Flow over Bicycle

Aim: To write a program to calculate drag force against a cyclist and to plot

1.Velocity vs Drag force

2.Drag Co-efficient vs Drag force

Software used: octave

Theory:

A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. Drag always acts in the direction opposite to the motion.

The Drag force formula is given by,

F_D = ½*`rho`*A *V²*C_D

Where, `rho`=Density (kg/m^3)

A=Frontal area (m^2)

V=Velocity(m/s)

C_D =Drag Co-efficient

The Drag force depends upon the shape of the object, velocity, size and the fluid in it.

Lower the drag coefficient, the object will have less aerodynamic drag.

If the area is more, it means more of the area is in contact with the air which results in more drag.

The cyclist will experience drag force when the cycling velocity increases, hence the cyclists change their riding position frequently so as to reduce drag force i.e. change in the position will change the frontal area and the drag force experienced by the cyclist will be reduced.

To plot Velocity vs Drag force

clear all
close all
clc

% Program to calculate the drag force on a bicycle
% To plot Velocity vs Drag force

%inputs
%drag coefficient
Cd=0.8 ;
%frontal area in m^2  
A=0.1 ;
%density in kg/m^3   
rho=1.2 ; 
% velocity in m/s 
V=[1:50]; 

%drag force formula
drag_force=rho*A*V.^2*Cd*0.5 

%plotting
plot(V,drag_force)
title('Veloity vs Drag Force')
xlabel('Velocity (m/s)')
ylabel('Drag Force(N)')
grid on

Explanation of code

1. Start the program with clear all, close all and clc
2. Creating the variables required and assigning values to them
3. Here velocity is considered as an array so as to calculate different values of drag force for different velocities
4. Writing the formula to calculate drag force
5. Plot command is used to plot the graph and xlabel and ylabel commands are used to label the X-axis and Y-axis respectively
6. ‘grid on’ command is used to enable grid lines in the graph

To plot Drag-coefficient vs Drag Force

clear all
close all
clc

% Program to calculate the drag force on a bicycle
% To plot Drag-coefficient vs Drag Force

%drag coefficients
Cd=[0.47; 0.42; 0.50; 1.05 ; 0.80 ; 0.82 ; 1.15 ; 0.04 ; 0.09 ];
%area in m^2 
A=0.1 ; 
%density in kg/m^3   
rho=1.2 ;
% velocity in m/s 
V=3; 

%Drag force formula
drag_force=rho*A*V.^2.*Cd*0.5 

%Plotting
plot(Cd,drag_force)
title(' Drag-coefficient vs Drag Force')
xlabel('Drag Coefficient')
ylabel('Drag Force(N)')
grid on

Explanation of code

1. Start the program with clear all, close all and clc
2. Creating the variables required and assigning values to them
3. Here the coefficient of drag for different shapes are considered to get a varying drag force
4. Writing the formula to calculate drag force
5. Plot command is used to plot the graph and xlabel and ylabel commands are used to label the X-axis and Y-axis respectively
6. ‘grid on’ command is used to enable grid lines in the graph

Plots

Errors in programming

No errors were obtained.

Result:

1. For Velocity vs Drag force, a parabolic curve is obtained as Drag force varies proportionally to V²
2. For Drag Co-efficient vs Drag force, they vary linearly, hence a straight line is obtained

Conclusion

The drag force experienced by the cyclists can be reduced by getting down low in a crouched position with elbows in, as there is more streamlined shape and there is less frontal area.