ANALYSIS OF FLOW OVER A BICYCLE

OBJECTIVE: To analyse the flow of fluid(Air) over a bicycle in Matlab by plotting:

• Velocity vs Drag force.
• Drag Co-efficient vs Drag force.

THEORY: In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is:

is the drag force, which is by definition the force component in the direction of the flow velocity,

is the mass density of the fluid,[1]

is the flow velocity relative to the object,

is the reference area, and

is the drag coefficient – a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag. In general, depends on the Reynolds number

CODE FOR VELOCITY vs DRAG FORCE:

% A program to plot the velocity vs drag force over a bicycle
clear all
close all
clc

% Inputs

% A is frontal area in m^2
A = 0.1;
% Density kg/m^3
rho = 1.225;
%c_d is coefficient of drag
c_d = linspace(0.10,1.8,20);
%Velocity m/sec^2
v = linspace(1,7,20);
% F is drag_force in N
F = rho*A*v.^2.*c_d*0.5;

%Plotting Velocity vs Drag force
xlabel('Velocity (m/sec)')
ylabel('Drag Force (N)  ')
plot(v,F,'color','b')

CODE FOR DRAG CO-EFFICIENT vs DRAG FORCE:

% A program to plot the Drag Co-efficient vs Drag force over a bicycle
clear all
close all
clc

% Inputs

% A is frontal area in m^2
A = 0.1;
% Density kg/m^3
rho = 1.225;
%c_d is coefficient of drag
c_d = [0.1 0.42 0.50 0.82 1.05];
%Velocity m/sec^2
v = 7;
% F is drag_force in N
F = 0.5*rho*A*v^2.*c_d;

%Plotting Drag Co-efficient vs Drag force
plot(c_d,F,'color','r')
axis([0 1.2 0 3.5])
xlabel('Drag Co-efficient')
ylabel('Drag Force(N)')

RESULT:

Program 1 : VELOCITY vs DRAG FORCE:

In this plot of Velocity of a cyclist vs Drag force is an exponential if Area and Drag Coefficient are kept constant. This graph implies that the Drag Force is directly proportional to the square of velocity of the cyclist.

Program 2 : DRAG CO-EFFICIENT vs DRAG FORCE:

In this plot it can be seen that the graph for Drag coefficient vs Drag Force is linear. That means drag force is directly proportional to the drag coefficient.