Flow over Bicycle

FLOW OVER BICYCLE:

AIM:

To write a Matlab program to calculate drag force against a cyclist.

GOVERNING EQUATIONS:

`F_d=1/2xxrhoxxAxxV^2xxC_d`

Where,

F_d = Drag Force in N

`rho` = Density in Kg/m³

A = Frontal Area in m²

V = Velocity in m/s

C_d = Drag Co-efficient.

This equation determines the drag force using the four factors: density, frontal area, velocity, drag co-efficient.

OBJECTIVES:

• To calculate the drag force experienced by the cyclist
• To plot velocity vs drag force
• To plot drag co-efficient vs drag force

PROGRAM:

Programming Language Used: MATLAB

To plot Velocity vs Drag force:

%program to calculate drag force and to plot velocity vs drag force
clear all
close all
clc

%Inputs
%drag Co-efficient
c_d = 0.8;

%area m^2
a=0.1;

%density kg/m^3
rho=1.2;

%velocity m/s
v=[1:5];

%drag force N
drag_force= rho*a*v.^2*c_d*0.5;

plot (v,drag_force)
xlabel('Velocity(m/s)')
ylabel('Drag Force(N)')
grid on

To plot Drag Co-efficient vs Drag force:

%To plot drag co-efficient vs drag force
clear all
close all
clc
%inputs
%drag Co-efficients different values 
c_d1 = [0.48 0.58 0.75 1.0 1.4] 
 
%area m^2
a=0.1;
 
%density kg/m^3
rho=1.2;
 
%velocity m/s
v=1;
 
%drag force N
drag_force1= rho*a*v^2*c_d1.*0.5;
 
plot (c_d1,drag_force1)
xlabel('Drag Co-efficient')
ylabel('Drag Force(N)')
grid on

INPUTS:

• Density is taken as 1.2 kg/m^3.
• Frontal Area is taken as 0.1 m^2.
• In 1st case, Velocity varies from 1 m/s to 5 m/s in which Drag co-efficient is 0.8.
• In the 2nd Case, Drag co-efficient varies from 0.48 to 1.4 in which Velocity is 1 m/s

OUTPUT:

Plot of Velocity vs Drag Force:

Plot of Drag co-efficient vs Drag Force:

EXPLANATION:

• The drag force is dependent on density of air, frontal area, velocity, drag co-efficient which are taken as input values.
• Drag force is calculated by varying Velocity from 1 m/s to 5 m/s and taking drag coefficient as 0.8 and Velocity vs Drag Force plot is made using these Values.
• As Velocity has Multiple Values, Element wise operator is used.
• Now, Drag Force is calculated by varying Drag Co-efficient from 0.48 to 1.4 and taking velocity as 1m/s and Drag Co-efficient vs Drag Force plot is made using these Values.
• As Drag Co-efficient has Multiple Values, Element wise operator is used.

CONCLUSION:

Plots of Velocity vs Drag Force and Drag Co-efficient vs Drag Force are made and it is observed that the variation of velocity with drag force is parabolic whereas variation of drag co-efficient with drag force is linear.