MATLAB PROGRAM FOR CALCULATING A DRAG FORCE AGAINST A CYCLIST

AIM:-

• Study the effect of varying velocity & drag co-efficient on drag force from plots generated by MATLAB program.

INTRODUCTION:-

• Drag force:-

When a body (Cyclist) moves with the particular velocity in the fluid (here air), it experience a resisting force, these resisting force is known as drag force, Drag force is generated due to difference in velocity between cyclist and air.

Drag force is act opposite to the direction to the flow velocity.

• Drag Co-efficient:-

It is used to calculate drag or resistance of an object in a fluid (here Air). A lower drag co-efficient indicates the object will have less aerodynamic or hydrodynamic drag.

It is always associated with a particular surface area.

Drag Co-efficient value is changes for different shape of same frontal area.

GOVERNING EQUATION:-

Drag force = 0.5 * ρ * A * v² * c_d

Where,

• ρ = Density of air through which bicycle is moving ( Kg/m³)
• A = Frontal area of bicyclist perpendicular to the flow direction (m²)
• v = Velocity of body relative to air (m/s)
• c_d = Co-efficient of drag ( dimensionless quantity)
• Drag force (Kg*m/s)

OBJECTIVE:-

• Program to calculate drag force against a cyclist.
• Program to plot velocity Vs drag force.
• Program to plot drag co-efficient Vs drag force.
• By above plot we can derive that what changes will occur in the value of drag force while changing the velocity and co-efficient of drag.

PROGRAM:-

• Program for calculating the drag force:-

% A program for calculating the drag force on a bicycle for different velocity and drag co-efficient.

clear all
close all
clc

% inputs for calculating drag force 

% drag co efficient( dimension less)
c_d = [ 0.02: 0.02 : 1 ]

% density of air ( Kg/m^3)
rho = 1.2

% Frontal area of bicyclist ( m^2)
A = 0.1

% velocity of cyclist relative to fluid ( m/s)
v = [ 1 : 1: 50 ]
V = 10

% Governing equation of drag force
drag_force = 0.5*rho*A*c_d.*v.^2
drag_force1 = 0.5*rho*A*c_d.*V.^2

% plot 'velocity vs drag_force)
% figure command used for specifying one perticular plot.
figure(1)                                     
plot(v,drag_force,'color','g')             
xlabel('velocity')
ylabel('drag force')
title('velocity Vs drag force')
grid on 


% plot 'drag_co_efficient vs drag_force)
% figure command used for specifying one perticular plot.
figure(2)
plot(c_d,drag_force1,'color','g')
xlabel('drag co-efficient')
ylabel('drag force')
title('drag co-efficient Vs drag force')
grid on

First of all we have to give all the input values for calculation

So,

1. drag co-efficient= c_d = [0.02 : 0.02 : 1]

From above command we will get the 50 value of drag force starting from 0.02 to 1 with the interval of 0.02.

2. Density of air ( Kg/m³) = ρ = 1.2

3. Frontal area of cyclist (m²)= A = 0.1

4. Velocity of cyclist (m/s) = v = [ 1 : 1 : 50 ]

From above command we will get the 50 values of velocity starting from 1 m/s to 50 m/s with the interval of 1 m/s.

5. Command for calculation => drag_force = 0.5*rho*A*c_d.*v.^2

From above command all the 50 values of drag force will be calculated.

• Program for plotting velocity Vs Drag force:-

figure(1)

plot(v,drag_force,'color','g')

From these command we can generate plot between velocity and drag force. In which first two term are the terms between we have to generate plot, than 'color','g' term is for giving a color green.

xlabel('velocity')

ylabel('drag force')

These two commands use to give name of x-axis & y-axis in the graph. In which xlabel('velocity') , first is axis and in bracket is the name of that axis which you want to give.

title('velocity Vs drag force')

These command use to give title of the plot.

grid on

These command is use to on the grid in the graph.

• Program for plotting the drag co efficient Vs drag force

figure(2)

plot(c_d,drag_force1,'color','g')

From these command we can generate plot between velocity and drag force. In which first two term are the terms between we have to generate plot, than 'color','g' term is for giving a color green.

xlabel('drag co-efficient')

ylabel('drag force')

These two commands use to give name of x-axis & y-axis in the graph. In which xlabel('drag co-efficient') , first is axis and in bracket is the name of that axis which you want to give.

title('drag co-efficient Vs drag force')

These command is use to give title of the plot.

grid on

These command is use to on the grid in the graph.

CONCLUSION:-

• We know drag force is proportional to square of velocity, from graph we can see by increasing velocity drag force is increasing vastly.
• Drag force and drag co-efficient have linear relationship, drag force is considerably increasing with increasing drag co-efficient.
• With increase in the drag force, resistance to motion of cyclist will increase so one have to put some extra effort for same distance travelling, that’s why to reduce that extra effort in races cyclists are changes their upper body position to reduce drag co-efficient, indirectly drag force.