Flow against bicycle

Aim:

To calculate the drag force against a cyclist.

Governing Equation:

Fd= 1/2*r*A*V^2

where

Fd=drag force

r=density of the fluid which the body is resisting

A=frontal area

V=velocity

Objective:

• To plot a graph between velocity and drag force at a constant drag coefficient.
• To plot a graph between drag coefficient and drag force at a constant velocity.

Assumptions:

• Frontal area of the cyclist is assumed to be 0.1 m^2.
• Fluid is taken as air and density is taken as 1.225 kg/m^3.
• Velocity is assumed from 5 to 15 m/s.
• For plotting velocity and drag force, drag coefficient is taken as 0.8.
• For plotting drag coefficient and drag force, velocity is taken as 10 m/s.

Description:

Drag force is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. It depends upon frontal area, density of the fluid which it is resisting, velocity of the body and a dimensionless quantity called drag coefficient.

Code:

Programming language used – Python

# Program to calculate the drag force
# By : Anubrat Padhee

# Importing matplotlib for plotting
import matplotlib.pyplot as plt

# Inputs

# Drag coefficient unit-dimensionless
c_d=0.8

# Frontal area unit-m^2
a=0.1

# Density of air unit=kg/m^3
rho=1.225

#velocities unit-m/s
velocities=[5,6,7,8,9,10,11,12,13,14,15]

# Declaring an empty dragforce array
drag_forces=[]
# Calculating drag forces
for velocity in velocities:
	drag_forces.append(0.5*rho*a*c_d*velocity*velocity)

# Plotting velocity vs. drag force at constant drag coefficient
plt.figure()
plt.plot(velocities,drag_forces)
plt.xlabel("Velocity")
plt.ylabel("Drag force")
plt.title("velocity vs. drag force")
plt.show()

# Now to plot drag force vs drag coefficient at constant velocity

# Taking velocity constant unit-m/s
c_velocity=10

# Drag coefficient for different shapes
# Sphere=0.47
# Half sphere=0.42
# Cone=0.50
# Cube=1.05
# Angled cube=0.80
# Long cylinder=0.82
# Short cylinder=1.15
# Streamlined body=0.04
# Streamlined half body=0.09
C_d_s=[0.47,0.42,0.50,1.05,0.80,0.82,1.15,0.04,0.09]
Drag_forces=[]

# Calculating drag forces
for C_d in C_d_s:
	Drag_forces.append(0.5*rho*a*C_d*velocity*velocity)

# Plotting drag coefficient vs. drag force at constant velocity
plt.figure()
plt.plot(C_d_s,Drag_forces)
plt.xlabel("Drag coefficient")
plt.ylabel("Drag forces")
plt.title("drag coefficient vs. drag force")
plt.show()	

Steps :

• First the matplotlib library was imported for using plot function.
• First, to plot drag force vs velocity certain inputs were given.
• Drag coefficient was taken as 0.8.
• Frontal area was assumed 0.1 m^2.
• Density of air is taken as 1.225 kg/m^3.
• An array of velocities were taken from 5 to 15 m/s.
• Then for each velocity drag force was calculated using for loop and the formula mentioned above.
• Drag forces were stored in an array.
• Then, drag force vs velocity was plotted using plot function of matplotlib.
• Second, to plot drag force vs drag coefficient.
• Same input were taken except velocity which was taken as 10 m/s.
• Drag coefficient of different shapes were stored in an array.
• Then for each drag coefficient drag force was calculated using for loop and the formula mentioned above.
• Drag forces were stored in an array.
• Then, drag force vs drag coefficient was plotted using plot function of matplotlib.

Output:

Conclusion:

As we can see from the graph drag force varies quadractically with velocity and linearly with drag coefficient.