Calculation of Drag force on flow over a bicycles and obtaining different plots using Matlab

Aim- Calculation of Drag force on flow over a bicycles and obtaining different plots using Matlab

Description - A drag force is a resistance caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is relative velocity between the body & the fluid. The drag Force F is exerted on a body travelling through a fluid is given by

F=0.5×ρ×A×Cd×V2">F=0.5×ρ×A×Cd×V2F=0.5×ρ×A×Cd×V2

where,

rho = density of fluid through which body is moving

A = Frontal Area

Cd = Drag Coefficient

V = Speed of body relative to the fluid

Coefficient of Drag is a dimensionless number that relates an object's drag force to its ares and speed, it ranges upwards from 0. An object with a drag coefficient of 0 could not exist on earth, while teardrops or wing shapes have some of very lowest drag coefficients. As different values of Drag coefficient is listed below-

Wing = 0.005

Ball = 0.5

Person stood upright = 1.0

Flat Plate face-on to airflow = 1.17

Brick = 2.0

Cyclist(Tops) = 1.05

Cyclist(Hoods) = 1.0

Cyclist(drops) = 0.88

Cyclist(Aero bars) = 0.70

A riders aerodynamic drag is a critical factor in the speed he can achieve at a given level of power output and therefore a given level of fitness.

Frontal Area is typically measured in metres squared. A typical cyclist presents a frontal area of 0.1 to 0.6 m^2 depending on position.

Velocity has been taken in a range of 0-25 m^2.

THE PROGRAM FOR THE CALCULATION OF THE DRAG FORCE AND VARIOUS PLOTS IS GIVEN BELOW WITH THE PLOT RESULTS

* In the code attached below, two separate functions have been used both of the graphs. As for plotting Drag force vs Velocity, the velocity is to be an array as we have to plot drag force for different values of velocity(indicated by v) and for its calculation we used drag_force1 and similarly for plotting Drag force vs drag coefficient, the drag coefficient is to be an array as we have to plot drag force for different values of drag coefficient and with assuming contsant velocity V=15m^2 (indicated by V) and for its calculation we used drag_force2.

* Subplot Function has been used to accomodate both the functions in the same graph alongwith their titles.

% Program to calculate drag force
clear all
close all
clc

%Inputs%
%Drag coefficient%
c_d = [0:30];

%Area m^2%
A = 0.2;

%Density kg/m^3%
rho = 1.1;

%Velocity m/s^2%
v = [0:30];
V = 15;

Drag_force1 = 0.5*rho*A*v.^2.*c_d;
Drag_force2 = 0.5*rho*A*V^2.*c_d;

%Plotting%

subplot(2,1,1);
plot(Drag_force1,v)
xlabel('Drag Force')
ylabel('Velocity')
title('Drag Force vs Velocity')
grid on

subplot(2,1,2);
plot(Drag_force2,c_d)
xlabel('Drag Force')
ylabel('Drag Coefficient')
title('Drag Coefficient vs Drag Force')
grid on

Results- The following plots are obtained and different values of cd can be obtaines from the graph.