Study of Drag Force on cyclist and Flow over Bicycle using MATLAB

AIM

To study drag force on cyclist and major performances parameter in cycling using MATLAB.

GOVERNING EQUATIONS:

`bb "Drag Force " F_d=(1/2)*v^2*A*C_d*rho`

where,

`C_d " = drag coefficient "`
`v " = speed of the body "`
`A " = projected cross-sectional area of the body "`
`ρ " = density of the fluid "`

Program to plot Velocity vs Drag force

% program to plot Velocity vs Drag force

close all
clear all
clc

%Inputs

% Desity kg/m^3
rho = 1.225;

% Frontal Area m^2
A = 0.5;

% Drag coefficient
c_d=0.5;

% Velocity m/s^2
v = [1:50];

% Calculate Drag Force N
D = 0.5*rho*A*v.^2*c_d;

% Ploting
plot(v,D,'color','b');
title('Velocity vs Drag force');
xlabel('Velocity in m/s^2')
ylabel('Drag force in N')
grid on

MATLAB Plot:

Result:

In the drag force equation

`F_d=(1/2)*v^2*A*C_d*rho`

drag force is proportional to the square of velocity v which is in accordance with the above plot.

So it is necessary to focus on decreasing drag force on high velocity moving bodies.

Program to plot Drag Co-efficient vs Drag force

% program to plot Drag co-efficient vs Drag force

close all
clear all
clc

%Inputs

% Desity kg/m^3
rho = 1.225;

% Frontal Area m^2
A = 0.5;

% Drag coefficient
c_d = [0.04 0.09 0.42 0.47 0.5 0.8 0.82 1.05 1.15];
labels = {'Streamlined Body', 'Streamlined Half-body', 'Half-sphere', 'Sphere', 'Cone', 'Angled Cone', 'Long Cylinder', 'Cube', 'Short Cylinder'};
% Velocity m/s^2
v = 5;

% Calculate Drag Force N
D = 0.5*rho*A*v.^2*c_d;

% Ploting
plot(c_d,D,'color','b','marker','o','markerfacecolor','g')
text(c_d,D,labels,'VerticalAlignment','top','HorizontalAlignment','left')
title('Drag co-efficient vs Drag force')
xlabel('Drag co-efficient')
ylabel('Drag force in N')
grid on

Drag co-efficient source:

MATLAB Plot:

Result:

From the above plot, different Drag force for different object shapes plotted and streamlined Body has lower drag force so that these shapes are widely used.