Flow over Bicycle.

AIM – Write a MATLAB program to calculate drag force against a cyclist.

Governing Equations –

`F= 1/2 ρAv^2 C_d`

`F` = Drag Force in `N`

`rho` = Density of air in `(kg)/m^3`

`A`= Frontal Area of the bicycle in `m^2`

`v` = Velocity of bicycle in `m/s`

`C_d` = Drag co-efficient which is dimensionless quantity

Objectives-

1. To calculate the drag force with respect to different velocities and then plotting their graph.
2. To calculate the drag force with respect to different drag co-efficient and then plotting their graph.

Theory -

1. Drag Force- 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. S.I. unit = Newton (`N`)

2. Density (`rho`)- The density, of a substance is its mass per unit volume. S.I. unit = Kilograms per cubic metre (`(kg)/m^3`)

3. Frontal area- Imagine that you are exactly in front of a cyclist on his bicycle in front of a white wall, the projected frontal area represents the whole visible area of this cyclist on his bicycle. S.I unit = meter square (`m^2`)

4. Velocity- The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. S.I. unit = meter per second (`m/s`)

5. Drag coefficient- The 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.

Procedure-

Inputs

Code File:

1. Calculating the drag force w.r.t. different velocities and plotting their graph -

%Flow over Bicycle

clear all
close all
clc

%1)calculating drag force w.r.t. different velocities and plotting their graph

%Inputs
%drag coefficient
C_d = 0.88;
%density in kg/m^3
rho = 1.8;
%Frontal area of bicycle in m^2
A = 0.370;
%velocity in meter per second(m/s)
v = [1:50];

%drag force in Newton(N)
drag_force = rho*v.^2*A*C_d*0.5;

%plotting
figure(1)
plot(v,drag_force)
title('Drag force variation w.r.t. velocity')
xlabel('Velocity')
ylabel('Drag force')
grid on

2) Calculating drag force w.r.t. different drag coefficient and plotting their graph -

%Flow over Bicycle

clear all
close all
clc


%2)calculating drag force w.r.t. differenr drag co-efficient and plotting
%their graph

%Inputs
%drag coefficient
C_d = [0:0.1:2];
%density in kg/m^3
rho = 1.8;
%Frontal area of bicycle in m^2
A = 0.370;
%velocity in meter per second(m/s)
v = 30;

%drag force in Newton(N)
drag_force = rho*v.^2*A*C_d*0.5;

%plotting
figure(2)
plot(C_d,drag_force)
title('Drag force variation w.r.t. drag co-efficient')
xlabel('Drag coefficient')
ylabel('Drag force')
grid on

Results -

Outputs

Result 1 - Graph 1 (Drag force vs velocity)

Result 2 - Graph 2 (Drag force vs drag coefficient)

Conclusion -

1. From Result 1(graph 1) we can see that `Fproptov^2`. Therefore, it follows parabolic path.

2. From Result 2(graph 2) we can see that `F propto C_d`. Therefore, it follows straight line.

3. Drag force (`F`) is directly proportional to frontal Area. Therefore more the area more the drag force. So,the cyclist adjust their body position while racing to face minimal drag force.

4. Drag force (`F`) is directly proportion to density(`rho`). Therefore denser the medium more will be the drag force.