Drag force over a Bicycle.

Aim:

To see how Drag force varies with velocity and drag coefficient.

Governing Equation:

Drag force, `Fd=0.5×Cd×ρ×A×V^2.`

Where, `rho` = Density (Kg/m^3).

A = Frontal area (m^2).

V = Flow Velocity relative to object (m/s).

Cd = Drag coefficient.

Objectives:

• Writing a program to plot Velocity vs Drag force.
• Write a program to plot Drag Co-efficient vs Drag force.

Body of Content:

The programming is done in MATLAB. To see the variation of drag force with velocity first of all the inputs are defined, the range of velocity is taken between 1 to 15 m/s with 50 intervals using linspace command. So, V is an array in this case for that I have included element wise operator while defining drag force equation. Then Velocity vs Drag force graph is plotted.

%Program to plot Velocity vs Drag force.

clear all
close all
clc

%Inputs
Cd = 0.7;    %drag coefficient
A = 0.4;     %frontal area (m^2)
rho = 1.2;   %Density of air (Kg/m^3)
V = linspace(1,15,50);   %Velocity range of bicycle(m/s)

Fd = 0.5*rho*A*V.^2*Cd  %Drag force

%Plotting
color = [1 0.8 0];  %color = [r g b]
plot(V, Fd, 'color', color)
xlabel('Velocity')
ylabel('Drag Force')
grid on

To see how the drag force varies with drag coefficient, the range of Cd is taken between 0.5 to 0.7 with 50 intervals with other inputs as given in the program. Here linspace command is used for Cd. Finally Drag coefficient vs Drag force graph is plotted.

%Program to plot Drag Co-efficient vs Drag force.

clear all
close all
clc

%Inputs
Cd = linspace(0.5,0.7,50)    %drag coefficient range over bicycle for the same frontal area.
A = 0.4;     %frontal area (m^2)
rho = 1.2;   %Density of air (Kg/m^3)
V = 3;   %Average Velocity over bicycle(m/s)

Fd = 0.5*rho*A*V^2.*Cd  %Drag force (N)

%Plotting
color = [1 0 0.8];  %color = [r g b]
plot(Cd, Fd, 'color', color)
xlabel('Drag coefficient')
ylabel('Drag Force')
grid on

The final graphs are given below.

Conclusion:

• There is a parabolic variation between velocity and drag force. It is also noticeable that at higher values of velocity, the small change in V will result in drastic change in drag force.
• Variation between drag coefficient and drag force is linear.