STUDY, DESIGN AND SIMULATION OF A PROGRAM FOR NUMERICAL EVALUATION OF VEHICLES’ FUEL CONSUMPTION DUE TO DRAG FORCE; CASE OF LIGHT VEHICLES DESIGN AND SIMULATION OF A PROGRAM FOR NUMERICAL EVALUATION OF VEHICLES’ FUEL CONSUMPTION DUE TO DRAG FORCE; CASE OF LIGHT VEHICLES.”

: Nowadays, vehicles are being abandoned by their users due to their high fuel consumption which had not been studied by the user from the start. Thus, the need to study the fuel consumption of vehicles due to one of the factors which greatly affects it; drag force, so as to produce information which vehicle users can have before purchasing their vehicles. With regards to this, this work is focused on the development of a computer program able to evaluate the fuel consumption of light vehicles. To achieve this, the basic equations of consumption are used to arrive at a mathematical relation between drag force and fuel consumption. This mathematical model is further implemented on the analytical software Matlab in order to produce the various consumption curves of the vehicles case study. A simulator which takes into consideration a vehicle’s engine data in order to produce specific consumption curves and provide valid information on the fuel consumption of the vehicle is developed from this mathematical model. It can be used in automotive construction companies and also by any individual .


Introduction
The rise in petroleum products especially fuel in automobile industry has for many years been a topic of concern to vehicle users and manufactures. Hence, there is a great need for studies to be carried out in order to determine the rate of fuel use during vehicle functioning in so as to avoid sudden car breakdown on the roads. Some faults have proven to be causes of high vehicle consumption such as; engine malfunction, electric and electronic problems in the vehicle, as well as transmission faults. This paper presents one of the factors which greatly influence a vehicle's fuel consumption, being the vehicle's drag force and is directly related to the vehicle's shape and size. As such, this paper is aimed at providing useful information to users on their vehicle's fuel consumption as well as, educating them on how to choose a vehicle depending on its size thus inherently its drag force in order to minimize fuel consumption.

Materials
Aerodynamics is a part of fluid mechanics, applied specifically to air. As such, the mathematical laws that on which this model will be based are: • The Navier-Stokes equations in which the viscous effects are non-negligible.
• Euler or perfect fluid equations, in which the viscous effects are negligible; (2) • With ⃗⃗⃗ a normal vector to the wall and ⃗ ⃗ a vector tangential to the wall, P corresponds to the local static pressure, Pref the reference pressure and dS the integration surface element. The aerodynamic moment defined at point P relative to the center of gravity G is: The pressure field exerted on a road obstacle generally induces a set of efforts where one considers usually: • A drag force Fx, parallel to the mean flow direction.
• A drift force Fy, perpendicular to the mean flow direction, in the horizontal plane.
• A force of lift Fz, perpendicular to the mean flow direction, in the vertical plane. The expression of force is of the general form: With q= Thus, "q" in equation (4) above, Force becomes the following;

Aerodynamic Coefficients
The aerodynamic coefficients are dimensionless coefficients used to quantify the forces in x, y, z.
• Cx: the drag coefficient; • Cy: The coefficient of lateral drift; • Cz: The coefficient of drift.
As the forces are calculated or measured experimentally (in the wind tunnel), the coefficients are determined by: Substituting the expression for q in equation (6) above, the final expression for determining the aerodynamic coefficients is gotten:

The Drag
The drag coefficient is the ratio of drag to the product of the reference surface and the dynamic pressure. The drag force is: With Cx = 1. We can also determine this force by considering the inertia force defined by:  [4] Therefore, replacing these expressions of mass and air into equation (9), the inertia force becomes; F x = 1 2 ρ air × V 2 × S × C x (10)

The Lift
The lift equation is similar to that of the drag with Cx replaced by Cz or Cy, for lateral lift [7];

The Drift
The drift equation is similar to that of the drag with Cx replaced by Cy where:

Aerodynamic Moments
It is defined according to three components [8]: The moment of roll Mx = L = 1 2 ρC l lSV 2 The pitch moment The yaw Moment Mz = M = 1 2 ρ C m lSV 2 (15)

The Adherence of Tires
This part will deal with the mechanical effects between the ground and the tire. The adhesion between the tire and the ground depends on two basic parameters: • The adhesion coefficient; • The adhesion forces.

The Adherence Coefficient
It depends on the state of the tyre and the nature of the soil; one note it to be µ.

The Adherence Strength
The adhesion strength corresponds to the action (A) of the ground on the wheel.  The following points are important for these analysis:  2) Effective Specific Consumption The specific consumption " "is the mass of fuel (in grams) that the engine would consume to deliver a power of 1kW for one hour (i.e. work of 3600 KJ).

Consumption Per Hundred Kilometers
This refers to the amount of fuel in liter burned to travel one hundred (100) kilometers The fuel consumption per hundred kilometers is calculated thus:

Relationship Between Consumption in One Hundred Kilometers and The Drag Force
The consumption over one hundred kilometers is defined by equation (19)  For a given vehicle, all these values represent constants in the course of its displacement; thus, only speed is the parameter which varies during the movement of the vehicle.

Experimental Determination of Drag Coefficient (Wind Tunnel Method)
This section deals with experimentally determining the wind drag coefficient. To achieve this, the SOLIDWORKS software was used to simulate the effects of wind on the bodywork of a CHEVROLET CAMORO vehicle, drawn on the same software.

Presentation of Results and Discussions
To better explain this paragraph, we will present the results of some simulation plans and we recorded the elementary pressures on the elementary surfaces.   The flow at the rear of the vehicle creates a high-speed (swirling) vacuum that generates a drag force opposing the vehicle's advancement.  Let's introduce the characteristics of each of these vehicles in the software in order to evaluate their respective consumption per hundred kilometers according to the drag force. This being done click on draw; then export to get the analysis report and its consumption curve.

Conclusion
This main objective of this paper was to realize a software for the evaluation of a fuel consumption with respect to the effect of its drag force. To achieve this, Matlab was used to quantify and plot the characteristic curves of some light vehicles through the programming of the existing mathematical relationship between consumption over one hundred kilometers and the drag force. The preliminary studies allowed us to find the real program capable of generating a source code necessary for the compilation and realization of the software. This software will greatly help vehicle users to evaluate how much quantity of fuel consumption their vehicle can consume. Automotive engineers will see in this software an important tool in the quest for producing better, reliable and affordable engines.