PAPER NO. 73-1528
Optimum
Width
and
Speed
for Least Cost Tillage
by
Frank M. Zoz
Engineer, Product Test and Evaluation
John Deere Waterloo Tractor Works
Waterloo, Iowa 50704
For presentation at the 1973 Winter Meeting
AMERICAN SOCIETY OF AGRICULTURAL ENGINEERS
Conrad Hilton
Chicago, Illinois
December 11 - 14, 1973
SUMMARY:
Equal productivity can be obtained with various combinations of
width and speed. Investment costs tend to increase at slow speeds
due to weight of tractor and implement. Operating costs increase
at higher speeds due to higher (per acre) energy consumption. An
optimum width and speed exist for given conditions.
Papers presented before ASAE meetings are considered to be the property of the
Society. In general, the Society reserves the right of first publication of such papers,
in complete form. However, it has no objection to publication, in condensed form,
with credit to the Society and the author. Permission to publish a paper in full may
be requested from ASAE, P.O. Box 229, St. Joseph, Michigan 49085. The Society is
not responsible for statements or opinion advanced in papers or discussions at its
meetings.
OPTIMUM WIDTH AND SPEED FOR LEAST COST TILLAGE
Summary
Advantages and disadvantages of the alternative means of increasing productivity of tillage operations
are discussed. Tractor performance and plow draft predictions are made. Tractor and plow prices are
estimated, .total costs are determined and the optimum width and speed is calculated for least total
cost/acre. Investment costs tend to increase at slow speeds due to size and weight of tractor and
implement. Operating costs increase at high speed due to higher (per acre) energy consumption. Total
tractor costs per hour increase for slower design plowing speeds due to weight and strength
requirements. Since other tractor operations are also subject to these higher costs, the optimum
plowing speed may be even higher than shown in this paper.
Primary tillage has always been one of the larger
power consuming operations on a farm. As such
it is the operation that most influences the size
of the power unit required for the total farm
operation. Over the years the moldboard plow
has been the most accepted primary tillage tool,
only recently being challenged by various
systems offering types of reduced tillage.
Reasons for this are varied but a primary
stimulus is the desire to increase productivity
and minimize cost.
Increases in productivity in field operations can
be accomplished in at least three ways: 1)
increasing size and width of machine, 2)
increasing travel speeds, or 3) combining
operations to limit the number of trips across
the field.
For an analysis of total farm system, alternative
number 3 can be very important. However, for
purposes of this paper we are limiting
considerations to the first two alternatives-increasing size and increasing speed. Productivity
of the tractor primary tillage system is usually
limited by the power available from the tractor.
With an increase in power either may be a
satisfactory alternative to increase productivity.
What are some of the advantages and
disadvantages of each approach?
Increasing Width It is a relatively simple
engineering matter to scale up the tractor
implement combination to increase the unit size.
No new technology is involved. Remaining at
the same travel speeds creates no new functional
problems in the field. With increasing farm size
and some increase in field size, field efficiency
should not be adversely affected.
However, the larger implements are much more
difficult to transport when farm operations are
spread out geographically as is often the case.
Larger implements can be expected to increase
in cost at least in proportion to their width and
likely more due to heavier frames required for
the larger machine, if the ground is level no
operational problem is likely to result from
increased width. However, in the normal
situation or in the special case where terraces are
involved, an excessively wide implement may
not have the required flexibility to follow the
contour of the ground. Larger implements also
require larger components at the tractor
implement interface and result in more
difficulty in hitching. Tractor weight and ballast
required is directly proportional to the size of
the implement. Increasing width not only
requires a heavier and thus more expensive
tractor but also one with design to transmit high
power at low speeds (also resulting in increased
cost).
Increasing Speed History has seen a gradual
increase in plowing speeds in spite of some
disadvantages that may result from it. The cost
per unit of implement width may increase if
higher speeds are utilized because of functional
and durability requirements. Under certain soil
conditions, accelerated wear may occur on the
soil engaging elements unless better and more
expensive materials are used. High speed
2
Optimum Width and Speed for Least Cost Tillage
operation in rocky soil may be impossible
without the extra expense of automatic resetting
bottoms or spring cushion standards. Fatigue
life may be decreased because of the higher
frequency of loadings at increased speeds. New
technology may be required to obtain
satisfactory function and durability. Operator
ride and control factors become more critical
items at higher speeds. Also, since the draft of
nearly all soil engaging elements increases with
speed, more energy is required to till an acre of
ground at higher travel speeds.
Utilization of increased power by higher travel
speeds does have several important advantages.
Since machines usually cost in proportion to
their weight, the smaller size plow and tractor
required for higher speed operations have a
lower investment cost. The tractor may have
lower cost per unit of power. The smaller size
not only results in a more maneuverable
tractor-plow combination but results in a tractor
more adaptable to other farm operations where
power may not be the biggest requirement.
There are, of course, both economic and
non-economic factors involved in determining
the optimum width and speed for a given
situation. Economics will not always be the
most important factor. However, for most
farms, it is important and for the industry as a
whole, it is the single most important factor
involved in the design of future tractor
implement systems.
A review of a number of publications pertaining
to cost analysis of farming operations shows that
quite often these analyses result in the widest
and slowest combination being the most
economical. Since this is not in line with current
farming practices, it is the purpose of this paper
to show where these analyses may be in error
and to present new methods of optimizing the
tractor implement systems.
In order to predict the economics of
tractor-tillage systems, the following steps are
necessary:
Prediction of tractor performance.
Prediction of implement draft requirement.
Matching of tractor and implement.
Prediction of productivity.
5. Estimation of tractor and implement
investment cost.
6. Fixed and variable cost determination and
optimization.
1.
2.
3.
4.
Predicting Tractor Performance Methods for
predicting the performance of tractors in the
field were outlined in a previous ASAE paper by
the author.(1)* A graphical approach was used
to predict the performance of any tractor for
given soil conditions. In that analysis the
tractors were usually assumed to be a specific
unit with a given operating weight. For this
paper a more generalized mathematical approach
was necessary. Luth and Wismer(2) have
established mathematical relationships for the
performance of tires in soils whose strength is
specified by Cone Index. They also suggest
design
points
for
optimizing
vehicle
performance. These design points are very much
in line with the author's experience and a similar
approach is used in this paper. The design points
establish the optimum tractive efficiency,
dynamic ratio and travel reduction for the
performance prediction.
Using design points, the performance can be
predicted by the following relationships from
author's previous paper(1):
Using Dynamic Ratio
P = RWS/(1/DR-DWC)
Using Tractive Efficiency
P = (TE)(AHP)(375)/SO(1-TR)
And combining to give
(WT)(RWR)(SO) = (375)(TE)(PTAXE)(I/DR-DWC)
PTO HP
(1 - TR)
Where:
RWS = Static Rear Weight, Ibs.
RWR = Ratio of Static Rear Weight to Total
Wt.
WT = Total Tractor Weight, Static, Ibs.
*Numbers in parenthesis refer to references listed at end of paper.
Optimum Width and Speed for Least Cost Tillage
AHP = Axle Horsepower
PTOHP = PTO Horsepower
PTAXE = Ratio of Axle Horsepower to PTO
Horsepower
SO = No-Slip Travel Speed, mph
TE = Tractive Efficiency Ratio
DR = Dynamic Ratio
DWC = Dynamic Weight Transfer Coef.
TR = Travel Reduction Ratio
In using the above relationships, the tractive
efficiency, dynamic ratio and travel reduction
are selected from the design points. PTO to axle
horsepower
relationships
are
estimated
(normally PTAXE - 0.96) or can be determined
from Nebraska tests on concrete through
procedures outlined in previous paper.(1) The
following are estimates for DWC and RWR for
three hitch types in the field and for horizontal
pull from the drawbar on concrete:
Concrete
Towed Implement
Semi-Integral Hitch
Integral Hitch
DWC
RWR
0.20
0.25
0.45
0.65
0.75
0.75
0.70
0.65
3
Using these relationships and soil data from Luth
and Wismer(2), it is possible to predict tractor
weight requirements under various soil strength
conditions as shown in Figure 1.
DESIGN POINTS*
Cone
Travel
Index, psi Reduction, %
Tractive
Eff. %
Dynamic
Ratio
50
25
.24
45
75
21
58
.34
100
65
19
.41
150
.49
16
72
200
.54
76
14
Cone
90
.58
7
*For single R1 tires loaded to approx. 90% of maximum
Tire and Rim Ratings.
TRACTOR WEIGHT REQUIREMENTS
2WD-SINGLE R1 TIRES
NO-SLIP TRAVEL-SPEED, MPH
FOR TIRES LOADED TO APPROX. 90% MAX. TIRE & RIM RATINGS.
FOR SEMI-INTEGRAL HITCH IN FIELD; HORIZONTAL PULL FROM DRAWBAR ON
CONCRETE
FIGURE
1
4
Optimum Width and Speed for Least Cost Tillage
Weight determinations are very essential to this
analysis as weight contributes to cost as will be
shown later.
several general soil types. Tests show that a
relationship of the following type generally can
be used for moldboard plows:
Determination
of
Implement
Draft
Requirements
Implement draft data for a
range of soil strengths is not so readily available
as traction data. Much work has been done
throughout the years but the data were not
generally related to soil strength and in a form
to be readily useable. It is a well known
fact that draft increases with travel speed for
nearly all soil engaging tools and that for
moldboard plow the draft generally varies with
the square of the travel speed. ASAE
Yearbook(3) shows draft relationships for
Specific Draft = XK1 + XK2 (SA)2
Where:
Specific Draft = Draft per square unit of
furrow cross section, psi
XK1 = Specific draft at zero velocity, psi
XK2 = Velocity coefficient
SA = Actual Travel Speed, mph
This relationship is plotted in Figure 2. Using
this or known data for given plow bottoms, the
total draft can be determined as a function of
plow width, depth and travel speeds.
TYPICAL MOLDBOARD PLOW DRAFT
TRAVEL SPEED, MPH
FIGURE 2
Considerably less draft data are available for
chisel plows, probably because their use history is
shorter and perhaps because of the less standard
tool shapes. However, it is interesting to
compare the energy requirements for moldboard
and chisel plowing in similar soil at the same
depth, Figure 3. At 5-1/2 mph the energy
requirement per acre for moldboard plowing is
nearly twice that of chisel plowing. Also note
that the increase with speed is much greater. This
may help somewhat to explain the general trend
toward chisel plowing.
Optimum Width and Speed for Least Cost Tillage 5
ENERGY REQUIREMENTS
TRAVEL SPEED, MPH
8
IN.
DEPTH,
MEDIUM
DRAFT
SOIL
GOOD TRACTIVE CONDITIONS
FIGURE 3
Matching of Tractor and Plow; Prediction of
Productivity Tractor and implement are
matched on the basis of the implement draft
requirement and tractor pull capability. The
power limited travel speed is determined and is
combined with the implement width and
estimated field efficiency to predict the
productivity in acres/hour.
APH = (SA)(W)(FE)
8.25
Where:
APH = Acres/Hour
SA = Actual Travel Speed, mph
W = Width, ft.
FE = Field Efficiency Ratio
The combination of tractor, implement, and
productivity relationships is shown graphically
in Figures 4 and 5 for moldboard and chisel
plowing under given conditions. This method
resulted from unpublished work by Luth. It
shows the interaction of plow size, tractor
horsepower, tractor weight and travel speed and
the resulting productivity. The figures are only
valid, of course, for the constants shown. Any
two values locate a point on the graph. For
example, in Figure 4, five bottoms (16") at 5.5
mph no-slip travel speed results in 4.7 mph
actual travel speed, requires about 120 Ibs.
tractor weight per PTO HP, about 112 PTO H P,
9500 Ibs. on the tractor drive wheels (2WD)
and will result in about 3.4 acres per hour. From
a given point any value can be held constant and
another point determined. For example, if a
constant 112 PTO HP is followed going down in
travel speed, we would find that eight bottoms
could be pulled at about 3.4 mph with an
increase of about 0.6 acre/hr (increased to 4.0
acre/hr). However, this combination requires
13,000 Ibs. on the tractor drive wheels, and
expensive design for high strength in the lower
gears.
6
Optimum Width and Speed for Least Cost Tillage
MOLDBOARD PLOW PRODUCTIVITY
APPROX. TRACTOR WEIGHT TO PTO HORSEPOWER RATIO REQUIRED, LB/PTO HP
FIGURE 4
Optimum Width and Speed for Least Cost Tillage
CHISEL PLOW PRODUCTIVITY
APPROX. TRACTOR WEIGHT TO PTO HORSEPOWER RATIO REQUIRED, LB/PTO HP
FIGURE
5
..
7
8
Optimum Width and Speed for Least Cost Tillage
Tractor and Plow Price Relationships Specific
price information is available for any given
implement or tractor. However, for this analysis
it was necessary to determine implement and
tractor costs in general terms, particularly in
terms of the performance parameters of width,
travel speed, power, and weight. Price
information for all tractors currently on the
market is readily available and can be used to
establish price relationships at current travel
speeds.
Recognizing that manufacturing cost varies with
weight, the following type of relationship has
been used to project purchase price of the
tractor (2WD) over a range of travel speeds:
PURT = C1 (PTOHP) + C2
Where:
PURT = Tractor Purchase Price, $
C1 and C2 = Constants
SA = Actual Travel Speed, mph
Travel speed and operating weight are related as
shown in Figure 1. The constant C2 represents
items such as cabs and operator stations whose
cost is not directly related to the size, power or
weight of the tractor.
The price relationships for plows are not so well
defined as that for tractors. In general, there is
less need for precision in plow price estimates as
it is a relatively low contributor to the total
costs. Plow prices have been determined to be a
function of the width, and a speed factor is
applied to allow for probable increase in cost per
unit width for satisfactory life at increased
speeds. The following type of relationship has
been used:
)
PURP = C3 (W) (
Where:
PURP = Purchase Price of Plow, $
W = Width of Plow, ft.
SA = Actual Travel Speed, mph
C3 = Constant
Values of the constants have been selected to
provide purchase prices representative of
tractors and plows presently on the market at
current travel speeds.
Curves of tractor and plow prices used in this
paper are shown respectively in Figures 6 and
7 on a width and speed coordinate system.
If a constant horsepower curve is followed in
Figure 6, one can see that increasing speed
results in a less expensive tractor, that is, the
cost per hp is not constant but decreases at
higher design travel speeds. A similar analysis
can be made in Figure 7 for plows showing
increased cost for the same sized plow at higher
speed. Following a constant hp line, (Figure 7)
shows that a more expensive plow is required for
the same PTO HP at the slower speed.
Optimum Width and Speed for Least Cost Tillage
GENERAL TRACTOR PRICE RELATIONSHIPS
FOR MOLDBOARD PLOWING
(FIELD
BALLASTED
2-WHEEL
DRIVE
FIGURE 6
TRACTORS)
9
10
Optimum Width and Speed for Least Cost Tillage
GENERAL MOLDBOARD PLOW PRICE RELATIONSHIPS
FIGURE 7
Cost Determinations and Optimization After
the performance and purchase prices have been
predicted, the fixed and operating costs can be
calculated. Optimization is really the process of
determining the trade-off between fixed and
operating costs to determine the best combination
of width and speed for the least total cost per
unit of area plowed. The higher investment costs
of slow speed operations are balanced against
the higher energy cost at increased speeds. Cost
factors considered are:
1. Depreciation - Straight line depreciation is
used. The total costs are the average over the
life of the tractor and plow.
2. Interest-Calculated at current annual rates.
3. Taxes, Insurance, Shelter - Estimated as a
percentage of purchase price.(6)
4. Labor- Current on-farm hourly rates.
5. Fuel - Current cost/gallon. Consumption is
calculated, based on PTO HP required.
Optimum Width and Speed for Least Cost Tillage
6. Repairs and Maintenance - Estimated as a
percentage of the purchase price.(6)
The following are the primary variables used in
the optimization shown in following figures:
Tractive Efficiency Ratio - TE = .70
Dynamic Ratio - DR= .50
Travel Reduction - TR = .15, (15%)
Ratio of Tractor Rear Weight to Total Weight
- RWR = .70
Dynamic Weight Transfer Coef.- DWC = .45
PTO to Axle hp Ratio - PTAXE = .967
Specific Draft at Zero Velocity (medium draft
soil) - 7 psi
Plowing Depth - DE = 8 inches
Field Efficiency- FE = .90, (90%)
Tractor Use - Tractor is used 400 hours per
year exclusive of plowing. Plow hours are
added to obtain the total.
Tractor Life - Life of tractor is 7000 hours
or I0 years, whichever comes first. Plowing
hours are calculated, added to the tractor
hours and life is calculated.
Tractor Fuel Efficiency - Tractor PTO HPHR/GAL. = 15
Plow Life- Life is assumed to be 10 years.
Interest Rate - Annual rate of 8% is used.
Salvage Values - 10% of purchase price after
useful life is complete.
Plow Use - 400 acres/year are plowed; also
varied.
11
Fuel Cost- $.20/gallon; also varied.
Labor Cost - $2.00 per hour; also varied.
A computer program was developed to calculate
the performance of the tractor and the
requirement of the plow, to predict the
productivity, to calculate the individual cost
items, and to plot them on a width and speed
coordinate system. The optimum point (least
total cost/acre) is determined and contours of
equal cost, at percentages greater than the
minimum, can be plotted.
Figure 8 shows an example of the program
output using assumed inputs previously listed.
For this set of variables, the minimum cost/acre
was determined to be at 6.4 ft. wide and 5.2
mph. Other values from the graph are 125
PTO HP, 3.6 acres/hour, approximately five 16
inch bottoms and required tractor weight of 110
Ibs./PTO HP. For these variables the minimum
cost was determined to be $3.38 per acre. The
contour shown represents total costs/acre 5%
greater than the minimum. In other words, all
the area inside the contour is within 5% of the
minimum cost. It is interesting to note that 200
PTO HP at 8 mph can have total costs equal to
100 PTO HP at less than half this speed. This is
due in part to the small change in operating
costs (fuel and labor) in this area as shown in
Figure 9. As speed is increased the energy cost
per acre increases but is offset by diminishing
labor costs.
12
Optimum Width and Speed for Least Cost Tillage
TYPICAL COST OPTIMIZATION
MOLDBOARD
PLOWING
FIGURE 8
Optimum Width and Speed for Least Cost Tillage 13
TYPICAL CURVES OF CONSTANT FUEL AND LABOR COST
MOLDBOARD
CALCULATED
AND
FOR
$2.00
PLOWING
$.20
PER
PER
HOUR
GALLON
FUEL
LABOR.
FIGURE 9
Figure 10 shows how the fixed and variable
costs for tractor and plow add to obtain the
total costs. Costs are shown for a 125 PTO HP
tractor at design speeds from 2.5 to 9 mph. At
five mph, the plow costs are about 25% of the
total plowing cost per acre. The minimum total
cost/acre for variables used is as previously
shown -- about five mph. Perhaps most
significant on Figure 10 is the total tractor cost
per hour for design speeds from 2.5 -9 mph.
Heavier weights required for the slow speeds
(with large plows) results in a tractor that has a
higher total cost/hour. A tractor designed for
plowing at slow speeds costs more per hour
for the other 400 hours (this example) when it is
not plowing. For this reason, the optimum
tractor for a least cost total machinery
complement may have a still higher optimum
plowing speed.
14
Optimum Width and Speed for Least Cost Tillage
COST
RELATIONSHIPS
MOLDBOARD
125 PTO HP TRACTOR
PLOWING
TRACTOR USE 400 HOURS/YEAR (Except Plowing) - PLOW USE 400 ACRES/YEAR
FIGURE 10
All curves shown are, of course, dependent upon
the values of the variables used. A sensitivity
analysis has been conducted on several
important variables.
Fuel Cost, $/Gallon With increasing evidence
of an energy shortage in this country, it is likely
that fuel costs will increase. In Figure 11 the
cost per gallon is varied from $.10 to $.60 and
the optimum points are determined. As expected,
an increase in fuel cost reduces the optimum
travel speed and increases the total cost per acre.
Total costs/acre with $.60 per gallon fuel are
26% above those at $.20 per gallon.
Labor Cost, $/Hour Figure 11 also shows the
effect of increasing the labor cost from $2.00
per hour to $6.00 per hour. Increasing labor
costs pushes the optimum point to a larger size
tractor and implement at increased travel speed.
Total costs/acre increase 24% as labor cost is
varied from $2.00 to $6.00 per hour.
Acres/Plowed Per Year In Figure 11 the effect
of increasing the number of acres plowed per
year is also shown. Total costs/acre are
decreased 19% as the acreage is increased from
400 up to 1000 acres/year. The optimum point
increases in width and decreases in speed.
It is easy to see that there is no single optimum
width and speed but that it varies with assumed
conditions. When average values are used, the
optimum comes close to the most popular size
tractor and plows in use today. It is also
interesting to note the large variation in width
and speed possible to remain within a few
percent of the optimum point. This, perhaps,
explains the variety of tractors and plows
demanded by today's farmers, with the tractor
size and type probably influenced by other
considerations on the farm.
Optimum Width and Speed for Least Cost Tillage 15
EFFECT OF FUEL COST, LABOR COST, AND
ACREAGE PLOWED ON OPTIMUM WIDTH AND SPEED
(MOLDBOARD PLOWING)
FIGURE 11
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Zoz, F.M, "Predicting Tractor Field Performance", ASAE Paper No. 70-118, July 1970
Wismer, R.D. and Luth, H.J., "Off-Road Traction Prediction for Wheeled Vehicles", ASAE Paper No. 72-619, Dec 72
ASAE 13230.1, "Farm Machinery Cost and Use", Agricultural Engineers Yearbook, 1973
Davidson, J.B., Fletcher, L.J., and Collins, E.V., "Influence of Speed Upon the Draft of Plow", Transactions of the
ASAE, Volume 13, December 1919.
Hunt, Donnell, "Selecting an Economic Power Level for the Big Tractor", ASAE Paper No. 71-147 June 1971
Hunt, Donnell, Farm Power and Machinery Management, Iowa State University Press
Reaves, Carl A., "Moldboard Plow Design and Use for Higher Horsepower-Lower Weight Tractors", SAE Paper
710681, September 1971
Coleman, R.N. and Wilkins, i.D., "High Field Speed Tractors, Why?" SAE Paper 710686, September 1971
University of Nebraska, Agricultural Engineering Department, "Tractor Test Reports"