Calculation of Drag Force on a Cyclist using Matlab program

Aim: To calculate the drag force acting on the cyclist and plotting the relation for velocity and drag Co-efficient against Drag force using Matlab program.

Governing Equation:

When a cyclist is moving in a certain direction, he experiences a resisting force acting in opposite direction of movement of cycle. This resisting force is the Drag Force and depends on various factors like Velocity, Density of medium, Frontal Area, Drag Co-efficent.

The equation to calculate the Drag Force is given by,

`D=1/2×Cd×ρ×v^2×A`

Where D = Drag Force acting on the cyclist in N,

`ρ` = Density of medium in `frac{kg}{m^3}`,

V = velocity of cyclist in `frac{m}{s}`,

A = Frontal Area of cyclist in `m^2`,

Cd = Drag Co-efficient.

Matlab Program:

Case (1)- Program for plotting Drag force vs Velocity relation:

Here, we first give inputs for Drag co-efficient, Frontal area, and Density by keeping them constant and give different values of velocity as input in form of an array and calculate drag force for these values. After calculating drag force use the plot command to get the variation between velocity and drag force.

% A program to calculate the drag force on a cyclist and
% plotting of drag force vs velocity
clear all
close all
clc

%Inputs
%Drag co-efficient
c_d = 0.8;
%Area in m^2
A = 0.1;
%density of the medium in kg/m^3
rho = 1.2;
%velocity in m/s
v = [1:30];

%Calculating Drag force
drag_force = rho*A*v.^2*c_d*0.5;

%Plotting of Drag force vs velocity
plot(v,drag_force)
xlabel('Velocity')
ylabel('Drag force')
grid on

Case (2) - Program for plotting Drag force vs Drag Co-efficient relation:

In this program, we give inputs for velocity, frontal area and density by keeping them constant and give different values of Drag Co-efficient in form of array and calculate drag force for these values. After calculating the drag force use the plot command to get the variation between drag co-efficient and drag force.

% A program to calculate the drag force on a cyclist and
% plotting of drag force vs drag coefficient
clear all
close all
clc

%Inputs
%Drag co-efficient
c_d = [0.15 1.4 0.05 0.5 0.6 0.65 0.7 0.8 0.85 0.9]
%Frontal Area in m^2
A = 0.1;
%density of the medium in kg/m^3
rho = 1.2;
%velocity in m/s
v = 30;

%Calculation of Drag force
drag_force = rho*A*v.^2*c_d*0.5;

%plotting of drag force vs drag coefficient
plot(c_d,drag_force)
xlabel('Drag Co-efficient')
ylabel('Drag force')
grid on

Result:

After execution of Case (1) program we get the plot of Drag force Vs Velocity as shown in figure below:

figure(1): Drag Force vs Velocity

After execution of Case (2) program we get the required plot of Drag force vs Drag Co-efficient as shown in figure below:

figure (2): Drag force vs Drag Co-efficient

Conclusion:

• From figure (1), we can see that velocity increases drag force increase quadratically which can have adverse effect on the performance.
• From figure (2), we can see variation of Drag Co-efficient vs Drag force is linear.