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: