FLow over a Bicycle

clear all
close all
clc

% Calculating Drag Force experienced by a Cyclist (in Upright position)

% Inputs

% Density of Air (kg/m^3)  
rho = 1.2 ;

% Frontal Area (m^2)
A = 0.51 ;

% Velocity of cyclist (m/s^2)
v = linspace(0,10,10)

% Drag coefficient (in Upright Position)
c_d = 1.1;   

% Drag Force on a cyclist can be calculated using the below formulae : 

F_d = 0.5*rho*A*v.^2*c_d ;


plot(v,F_d)
xlabel('Velocity,v')
ylabel('Drag force,F_d')

Plot :

Explaination :

• Fomulae for calculating drag force is given by : F_d= 0.5*rho*A*v^2

Here, F_d=Drag Force experienced by the cyclist

rho = Density of fluid (here air at STP/NTP)

A = Frontal area in contact with the fluid (i.e., cyclist + bicycle)

v = Velocity of the cyclist

c_d = Drag coefficient

• Above parameters for calculating drag force will be inputed by us for calculating drag on the cyclist.
• Defining all the parameters in MATLAB as shown in code attached.
• I'm calculating the drag force when the cyclist is in upright position in which he has Drag coefficient=1.1.
• Actually, for the same frontal area value ,the variation of drag is observed with different shapes of the area.
• Defining,velocity of the cyclist with help of linspace command for plotting purpose with 10 values of velocity between 0 and 10.
• Ultimately,plot the graph of Drag Force (F_d) v/s Velocity (v) using plot command.
• And,labelling it using xlabel and ylabel command with the respective names and symbols.
• So,we're getting a parabolic variation of Drag with velocity and the velocity is eventually the most dominant parameter while calculating drag due to its square variation.

Therefore,while designing Supersonic jets and other spacecrafts ,the size of the jets are kept small in order to get small frontal area (A) & coefficient of drag (c_d) to reduce the value of F_d low as possible.

Code 2 :

clear all
close all
clc

% Calculating Drag Force and plotting Drag Force v/s Drag coefficient

% The formulae for calculating Drag Force is given by :
% Drag = 0.5 * Density of Air * Frontal Area * Velocity^2 * Drag coefficient

% Inputs

% Density of air (rho,kg/m^3)
rho = 1.2

% Frontal Area (A,m^2)
A = 0.51

% Velocity of Cyclist (v,m/s^2)
v = 1.2 

% Drag Coefficient (c_d)
c_d = [ 0.12 0.5 0.9 1.1 ]

% Calculating Drag force (Drag) using above parameters : 

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

% Plotting 
plot(c_d,F_d)
xlabel('Drag Coefficient,c_d')
ylabel('Drag Force,F_d')
grid on 

Plot :

Explantion :

• The above code calculates and plots the linear variation of the Drag Force (F_d) with Drag Coefficient (c_d) using the same formulae as above for different values of the drag coefficient.
• Here,an array of 4 values of the drag coefficient is created and a plot is generated which also includes all the values of the c_d including the defined values between 0.12 and 1.1.
• The values and c_d is calculated experimentally and is taken from the internet for assignment purpose.