Calculation of drag force against a bicyclist

Objective- Write a MatLab program to calculate drag force against a cyclist

Software Used- MATLAB

Drag force

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

solution 1- Now we would plot the variation of drag force and velocity-

let us take a velocity range from 1m/sec to 50 m/sec

so now we take a vector of velocity while writing code (v=[1:50])

we take area(A), C_d as constant to plot the variation.

Density is constant as we considered the fluid is air so (rho=1.2)

Program-

%Program for calculating drag force
%matlab program to calculate flow over bycycle
clear all
close all
clc
%input
%drag coefficient
C_d=.9
%area m^2
A=0.2
%density kg/m^3
rho=(1.2) 
%velocity m/sec
V=[1:50]
%formula of drag force
drag_force=rho*A*V.^2*C_d*0.5
plot(V,drag_force)
xlabel('Velocity')
ylabel("drag_force")
grid on 

Output-

the Graph between Drag force (Y-axis) and Velocity (X-axis)

As we know the formula the drag force changes quadratically with the velocity which is also portrayed in the output graph

Situation 2-

As we know that when the rider changes position of the bode, there will be a change in the shape of the frontal area. So for the same frontal area but different shapes there will be a different drag force coefficient.

That's why during the cycling the bicyclist keeps changing their body position and wear thinner clothes so that they make sour that the frontal area is minimal to experience less drag force and can finish the race quickly.

for the various position, the coefficient of drag varies. let us take the common value of C_d.

So now plot the variation of drag force with the variation of drag coefficient keeping other constant.

Program-

%matlab program to calculate flow over bycycle
clear all
close all
clc
%input
%drag coefficient (changes with position of bicyclist)
C_d=[.5,.9,1.3]
%area m^2 (Frontal area)
A=0.2
%density kg/m^3
rho=(1.2) 
%velocity m/sec
V=50;
%formula of drag force
drag_force=rho*A*V.^2*C_d*0.5
plot(C_d,drag_force)
xlabel('C_d')
ylabel("Drag Force")
grid on

Output-

The graph between drag force (Y-axis) and C_d (X-axis)

So the drag force is calculated using MatLab and the observations made are-

1. Drag force varies quadratically with the velocity.

2. Drag force varies linearly with the drag coefficient.

In this way, the drag force can be calculated against any moving object in a specific fluid or air whose density is known.