MATLAB Basics : Flow Over a Bicycle

1. AIM :

• To write a code to plot a graph of VELOCITY vs DRAG FORCE.
• To write a code to plot a graph of DRAG COEFFICIENT vs DRAG FORCE

2. GOVERNING EQUATION :

`F_d = 0.5*ρ*A*v^2*C_d`

Where;

`F_d` = Drag Force (N)

`ρ` = Density of Air (kg/m³)

A = Frontal Area (m²)

v = Velocity (m/s)

`C_d` = Coefficient of Drag

3. OBJECTIVE :

• The objective of this project is to represent the variation in Drag Force with respect to change in Velocities as well as the drag Coefficient.
• This is achieved by plotting a graph VELOCITY vs DRAG FORCE & DRAG COEFFICIENT vs DRAG FORCE respectively.

4. BODY OF THE CONTENT :

• The programming language used in this project is MATLAB.
• In this project, the medium through which the object moves is taken as AIR.
• There are two differnt possibilities are taken into consideration :

1. Varying Velocity

2. Varying Drag Coefficient.

• For the first program, Frontal area , Density and Drag coefficient are kept constant. The velocity of the object is made to vary between 1& 20 m/s.
• The change in Drag Force with respect to the change in velocity is plotted on a graph.

• For the second program, Frontal area , Density and Velocity are kept constant. 5 different objects are taken (cube,sphere,cone,cylinder & aerofoil) with different Drag Coefficients respectively.
• The variation in Drag Force with respect to the change in Drag Coefficient is plotted on a graph.

clear
close all
clc
% This code is to plot a graph of Velocity vs Drag Force
% Drag Coefficient & Area are kept constant with varying velocities

% Inputs
% Density kg/m3
rho = 1.2;
% Area m2
A = 0.2;
% drag_coefficient
c_d = 0.47;
% velocity m/s
v = [1:20];
drag_force = 0.5*rho*A*v.^2*c_d;
plot(v,drag_force,'linewidth',3,'color','b');
xlabel('Velocity');
ylabel('Drag Force');
grid on



close all
clear
clc

%  This code is to plot a graph of Drag Coefficient vs Drag Force
% Velocity & Area are kept constant with varying Drag Coefficients

% Inputs
% Density kg/m3
rho = 1.2;
% Area m2
A = 0.2;
% drag_coefficient
% cube = 1.05 sphere = 0.47 cone = 0.5 cylinder = 0.82 aerofoil = 0.045
C_d = [1.05 0.47 0.5 0.82 0.045];
% velocity m/s
V = 2;
d_f = 0.5*rho*A*V^2*[C_d];
plot(C_d,d_f,'linewidth',3,'color','r');
xlabel('Drag Coefficient');
ylabel('Drag Force');
grid on

• ERROR FACED :

5. CONCLUSION :

• We can clearly see that the Drag Force changes exponentially with respect to change in velocity while it shows a linear variation with respect to change in Drag Coefficient.