## Matlab Program To Calculate Drag Force Against A Cyclist In Different Positions

Aim :

Calculate the Drag Force of a cyclist in different positions by varying Velocity.

Objective :

• Plot Velocity (vs) Drag Force using codes in matlab.
• Plot Drag Co-efficient (vs) Drag Force  using codes in matlab

Theory :

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. This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity.

Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag_equation:

F_D = 1/2 rho v^2 C_D A

where ,

is the drag force,
is the density of the fluid
v     is the speed of the object relative to the fluid,
is the cross sectional area or said frontal area
is the drag coefficient (a dimensionless number).

Required inputs

• the following drag coefficient values of the cyclist in different positions

1. AEROBARS

2. DROPS :

3. HOODS :

4. TOPS :

5. STANDING :

• value of the frontal area 'A' is taken as A= 0.4 in m^2

• value of the density is taken as rho = 1.2 in kg/m^3

• value of the velocity is taken as v = 1 : 10 in m/s  ( here we are using range operator for the variation of values in  'v' )

Matlab code

• for the first pogram to show the plot of velocity (vs) drag force

% a program to calculate drag force of different shapes
close all
clear all
clc
% inputs
% drag coefficient of shapes
% drag coefficinet for different shapes of cyclist like
% aerobars,drops,hoods,tops and standing
c_d =[0.37 0.40 0.42 0.45 0.5];
% frontal area in m^2
A = 0.4
% density in kg/m^3
rho = 1.2
% velocity in m/s
v = [ 1 : 10 ] ;
for i=1:5
%drag force in N
drag_force = rho*A*v.^2*c_d(i)*0.5;
% plotting
plot ( v , drag_force )
xlabel ('velocity')
ylabel ('drag force')
axis ( [ -1 10 -1 10] )
grid on
hold on
end

• for the second pogram tos how the plot of drag co-efficient (vs) drag force
% a program to calculate drag force of different shapes
close all
clear all
clc
% inputs
% drag coefficient of shapes
% drag coefficinet for different shapes of cyclist like
% aerobars,drops,hoods,tops and standing
c_d =[0.37 0.40 0.42 0.45 0.5];
% frontal area in m^2
A = 0.4
% density in kg/m^3
rho = 1.2
% velocity in m/s
v = [ 1 : 10 ] ;
for i=1:10
%drag force in N
drag_force = rho*A*v(i)^2*c_d.*0.5;
% plotting
hold on
plot ( c_d , drag_force )
xlabel ('drag co-efficient')
ylabel ('drag force')
grid on
end

Result and Explaination

here in the pogram (1) we have taken the velocity 'v' as the dot product vector and drag co-efficient as the array 'c_d' . the value of the following shows in the fig (1) given below ,that shows the plot of velocity (vs) drag force .

here in second pogram we have taken the velocity 'v' as the array and the 'c_d' drag co-efficient as the dot product. the values of the following shows in fig (2) given below, which shows plot of drag co-efficient (vs) drag force .

Reference :

the values and the different shapes of the cyclist taken from the link

https://ridefar.info/bike/cycling-speed/air-resistance-cyclist/

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