FLOW CHARACTERISTICS OVER A BICYCLE

OBJECTIVE:

The drag force exerted on the bicycle is to be computationally extracted and its effects posed;

ABSTRACT:

A drag force is the resistance force 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 the relative velocity between the body and the fluid. 
 
 The drag force D exerted on a body traveling though a fluid is given by

Where: 
 
 C is the drag coefficient, which can vary along with the speed of the body. But typical values range from 0.4 to 1.0 for different fluids (such as air and water) 
 
 ρ is the density of the fluid through which the body is moving 
 
 v is the speed of the body relative to the fluid 
 
 A is the projected cross-sectional area of the body perpendicular to the flow direction (that is, perpendicular to v).

MATLAB CODE:

% Calculation of drag force for different frontal areas with respect to velocity

clear all
close all
clc

% Input Parameters

% Frontal area(flat surface)m^2
A = 0.76;

% Density of the fluid that the frontal area is resisting (air) kg/m^3
rho = linspace(1.292,1.127,20);

% Velocity at which the cyclist is cycling m/s^2
v = linspace(5,35,20);

% Drag co-effecient of the frontal arrea

% drag co-effecient of a flat surface
Cd1 = 1.280; 

% drag co-effecient of a prism
Cd2 = 1.140;

% drag co-effecient of a bullet
Cd3 = 0.295;

% drag co-effecientof a sphere
Cd4 = 0.070;

% Calculating drag co-effecient

% Calculating drag force for a flat surface
Fd1 = rho*A.*v.^2*Cd1*0.5

% Calculating drag force for a prism surface
Fd2 = rho*A.*v.^2*Cd2*0.5

% Calculating drag force for a bullet surface
Fd3 = rho*A.*v.^2*Cd3*0.5

% Calculating drag force for a sphere surface
Fd4 = rho*A.*v.^2*Cd4*0.5

% Plot of velocity vs drag force
figure(1)
subplot(3,3,1)
plot(v,Fd1)
xlabel('velocity')
ylabel('drag force-flat surface')

subplot(3,3,2)
plot(v,Fd2)
xlabel('velocity')
ylabel('drag force-prism')

subplot(3,3,3)
plot(v,Fd3)
xlabel('velocity')
ylabel('drag force-bullet')

subplot(3,3,4)
plot(v,Fd4)
xlabel('velocity')
ylabel('drag force-sphere')

% plot of Drag co-effecient vs Draf force
figure(2)
subplot(2,2,1)
plot(Fd1,Cd1)
xlabel('drag force')
ylabel('drag co-effecient-flat surface')

subplot(2,2,2)
plot(Fd2,Cd2)
xlabel('drag force')
ylabel('drag co-effecient-prism')

subplot(2,2,3)
plot(Fd3,Cd3)
xlabel('drag force')
ylabel('drag co-effecient-bullet')

subplot(2,2,4)
plot(Fd4,Cd4)
xlabel('drag force')
ylabel('drag co-effecient-sphere')

RESULTS:

Fd1 =

Columns 1 through 16:

15.711 27.017 41.260 58.377 78.305 100.980 126.339 154.319 184.856 217.888 253.352 291.184 331.321 373.699 418.257 464.930

Columns 17 through 20:

513.655 564.369 617.009 671.512

Fd2 =

Columns 1 through 16:

13.992 24.062 36.748 51.992 69.740 89.935 112.520 137.440 164.638 194.057 225.642 259.336 295.083 332.826 372.510 414.078

Columns 17 through 20:

457.474 502.641 549.524 598.065

Fd3 =

Columns 1 through 15:

3.6208 6.2266 9.5093 13.4542 18.0469 23.2727 29.1171 35.5656 42.6036 50.2165 58.3897 67.1088 76.3591 86.1260 96.3951

Columns 16 through 20:

107.1517 118.3813 130.0694 142.2013 154.7625

Fd4 =

Columns 1 through 15:

0.85918 1.47750 2.25643 3.19252 4.28230 5.52233 6.90915 8.43930 10.10933 11.91578 13.85519 15.92412 18.11910 20.43669 22.87342

Columns 16 through 20:

25.42583 28.09049 30.86392 33.74267 36.72330

GRAPHS: