Traction prediction modelling, a key factor in farm tractor design, has been driven by the need to find the answer to this question without having to build physical prototypes. A wide range of theories and their respective algorithms can be used in such predictions.

The “Tractors and Tillage” research team at the Polytechnic University of Madrid, which engages, among others, in traction prediction for farm tractors, has developed a series of programs based on the cone index as the parameter representative of the terrain. With the software introduced in the present paper, written in Visual Basic, slip can be predicted in two- and four-wheel drive tractors using any one of four models. It includes databases for tractors, front tyres, rear tyres and working conditions (soil cone index and drawbar pull exerted). The results can be exported in spreadsheet format

Catalán Mogorrón, Heliodoro Fco.

Linares Anegón, Pilar

Mendez Fuentes, Valeriano

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Tractor PT: A traction prediction software for agricultural tractor

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Short communication
Tractor PT: A traction prediction software
for agricultural tractors
Heliodoro Catala´na, Pilar Linaresb, Valeriano Me´ndeza,∗
a Dpto. Matema´tica Aplicada, E.T.S. Ingenieros Agro´nomos, Universidad Polite´cnica de Madrid,
Ciudad Universitaria s/n, 28040 Madrid, Spain
b Dpto. Ingenierı´a Rural, E.T.S. Ingenieros Agro´nomos, Universidad Polite´cnica de Madrid,
Ciudad Universitaria s/n, 28040 Madrid, Spain
a r t i c l e i n f o
Article history:
Received 15 January 2007
Received in revised form
30 July 2007
Accepted 30 July 2007
Keywords:
Traction prediction
Tractor performance
Simulation
Visual programming
a b s t r a c t
Traction prediction modelling, a key factor in farm tractor design, has been driven by the
need to ﬁnd the answer to this question without having to build physical prototypes. A wide
range of theories and their respective algorithms can be used in such predictions.
The “Tractors and Tillage” research team at the Polytechnic University of Madrid, which
engages, among others, in traction prediction for farm tractors, has developed a series of
programs based on the cone index as the parameter representative of the terrain. With the
software introduced in the present paper, written in Visual Basic, slip can be predicted in
two- and four-wheel drive tractors using any one of four models. It includes databases for
tractors, front tyres, rear tyres and working conditions (soil cone index and drawbar pull
exerted). The results can be exported in spreadsheet format.
© 2007 Published by Elsevier B.V.
1. Introduction
Computerized tractor simulation and prediction models,
which economize on time and ﬁeld trials, constitute an essen-
tially cost-free approach to the determination of the relative
importance of a number of factors affecting actual tractor
operation. Gradually but steadily rising energy prices oblige
engineers and users to improve tractor operation by compar-
ing and analyzing the various parameters involved. Tractor
performance on actual soil conditions differs substantially
from the results of laboratory track testing. The physical laws
governing movement and behaviour in general vary from one
surface to the other, while constant changes in terrain and
drawbar pull generate ongoing variations in the dynamic load
on each wheel.
∗ Corresponding author. Tel.: +34 913 365 854; fax: +34 913 365 845.
E-mail addresses: h.catalan@upm.es (H. Catala´n), pilar.linares@upm.es (P. Linares), valeriano.mendez@upm.es (V. Me´ndez).
The soil–vehicle interface is the primary cause of low
traction efﬁciency (estimated to be on the order of 60% on
farmland, for transmission performance of nearly 90%). In
1935 the National Tillage Machinery Laboratory at Auburn,
Alabama, was created (Bekker, 1969). The soil bins built there
to test farm implements soon proved to be a valuable tool for
analyzing soil response to the mechanical stress caused by
ploughing vehicles and implements. The Vicksburg, Missis-
sippi Waterways Experiment Station (WES) was designated to
launch a trafﬁcability programme in 1945. In the 1950s, a host
of papers dealing with vehicle behaviour on natural terrain
appeared, scattered across a variety of journals (Upadhyaya
et al., 1997). Bekker’s studies on the occasion of the NASA
moon ﬂight programmes fathered TERRAMECHANICS. Many
surveys have been based on strain-deformation relations at
0168-1699/$ – see front matter © 2007 Published by Elsevier B.V.
doi:10.1016/j.compag.2007.07.009
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290 computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295
the soil–vehicle interface, such as the Nepean Tracked Vehicle
Performance Model (NTVPM) (Wong, 1986).
Deere & Co. implemented a vast experimental programme
to analyze the conditions deﬁning maximum traction per-
formance in farm tractors, using the cone index as the sole
parameter to represent the terrain. A series of associated
parameters were likewise employed, such as wheel number
(Wismer and Luth, 1972) and mobility number (Brixius and
Wismer, 1975). In England, the National Institute of Agricul-
tural Engineering (NIAE, Silsoe) studied the traction capacity
of farm tyres using vehicles such as the single wheel tester
and developed a theory likewise based on the cone index (Gee-
Clough et al., 1978; Gee-Clough, 1984).
Computer models or simulation software to predict tractor
response contribute to determining the relative importance
of different factors that affect soil–tractor behaviour with-
out the need for costly and time-consuming ﬁeld trials.
Moreover, this software helps researchers and tractor man-
ufacturers to improve performance. Al-Hamed et al. (1994)
introduced a spreadsheet to calculate tractive efﬁciency
in radial wheels. Subsequently used by authors such as
Grisso and Zoz (2004), Zoz and Grisso (2003) and Goering
and Hansen (2004), it has gradually evolved into a sys-
tem that covers the entire tractor. Simulation software to
predict tractor performance may draw from different pro-
gramming tools. Presently Visual Basic and Visual C++ are
widely used to develop such software. The Visual Basic
environment facilitates user access to and implementa-
tion of program functionalities. Al-Hamed and Al-Janobi
(2001) developed prediction software that calculates draw-
bar pull and slip from engine power and theoretical forward
speed.
The “Tractors and Tillage” research team at the Polytech-
nic University of Madrid, which engages, among others, in
traction prediction for farm tractors, has developed a series
of programs based on the cone index as the parameter rep-
resentative of the terrain. With the software introduced in
the present paper, written in Visual Basic, slip can be pre-
dicted in two- and four-wheel drive tractors using any one
of four models. It includes databases for tractors, front tyres,
rear tyres and working conditions (soil cone index and draw-
bar pull exerted). The results can be exported in spreadsheet
format.
2. Traction prediction models
Fig. 1 represents the general outline for traction prediction
models. The input data refer to the vehicle, terrain and work-
ing conditions (drawbar pull exerted).
Themodels used yield an exponential equation that relates
traction coefﬁcient and slip as follows:
 = max(1 − e−˛ı)
where ı is slip, ˛ is a parameter that characterizes the
soil–vehicle system,  is the traction coefﬁcient (max is the
maximum traction coefﬁcient).
Fig. 1 – Traction prediction theory ﬂow diagram.
3. Models used
As a differencewith other prediction software programs, Trac-
tor PT deploys the four prediction models characterized in
Table 1, all of which use the cone index to represent soil
conditions. The ﬁrst three are well known: the ASAE or Cn
(Wismer and Luth, 1972); Deere or Bn (Brixius and Wismer,
1975); and NIAE or MN (Gee-Clough, 1984) models. The fourth,
the modiﬁed Cn (ASAE) model, was developed by the Poly-
technic University of Madrid’s Rural Engineering Department
based on years of comparative studies of predicted and exper-
imental testing.
Program output consists of two- and four-wheel drive trac-
tor slip values for the four prediction theories. For greater
convenience, the software is provided in Spanish, Portuguese,
English or French. Before predictions can be processed, the
input values must be entered into four databases: tractor, test
conditions (cone index and drawbar pull exerted), rear tyres
and front tyres.
The primary difference between this software and the
Grisso-Zoz Goering spreadsheet and Al-Hamed and Al-Janobi
program lies in the input data. Tractor PT uses drawbar pull
rather than engine horsepower.
4. Modiﬁed ASAE model
The Madrid School of Agricultural Engineering’s Rural Engi-
neering Department has engaged in terramechanics research
(or land locomotion) since 1970. Linares et al. (1993), test-
ing tractors under actual ﬁeld conditions based on electronic
instrumentation able to record test variables in situ (Camps
et al., 2000a; Catala´n and Linares, 1998). With these facilities,
comparisons could be drawn between prediction and experi-
mentation, applying cone index-based theories.
In these surveys, predictions were made on a LOTUS
spreadsheet. When the Cn theory was used, the comparison
revealed deviations: the theory proved to be pessimistic for
soft soils (with higher predicted than experimental ﬁgures)
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computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295 291
Table 1 – Prediction models used in the Tractor PT program
and optimistic for hard soils. An adjustment between pre-
diction and experiment was made, maintaining the original
equation that related traction coefﬁcient t to slip ı:
t = 0.75(1 − eA1Cnı)
In the original model A1, the value was 0.3. For the adjust-
ment, Cervantes (1993) proposed 0.16 for hard soil and 0.61 for
soft soil.
Further comparisons were made with four-wheel drive
tractors on hard and soft soil. DOS software titled TRACCIO´N
(Catala´n, 1996) was used to calculate the predictions. The pat-
tern found was the same as in the two-wheel drive tests and
the ﬁt between the experimental and predicted results was
improved by changing the parameters.
This consistency in the results obtained prompted the ini-
tiation of a study that attempted to expand the range of
soils tested from 200 to 1200kPa, although for theory Cn
and two-wheel drive vehicles only (Herna´ndez, 1998). In light
of the results of that study, a change was proposed in the
slip coefﬁcient in the original Cn theory, to be replaced by
slip-dependent parameter A1 (Table 2). This led to a sub-
stantial improvement in the comparison between predicted
and experimental ﬁndings. In this case, prediction was con-
ducted with an Excel spreadsheet, using the radii measured
in the experimental trials (Cervantes et al., 2000). The same
operating procedure was deployed in subsequent years, using
“catalogue” radii for the prediction (Catala´n and Linares, 1998;
Camps et al., 2000b) obtaining the A1* parameter (Table 2).
The software developed for this purpose, written in C++, was
named MITRA (Spanish acronym for farm tractor modelling
software) (Camps et al., 2005).
The problems encountered to export the results obtained
with MITRA software hindered its dissemination, however. A
stage in which the effect of tyre weight and width on tractor
performance was studied with a Mathcad spreadsheet (Mahl
Table 2 – Parameter A1 used in modiﬁed Cn model
Radii Parameter
Measured in experimental tests A1 = 182
CI1.0231
Theoretical (catalogue) A1∗ = 253
CI1.09
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292 computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295
Fig. 2 – Tractor PT program structure.
et al., 2005; Linares et al., 2005) was followed by the devel-
opment of new prediction software, Tractor PT (Linares et al.,
2006).
5. Tractor PT program structure
Object-oriented programming is ﬂexible and easy to use.
For this reason, the program for predicting traction in 2WD
and 4WD tractors on farm land was developed in Visual
Basic 6.0. TRACTOR PT has a Windows graphic user inter-
faced (GUI) developed in Visual Basic, Access to store the
data model and Excel as interface to print form and to export
data. It runs on computers with Windows 98/NT/2000 or XP
operating systems and Microsoft Ofﬁce Access, Word and
Excel. The program has two Access data base ﬁles, one to
store the parameters depending on the language selected.
All the ﬁxed text is stored in this database, the windows
labels, the pop-up message texts, the Excel form texts, and
the dropdown list options. The program can manage four
languages (English, French, Portuguese and Spanish), but lan-
guages can be added to the database without modifying
Fig. 3 – Tractor PT program operation procedure.
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computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295 293
Fig. 4 – Calculation ﬂow chart for ASAE theory, MFWD:4WD.
Fig. 5 – Summary screen showing results obtained.
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294 computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295
the hard code in the Visual Basic modules (Linares et al.,
2006).
In the other database the user stores the prediction data
using the Visual Basic GUI. This database has ﬁve tables,
conditions, tractor, rear tyres, front tyres and predictions.
The GUI is very easy to manage and is perfectly inte-
grated with the Windows utilities and programs. It uses the
Newton iteration algorithm to obtain the root of the slip
function.
The software covers two- and four-wheel drive tractors
working on horizontal terrain with parallel-horizontal draw-
bar pull. All other conditioning factors are deﬁned by the
prediction theories used.
The program ﬂow chart is given in Figs. 2 and 3. The
data sheet and prediction menus are accessed from the main
menu, to create the databases relating to the tractor, front and
rear tyres and test conditions. The user may create, correct,
add or remove data sheets from any of the databases.
To predict the performance of a given tractor, the user
selects “new prediction” on the “predictions” submenu to dis-
play the screenwhere the respective data, including the choice
of drive (two- or four-wheel) andmodel, are to be entered. The
calculation procedure for a 4WD tractor usingmodel Cn is out-
lined in Fig. 4. Prediction results can be visualized both on a
summary screen (Fig. 5) or as a preview (Fig. 6) and exported
to a spreadsheet.
Fig. 6 – Full prediction results, exportable to Excel spreadsheet.
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computers and electron ics in agr iculture 6 0 ( 2 0 0 8 ) 289–295 295
6. Conclusions
A computerized model in Visual Basic has been developed to
predict 2WD and 4WD:MFWD tractor performance on farm-
land. Themodel is designed for use in education and research.
The menus and windows guide the user through a series of
fairly easy steps. The interface is intuitive and user-oriented
with screens for selecting the type of tractor, tyres and condi-
tions.
The software uses four prediction models that calculate
dynamic axle load, soil–vehicle parameters and slip from the
drawbar pull.
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Tractor PT: A traction prediction software for agricultural tractor

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