calculating drag force for flow over cycle

Objective :

1. calculating the drag force .

2. plotting the graph between coefficent and drag force

3. plotting graph between velocity and drag force

Theory :

Drag is the resistive force against motion of object in fluid it is a mechanical force devloped due to solid and fluid interaction.Drag is generated by the difference in velocity between the solid object and the fluid. if there is no difference there will be no drag .

in our case cyclist is moving in and the air resistance which oppose the motion is basically drag.

now from above figure we can see that how drag is acting and the frontal area will continuosly will change as cyclist will move crank so here most imporant parameter is drag coefficient which will affect the drag force . drag coefficent values will depend upon various geometrical shapes , velocity,frontal area,etc.

Matlab code:

% programme to calculate drag force against cyclist 
% input values 
c_d = linspace(0.01,0.99,50);
a = 0.85;
v = linspace(5,25,50);
v_0 = 12.5 
rho = 1.225
% drag force formula 
f_d = a*0.5*rho.*v.*v.*c_d    % here both varies drag coeffcient and velocity 
F_D = 0.5.*c_d*a*v_0^2*rho  % here drag coefficent varries but velocity is constant 
figure(1)
plot(c_d,F_D)
xlabel('drag coefccient')
ylabel('drag force')
figure(2)
plot(v,f_d)
xlabel('velocity')
ylabel('drag force')

here we have taken input values first ,

c_d = drag coefficient which we will take in between 0.01 to 0.99 in 50 equal interval which will give us an array with 50 column and 1 row .

a = frontal area in m^2

v = velocity of cyclist in m/s^2

here we hqve taken v and v_0 which both are values here v is an array of 50 values of velocity and v_0 is a constant velocity by both velocity we will find out the two diffrent values of drag force.

rho = density of air which is in kg/m^3

f_d = 0.5*c_d*rho*v^2*a

now here we have calulated the two values of drag force why

because then we can get the plot between c_d and f_d and v and f_d in which all other parameters are constant . and so we can get the plot result between c_d and F_D in this only variable is c_d so we get one plot and we calculate f_d in this case v and c_d both are variable parameters so we get diffrent plot.

Ruslts:

Plot 1 = plot between drag coefficient and drag force here we se that in this plot we use v_0 which is constant value so from drag force formula we see that relation between f_d and c_d should be linear and from plotting the result we get the linear graph .

Plot 2 : In this plot values of v and c_d both are changing and we see that f_d is directly proportional to v^2 so we will be getting parabola which indeed we are getting by plotting the results so here we see the graph between the f_d vs v and we can get any values of f_d if we know the velocity .