Flow Over Bicycle

Aim: Program to calculate Drag Force against a cyclist and to plot :

1) Velocity Vs Drag Force

2) Drag Co-efficient Vs Drag Force

Governing equation : F_D = ½*ρ* A* V² *C_D

where;

F_D -------> Drag Force (Kg m/s^2)

C_D -------> Drag coefficient

ρ ---------> Density (Kg/m^3)

A ---------> Frontal Area (m^2)

V ---------> Flow velocity relative to the object (m/s)

Theory :

Drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as bicyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force F_D is found to be proportional to the square of the speed of the object. We can write this relationship mathematically as,

F_D ∝ V²

When taking into account other factors, this relationship becomes,

F_D = ½* ρ * A* V² *C_D

Software used: Octave

(1) A program to calculate drag force against a cyclist and to plot Velocity vs Drag Force.

% A program to calculate the drag force on a bicycle
clear all
close all
clc

%Input

%Drag coefficent
c_d = 0.8  

%Area m^2
 A=0.1
 
%Density kg/m^3
rho =1.2

%velocity m/s
v=[1:50]

drag_force = rho*A*v.^2*c_d*0.5

plot (v,drag_force);

xlabel('velocity')
ylabel('drag force') 
 
grid on

Explanation of the code :

The code is determined by our inputs in the formula mentioned above. The values of velocity were given using the range operator. By plotting Velocity vs Drag Force, we can get our result. In this instance, velocity is interpreted to be an array so that we have different velocity values that provide us with different drag force values. When the bicycle is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. The resultant plot depicts the same.

Outcome:

No errors were obtained after executing the code.

Plot :

Velocity vs Drag Force

The above plot depicts that the drag force is directly proportional to the square of the velocity. The plot is a parabolic curve.

(2)A program to calculate drag force against cyclist and to plot Drag Co-efficient vs Drag force.

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

%drag coefficients 
Cd = [0.04  0.09 0.42 0.47 0.50 0.80 0.82 1.05 1.15]

%area m^2
A=0.1;

%density kg/m^3
rho=1.2;

%velocity m/s
V=5;

%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')

grid on

Explanation of the code:

Multiple drag coefficients for different shapes are taken from the internet and a matrix is generated, and with respect to drag force, velocity is the most important variable.

Outcome:

No errors were obtained during execution.

Plot :

This resultant plot shows that the drag force is increasing linearly with the drag coefficient values. Hence, we can say it is linearly proportional.

RESULT :

Thus, the drag forces were calculated and the two graphs are plotted for the questions mentioned.