MATLAB program to calculate drag force against a cyclist

AIM

To calculate drag force against a cyclist

Governing Equation

F = `1/2*rho*S*V^2*C_d`

Here,

F = Drag force experienced by the cyclist in Newton(N).

`rho`= Density of air (kg/`m^3`)

S = Frontal area or the area suffering air resistance (`m^2`)

V = velocity of the cyclist (m/s)

`C_d`= drag coefficient (unitless quantity)

Drag force is the force caused due to motion of the body through a fluid like air and it opposes the direction of velocity.

There is no object on the earth that would have value of drag coefficient equal to 0 as every object suffers some resistance to motion. However, efforts are made to minimise the drag coefficient and hence resistance experienced by the body with the help of aerodynamics.

Objective

The objective of this program is to determine the drag force experienced by the cyclist while cycling. From the equation, we can see that the drag force is directly affected by the frontal area. Therfore, in the professional cycling events, we can observe that the cyclist adjust their body posture in order to minimise the frontal area, which minimises the drag force experienced by them and increases their speed.

In this project, we would see the effect of velocity of cycling and drag coefficient on the drag force respectively and plot the graphs of the same.

Program

% program to calculate drag force on a cyclist
clear all
close all
clc

%inputs
%Frontal area,S (m^2)
S = 0.3;
%constant velocity,V (m/s)
V = 10;
%Changing velocity,v (m/s)
v = linspace(2,20,10);
%drag coefficient, C_d
C_d1 = linspace(0.6,0.7,6);
C_d2 = 0.64
%density of air (kg/m^3)
rho = 1.223;

%drag force,F_d = 0.5*rho*S*v^2*C_d

%For constant velocity
F_d1 = 0.5*rho*S*V^2.*C_d1

%for varying velocity
F_d2 = 0.5*rho*S*v.^2*C_d2

%plotting drag coeff vs drag force
subplot(2,1,1)
plot(C_d1,F_d1,'linewidth',4)
xlabel('drag coefficient')
ylabel('drag force')
grid on

%plotting velocity vs drag force
subplot(2,1,2)
plot(v,F_d2,'linewidth',4)
xlabel('velocity')
ylabel('drag force')
grid on

i) Initially, the required inputs are provided. These include the value of frontal area, velocity of the cycle, drag coefficient and the density of air. In order to deduce a relationship between drag force with drag coefficient and velocity respectively, we define different values for velocity and drag coefficient.

ii) To study the effect of drag coefficient on drag force, a constant velocity is assumed and an array containing different values of drag coefficient for different cycling positions is taken. A plot is then generated between `C_d` and drag force.

iii) To study the effect of cycling velocity on drag force experienced, an array containing different values of velocities is generated and used to calculate drag force for each of the velocities in the array, keeping `C_d` constant. The plot is then generated.

iv) Subplot command is used to get both the plots in same figure and labels are provided to the axes.

OUTPUT

Conclusion

i) From this project, following conclusions can be drawn. For same velocity of cycling, lower the value of drag coefficient, lower will be the resistance offered to the cyclist which would help in achieving higher acceleration. Thus, the cyclist would be able to cycle faster with similar effort, by changing his position to minimise drag force experienced.

ii) For same value of drag coefficient, that is, same position of cycling, if the cyclist increases the velocity by applying more effort, the drag force experienced by him/her increases parabolically, which tends to make him/her tired at faster rate.