Drag Force calculation for different position of cyclist using MATLAB

AIM: Calculate the drag force for different position of cyclist with varying velocity.

THEORY :

1. Calculating Drag Force

In order to better understand the aerodynamics of cycling, it is important to first understand how air resistance is calculated. Below is the drag equation that represents the drag force, , experienced by a cyclist’s body due to the movement through the air. The first element of the equation is the density of the air, , which decreases with altitude, thus one way to experience less drag is to move from the sea level to the mountains.

The second factor is , the projected frontal area of the cyclist on a bike. In general, the smaller the frontal area, the smaller the drag—thus in order to minimize air resistance, the cyclists have to make themselves as small as possible on the bike. The next component—the drag coefficient —depends on a number of factors including speed and surface roughness, and it has to be measured directly. Finally, , the cyclist’s velocity relative to the air around them plays a role. The velocity is squared, which means the cyclist that goes twice as fast experiences four times the drag.

`F_D =1/2*rho*A*V^2*C_D`

where `rho = 1.225`kg/m^3 Air density

V = velocity 10.28 m/sec average cyclist speed

2 Different position of cyclist:

There are mainly three position.The first is an upright position with the hands on top of the handlebars. Here most of the cyclist’s torso is presented to the wind, so it is not expected to be a very aerodynamic position.

The second position puts the rider’s hands lower on the handlebars in what cyclists call the “drops”—it leans the rider further forward and is a typical racing position both on flat terrain and on the descent.

The third position has the rider crouched even lower, on the bike’s top tube—it’s extremely hard to pedal in this position so it’s only used when riding downhill.

3 Value of Drag coefficient for the various position of cyclist:

1. Upright position `C_D` = 1.00
2. Drop position `C_D` = 0.88
3. top tube position `C_D`=0.70

MATLAB Code:

% Write a program to plot Drag Co-efficient vs Drag force.
clear all
close all
clc

%input
%density of air kg/m^3
d=1.225;

%frontal area 0.3 to 0.6 m^2 depending on position we take average
a=0.45;

%Drag co-efficient for different position like tops*,hoods* and Drops*
c_d=[1 0.88 0.70];
%*Source = "Bicycling Science" (Wilson, 2004). It is unlikely these values included helmets.
%velocity* in m/sec 
v=1:50;

for i=1:3
%Drag force in N
d_f= d*a*v.*v.*c_d(i)*0.5;

plot(v,d_f,'marker','*')
hold on
xlabel('Velocity')
ylabel('Drag force')
end
title('Velocity vs Drag Force')
grid on

CODE EXPLAINATION AND RESULT:

Here in code, area and air density is assumed as constant and we make an array of drag coefficient and velocity as shown in the figure. I use for loop to get different value of drag force at a different velocity so I can able to plot graph. here graph is parabolic since drag force is proposonal to velocity^2.

As A result, we get below graph:

Here different colour shows a different position of the cyclist.

however, a rider’s position can give the cyclist an aerodynamic advantage without violating the rules. Also, we can use this result to design such a cycle.