MATLAB program for Drag force against Cyclist ( Calculation and Graphical Demonstration )

AIM

MATLAB program to calculate Drag Force on the cyclist and demonstrate graphically its variation with respect to cyclist speed and drag coefficient.

GOVERNING EQUATION

Consider a cyclist running cycle at normal atmospheric temperature and pressure condition will face a force against its motion due to air which is known to be drag force which is arises due to "NO SLIP PHENOMENON" of air particles over its body lead to Viscous Force between fluid layers and give birth to Drag.

This Drag is proportional to square of Velocity of cyclist, Density of air, Frontal Area and Drag Coefficient.

Drag Coefficient is dimensionless and depends on different shape and is determined empirically.

The relation is as follow:

`F_d=1/2*ρ*A*V^2*C_d`

where,

F_d = Drag Force (N).

rho = Density of air (kg/m³ ).

A = Frontal Area(m² ) that is the area of cyclist facing the wind.

V = Velocity of Cyclist(m/s).

C_d = Drag Coefficient(dimensionless).

OBJECTIVE

To write a program to plot Velocity vs Drag Force.

To write a program to plot Drag Coefficient vs Drag Force.

BODY OF CONTENT

Coefficient of Drag generally vary from 0.05 to 1.28 with different shapes.

(Reference: https://www.grc.nasa.gov/WWW/K-12/airplane/shaped.html)

Velocity of Cyclist generally varies from 1m/s to 13 m/s.

Now the MATLAB program.

% A MATLAB program to calculate and demonstrate graphically DRAG FORCE
% against cyclist with respect to variable velocity and drag coefficient

clear all %clear workspace
close all %close all plots
clc       %clean command window

%Formula used (Drag = 0.5*rho*frontal area*velocity*drag coefficient)

%Inputs

%density of air in kg/m^3
rho = 1.28;

%frontal area in m^2
A = 0.1;

%drag coefficient (dimensionless) ( it depends on shape)
c_d = [0.05:0.05:1.30]; %usually it varies from 0.05 to 1.28

%velocity of cyclist in m/s
v = linspace(1,13,26); %usually cyclist range is 1 to 13 mps

%drag force in Newton
D = 0.5*rho*A.*c_d.*v.^2 %drag force values are obtained in array of size 1X26

%ploting velocity and drag coeff vs drag
figure(1) %open a figure

hold on   %plot all graph on that figure only

plot(v,D,'linewidth',4,'color','r') %plot velocity vs drag in red color with 4mm linewidth

plot(c_d,D,'linewidth',3,'color','b') %plot drag coeff vs drag in blue color with 3mm linewidth

xlabel('Velocity and Coefficient') %name x-axis as velocity and coefficient

ylabel('Drag') %name y-axis as Drag

grid on  %switch on the grid on graph

legend('velocity','drag coefficient') %signifies which graph represents what

RESULT

The above graph signifies that Drag increases parabollicaly with velocity and almost linearly with Coefficient of Drag.

CONCLUSION

• Since the Drag is not Desirable but also it cannot be eliminated fully but the effect can be reduced by decreasing Frontal Area and engaging shapes for which Drag Coefficient is Small.
• In the above Problem we have taken Frontal Area as constant but it changes with cyclist different position.
• This can be taken into account by considering Frontal Area as a variable also that is taking different values for that.