STUDY AND SIMULATION OF THE FUEL CONSUMPTION OF A VEHICLE WITH RESPECT TO AMBIENT TEMPERATURE AND WEATHER CONDITIONS AND SIMULATION OF THE FUEL CONSUMPTION OF A VEHICLE WITH RESPECT TO AMBIENT TEMPERATURE AND WEATHER CONDITIONS.”

: The consumption of fuel in vehicles depends on many factors such as the state of the roads, the state of the engine and the driver’s behavior. A mathematical model for evaluating vehicle fuel consumption on a 100 km interval at standard operating weather conditions was developed. This mathematical model developed took into consideration many factors, but the main factors were those related to weather conditions and temperature. Here a new simulation program for determining the influence of temperature and weather conditions on fuel consumption is built using the software Matlab. For efficient simulations the model uses a set of data for an SUV and then makes varying only the parameters that are related to weather and temperature for the simulation. During the simulation process, a set of 10 vehicle models and 8 roads conditions were chosen to run down the simulations and only the parameters of temperature, the drag coefficient and coefficient of rolling resistances respectively were subjected to variations during each of the simulations. Upon simulation, different results were obtained for the different parameters considered. For every 15% drop in temperature, 0.1litre, 0.12litre and 0.04litre increase in fuel consumption for the set of parameters chosen was noticed. These results were analyzed and interpreted with the help of Microsoft Excel and were found to be satisfactory given that it permits manufacturers and car users to have a notion of the impact of ambient temperature and weather conditions on fuel consumption, thereby promoting optimum usage of fuel, hence reducing the effect of greenhouse emissions in the atmosphere .


Introduction
In an automobile, fuel consumption is important to the users as well as the manufacturer. Given that the aim of every user is to obtain a minimal fuel consumption while maintaining the best performances of his vehicle, this article is going to raise awareness on the users on how fuel is being consumed and when best to use your vehicle ensuring optimum usage of fuel hence saving a lot of money and contributing to the reduction of environmental damages through air pollution caused by the fuel in the form of exhaust gases. In the literature, multiple dependencies of fuel consumption were constructed based on experimental data (approximation), but their purpose is largely confined to analyzing the influence of various factors on the fuel consumption of specific vehicles such as the power train, the driving style and many others. Most of them failed to consider natural factors such as weather conditions, whereas it has a great and significant influence on fuel consumption. The amount of fuel consumed depends on the engine, the type of fuel used, and the efficiency with which the output of the engine is transmitted to the wheels and many other parameters. This fuel's energy is used to overcome rolling resistance primarily due to flexing of the tires, aerodynamic drag as the vehicle motion is resisted by air, and inertia and hill-climbing forces that resist vehicle acceleration, as well as engine and drive line losses.

Materials and Methods
This section is concerned with the materials and the methods which were used in order to achieve a numerical relation between fuel consumption and ambient temperature, and also comprises the choice of the software which is going to be used in this project. Below is the list of the materials used for this project.

Analytical Modeling Study
A study of the mathematical relations of the main factors that influence the fuel consumption of our vehicle and the manipulation of some equations to derive an equation that relates fuel consumption and temperature is done, taking into account the assumptions and the specifications of our model.  The following assumptions were made as regard to this model for the simulation of fuel consumption of this model;

Aerodynamic Drag
Aerodynamic drag is the resisting force that air applies on a moving object like a ball, car, or aircraft. Basically, the object crashes into the air molecules in front of it. The air has to be pushed out of the way and the drag force comes from that air pushing back against the object. The drag force on an object, for instance a car, can be quantified using the formula: (1) Where: FD is the drag force, ρ is the air density, v is the velocity, CD is a dimensionless drag coefficient, and A is the frontal area.
The magnitude of the density will decrease at higher humidity and/or elevation, but the trend as a function of temperature is essentially unchanged. Cold air is denser than warm air and the aerodynamic drag force is proportional to the air density.

Derivation of The Formula of Fuel Consumption with Respect to Ambient Temperature
In this paper, an estimation of fuel consumption Q S measured inlitersper100km, with respect to the engine power via the following relation (Michael Ben Chaim, 2013); Assuming that the vehicle is constantly operating in acceleration mode and the engine power is determined according to this assumption. Specific fuel consumption is assumed to be constant and optimal. Based on the equation of fuel consumption above, the calculations can be made providing the values for the following; • Specific fuel consumption • Power to overcome rolling resistance • Power to overcome aerodynamic drag • Power to overcome inertial acceleration • The fuel density • The efficiency of the transmission The lower the brake specific fuel consumption, the more efficient the engine is. For spark ignition (gasoline engine) the BSFC is around 250 g/kWh and for compression ignition (diesel) around 200 g/kWh.(x-engineering.org, 2019)

Determination of Power to Overcome Rolling Resistance
According to Wong, 1993, 90-95% of the rolling resistance is caused by internal hysteresis, 2-10% by friction between the tire and the ground and1-3% is caused by air resistance. Below is the formula that can be used to calculate the rolling resistance of the wheels of a vehicle.

= (3)
Upon obtaining the rolling resistance force, the power required to overcome rolling resistance can be calculated as follows; Where frl is the rolling resistance coeficient,

Power to Overcome Aerodynamic Drag Force
Aerodynamic drag force is the resisting force that air applies on a moving object like a ball, car, or aircraft. Below is the formula used to calculate the aerodynamic drag of a vehicle; In order to calculate the power, we have to make use of the relation; = Where the power to overcome aerodynamic drag is, is the force due to aerodynamic drag and V is the velocity of the vehicle. Substituting in the equation of , we obtain the following; From the ideal gas equation, assuming dry air in our model, we can obtain the relation between temperature and density as (Charles' Law); Where P is the pressure of air, Rd is the gas constant (8.314J/molK), and T the ambient air temperature.
In the case of moist air, we have; Where Tvis the virtual temperature expressed as Tv= T. (1+0.61r) with r being the water vapor mixing ratio.

Determination of Fuel Density
An engine which uses diesel as its fuel is the case study. The density of diesel is given as ρf=0.8325kg/l. The measurements were made at 15.5 o C and standard atmospheric pressure.

Determination of The Efficiency of Transmission
After measuring the power throughout the entire rpm range, transmission efficiency can be calculated using the relation; In order to obtain the relation between the fuel consumption and temperature, we replace equations  The relation shows the dependence of temperature on the overall consumption of the vehicle. Replacing all the values of the respective parameters and the necessary assumptions made for this model leads us to a simpler relation of fuel consumption and temperature which can then be simulated.  To validate the obtained formula, estimates of fuel consumption obtained by calculations via the formula were compared to experimental data available from manufacturers. The vehicle-specific parameters used were the engine type, automobile mass, maximum power and engine speed at maximum power.

Results and Discussions
The data for the following vehicles were run in the Matlab/Simulink software; For the first simulation, the results obtained were due to the variations of frontal areas at different temperatures. Below is the graph obtained from the simulation with varying frontal areas.  The respective curves represent the different vehicles alongside their fuel consumption measured in litres/100km at respective temperatures during the driving cycle of 100km. The graph shows that the higher the temperature, the lower the fuel consumption for all the tests vehicles. It can also be observed that the vehicle frontal area affects the vehicle's fuel consumption linearly.
Another program was written to simulate the fuel consumption of the test vehicles with respect to temperature, while varying both the vehicle frontal area and the coefficient of aerodynamic drag force. Below is the result of its simulation; It can be observed from the above histograms, the value of fuel consumption obtained varies according to the temperature in a similar manner for all the test vehicles. Also it was noticed that for every 15°C drop in temperature, there is 0.1 litre increase in fuel consumption for the same vehicle and same frontal area and at the same speed. For the second simulation, the results obtained were due to the variations of both the frontal areas and coefficient of aerodynamic drag at different temperatures. It can also be observed from this graph that the impact of higher drag coefficients and frontal area is of more significance, hence greater fuel consumption. The interpretation of this graph for each temperature range of 15°C using histograms was done. Below are the results for the temperatures of -15°C and 30°C. Figure 5: Graph of fuel consumption against drag coefficient and frontal area at a constant temperature of -15°C and 30°C for the ten test vehicles.
From the above histograms, one can notice that the value of fuel consumption obtained varies according to the temperature in a similar manner for all the test vehicles. Also, it was noticed that for every 15°C drop in temperature, there is 0.12litres increase in fuel consumption for the same vehicle and same frontal area, same drag coefficient and same speed.
For the third simulation, the results obtained were due to the variations of the rolling resistance coefficients at different temperatures. Below is the graph obtained from the simulation.  The fuel consumption for the test vehicles was estimated for varying coefficients of rolling resistances at temperature ranges of -15°C to 45°C so as to explain the effects of different roads or different tires on the fuel consumption of the vehicle. The graph above shows the relationship between fuel consumption, coefficient of rolling resistance and temperature.
The interpretation of this graph for each temperature range of 15°C using histograms was done. Below are the results of the temperatures of -15°C, 30°C and 45°C Figure 7: the graph of fuel consumption against rolling resistance for a constant temperature of -15°C for different road conditions.
The values of the coefficients of rolling resistance frl for each vehicle corresponds to the height of the rectangle of the said vehicle taken from the left of our graph, and the fuel consumed is the corresponding meeting point or extrapolation of the rectangle to the curve and then reading the value on the right hand side of our graphs to have the amount of fuel consumed by that vehicle. Also, it was noticed that for every 15°C drop in temperature, there is 0.04litre increase in fuel consumption for the same vehicle under the same road conditions and the same speed.