Flow over a Bicycle

Drag force is the resistance force of a fluid. This force applies acting opposite towards the motion of the object which is moving submerge in a certain fluid. Thus Drag Force is defined as the force which resists the motion of a body with fluid.

AIM: To evaluate the drag force experienced by a bicycle rider we shall look at the following governing equation.

Drag force= p A v²C_d

p: Density of fluid

A: Frontal area of the body

v: is the speed of the object relative to the fluid

C_d: Drag coefficient, a dimensionless number

To visualize the force relationship on depending factors lets take a example from the referenced paper.

Here is a MATLAB code to generate plots to visualize this relationship.

%To Evaluate Drag Force experienced by a Cyclist 
clear all
close all
clc

%Density of fluid
p=1.2; %Kg/m3

%Frontal area
A= 0.6; %m2


%Array of Velocity values (from reference data)
v=linspace(4.8,21,50); %m/sec
%constant velocity
v_cons=15; %m/sec
%Array of Drag coefficient due to change in velocity  (from reference data)
Cd=linspace(0.9,1.14,50);

%Drag Force
F=0.5*p*A*v.^2.*Cd;
%To visualize effect of Cd on Drag force assuming constant velocity
f=0.5*p*A*v_cons^2.*Cd;

%To obtain Both plots in same figure
subplot(2,1,1)
plot(v,F,'linewidth',2,'color','r')
xlabel('Velocity')
ylabel('Drag Force')
grid on
title('Effect of velocity on Drag Force')
subplot(2,1,2)
plot(Cd,f,'linewidth',2,'color','g')
xlabel('Drag Coefficient')
ylabel('Drag Force')
grid on
title('Effect of Drag coefficient on Drag Force')

On using the code, we can visualize the Drag Force relationship through the graphs as follows:

OBSERVATIONS:

• We can observe that the Drag force varies velocity according to velocity squared. We can see the parabolic nature of the curve validating our governing equation.
• For the Drag force dependence on the Drag Coefficient we can observe that the relationship is linear. That is due to our assumption of taking the velocity as constant and then varying the drag coefficient due to change in the area.