Drag force calculation on a cyclist.

Aim – Program to calculate the drag force against a cyclist.

Governing Equation – [ F_D = 0.5*c_D*ƍ*A*v² ]

Where,

F_D = Drag force on the cyclist (N);

C_D = Drag coefficient;

A = Frontal Area (m²);

ƍ (rho) = Density of air (kg/m³);

v = Velocity of the cyclist (m/s).

Above written formula can be used to calculate the drag force on any moving body. According to Bernoulli’s equation, when a body is moving, its kinetic energy gets converted into pressure energy due to fluid particle in the environment. This results in pressure gradient and thus due to difference in pressure, a force is applied on the body, which is called the drag force.

Drag force depends upon density of the medium, area of the body which is exposed to the medium, drag coefficient and velocity of the moving body.

Assuming frontal area of every object is same and C_D varies for different shapes as written below -

1. Sphere – 0.07 – 0.5, 2. Airfoil – 0.045, 3. Bullet – 0.295, 4. Prism – 1.14, 5. Flat Plate – 1.28

Objectives –

1 - To calculate the drag force

2 -To plot a graph between – (i) Drag force and velocity, (ii) Drag force and C_D.

Code 1 – Program for plot between Drag force and velocity – (C_D = constant)

% program to calculate the drag force on a bicycle

%inputs

%drag coefficient
c_d = 0.8;

%density kg/m^3
rho = 1.2;

%area m^2
a = 0.1;

%velocity m/s
v = [1:20];

drag_force = rho*a*v.*v*c_d*0.5

plot(v,drag_force)
xlabel('velocity')
ylabel('drag force')
grid on

Explanation - First of all, the program need to know the value of all the parameters which are going to be used in the formula of drag force. So we address the value of drag coefficient (c_d), density (rho), frontal area (a) and an array for the values of velocity(v) byn using a semicolon operator.. The variation in velocity is given as we want a plot between the velocity and the drag force. The semicolon operator gives all the integer values in between the first term and the last term including these two.

After that, we write the formula the formula for the drag force. It is to be remembered that as the velocity is now an array so it can't be multiplied normally. Hence we do vector multiplication by using (.^) or (.*). Then we use the plot command to plot a graph between velocity and drag force and name the x-axis and y-axis.

Result –

Plot –

Code 2 – Program for plot between Drag Force and C_D – (velocity = constant)

% program to calculate the drag force on a bicycle
 
%inputs

%drag coefficient
c_d = [0.045 0.07 0.295 0.5 1.14 1.28];  

%density kg/m^3
rho = 1.2; 

%area m^2
a = 0.1; 

%velocity m/s
v = 20;

drag_force = rho*a*v.*v*c_d*0.5

plot(c_d,drag_force)
xlabel('c_d')
ylabel('drag force')
grid on

Explanation -Similar to the previous program, first we address the values of all the parameters which are being used in the formula of drag force calculation. The only difference is that this time the velocity (v) is constant and the drag coefficient (c_d) is varying. Then we write the formula for drag force and use the plot command to plot the graph between drag coefficient and drag force.

Result –

Plot -

Conclusion -

From the first result and the graph it is clear that the drag force varies parabolically with velocity (v). Hence during the manufacturing of a high speed vehicle, it is very important to consider the effect of drag force as the main factor of the drag force is velocity.

In the second result, the drag force varies linearly with the drag coefficient. For an Airfoil or streamlined objects, drag coefficient is very low so the drag force is also very low. Hence to reduce the effect of drag force, a body must be streamlined as much as possible.