APPLICATION OF BUCKINGHAM PI THEOREM IN DEVELOPMENT OF TRACTOR FUEL CONSUMPTION MODEL FOR PLOUGHING OPERATION

The estimation of tractor fuel consumption during ploughing operation has been consistently
receiving attention as a result of diverse nature, varieties and development in prime movers
and dynamic response of soil to tillage operation treatment. The need to use selected soilimplement-machine parameters as factors affecting fuel consumption is necessary. Fuel consumption model for estimating tractor fuel consumption per working area for ploughing operation has been developed using Buckingham’s pi theorem. Generalized reduced gradient
(GRG), a nonlinear method of Excel solver was used for the establishment of the model’s
constant. The model was validated by simulating the experimental results into the equation,
coefficient determination (r2), graphical comparison, root mean square error, and paired tTest. The field experiment was performed at Rivers Institute of Agricultural Research and
Training (RIART) Farm in Rivers State University, Port Harcourt. Port Harcourt lies on the
latitude of 4° 49′ 27″ N, and longitude of 7° 2′ 1″ E; with an altitude of 274mm above mean
sea level; and average annual rainfall depth of 2310.9 mm The experimental land area was
138 m by 50 m (6900 m2) which was divided into three blocks of 9 plots each. Each plot was
marked out 50 m by 2 m each along with the paths dimension of 1 m between each plot was
provided for different treatment options and with a space of 2 m between each block and 1 m
at the sides of the of the outer blocks. The group balanced block design (GBBD) was
adopted. The design consisted of 9 experimental treatments with three replicates. The
experimental fuel consumption per working area was determined by quantity of fuel used per
working area with the aid of fuel flow meter. The field test parameters (speed, depth, forward
speed, cone index, bulk density) were measured accordingly with their specific standards
procedures. The field test parameters (speed, depth, forward speed, cone index, bulk density)
results were simulated with fuel consumption to obtain the constants in the estimation model.
The developed model displayed good agreement between measured and estimated results
with high coefficient of determination (r2) of 0.9974, and low root mean square error of 0.74.
The paired t-Test results also showed no significant difference at 95 and 99 % confidence
levels. It is as a result, recommended that the model be used for estimating tractor fuel
consumption during ploughing operation.