Flow over Bicycle

AIM : To calculate the drag force against a cyclist using MATLAB program.

OBJECTIVES:

To plot a graph between velocity vs drag force.

To plot a graph between Drag co-efficient vs drag force.

DESCRIPTION :

The formula to calculate the drag force is F_d = 1/2 * ρρ*A*V^2*c_d

• F_d = drag force (kg.m/s^2)

It is the force or resistance that is caused when an object moves through air.

• rho = Mass density of the fluid .(kg/m^3)

It is the density of the medium

• A = frontal area (m^2)

It is the area of the object which is facing the fluid.Drag force increases with an increase of surface area.

• V = Velocity or speed.(m/s)

Is the speed of the vehicle with which it is moving forward.

Drag force increases with square of the velocity.

• c_d = drag coefficient

Drag coefficient is a dimensionless value . It is used to quantify the drag or resistance of an object.

MATLAB CODE :

1.Matlab program to plot a graph between velocity vs drag force.

% A program to calculate the drag force on a bicycle
clear all
close all
clc
% Inputs 
% Drag coefficient 
c_d = 0.8
% Area m^2
A = 0.4
% Density kg/m^3
rho = 1.5
% velocity m/s
v = [1:50];
drag_force = 0.5*rho*A*v.^2*c_d;
figure(1)
plot(v,drag_force)
title('velocity vs drag force')
xlabel('velocity')
ylabel('drag force')
grid on

2. Matlab program to plot a graph between drag co-effiecient (for different values) vs drag velocity .

% A program to calculate the drag force w.r.t different drag co-efficients.
clear all
close all
clc
% Inputs 
% Drag coefficient for different values 
c_d = [0:0.1:2]
% Area m^2
A = 0.4
% Density kg/m^3
rho = 1.5
% velocity m/s
v = 50
drag_force = 0.5*rho*A*v.^2*c_d
figure(1)
plot(c_d,drag_force)
title('Drag co-efficient vs drag force')
xlabel('Drag co-efficient')
ylabel('Drag force')
grid on

CONCLUSION:

From the obtained output we can observe that

i) Drag force is directly proportional to v^2. As v increases Drag force also increases simultaneously and forms a parabolic path.

ii) Drag force is directly proportional to drag coefficient.It forms a straight path.

iii) Drag force is directly proportional to density . The more denser medium the more drag force.

iv) Drag force is directly proportional to Frontal Area. It increases with an increase of surface area`