Flow Over Bicycle

AIM:

TO CALCULATE DRAG FORCE AGAINST CYCLIST.

GOVERNING EQUATION:

F_D = `1/2`×A×C_D×v²×`rho`

Where,

F_D = Drag force on cyclist(N).

A = Frontal Area of cyclist(m²).

C_D = Drag coefficient(unitless).

v = velocity of cyclist (m/s).

`rho` = Density(kg/m³)

OBJECTIVE:

The main objective of the program is to find the drag force on a cyclist by varying the velocity and drag coefficient.

The above figure shows the position of cyclist and different forces.

WORKFLOW OF PROJECT:

!) Initially we assign the values of different variables.

2) Then obtain the value of drag force by using the formula.

3) At last , obtain the results and plot the graph.

PROGRAMMING LANGUAGE USED – MATLAB

CASE 1: Here we write program for plotting velocity v/s Drag force.

MATLAB CODE:

%A program to calculate drag force by varying velocity
%And plotting the graph of velocity v/s Drag force
clear all
close all
clc
 
%inputs
%Frontal area assumed(m^2)
A = 0.1;
 
%Drag coefficient assumed(unitless)
c_d = 0.8;
 
%density assumed(kg/m^3)
rho = 1.2;
 
%velocity assumed(m/s)
v=1:50;
 
%Formula for finding drag force
dragforce = 0.5*A*v.^2*rho*c_d;
 
%plotting the graph
plot(v,dragforce);
xlabel('velocity');
ylabel('Dragforce');
title('graph of velocity v/s Dragforce');
grid on;

CODE EXPLAINATION:

Initially all the parameters like area(A),density(rho) and Drag-coefficient(c_d) are assumed with some values .Velocity is varied from 1m/s-50m/s and drag force is obtained by substituting the values in the formula.

OUTPUT PLOT OF CASE-1:

CONCLUSION:

From the above graph we can conclude that as the velocity increases , drag-force increases quadratically . It means that if velocity increases by a factor of 2 then drag-force increases by a factor of 4.

CASE 2: Here we write a program to plot Drag-coefficient v/s Drag-force.

MATLAB CODE:

%A program to calculate drag force by varying Dragco-efficient
%And plotting the graph of Dragco-efficient v/s Drag force
clear all
close all
clc
 
%inputs
%Frontal area assumed(m^2)
A = 0.1;
 
%density assumed(kg/m^3)
rho = 1.2;
 
%velocity assumed(m/s)
v=10;
 
%drag co-efficient for different shapes
%these values have been found out from google
%c_d=(airfoil,bullet,sphere,prism,flatplate)
c_d = [0.045,0.295,0.7,1.14,1.28];
 
%Formula for finding drag force
dragforce = 0.5*A*v^2*c_d.*rho;
 
%plotting the graph
plot(c_d,dragforce,'marker','*','color','red');
xlabel('Drag co-efficient');
ylabel('Dragforce');
title('graph of Drag co-efficient v/s Dragforce');
grid on;

CODE EXPLAINATION:

Initially all the parameters like area(A),density(rho) ,velocity(v) are assumed with some values. Drag co-efficient of different shapes like (airfoil, bullet, sphere, prism, flatpate) is found from google. At last drag force is obtain by applying its formula for different values of drag co-efficient.

OUTPUT PLOT OF CASE-2:

CONCLUSION:

From the above graph we can conclude that as the drag co-efficient increases the drag force also increases linearly.