ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT
AZOJETE - CIGR Section VI Special Issue:

Innovation & Technologies for Sustainable Agricultural Production & Food Sufficiency
AZOJETE, December, 2018. Vol. 14(SP.i4): 8-19

Published by the Faculty of Engineering, University of Maidiguri, Maidiguri, Nigeria.

Print ISSN: 1596-2490, Electronic ISSN: 2545-5818
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ORIGINAL RESEARCH ARTICLE
MODELLING OF TRACTOR FUEL CONSUMPTION FOR HARROWING OPERATION IN A

SANDY LOAM SOIL
O. A. Oyelade1* and K. C. Oni2

1*Farm Power and Machinery Department, National Centre for Agricultural Mechanization (NCAM), Ilorin, Kwara State,
Nigeria.

2Agricultural and Biosystems Engineering Department, University of Ilorin, Ilorin, Kwara State, Nigeria.

ARTICLE INFORMATION

Received October, 2018
Accepted December, 2018

Keywords:
Fuel
Harrowing
Evaluation
prediction
Tractor
consumption

ABSTRACT
In the study of agricultural machinery management, fuel
consumption is considered as a very important factor that plays a
significant role in the selection and management of tractors and
equipment. In Nigeria, there are no tractor fuel consumption
models developed for harrowing operation. Considering the
importance of harrowing operation to tillage practice in Nigerian
agriculture, it became necessary to embark on the study on the
modelling of tractor fuel consumption in litres per hectare (L/ha)
during harrowing operation in a sandy loam soil using available
information gathered from the National Centre for Agricultural
Mechanization (NCAM) Tractor Test Reports. A multiple linear
regression method was used to develop the model. A 10-repeated
10-fold cross-validation method was used to validate the model.
The study revealed that the model developed for harrowing
operation had a R2-value of 0.477 showing tractor power rating as
the only operation parameter contributing to the model developed.
Cross-validation revealed that the harrowing operation model had a
test error value of 0.986 L/ha. The study also identified other
contributing factors to tractor fuel consumption during harrowing
operation in a sandy loam soil. The model developed for tractor fuel
consumption during harrowing operation in a sandy loam soil is
recommended for use in budgeting for diesel consumption.
© 2018 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved.

1.0 Introduction
Tillage of soil is considered to be one of the biggest farm operations (Al-Suhaibani and Ghaly,
2010). It is also a conventional farming system involving the use of the tractors which results in
high energy costs. The sustainability of such a system requires a well-controlled resource
management leading to a significant reduction in crop production costs derived from savings in
fuel consumption (Serrano et al., 2009). Agricultural machinery has become increasingly
important in carrying out farm work. The application of machines to agricultural production has
been one of the outstanding developments in agriculture. Machinery contributes a major capital
input cost in most farm businesses.
In agriculture, the tractor remains a very important machine due to its ability to provide
mechanical power to farm implements both on and off the farm. The choice of a tractor based
on field performance can be very challenging due to limited information with regards to
performance on the field. According to Sirelkatim, et al. (2001), land preparation is one of the
most energy demanding operations in agriculture, it involves soil cutting, turning and
pulverizing and thus demands high energy, hence there is need to optimize tractor performance

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in order to utilize the available energy. This energy utilization depends on many factors such as
soil type and condition, operating depth and speed, and hitch geometry.

The use of models for budgeting of tractor fuel consumption has been of great use to farmers in
developed nations. Most studies on model development for tractor fuel consumption centres
mainly on ploughing operation which is the first tillage operation carried out on the soil.
Harrowing operation has been considered as a very important tillage operation that needs to be
carried out during land preparation in Nigerian agriculture.

Considering the importance of harrowing operation to tillage practice in Nigerian agriculture,
there is a need to develop a simple model equation for predicting tractor fuel consumption in
litres per hectare (L/ha) during harrowing operation. The study is aimed at developing a
statistical model for predicting tractor fuel consumption during harrowing operation in a sandy
loam soil.

2.0 Materials and Methods
2.1 Experimental procedure
The study involves the use of information gathered from the National Centre for Agricultural
Mechanization (NCAM) Tractor Test Reports on 41 agricultural tractors compiled by Oyelade
(2016) which were tested during harrowing operation on a sandy loam soil. Each tractor was
tested on an area of 0.25 hectare (25 m x 100 m) in a randomized complete block design (RCBD).
The implement used for the trials was tractor mounted off-set disc harrow. Parameters measured
during harrowing operation include speed of operation, fuel consumption, field capacity, field
efficiency, wheel slip, duration of operation, draught force, the width of cut, depth of cut, soil
cone index, soil moisture content, and soil bulk density. The three soil properties, namely, soil
cone index, soil moisture content and soil bulk density were all measured at depths 0 – 7 cm, 7 –
14 cm and 14 – 21 cm. The resulting average values of these three soil properties were part of
the data collated. All the parameters of the tractor-implement performance were measured and
recorded in line with the recommendations of RNAM test codes and procedures for farm
machinery technical series (1983). Out of the 41 tractor test data, 37 tractor test data termed
model development data-set was used to generate multiple regression for use in future
predictions of tractor fuel consumption in litres per hectare during harrowing operation on a
sandy loam soil. The remaining four tractor test data termed model validating data-set were
used to validate the model developed.

2.2 Description of the Study Area
The study was carried out at the National Centre for Agricultural Mechanization (NCAM), Ilorin,
Kwara State which is located at 370 m above sea level in the Southern Guinea Savanna
ecological zone of Nigeria by Longitude 4o 30′ E and Latitude 8o 26′ N. The various test
locations where these tractors were tested fall under the sandy loam soil textural class with the
following fractions: sand - 56.79% to 69.92%, silt - 15.33% to 28.64% and clay - 6.44% to 18.33%.
The soil in the various test locations of the study area were classified as Alfisols (Soil Survey Staff,
1975) under the USDA soil order.

2.3 Particle Size Analysis
Particle size analysis was carried out using the hydrometer method described by Gee and Or
(2002). Sodium hexametaphosphate (calgon) was used as the dispersant. The textural class of the
soil was determined using the USDA Textural Triangle.

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2.4 Test Parameters
2.4.1 Speed of Operation
The speed of operation was determined by placing two poles 20 m a part in-between the
longest distance of the test plot. On the opposite side of the test plot, two poles were placed in
a similar position 20 m apart. The speed of operation for each tractor evaluated during
harrowing operation was mathematically expressed as:











1

206.3
t

VS (1)

where,
Vs = Speed of operation (km/h)
t1 = Time taken to cover 20 m (sec)

2.4.2 Depth and Width of cut
The depth and width of cut during field operation were measured using a steel rule and
measuring tape, respectively.

2.4.3 Draught of the Implement
The draught of implement was measured using the trace tractor technique described by Oyelade
(2016).

2.4.4 Theoretical Field Capacity
Theoretical field capacity measured in ha/h was expressed mathematically as:

 
T
3600

a

EG
(2)

where,
G = Theoretical field capacity (ha/h),
E = Area of field (ha)
Ta = Actual time taken in doing the main tillage work (sec)

2.4.5 Effective Field Capacity
Effective field capacity measured in ha/h was expressed mathematically as:

T t

EX )3600(
5 

(3)
where,

X5 = Effective field capacity (ha/h)
E = Area of field (ha)
Tt = Total time taken in completing the whole tillage operation (sec)

2.4.6 Field Efficiency
Field efficiency, according to ASAE (2000), is the ratio of effective field capacity to theoretical
field capacity, expressed in percent. It was expressed mathematically as:

%100
G

5 xXH 
(4)

where,
H = Field efficiency (%)
X5 = Effective field capacity (ha/h)
G = Theoretical field capacity (ha/h)

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2.4.7 Fuel Consumption
The fuel required for each tillage operation was determined by filling the tank to full capacity
before and after the test. Amount of refueling after each test is the fuel consumption for the test.
The filling of fuel tank before the operation and then refilling after completing the operation in
determining the amount of fuel consumed during operation is a common method used in the
field for determining tractor fuel consumption in litres per hectare. This same method was as
reported by (Ajav and Adewoyin, 2011; Ikpo and Ifem, 2005; Kudabo and Gbadamosi, 2012;
Meshack-Hart, 1997; Sirelkatim et al., 2001; Udo and Akubuo, 2004) in determining tractor fuel
consumption in litres per hectare.

Fuel consumption measured in either L/ha or L/h was expressed mathematically as:

E
JI 

(5)
IxK 5X (6)

where,
I = Fuel consumption (L/ha)
J = Volume of fuel consumed (L)
E = Area of field (ha)
K = Fuel consumption (L/h)
X5 = Effective field capacity (ha/h)

2.4.8 Travel Reduction (Wheel slip)
In determining the wheel slip (travel reduction), a mark was made on the tractor drive wheel with
coloured tapes. This was used to measure the distance covered by the tractor drive wheel at
every 10 revolutions under no load and the same revolution with a load on the same surface.
The travel reduction (wheel slip) measured in % was expressed mathematically as:

%100
M

 M - M

2

12 L
(7)

where,
L = Travel reduction (wheel slip) (%)
M2 = Distance covered at every 10 revs of the wheel at no-load condition (m)
M1 = Distance covered at every 10 revs of the wheel at load condition (m)

2.4.9 Tractive Efficiency
Tractive efficiency measured in % is the ratio of drawbar power to wheel power and was
expressed mathematically according to (Macmillan, 2002) as:

%100
w

p
t Q

D
Q

(8)
where,

Qt = Tractive efficiency (%)
Dp = Drawbar power (kW)

Qw = Wheel power (kW), power losses in the transmission from engine to the
wheels of, say 10% is assumed, it can be written as:

%100
9.0





e

p
t Q

D
Q

(9)
where, Qe = Engine power (kW)

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2.4.10 Duration of Operation
The duration of operation measured in h/ha which is the time spent in completing the whole
operation was mathematically expressed as:

5
9

1
X

X 
(10)

where,
X9 = Duration of operation (h/ha)
X5 = Effective field capacity (ha/h)

2.5 Soil Parameters
2.5.1 Soil Bulk Density
Soil bulk density (ρb ) is a measure of the mass of soil per unit volume and is usually reported on
an oven-dry basis. The soil bulk density was determined by the core method described by
Anwanane (2014). The core samples were oven dried at a temperature of 1050C to a constant
weight.

ρb =
Ms
VT

(11)
where,

ρb = Soil bulk density (g/cm3)
Ms = Mass of dry soil (g)
VT = Total volume of soil (cm3)

2.5.2 Soil Moisture
Klenin et al. (1985) defined soil moisture content as the amount of liquid, usually water that is
present in the soil. It is expressed as a percentage of the mass of water in the soil to the mass of
the dried soil (for dry weight classification). The soil moisture content (in dry basis) measured in
%, can be expressed mathematically as:

%100
s

w
c W

W
M

(12)
where,

Mc = Soil moisture content (%)
Ws = Mass of oven dried soil (g)
Ww = Mass of water present in soil (g)

2.5.3 Soil Cone Index
The soil cone index (CI) is the soil resistance to penetration and was measured using a cone
penetrometer.

2.6 Statistical Tool
2.6.1 Regression Analysis
Multiple linear regression method which is a form of regression analysis was used for
establishing the relationship that existed between fuel consumption (the model response
variable) and other factors (or predictors of fuel consumption) identified to be factors
influencing tractor fuel consumption in litres per hectare during harrowing operation. Multiple
regression is when there is one dependent variable but more than one independent variables. In
this study, tractor fuel consumption in litres per hectare was the dependent variable while other
factors identified as factors influencing tractor fuel consumption in litres per hectare stands as
the independent variables.

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In developing this model, the following hypotheses were drawn:
Test of Hypothesis about Full Regression Model of Harrowing Operation
Hypothesis 1: [Test of significance about all regression parameters]
Null hypothesis H0 : The model does not fits the data/ The model is not adequate
Alternative hypothesis H0 :The model fits the data/ The model is adequate
Mathematically,
Null hypothesis H0 : βj = 0 [None of the predictors contributes significantly to the model]
Alternative hypothesis H0 : :βj = 0 for at least one j [At least one of the predictors contributes
significantly to the model]

Tests statistic: Fratio =
MSRegression
MSError

[Global F-test]

Decision rule: Reject thenull hypothesis in favour of the alternative hypothesis at 0.05
significance level if P − value < 0.05, otherwise do not reject the null hypothesis.
Hypothesis 2: [Test of significance about individual regression coefficient]
Null hypothesis H0 : βj = 0 [Predictor xj is not statistically significant in the model given that
others are included in the model]
Alternative hypothesis H0 : : βj ≠ 0 [Predictor xj is statistically significant in the model given that
others are included in the model]
Tests statistic: tvalue =

βj

Cjjσ2
[Individual t-test]

jjC diagonal element of the covariance matrix corresponding to j

2 variance of j

This same tests statistic was also used by James et al. (2013)
Decision rule: Reject the null hypothesis in favour of the alternative hypothesis at 0.05
significance level if P − value < 0.05, otherwise do not reject the null hypothesis.

2.7 Developing models without an intercept term
Models with intercept term are common to all models built round multiple linear regression
models. In this study, the assumption was whether a tractor could consume some amount of fuel
before commencement of harrowing operation if such variable as air (ambient) temperature
could constitute measurable parameters. The study was therefore governed by building models
without intercept term because it is the most appropriate model type that fits this study based
on the cylinder method of measuring fuel consumption.

2.8 Model Validation
The model validation method adopted for this study is the cross validation method. This
validation method is an extremely flexible and powerful technique and widely used approach in
validation work for estimating prediction error. The measure of error for cross-validation is the
mean square error (MSE) for a quantitative response. The 10-fold cross-validation is commonly
used. According to Bouckaert (2003), 10-fold cross-validation remains the most widely used
validation procedure.

3.0 Results and Discussion
3.1 Model Development and Validation
One model with p-value < 0.05 was statistically developed for harrowing operation on a sandy
loam soil. Details of the pair-wise correlation analysis showing the result of the correlation
strength of the developed model for harrowing operation is presented in Table 1. Results

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obtained for parameter estimates and Analysis of Variance (ANOVA) for the model developed
for harrowing operation are presented in Tables 2 and 3, respectively.

Table 1. Pair-wise Correlation result of Fuel Predictive Values of Model 2 with Observed Fuel
Values during Harrowing Operation

* = significant at 5% level when r-value ≥ 0.338788

Table 2. Table of Parameter Estimates for Model 2 of Harrowing Operation

*significant at 5% level

Table 3. ANOVA Table for Model 2 of Harrowing Operation
Source of Variation Degree of

Freedom
Sum of
Squares

Means
Squares

F-value P-value

Tractor power rating 1 234.430 234.430 151.6806 4.503e-11 *
Width of cut 1 6.257 6.257 4.0487 0.05721
Depth of cut 1 3.660 3.660 2.3684 0.13875
Draught force 1 4.110 4.110 2.6594 0.11785
Effective field capacity 1 3.300 3.300 2.1349 0.15879
Tractive efficiency 1 11.101 11.101 7.1828 0.01401 *
Field efficiency 1 4.096 4.096 2.6499 0.11847
Wheel slip 1 1.576 1.576 1.0200 0.32401
Duration of operation 1 0.086 0.086 0.0556 0.81594
Speed of operation 1 11.162 11.162 7.2223 0.01379 *
Average soil moisture content 1 0.750 0.750 0.4851 0.49378
Average soil bulk density 1 2.365 2.365 1.5301 0.22975
Average soil cone index 1 0.020 0.020 0.0131 0.90999
Residuals 21 32.457 1.546
*significant at 5% level

Model developed Observed
Model 2 of Harrowing operation 0.690468*

P-value of
Model

Model
Multiple
R-square
value

Model
Adjusted
R-square
value

Coefficients Estimates Std. Error t value P-value

1.519e-07 0.4767 0.1778 Tractor power rating 0.055996 0.059842 0.936 0.3601
Width of cut -0.050569 0.029628 -1.707 0.102
Depth of cut 0.059737 0.062936 0.949 0.3533
Draught force -0.698953 0.954827 -0.732 0.4722
Effective field capacity 10.673913 8.512772 1.254 0.2237
Tractive efficiency 0.250983 0.190038 1.321 0.2008
Field efficiency -0.031328 0.059421 -0.527 0.6036
Wheel slip -0.060759 0.054501 -1.115 0.2775
Duration of operation 5.464993 3.336067 1.638 0.1163
Speed of operation -1.523374 0.598055 -2.547 0.0188 *
Average soil moisture
content

-0.085734 0.115415 -0.743 0.4658

Average soil bulk
density

2.768087 2.346524 1.180 0.2513

Average soil cone index 0.003298 0.028825 0.114 0.9100

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Model 2 of harrowing operation with p-value < 0.05 recorded a R-squared value of 0.4767. The
model explains 48% of the proportion of variance in the mean squared errors of tractor fuel
consumption for harrowing operation with only speed of operation showing statistical
significance with a p-value of 0.0188 in the model. In terms of marginal (individual) significance
of the predictor variables, results in Table 4 reveal that we reject the null hypothesis about only
tractor power rating, tractive efficiency and speed of operation with corresponding p-values of
4.503e-11, 0.01401 and 0.01379, respectively. This means that each of these variables is
statistically significant in the model provided others are included in the model. It also implies
that they cannot be removed from the model.

The equation used for expressing Model 2 of harrowing operation as contained in Table 2 was
given as:

The equation used for expressing Model 2 of harrowing operation as contained in Table 2 was given as:
�� = 0.055996X1 − 0.050569 X2 + 0.059737X3 − 0.698953X4 + 10.673913X5 + 0.250983X6 −
0.031328X7 − 0.060759X8 + 5.464993X9 − 1.523374X10 − 0.085734X11 + 2.768087X12 +
0.003298X13

where,
Y� = Tractor fuel consumption (L/ha),
X1 = Tractor power rating (hp),
X2 = Width of cut (cm),
X3 = Depth of cut (cm),
X4 = Draught force (kN),
X5 = Effective field capacity (ha/h),
X6 = Tractive efficiency (%),

X7 = Field efficiency (%),
X8 = Wheel slip (%),
X9 = Duration of operation (h/ha),
X10 = Speed of operation (km/h),
X11 = Average soil moisture content (%),
X12 = Average soil bulk density (g/cm3) and
X13 = Average soil cone index (N/cm2).

The model equation generated for Model 2 of harrowing operation was used for predicting
tractor fuel consumption using the 37 model development dataset. Results obtained from the
fuel prediction values of Model 2 of harrowing operation is presented in Table 4. The values for
both observed and predicted tractor fuel consumption of Model 2 of harrowing operation as
shown in Table 4 were correlated together and gave a correlation coefficient of 0.690468 as
shown in Table 1. According to the rule of thumb as provided in
http://www.westgard.com/lesson42.html for evaluating correlation coefficient, noted that size of
r with correlation values between 0.50 and 0.69 are said to be moderate. It indicates that tractor
fuel consumption predictions of Model 2 of harrowing operation is moderately correlated with
the observed tractor fuel consumption values obtained during harrowing operation on a sandy
loam soil. Figure 1 shows the graph plot of observed and predicted tractor fuel consumption
using Model 2 of harrowing operation.

(13)

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Table 4. Results of Predicted Tractor Fuel Consumption values during Harrowing Operation on a
Sandy Loam Soil using Model 2 of Harrowing Operation

Figure 1. The plot of Observed and Predicted Tractor Fuel Consumption using Model 2 of Harrowing
Operation

Tractor
Observations

Observed fuel values
(L/ha)

Predicted
fuel values (L/ha)

Residuals
(L/ha)

1 3.28 2.711058 0.568942
2 4.12 3.783405 0.336595
3 5.47 4.624426 0.845574
4 1.44 1.972107 -0.53211
5 4.76 3.74173 1.01827
6 5.26 3.453034 1.806966
7 3.2 3.192731 0.007269
8 0.9 2.68324 -1.78324
9 3.8 2.452152 1.347848
10 3.53 4.300108 -0.77011
11 3 2.040149 0.959851
12 0.85 1.749665 -0.89966
13 3.92 3.35114 0.56886
14 0.92 1.557942 -0.63794
15 2.32 2.938795 -0.6188
16 2.24 1.525242 0.714758
17 1.84 2.549917 -0.70992
18 0.8 1.956347 -1.15635
20 1.68 2.904075 -1.22407
21 1.04 1.58534 -0.54534
22 0.9 1.847902 -0.9479
24 3.4 2.173657 1.226343
25 3 2.561103 0.438897
26 4 3.364288 0.635712
27 1.6 3.417445 -1.81745
28 1.9 2.857485 -0.95749
29 2.8 3.153878 -0.35388
30 2.1 1.820463 0.279537
32 2.88 1.907434 0.972566
33 2 2.748966 -0.74897
34 4.53 5.363732 -0.83373
35 4 2.156639 1.843361
36 1.2 1.338286 -0.13829
37 4.13 3.083001 1.046999

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3.2 Model Predictors for Harrowing Operation
The results of the parameter estimates and Analysis of Variance (ANOVA) for the only model
developed for harrowing operation on a sandy loam soil as shown in Tables 2 and 3, respectively,
have revealed that the only developed model for harrowing operation contains some important
predictors found to be significant at 5% level. These predictors include tractor power rating,
tractive efficiency and speed of operation. These three set of predictors are harrowing operation
parameters affecting tractor fuel consumption in litres per hectare during harrowing operation
on a sandy loam soil. Among these three factors affecting tractor fuel consumption during
harrowing operation on a sandy loam soil, only tractor power rating contributed highly to the
model developed. Therefore, tractor power rating, strongly determine tractor fuel consumption
in litres per hectare during harrowing operation on a sandy loam soil.

3.3 Model Validation for Harrowing Operation Model
Result of 10-repeated 10-fold cross-validation method as presented in Table 5 was used for
validating the model developed for harrowing operation on a sandy loam soil. It can be deduced
from Table 5, that Model 2 of harrowing operation recorded a root mean square error of
0.98643 L/ha serving as the model’s test error value using the four model validating datasets
presented in Table 6.

Table 5. Results of 10-repeated 10-fold Cross-validation for Model 2 of Harrowing Operation
Replicate No. MSE Value
1. 0.967218
2. 1.023916
3. 0.967739
4. 0.967430
5. 0.967155
6. 0.967337
7. 0.967429
8. 0.967726
9. 0.967282
10. 0.967218
Average MSE (L2ha-2) 0.973045
Average RMSE (Lha-1) 0.98643
Key:
MSE – Mean Square Error
RMSE – Root Mean Square Error
Note that each replicate contains the average mean square error value of 10-fold cross-
validation

Table 6. Results of Fuel Predictive and Residual values of Model 2 of Harrowing Operation used
for Model Validation data
Observed fuel values (L/ha) Predicted Fuel values (L/ha) Residual (L/ha)
4.00 3.384845 0.61516
1.60 3.1639 -1.5639
2.60 1.671801 0.9282
1.42 0.802705 0.6173

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Oyelade and Oni. Modelling of tractor fuel consumption for harrowing operation in a sandy loam soil.
AZOJETE, 14(sp.i4): 8-19. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: yemibamigbedjdoyelade@gmail.com 18

4.0 Conclusion
A study was carried out to develop a model for future prediction of tractor fuel consumption
during harrowing operation in a sandy loam soil using information gathered from NCAM Tractor
Test Reports. From the outcome of this study, it can be concluded that:

One effective model with p-value < 0.05 was developed for harrowing operation. Model 2 of
harrowing operation developed for future prediction of tractor fuel consumption in litres per
hectare during harrowing operation on a sandy loam soil recorded a coefficient of multiple
determination (R-squared) value of 0.4767.

Harrowing operation parameters such as tractor power rating, the speed of operation and
tractive efficiency were found to be statistically significant at 5% level in Model 2 of harrowing
operation with only tractor power rating contributing highly to the model developed.

The model for harrowing operation based on cross-validation result had a test error of 0.98643
L/ha.

Acknowledgement
We want to thank members of NCAM tractor testing team for the tremendous work they have
been doing over the years in the testing of agricultural tractors imported into the country for use
in Nigerian agriculture.

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