Numerical Modelling Formula 1 Vehicle Resistive Forces in Scilab-Xcos
By: Shiv Pratap Singh Rajawat
Tags: Formula 1, Model Based Design, Electric Vehicles, Electric Car, Scilab

Created by: Shiv Pratap Singh Rajawat

Problem statement: Model the Formula 1 Vehicle Resistive Force in Scilab-Xcos to plot the vehicle resistive force.

Track Drive Cycle Graph: A series of data points representing the speed of vehicle versus time. With the help of the drive cycle; we can calculate: Rolling Resistance Force, Gradient Force Aerodynamic Force, Acceleration Force, can predict the Fuel Consumption, and can also estimate the Battery capacity, Battery Discharge Current & Polluting Emissions. Various Drive Cycles standards around the world: NEDC, WLTP, and FTP75.

Drive Cycle can also be used to estimate the highest Torque requirement with the help of Top Speed.

Track Drive data

Model Inputs:

Program:

Program to import the Drive Cycle data and the Gradient angle data.

2. Defining the input parameters to initialize the model.

Vehicle Resistive Forces Calculation Model on Scilab-Xcos:

Rolling Force(Fr) = GVW*Crf*Cos(theta)

where;

Crf denotes the Coefficient of Rolling Friction

Table of Crf wrt Surface

Theta denotes the Grade angle

GVW denotes the gross vehicle weight

GVW = GVM*g

where GVM = (Kerb mass of vehicle + Driver Mass) and g= 9.81 m/s

2. Gradient Force(Fgr) = GVW*sin(theta)

where;

Theta denotes the Grade angle

GVW denotes the gross vehicle weight

3. Aerodynamic Force (Fa) = 0.5*rho*A*Cd*V²

Figure showing the aerodynamic forces acting on the vehicle

The frontal area (A) is projected on a plane, we consider to calculate or model, upon which the aerodynamic force acting on the car. As Area is directly proportional to aerodynamic force, upon increasing the Area, the aerodynamic force increases proportionality.

The density of air (rho) is considered to be constant. It does vary wrt altitude and temperature, but the variation of density has lesser significance on the aerodynamic force.

The coefficient of drag (Cd) is a constant that represents the effectiveness of the body in reducing air resistance. The drag coefficient varies with respect to the shape of the body as described in the image. That’s why, shapes of airplanes, ships, space shuttles, or even in nature: the body of fish is streamlined to have the lowest possible coefficient of drag. So the object can slice through the air, creating lesser turbulence. With this we understand, lesser the Cd is, the lesser the Af.

Table for Cd along with the corresponding shapes

Velocity (V) creates a compounding effect on the aerodynamic force. As aerodynamic force is directly proportional to the square of velocity, the force on the car shoots up very high at higher speeds.

That’s why the engine needs to produce very high power to overcome aerodynamic force at higher velocity.

4. Acceleration Force (Facc) = GVM*a

where;

GVW denotes the gross vehicle mass

‘a’ denotes the vehicle acceleration in m/s²

Wheel Speed Calculation:

Wheel Speed (Nw) = V*60/2*pi*Rw

Wheel Torque Calculation:

Total forces acting on the Car (TTE) = Fr+Fgr+Fa+Facc

Wheel Torque (Tw) = TTE*Rw

Vehicle Resistive Forces Calculation Model on Scilab-Xcos

Results:

The Results Output obtained after running the model.

The Various Vehicle Resistive Forces — Rolling Force, Gradient Force, Aerodynamic Force & Acceleration Force wrt time.

2. The Wheel Speed and Wheel Torque with respect to time.

Output Results of the vehicle Resistive Forces

Output Results of Wheel Torque and Wheel Speed

Conclusion:

The Conclusion can be further used in the design and estimation of various parameters of the physical model.