Drag force calculation over bicycle using matlab - skill lync

• AIM

To calculate the drag force against a cyclist and to plot drag force vs velocity and drag force vs drag coefficient

• Objective:

To Study and Calculate the drag force and to find out the relationship between Drag Force VS Velocity of the Bicycle and Drag Force VS Coefficient of Drag -- for various positions during cycling.

• Theory :

Drag is the resistive force against motion of object in fluid it is a mechanical force developed due to solid and fluid interaction. Drag is generated by the difference in velocity between the solid object and the fluid. if there is no difference there will be no drag .in our case cyclist is moving in and th resistance which oppose the motion is basically drag.

now from above figure we can see that how drag is acting and the frontal area will continuously will change as cyclist will move crank so here most important parameter is drag coefficient which will affect the drag force . drag coefficient values will depend upon various geometrical shapes , velocity, frontal area,etc.

• Case1:

Initially we take input from user of Drag coefficients, Area and velocity. We consider drag coefficient is 0.8 , density of air 1.2 kg/m^3 and area is 0.1 m^2 also drag force is calculated with different values of velocity stored in the array to understand the variation of velocity with drag force in Matlab. then we can calculate drag coefficient from the drag force equation which is ,

Drag force f= 12pV2A2Cd">f= 12pV2A2Cdf= 12pV2A2Cd

Where ,

p= density of air in kg/m3

A= Frontal area of bicycle in m2

v= velocity of bicycle in m/S

f= drag force

Cd= drag coefficent

With the help of given data we can plot a graph of drag force wrt velocity And lebel it by considering velocity is on xlabel and drag force on ylable ,

% A program to calculate the drag force on a bicycle 
clear all
close all
clc
% Inputs
% Drag coefficient 
c_d = 0.8
%Area (unit m^2)
A = 0.1
%Density (unit m^3)
rho = 1.2
%Velocity (unit m/s )
v = [1:50];
%calculation of drag force
drag_force = 0.5*rho*c_d*v.^2*A;
%graph of velocity  and Drag force 
plot(v, drag_force,'color','b')
xlabel('velocity')
ylabel('Drag force')
grid on

• Case2:

To draw the graph between drag coefficient and drag force here we will take some different values of drag coefficient in array form by considering its shapes which is bullet,airfoil,prism,sphere,flatplate.Then will can calculate drag coefficient from drag force equation

%Program to calculate the drag force
clear all 
close all
clc
%inputs
%Drag coefficient ( unitless)
%drag coefficient values for various object 

% according to there shapes  bullet, airfoil, prism,sphere, flatplate
c_d = [ 0.295,1.14, 0.045, 0.07, 1.28 ]; 
%velocity (unit m/s)
v = 4
%Density ( unit kg/m^3)
rho = 0.8
%Area ( unit m)
A = 0.4
%Calculation of drag force 
drag_force = 0.5*rho*c_d*v.^2*A;
%graph of coefficient  of drag vs Drag force
plot(c_d,drag_force,'color','b' )
xlabel ('drag coefficient')
ylabel ( 'drag_force')
grid on

• output plot/results

plot on drag force vs velocity

plot on drag force vs drag coefficient

• conclusion : from the plot of velocity vs drag force it is clear that, drag force increase rapidly when velocity increase .

From Drag coefficient and drag force plot it can be concluded that drag force and drag coefficient varies linearly and with increase in value of drag coeffiecient, drag force increases.