FLOW OVER A BICYCLE ANALYSIS USING MATLAB

Aim - To calculate drag force against the cyclist

a. Plot Velocity vs Drag Force

b. Plot Drag Co-efficient vs Drag Force

The factors that are taken into consideration while calculations are -

1. Velocity

2. Drag coefficient

3. Frontal Area

4. Density of air

Drag is the aerodynamic force that opposes an aircraft's motion through the air. Drag is generated by every part of the airplane.

Drag is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field or an electromagnetic field, where one object can affect another object without being in physical contact. For drag to be generated, the solid body must be in contact with the fluid. If there is no fluid, there is no drag. Drag is generated by the difference in the velocity between the solid object and the fluid. There must be motion between the object and the fluid. If there is no motion, there is no drag. It makes no difference whether the object moves through a static fluid or whether the fluid moves past a static solid object.

Drag is a force and is, therefore, a vector quantity having both a magnitude and a direction. Drag acts in a direction that is opposite to the motion of the aircraft. Lift acts perpendicular to the motion. There are many factors that affect the magnitude of the drag. Many of the factors also affect lift but there are some factors that are unique to aircraft drag.

Drag force analysis is mainly done while carrying aerodynamic studies of various vehicles. It plays a very rigidly important role in carrying the proper analysis and increasing the aerodynamics of the vehicles for achieving higher speeds with high stability.

The equation to calculate the drag force is given by -

Drag Force = Drag co-eff * (Density * velocity square)/two * area

`f= d*0.5*rho*v^2*A`

For drag, this variable is called the drag co-efficient designated "d." This allows us to collect all the effects, simple and complex, into a single equation. The drag equation states that drag force F is equal to the drag coefficient d times the density rho times half (0.5) of the velocity V squared times the reference area A.

1. MATLAB/OCTAVE code to Plot Velocity vs Drag Force -

close all
clear all
clc

% MATLAB CODE FOR FLOW OVER BICYCLE ADN PLOT OF VELOCITY VS DRAG FORCE

% Drag coeffiecent
d= 0.5

% Area
A=0.4

% Density of air 
rho=1.225

% velocity
% To plot graph range of values is required, hence : operator can be used
v=[1:30]

% Drag force equation
% Dot product is used for squaring all the value in the array of velocity

f=d*0.5*rho*v.^2*A;

disp (f)

% Graph plot x-axis as velocity and y-axis as Drag force
plot(v,f)

xlabel('velocity')

ylabel('drag force')

grid on

The outut is shown below-

And the graph is -

2. MATLAB/OCTAVE code to Plot Drag Co-efficient vs Drag Force -

close all
clear all
clc

% MATLAB CODE FOR FLOW OVER BICYCLE ADN PLOT OF DRAG CO-EFFICIENT VS DRAG FORCE

% Drag coeffiecent for different shapes 

% LONG CYLINDER 
d1= 0.82

% SPHERE
d2= 0.47

% CONE
d3= 0.50

d = [d1 d2 d3]

% Area
A=0.4

% Density of air 
rho=1.225

% velocity
v= 10

% Drag force equation

f=A*rho*v^2.*d*0.5;

disp (f)

% Graph plot x-axis as drag coeffiecent and y-axis as Drag force
plot(d,f)

xlabel('Drag Co-efficient')

ylabel('drag force')

grid on

The output is shown below-

The graph is -