here has been denoted

xl' in order to show that it is a fixed value, which theoret-

A6

ically applies only, when the torque on the wheel is zero.

yo is a fixed value, determined as the axle height for
the loaded wheel on hard surface. It is exactly known and
therefore xl' can also be exactly calculated.

Because yo is close to D/2, equation A4 can approximately

be written:

D

x1 . 2” f.res'é'

Bekker (ref. 4) has theoretically derived for a rigid

wheel on soft ground (equations 182, 183 and 184)

2 -1 g -
F2 = const. F1 D or F2 = const F14 D or
9. .2.
F2 = const F13 D'-3

which gives

it

fres = const F1 D"1 or fres = const F1 D ' or
1-2.
fres = const F13 D 3
i 1
x '- const F or x ' - const F 2 D.5
1" i 1" 1 01‘
1 1

x1' = const F13 D 3

This shows that theoretically x ' varies equally with

1
the load as f and less than f with the wheel diameter.
res res

It should therefore be better suited to represent the rolling

resistance than fre . Both x1’ and f res will, however, be

8
used in the following. Incidentally, it may be mentioned that

rolling resistance for a steel wheel on a steel track is given

as a distance xl', not as a ratio fres‘

A7

When a torque is applied to the wheel, the value of x1
might change, but no research information on this is yet avail-
able.

xl can be determined experimentally for all values Of the

torque in the following way: A g

 

 

 

 

 

 

 

 

Z9: BZ=F2

T - F2Y0
1‘ 1 1 "1 F1

(”v . - - =

So far all factors included can be measured with good

~accuracy and x1 determined.

In order to relate this value for x1 to xl' or fres we

partly transform the expression for x1 to the four-force system

T

3 yo - v. R 3

(page A1). Using the definition of R4 3

Ru - R2 and 82 = F2 we get

:13" (YO'yQ) “(Ru-33) yo =RJyQ-RlLyI-&
F1 F1

 

 

x1
If Y4 is small enough to be neglected

R
x = 3’0

_ I D
1 F1 - fresyo e: rhea 2 as before.

A8

x1 might apparently also in this case be considered a
measure Of rolling resistance, but it must be remembered that
its value might now be another than when there is no torque.
Work done by Walters-Worthington (ref. 30) indicates a con-
siderable increase in x1 with increasing slip.

Table A1 shows some values for x1 calculated from tests,
performed by the Ford Motor 00., Birmingham, Michigan in which
F1,F2 and T were measured. The influence Of such factors as
axle load, slip or torque seems here to be small, or at least
much smaller than the influence Of irregularities in the field.

In Table A2 are given theoretical values for x1 for some

unorthodox cases of wheel-ground contact as an illustration Of
how x1 might vary and Of how it is influenced by e.g. F2 in
these cases. The x1 values given indicate the position when

enough torque is applied to utilize f i.e. to make the

opt,

wheel start spinning. The values will be Of Special interest

in the discussion Of the stability Of the power unit.

A9

Table A1. Examples on distance of rolling resistance, x1

 

Calculated from tests made by Ford Motor 00., August 1957.

A rear-wheel driven tractor and a tandem tractor was used.

 

 

 

Tractor Ordinary Tandem
Wheel Front ’ Rear Front Rear
5.50 x 16 11 x 28 11 x 28 11 x 28
Ave. load 925 3385 4630 3880
in work,
_lbs.

 

 

 

 

Mean and standard deviation of XI ft.”

 

ngpppg Mean S.D. Mean S.D. Mean S.D. Mean S.D.

 

Asphalt,
test track 0.024 0.077 -0.015 0.054 -0.025 0.037 0.007 0.149

Airfield
sod 0.134 0.099 0.063 0.079 0.209 0.084 0.090 0.077

Plowed and
disked field,
hard clods 0.256 0.137 0.375 0.121 0.

m
i:-
to

0.118j0.240'0.076

Plowed field
large hard
clods 0.253 0.136 0.335 0.144 0.430 0.104 0.297 0.093

 

 

 

 

 

 

 

 

 

 

 

*The deviation is due to both irregularities in the field,
different load and slip and to deviations in the instrumenta-

tion. The means are accurate within less than 1 0.040 ft S.D.

A10

Table A2. Calculated distance x1 for special cases Of wheel-

 

.A ground contact.

 

Dug-down wheel

 

 

 

Assume rcpt = 0.6 and fres = 0.1
F2/F1 = 0.6 0.4 0.2 0
x1
D2 = 0.1 0.25 0.42 0.6
Wheel_passing hindrance
Assume {Opt = 0.8 and fres = 0.05
= 0.8 0.4 0

 

0.05 0.33 0.67

 

2| 2* R
:3” NP.)
N NH\
’11
9..

ll

 

\
va‘l

 

= 0 0.03 0.22

 

 

The impression in the tire is
assumed negligible.

Log_attached to wheel with
chainygetc.

 

Maximum x1 at D/2.

 

Wheel ngainst high hindrance

 

 

Table A2. cont.

 

 

 

 

O(
- R;
‘ 1
.X
V<~e
8)
A

/ f

 

All

Wheel in a ditch (with hard Sides)

 

 

 

 

Assume fopt = 0.6 and fres = 0.1
CL = 60° 45° 30°
F2]?!

= 0 0.73 0.89 1.27

%%2 = = 0.3 0.32 0.43 0.81

0.6 -- 0.31 0.55
l

 

 

 

 

 

 

Another assumption is that the
wheel does not move. As soon
as it moves, x1 is the same as

for a dug-down wheel.

Wheel, fixed to the ground with
chainsy by frostygetc.

XI = T/Fl

A12

Stresses in the Soil in the Wheel-Ground Contact Area.
Pressures and Sinkage
The capacity Of the soil to support an unpowered wheel

has by Bekker (ref. 4) been expressed thus

kc
P =‘1; + kgjzn = k.zn

where p is pressure, 2 in sinkage, b is width Of the
wheel and kc, k9,, k and n are soil constants.
For a rigid wheel or a high-pressure tire the sinkage can

be derived from this formula and following expression found:

n+% F1 _
max = n* k
P - §)(BE + k?) bVTE‘

By a simple transformation we get

 

Z

n - F F
zmax - b D It 1 n z: __1_§‘ 1 n
z a- .- .. .—
( 3) b k (1 3)

 

 

1

pmax = 1 _ % Pave
F1
For a low-pressure tire p = 31’, which gives
n F1

 

z = ch + b k?9 L

For a low-pressure tire we further may put
P = pj + PC
where pi is the inflation pressure and pC is determined
by the stiffness Of the cord.
The inflation pressure can in its turn be related to the
carrying capacity Of the tire. An equation for this can be

written in the form:

A13

n

n n

F1 = A1 D

where B and D are tire dimensions and A

1

A , n , n , n are
2 1 2 3

J

1.
tire constants.
Traction as a function Of soil values.
The gross tractive force R4, which for a tire with lugs
is essentially a function of the shear stress in the soil, can
be written as (ref. 4)
R,+ = A (c + p tan 8) = A c + F1 tan 8
(low-pressure tire, p = Fl/b Z, A = 0.4.)
The net tractive force F2 is found by subtracting the
'rolling resistance' R3
F2 = A c + F1 tan 8 - R3
and the coefficient Of net traction f by dividing by F1

+ tan 0 -

.2
1 p

...,
II

"13' N51

.3313"

The rolling resistance of a tire can be written
B3=F+C+E

where F is due to tire deformation, C is due to vertical

b k
soil compaction = 3-1-1 2“”, and E is caused by bulldozing

the soil (ref. 5).
E: 22K2(b+lzK é) (1+x tanf')
I P 3 p p
The tire deformation work is in loose soil and with in-
flation pressures normally used Of minor relative importance
and can therefore be neglected here. Inserting 83 in the for-

) l/n F1

mula for f and then 2 = <2 and p = [—13 we get f expressed

k
in p and soil values.

A14

5h*

1 A1 n A2

c ._
f = - + tan 0 - ( ) - E'n -
p E [awn (k/ I; E 552
where A1 and A2 depend only on soil parameters.

This all shows that f decreases with increasing p.

Steering Forces on a Wheel

Steering forces are forces perpendicular to the wheel
plane. They arise similarly as driving forces in the contact
area between the wheel and the soil.

Because both the wheel and the soil generally are elastic,
an anglecx between the wheel plane and the direction of travel
is needed in order that steering forces be produced. This

angle is called the slip angle.

direction of

travel slip angle

  
 

wheel plane

steering
force

 

The slip angle causes a deflection of the tire and a de-
formation Of the soil. The forces needed for the deformation
are proportional to the deformation up to a certain value.
The steering force therefore increases with the slip angle.
Above a certain deformation, the shear force is almost con-
stant. A diagram of steering force versus slip angle there-
fore looks like the figure below. This is basically the same
relationship as for driving force versus travel reduction.

The steering force increases with an increasing load on

the wheel, but the relation between these forces is probably

not linear.

 

A16

/\ steering I—V; *"’
force '”' different

z” soils

\

slip angle /

 

 

The forces discussed above are either friction or shear
forces. In loose soil, there also is a bulldozing force when
the wheel pushes soil in front Of it.

When, besides the steering force, there is a tangential
force on the wheel, the contact force between wheel and soil,
which is limited by the soil strength, must be equal to the
resultantIOf the steering force and the tangential force. Two
consequences Of this should be observed. When a wheel is
driven with such high pull that it slips much, the steering
force it can give is very low.-On soft ground, the rolling re-
sistance can be so high that the wheel stops rolling when the
steering angle exceeds a relatively low value. Then the only
steering force is the bulldozing force, which is very inef-
fective. Theoretical considerations indicate that the slip
angle where the wheel stops rolling can be as low as 35° or

400 for conditions encountered in agricultural Operations.

A17

Resistive Moment on a Steered Wheel

In order to force a wheel to roll with a radius f’on the
ground, a steering moment around a vertical axis must be ap-
plied. This can be explained in the following way, figure

below.
/ fl
)1 L

 

 

 

 

 

 

The shaded area is the contact area between the wheel and
the ground. 1 is original position and 2 is final position of
the wheel. A point Of the wheel touches first ground at A and
remains there till the wheel is in position 2. When an element
of the tire settled at A, it had direction x', but when it
leaves ground, it has been forced to aSsume direction x". This
can have happened by the element sliding over the ground or by

distortion of the tire or the soil. All this requires a mo-

A18

ment. This resisting moment is related to the angle ’5 between
x' and x'; therefore, it increases when the length Of the con-

tact area increases and when the radius 59 decreases.

APPENDIX B. BASIC EQUATIONS OF MECHANICS FOR A POWER UNIT

 

System of Notations for ForcesL_DistancesL Etc.

A system Of notations will be used which was initiated
by McKibben (ref.20), has been developed by Buchele, and has
been changed and extended for this study.

Positions are indicated by coordinates in the following
right-handed orthogonal x-y-z system.

x-axis: When the power unit is standing still (static
load) with properly inflated tires on a hard surface, the
x-axis is in the surface. Positive direction forward in
normal direction of travel. The x-axis is fixed in this po-
sition relative to the power unit, always at the same dis-
tance from the rear and the front axle, as long as the front
wheels do not leave the ground. With changed load and corre-
spondingly changed inflation on hard surface, the x-axis should
remain tangent to the wheel circumferences. With overloaded
tires on hard ground, the tires would be deflected above the
x-axis; with normal load on soft ground, the tires would reach
below the x-axis, due to the lesser deflection of the tires.

y-axis: Through the center of the rear wheel and posi-
tive upwards.

z-axis: In the same ground surface as used to define the
x-axis. Positive to the right, when power unit is seen from
behind in normal direction Of travel.

xgygplane contains the center of gravity of the power

unit.

BZ

Nppg: This coordinate system is fixed relative the trac-
tor body and does not change with the position Of the wheel -
soil "contact point".

Units Of length: A non-dimensional system is used in
this study with the wheelbase, i.e. the x-coordinate Of the

front axle, as unity.

Distances might be positive or negative quantities, deter-
mined by their place relative tO the origin. This is necessary
in order to make the equations universal.

Linear speeds and accelerations are positive in the posi-
tive directions of the x-axis.

Angular displacements, speeds and acceleration§_ are
positive in the direction determined by the right-hand rule,

i.e. from the x-axis to the y-axis, etc.

Forces

All forces shown in pictures should be given as they act
on the power unit and the implement.

Three letters will be used for forces:

W for gravity and inertia forces;
R for reaction forces from the ground;
F for other forces.

Forces and torques are in general positive in the posi-
tive directions of the axis, see above. Exceptions are
forces and torques that very seldom change Sign, e.g., grav-
ity, implement resistance. These are positive in their

usual direction as indicated in figure.

BB

Dynamic conditions are treated by using d'Alembert's
principle, i.e. introducing inertia forces. These inertia
forces always have a direction opposite “their" acceleration
and are given positive Sign when the acceleration is positive.
This is another exception to the general rule above.

Indices: Distances, speeds, accelerations, and forces
will be given indices according to the following system:
index 0, 1.....9 quantities related to the body Of the power

unit (including the wheels when they are
treated together with the body as a unit);

10,11,...19 quantities related exclusively to the front
wheels or the front part Of a power unit;

20,21,...29 quantities related exclusively to the rear
wheels or the rear part Of a power unit;

50,51,...59 d:O to the implement or the implements when
more than one implement are treated as a
unit;

60,61,...69 d:o to the "second" implement if two imple-
ments are attached and each treated sepa-
ratelyo

The system is carried further as far as possible. SO
indicate e.g.:

index 0,10,20,...50... quantities related to the mass of resp.
unit, e.g.:

WO = weight of power unit body, 110 =
moment of inertia Of front wheels;

11,21,......51... (soil reaction) forces in the y-direc-
tion;

-12,22,......52... (soil reaction) forces in the x-direc-
tion;

13,23.......53... (soil reaction) forces in the z-direc-
tion.

The same index should be given to the coordinates as

that given to the main force in case.

B4

In the section on forces on a wheel, the first numeral

in the index is omitted.

Some Ratios
By using the dimensionless form, all distance indications
are actually ratios between the actual distance and the wheel-
base.
Also, for forces a non-dimensional form is wanted. Ten-
tatively, the gravity force on the power unit, W0, is used as

power unit and the following ratios for independent variables

introduced:
W
Implement weight ratio 1 = fi%9 (B1)
R
Implement self-support ratio .1 = WEE) (BZ)

'0

..L' is = 1 for fully-trailed implements and = O for

fully-mounted implements.

Basic Equilibrium Eqpations for a Power Unit
and Its Implement

There are a large number Of equally correct ways to write
the equations of equilibrium for a power unit and its attached
implement. Some ways, however, necessitate the determination
Of a smaller number of variables than others. This is the
case when the whole machine, in this instance both the power
unit and its implement, can be treated as a unity because in-
ternal forces do not then enter the equations. In a few cases,

however, internal forces, e.g. drive-shaft torque, must be in-

B5

cluded, making separate treatment Of the different parts of

the unity necessary.

Forces in the Longitudinal Plane on aegg-axle Power Unit with
Implement

The figure below shows the external forces on a two-axle
power unit with implement travelling horizontalIy_at constant
'ppggg (on horizontal ground and with equal sinkage front and
rear). Air resistances are neglected on account Of their

usually relatively low significance (discussion on pageifll).

A9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B6

Forces not explained earlier are:

weight of power unit, including wheels

1:
O
N

W50 = weight Of implement, including load on implement

R51 = perpendicular forces from the ground on the imple-
ment = implement self-support

R52 = parallel forces from the ground on the implement =
implement draft

R11 = perpendicular soil reaction on front wheels

R21 = perpendicular soil reaction on rear wheels

R12 = parallel soil reaction on front wheels

R22 = parallel soil reaction on rear wheels

Note that distances behind the rear axle or below the
wheels are negative quantities. Note also the direction Of

forces. They are all positive as drawn.

B7

When the baseline (x-axis) is inclined an angle £3 to the
horizontal, the changes shown in the above figure take place.
When the power unit accelerates, inertia forces according
to the following figure also enter the picture. This is the
most general case and can presumably be used for any power
unit plus its implements in any situation.
The equations Of equilibrium are:
Sum Of perpendicular forces, 2:’T= 0;
Sum Of parallel forces, Z» = 0;
Sum Of moment around the origin, 26‘ = 0.
For the Simple case in the first figure, horizontal trav-
el at constant speed, 9
Z. 1‘ = 0
Z—>=O=R12+822-R§2 (B4a)

R11 + R21 + R51 - W0 - W50 (838)

Era": 0 = Woxo + 14501150 - 811x11 - R21x21 -
‘351x51 " Bszysz (B58)

Corresponding equations for a power unit on a slope are:
ZT=O

Z—>=0

R11 + R21 + 1251 - WOOOSg - W5ocosp (B3b)

R12 + R22 - 352 - Wosinfl- Wsosinfl (B4b)

2: Q): 0 = Woxocosfl + W50x50cosgi - Woyosinfl-

‘ ”5033081“ " Rnxii " R213‘21 '

-R - R B b

51x51 52y52 ( 5 )
For an accelerating tractor, the equations are:
25 I = 0 = R11 + R21 + R51 - Wocosp - W50cosp-
Z» = 0 = 312 + R22 - 1252 - Wosin/g - Wjosin/d-

(B4c)

- w2 - w52

 

BB

....c: ..mioa .od
.6 5:95.83

 

Em
= X

 

Omd

«no j

\
w Loo

208035 .08
do 5:20.33

 

B9

2609: o = wcxocosp + W50x5ocosfi - Woyosin/A-
'3523'52 ” w1x0 I w51x50 " w25’0 "

" "52330 + To “ T10 + T20 + T50 (35°)

From the definitions, pages A4 and B4, we further have:

R12 = flRll; (B6a)
R22 = f2321; (B6b)
W50 = 1W0; (B7)
R51 ..[Wso =11W0, (B8)

Newton's law and d'Alembert's principle give:

W1 = 'E' 81 To = 100(0
”0
1.12 = '5 a2 T10 = I100‘10
W - E298 T - I
51 " s 51 20 ‘ 20920
W
.. 12- = 0(
w52 ‘ s 852 T50 I50 50
(B9) (B10)

Special care needs to be taken to Observe the sign of

forces and distances.

The following coordinates, accelera-

tions, and forces are usually negative, as they are written

in the equations: x50 x51<110<X20 T10 and T20. For a rear-

wheel-driven tractor, R12 and f1 are negative; for a front-

wheel-driven, 322 and f

B10

The Air Resistance
The air resistance for an automobile is usually calculated
according to the formula:
F = 0.00147 MZA lb
where M is the relative speed in mph,

A is the front area in sq. ft.,=’

O.8 height x width.

A tractor has probably higher coefficient of air resist-

ance. Say: I
F = 0.0025 M2A. (B11)

If a power unit velocity Of 20 mph is assumed and a wind~

velocity Of 25 mph, then:
F = 5A lb.

For a 5,000 lb. tractor frontal area might be 20 sq. ft.
The wind resistance for this should be 100 lb.' According to
this formula, this is a maximum value which seldom occurs.

For the same tractor at work with 5 mph, F = 45 lb. when work-
ing against the wind. Travelling on the road, the force with
no wind might be 20 lb.

The smallest coefficient of rolling resistance is of the
order of magnitude 0.02, which gives a minimum rolling resist-
ance for this tractor Of 100 lb. The air resistance is con-
sequently always smaller than the rolling resistance and usu-
ally is considerably smaller.

Such faster moving parts as the top of the wheels have a
higher resistance per area, but their area is so small that

alSo these forces are usually very small.

Bll

Usually the accuracy Of the calculations cannot be driven
down to figures of this magnitude. Change in weight Of fuel,
in weight Of dirt adhering to the power unit, etc., are usu-
ally neglected. These are of the same magnitude as the air
resistance; therefore, there is no reason in most cases to
include air resistance in the calculations, especially as

very little is known about e.g. its line Of action.

Forces in Planes, Peppendicular to the Direction Of Travel.

It is sometimes not enough to know the forces on the in-
dividual wheelpairs of the power unit, but also the forces
on each wheel must be known. The procedure is than first to
determine the load on the wheelpairs by earlier given equa-
tions B3-10, which were found in the vertical, longitudinal
plane. By similar equations, given below, the distribution
of the side forces can be derived by study in the horizontal,
longitudinal plane. Finally, the individual wheel forces are
found by studying forces in planes, perpendicular to the di-
rection of travel, i.e. to the x-axis. Equations, found in
that way, are also given below.

The same notations as in equations 83-10 are used in this
paragraph. The index I means left side (negative z-values),
index r, right side (positive z-values). The z-coordinate for
the center Of gravity of the power unit is by definition a 0.

The general purpose tractor (four-wheel tractor) as well
as some Ipur-wheel-drive tractors must be treated as two sep-

arate parts, because the joint between the front and the rear

812

part determines the moment that can be transferred from one to
the other. Because the joint is stiff in the y-direction (ver-
tically), the power unit can be studied as one body in the
horizontal, longitudinal plane, the first figure, and the sep-
aration made only when studying forces in the vertical planes
(y-z planes). In this way the only force in the joint which
is introduced in the equations is the moment, M, which Often
is = 0.

It should be noted that W0 refers to the whole power unit,
the weight of the parts being W10 and W20, and W0 2 W10 + W20.

The first figure gives (page B13):

2 Tx : Biz/Z + Rlzr + R22Z + R22r - R52 = o (B12a)

zzR R R -Wi -
2 —-> 1356+ 13.132221323,+ 53 08 “X

2 ®- R R R R z +

xz ° " 12,6 21%" 12,311,. " 22,6 zziz' 22,. 21,.
R132 X13 + B13,."13 + 32;? I23 I R23323 +

+ 852252 + 353x53 - Wosiano - WfiosingxsO =

= 0 (314a)
With only a slight change the figure on page B5 can be

used to give the corresponding equations to equations B3a

and B5a.

21" ”3115 + B11x. + E21% + R21,. + B51 '

- W0 cosg- “500085 = 0 (B15a)

le 1(neq.)

 

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R13: g l \ Rl3r
F— ——)=
‘l q . ,, r ¢
Rah/1* JT‘FRI2r
\J \J
ZZI? (neg. 22"? z|3
(\ {woigimy ("W T
R21?— “ ' \ R23? XUZ3 f0;
T
R22: fl /\j2r1 ?
X X
Of 1 "6590.) !(5:89.)
Wsofiin-Y
....o c g
|———-)>
' R
L I J 53
252/34 R52

 

Blllv

   
  

Front Port

iL

/\R \r
1“ R\3r \

     

Force; in the joint
not mdlcafed.

150 Rear Port

120“ ‘

a Q . 9“
W2032 1 w&5‘“7 “‘e

15%“ g %

815

2%.

xy . wocosxxo+w50cosdx5m (Ru/e + Burk“ -

In the y-z-planes we get for the front part (page Bib):

2 JOIHt: -M-311Z(ZIIZ-ZM) - Bllr(zllr - 2M) —
- RIB/£3:M - BlBry” + wlocos'zflz10 - 2M) -

- ”1031“ 25(y10 - y“) = 0 (317a)

and for the rear part:

2 m: M - 821,2 (221fl -2“) " 821r(221r - ZN) -

+ w20005‘3(220 - 2M) - wzosin75(y20 - y“) +

+ wjocosb’ (250 - 2M) - \«l5osin3(y5O - y”) = 0 (B18a)

The implement here has been treated as rigidly connected
to the rear part of the power unit. If there is a pivot be-
tween implement and power unit in the x-direction, equation
18a is not true. The corresponding equation must then be
found in a similar manner as used for the parts of the jointed
power unit.

By taking moments around the joint, we eliminate from the
equation the pure forces in the joint which are not indicated
in the figure and in which we are not interested. These forces,
however, prohibit us from taking sums of forces in two direc-
tions for each part. Instead we get the following relation-

ships:

B16

”0Y0 = w10Y10 + w20’20 (32°)
0 ‘ w10210 + w20220 (821)

Further, usually M = 0.
These equations are general for a two-part power unit
with rigidly mounted implements on the rear part. For the

special case where the front part is just the front axle g;

 

 

‘a general purpose tractor, M a 0 and W10 small compared to
wo, wherefore 220 = 0. Equations 812a - 16a remain unchanged
for this case but instead of equations 817a and 818a, we get

for the front axle:
411% (2111 -2“) ' 311,.(211, " ZR) ' 8131’. YR '
-3131!“ + w10°°sX(zio - 2M) - ”loSinXWm - 31M) =

= o (B17b)
and for the rest of the tractor:

-11le (2212 - ZM) - R21r(221r - ZN) - Rz3fl yM -
'RZBryM ‘ B51’251 ‘ 2M) + R53(5'53 ‘ YR) '

4.120003 62!“! - wzosin fly20 - y”) + w5ocos 34250 - ZM) -
-w505in 3(y5'0 - y”) = o; (Ble)
Wlocosjulo - 2M) and wlosinbdylo - y“) are often

small and can be neglected.

Most 'joined' tractors have a device which limits the

0. When this has happened the power unit may again be con-

B17

~k‘ ZM

. ‘ .N
‘ ,1» ~hl\
w

. d 9 w
YM “3“; \ Q~\\<
W‘

1»

\

’L

(o

«'51

 

 

1318'

sidered as one body and the forces and equations appear thus.
(For clarity the front and rear end are pictures separately,

page 817, but no inner forces are, of course, introduced.)

2 Ty: Bll’z cos X0 + Bllrcosb'O + RIB/Z sin 50 +

+ Bursinb’o + B + Bar + 351 - wocos X -

21E
- wjocosa = O; (Bljc)
E -—bz: -8111. 511150 - Bursinzjo + 813/) cos 3(0 +
x.

+ R13rcosb/O + 323% + 3231‘ + R53 - wosinb’ -

- w5osin3’ = 0; (8130)
E r()Viv’z: '311£(211Z + 20') ’ Elli-(2111‘ - 2°.) -
- 813/6 Yc' " BlBryC. ’ 32% 221,5- 8211-221? +

+ 3535'” - 851251 - woSiano - wwsinB’ySO +
+ wsocosa’z50 = O; . (8220)

From geometrical considerations we get:

370' yM(1 - 00330) + zMsin X0 (823)

zcv = zM(1 - cosb’o) - yMsin 3’0 (321+)
This is an undetermined case because all forces cannot

be found without further assumptions.
For a tricycle type tractor the equations can be found

by simplifying equations B12a - 16a and B220.

B19

2. TI : 812 + 322% + 8223. - B52 = 0 (812(1)

J

ZTy:Rll+R21L+R21r+R51-

- wocosg - wsocosg = 0 (B15d)

Z4: R13+ szfl+823r+353 -

- wosing- WSOsinb/z O (B13d)

E 0 ‘312211 " R22£ 221/ " R222.221,. +

+ 313x13 + 323£x23 + B23rx23 +

R52252 + R53x53 - wosinxxo -
- w50sin5x50 = 0 Blhd)
Z Coy): WOODS} + W50COSZ - Rllxll '-
.\
E. [392% '311311 - 321/1; 221/?" R21,921,. +
+ B53y53 - 1251251 - wosinb y0 -
- w5osinjy50 + ”500085250 = O (B22d)

Equation B22d could also be found from equations Bl7b

and Ble by introducing yM = 0, 211 = 211 and ”10 = O.
r

B20

The equations for the individual wheel loads as given here
are still more complicated than the equations for axle loads
because they contain more factors. They become slightly sim-
plified if more relationships are imposed upon them or by
assumptions, but they will probably still be too clumsy to
handle analytically in other cases than just to check a given
design. When trying to find the best combination of all quan-
tities involved, an analog computer seems to be the best solu-

tion here also.

The "Centrifugal” Force

There are many lateral forces on a turning tractor, but
the one of main interest in connection with stability problems
is the "centrifugal force”. This discussion will be limited
to a power unit in steady turn with the angular velocity 0)
and a constant radius z? to the xy-plane.

It can easily be seen that the radiqu’is different for
different points in the xy-plane; but also, that the component
of the centrifugal acceleration in the z-direction is con-
stant = -zf¢w2. The centrifugal acceleration in the z-direc-
tion for any point is therefore = '(Zf -z)q2. It also can be
shown that the acceleration component in the x-direction is
= (x-x59)uf. The axis of rotation being in the y-direction,

there is no y-component.

321

72

 

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03174