Flow over Bicycle

Aim - Write a Matlab program to calculate drag force against a cyclist.

Governing equations -

F=`1/2*ρ*A*v^2*Cd`

where F = Drag force in N

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

A = Frontal Area of the bicycle in `m^3`

v = velocity of bicycle `m/s`

Cd=">Cd= Drag co-efficient (Dimensionless)

Objectives -

• Write a program to plot Velocity vs Drag force.
• Write a program to plot Drag Co-efficient vs Drag force.

Procedure -

Theory -

Some terms that we have to know-

1. Drag force - Force acting opp. to the relative moyion of any object moving with respect to a surrounding fluid. its unit is in 'N' .

2. Density - Mass per unit volume is known as the density of the substance . it is denoted by `rho` and its unit is `(kg)/m^3`

3.Frontal area - It physically represented the area as projected right along the velocity vector. Unit is '`m^2`

4.Velocity - the rate of change of its position w.r.t frame of reference and is a function of time . Unit is `m/s`

5. Drag co-efficient - the drag co-efficient is used to quantify the drag or resistance of an object in a fluid encironment such as air , water etc.

Inputs -

MATLAB programe for plotting the drag force w.r.t different velocities is shown below-

clear all
close all
clc
% velocity m s^-1
v = [1:400];
% drag coefficient 
c_d=  .8 
% frontal area m^2
A = .1;
% density kg m^3
rho = 1.2; 
drag_force = rho*A*v.^2*0.5*c_d 
plot(v,drag_force)

xlabel('velocity')
ylabel('drag_force')
grid on

MATLAB programe for plotting the drag force w.r.t different drag cofficient is shown below -

clear all
close all
clc
% velocity m s^-1
v = 2;
% drag coefficient 
% for thin disk c_d=1.1
% for sphere c_d=0.5
% for bird c_d=.4
% for human c_d=.8
c_d=[1.1  0.5  .4  .8]
% frontal area m^2
A = .1;
% density kg m^3
rho = 1.2; 
drag_force = rho*A*v.^2*0.5.*c_d 
plot(c_d,drag_force)

xlabel('drag coefficient')
ylabel('drag_force')
grid on

Results-

Result 1 - graph 1 (Drag force vs velocity)

Result 2 - graph 2 (Drag force vs drag force co-efficient)

Conclusion-

1. From graph 1 we can say that drag force is directly proportional to the square of velocity as it follows parabolic path.

2.from graph 2 ,we can say that drag force is directly proportional to the drag co-efficient as it follows straight line

3.As drag force is directly proportional to density and frontal area ,so we can say that greater the density of the fluid greater is the force and vice versa and more the area more is the drag force .thats why during bicycling,cyclist has to make that posture so that their frontal area becomes small as possible .thus drag force has been reduced to minnimum .