Flow over Bicycle

Aim

To write a MATLAB program for Drag force on cyclist and also making a Plotof the following

1.Plot Between Velocity and Drag Force

2.Plot Between Drag_Coefficient and Drag Force

Solution

1.A Plot between veloctiy and Drag Force

In this part of program here the velocity substituted is from 1m/s to 10m/s with an common interval of 2 and for different velocity drag force is calculated and the formula is shown below;

Drag Force = 0.5*Area*Velocity^2*Density_of_Air*Coefficient_of_Drag

here the coefficient of drag is constant.And the program is attached and plot is shown below.

[note: in plot or graph the point or dotes shows each and every co-ordinates of x-axis and y-axis]

clear all
close all
clc

%constants
Dens = 1.2   %Density
Area = 0.1   %Area
C_d = 0.8    %Coefficient_of_Drag

%variable 
velo = [1:2:10];  %Velocity in m/s

%Formula

Drag_force = 0.5*Dens*Area*C_d*velo.^2;

%Graph
plot(velo,Drag_force,'ro-','linewidth',3)
grid on
legend data1
title('Drag of Bicycle')
xlabel('velo')
ylabel('Drag_force')

Hence first condition is solved.

2.A Plot between Coefficient of drag and Drag Force

In this part of program here the Coefficient of drag is substituted for various which are refered from vikipedia are shown in the table

S.No	Shapes	Drag Coefficient
1.	Sphere	0.47
2.	Semi-Sphere	0.42
3.	Cone	0.50
4.	Cube	1.05
5.	Angled Cube	0.80
6.	Long Cylinder	0.82
7.	Short Cylinder	1.15
8.	Streamlined Body	0.04
9.	Streamlined Half-Body	0.09

also it is a unit less term, denoted by C_d and for different C_d's ,drag force is calculated and the formula is shown below;

Drag Force = 0.5*Area*Velocity^2*Density_of_Air*Coefficient_of_Drag

here the velocity is constant.And the program is attached and plot is shown below.

clear all
close all
clc

%constants
Dens = 1.2  %Density
Area = 0.1  %Area
velo = 0.8  %Velocity

%variable 
C_d = [0.47 0.42 0.5 1.05 0.8 0.82 1.15 0.04 0.09]; %These are measured Coefficient of Drag refered from wikipedia


%Formula

Drag_force = 0.5*Dens*Area*C_d*velo.^2;

%Graph
plot(C_d,Drag_force,'ko-','linewidth',3)
grid on
legend data1
title('Drag of Bicycle')
xlabel('C_d')
ylabel('Drag_force')

Hence second condition is solved

Result

From this I found that for different Velocity, Drag Force changes and for higher velocity Drag force is high and also for different shape with the same velocity the Drag force changes because for different shape the drag coefficient varies.

Hence both the condition are verified and plots are formed.