Studying Drag Force acting on a Cyclist

Drag Force acting over a Cyclist

1.AIM:

• To calculate drag force acting on a cyclist driving the cycle using MATLAB.

2.GOVERNING EQUATIONS IF ANY:

`Drag(F)= 1/2 ρAV^2 C_d`

Where, ρ= density of the fluid in which cycle and cyclists exist (`(kg)/m^3`)

A= Frontal area / front area of exposure of cyclist (`m2`)

V = velocity of the cyclist respective to the fluid (`m/s`)

`C_d`= Drag coefficient (unitless)

Pressure = and thus, Drag Force = Pressure x Area x (some constant,`C_d` )

So, we get Drag Force (F) = `1/2 ρV^2 AC_d`

3.OBJECTIVES OF THE PROJECT:

• To find the total drag force acting on cyclist and cycle travelling with some velocity through a fluid medium.
• Write a MATLAB program to calculate drag force against a cyclist.
• Write a program to plot Velocity vs Drag force.
• Write a program to plot Drag Co-efficient vs Drag force.

4.FLOW OF THE PROJECT

1. Assign values to the input variables.
2. Get the value of drag force using the formula.
3. Plot the graphs mentioned in the objectives.

5.MATLAB CODE

clear all
close all
clc
%inputs

%drag coefficients for different shapes taken from:
%https://in.pinterest.com/pin/203576845632985496/
c_d = [0.04,0.09,0.42,0.47,0.82,1.15];

%assumed frontal area m^2
a = 0.1;

%assumed density of air kg/m^3
rho = 1.22;

%velocity variety
v=[1:50];

%Plotting velocity vs dragforce graph for every drag coefficient value:
%since dragforce directly proportional to velocity square, so we can safely
%assume that drag coefficient is constant for every curve on the graph
figure(1)
for i=1:length(c_d)
    dragforce = rho*a*v.*v.*c_d(i).*0.5;
    plot(v,dragforce,'color',rand(1,3))
    axis([0 50 0 140])
    xlabel('Velocity');
    ylabel('Drag Force');
    grid on
    hold on
end

%plotting coefficient vs dragforce for every velocity value:
%since coefficient directly proportional to dragforce square, so we can safely
%assume that velocity is constant for every line on the graph
figure(2)
for j=1:length(v)
    dragforce = rho*a*v(j)*v(j)*c_d.*0.5;
    plot(c_d,dragforce)
    axis([0 0.9 0 140])
    xlabel('Drag Coefficient');
    ylabel('Drag Force');
    grid on
    hold on
end

6.OBSERVATION

Figure 1: Velocity vs Drag Force

Figure 2: Drag Coefficient vs Drag Force

7.CONCLUSION:

• From figure 1, we can say that as velocity increases, drag force also increases. The plot verifies the quadratic nature of the direct proportion of drag force with velocity.
• From figure 2, we can say that as drag coefficient increases, drag force also increases. The plot verifies the linear nature of direct proportion of drag coefficient with drag force.