Matlab program to calculate drag force against a cyclist

AIM: Matlab program to calculate drag force against a cyclist.

The factors involved are Velocity,Drag coefficient,Frontal Area,Density of air.

THEORY

A drag force is the resistance force caused by the the motion of body through a fluid such as water or air. A drag force always acts opposite of the relatives motion of the body with respect to surrounfing velocity of the fluid. this can exist betwwen two fluid fluid layer or between a fluid layer and solid surface. Drag force is expressed as

F_d= (1/2)xC_dxAx rho x v^2

where C_d = drag coefficient

A = Frontal Area

rho = density

v = velocity of the object

Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. Lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag.

Typically, the drag coefficient of a cyclist ranges from approx 0.6 for a streamlined position to >0.8 for an upright position.

Assumption while writing the command

1. Frontal area doesn't change for different values of drag coefficient for different position of the cyclist.

2. Drag coefiicient is constant for different values of velocity.

%  calculate drag force against a cyclist
clear all
close all
clc

%inputs 
% Drag Coefficient
c_d1 = 0.8
c_d2 = linspace(0,1,8)

% Frontal Area (m^2)
A = 0.1
% Density (m^3/s)
rho = 1.2
 %Velocity (m/s)
 v = [0:20]
 V = 15
 
 %Drag Force (N)
 F_d1 = 0.5*rho*c_d1*A*v.^2
 figure(1)
 plot(v,F_d1,'color','blue')
 grid on
 title('velocity vs Drag force')
 xlabel('velocity (m/s)')
 ylabel('Drag force (N)')
 
 F_d2= 0.5*rho*c_d2*A*V.^2
 figure(2)
 plot(c_d2,F_d2,'color','r')
 grid on
 xlabel('Drag coeffiecient')
 ylabel('Drag Force')
 title('Drag Force vs Drag coefficient')

c_d1 =

    0.8000


c_d2 =

         0    0.1429    0.2857    0.4286    0.5714    0.7143    0.8571    1.0000


A =

    0.1000


rho =

    1.2000


v =

  Columns 1 through 17

     0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16

  Columns 18 through 21

    17    18    19    20


V =

    15


F_d1 =

  Columns 1 through 10

         0    0.0480    0.1920    0.4320    0.7680    1.2000    1.7280    2.3520    3.0720    3.8880

  Columns 11 through 20

    4.8000    5.8080    6.9120    8.1120    9.4080   10.8000   12.2880   13.8720   15.5520   17.3280

  Column 21

   19.2000


F_d2 =

         0    1.9286    3.8571    5.7857    7.7143    9.6429   11.5714   13.5000

Plot of Velocity vs Drag force

Plot of Drag Co-efficient vs Drag force.

Result:

From the governing equation and plot, it is concluded that drag force varies parabolically with the change in velocity and linearly with change in drag coefficient keeping frontal area constant.