MATLAB Report on: - Calculate Drag force against a cyclist.

Step 1: understanding Concept

Drag force means the force which can be withstood by the body under fluid flow (air or water). Drag force has a universal formula as given below: -

FD = Drag Force, N

Cd = Co-efficient of drag, no unit

A = Area, m^2

Rho = Density of Fluid, kg/m^3

V = Velocity, m/sec

Step 2: Note Down Given

As per this website http://physicalcycling.com/aerodynamic-coefficients/ we have got co-efficient of drag value is mentioned in the table: -

Cyclist drag co-efficient
Male:	Runner	Cyclist(Tops)	Cyclist(Hoods)	Cyclist(Drops)	Cyclist(Aero)
Cd	1.30	1.15	1.00	0.88	0.83
A	0.76	0.63	0.40	0.32	0.31

Figure(1) – Shows the cyclist position while cycling

• We know that as a cyclist is in the motion it's body moment changes so as its frontal area and which gives rise to change in a coefficient of drag and as the body is not in constant motion so it also varies the velocity of the cyclist. As problem statement states that we have to keep the area constant and only vary the coefficient of drag and velocity of the cyclist. So, we have the given as follows: -

Given: -

Cd = Co-efficient of drag = [0.83, 0.88, 1.0, 1.15, 1.30] , no unit

A = Area = 0.1 m^2

Rho = Density of Fluid = 1.225 kg/m^3

V = Velocity = [1 : 40] m/sec

Step 3: Preparing a suitable code

So, to get the desired solution we wrote the MATLAB code given below: -

close all 
clear all
clc

% Density has been mentioned as 'rho'
rho = 1.225
% frontal Area of cyclist denoted by 'a'
a = 0.1
% Velocity range from 1 to 40 m/sec.^2
v = 1:40;
% Co-efficent of drag 
Cd = 0.32

for i = 1:length(v)
    FD1 = 0.5*(Cd).*a*rho*v.^2
    figure(1)
    plot(v,FD1,'r','linewidth',3)
    hold on
    legend('Change in Drag Force')
    xlabel('velocity')               % xaxis name Velocity
    ylabel('Drag force')             % yaxis name drag force
    title('Variations in velocity in terms of Drag Force') %title of the graph
    grid on
end
  
% Velocity range from 1 to 40 m/sec.^2 
V = 10
% Co-efficent of drag varies as per the different shapes of cyclist
CD = [0.83 0.88 1.0 1.15 1.30];
   for  i = 1:length(CD)
    FD2 = 0.5*(CD).*a*rho*V.^2
    figure(2)
    plot(CD,FD2,'b','linewidth',3)
    hold on
    legend('Change in Drag Force')   
    xlabel('Co-efficent of drag')    % xaxis name Co-efficent of drag
    ylabel('Drag force')             % yaxis name drag force
    title('Variations in Co-efficent of drag in terms of Drag Force') %title of the graph
    grid on
end

Step 4: Results

Figure (2) – The Drag Force Vs. Velocity

• The drag force is directly proportional to the drag coefficient. So we can say that as drag force various the drag coefficient also varies.

Figure (3) – The Drag Force vs. Coefficient of Drag

• The drag force is proportionality constant to the square of velocity. The rate at which drag force is produced on the cyclist is proportional to the square of velocity.

Step 5: Conclusion

• From this, we understood that change velocity affects twice to the drag force which gives us Parabolic curve.
• As the formula itself tells us that drag force is directly proportional to the drag coefficient that's the reason we have got the inclined line in the results at first place.
• We also understood that maintaining the coefficient of drag is an important aspect to reduce the drag force on the cyclist.
• From this experiment got that When a cyclist is moving with varying velocity, we can not expect that we will get zero drag force. There will be a drag force of some amount as per the human body is a concern. so, we can only work on increasing its efficiency by working on cyclist gears like wearing a skinny suit, working on bicycle aerodynamics, etc things to achieve certainly fast speed.