Calculating Drag Force Using Python

Aim :- To write a Python program to calculate drag force against a cyclist.

Objectives :-

• To write a program to plot Velocity vs Drag force.
• To write a program to plot Drag Co-efficient vs Drag force.

Introduction :-

Drag force is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

Drag force can be found using formula,

Drag force = 0.5 x ρ x A x V² x C_d

The unit of drag force is newton or kg.m/s² .

Here,

A = Frontal area

V = Velocity

C_d = Drag coefficient. It is unitless.

ρ = Density

Program :-

1. Program to plot velocity vs drag force.

#Program to plot velocity vs drag force
#Program by Saurabh Kshirsagar

import matplotlib.pyplot as plt

#Inputs

#Drag coefficient
c_d = 0.8
#Frontal area
A = 0.1
#Density
rho = 1.2
#Bicycle velocity
velocities = [8,9,10,11,12,13,14,15]
drag_forces = []
for velocity in velocities:
	drag_forces.append((0.5*rho*A*velocity*velocity*c_d))

#Plotting

plt.plot(velocities,drag_forces)
plt.xlabel('Velocity')
plt.ylabel('Drag Force')
plt.show()

2. Program to plot Drag Co-efficient vs Drag force.

#Program to plot drag coefficient vs drag force
#Program by Saurabh Kshirsagar

import matplotlib.pyplot as plt

#Inputs

#Bicycle velocity
velocity = 10
#Frontal area
A = 0.1
#Density
rho = 1.2
#drag coefficient
drag_coefficients = [0.4,0.5,0.6,0.7,0.8]
drag_forces = []
for c_d in drag_coefficients:
	drag_forces.append((0.5*rho*A*velocity*velocity*c_d))

#Plotting

plt.plot(drag_coefficients,drag_forces)
plt.xlabel('Drag coefficient')
plt.ylabel('Drag Force')
plt.show()

Output:-

1. Velocity vs Drag force

Here, we wrote a program to plot velocity vs drag force. The above image is the output of the program.

Assumptions made were,

Frontal area = 0.1 m² .

Density = 1.2 Kg/m³ .

Coefficient of drag = 0.8

Velocity of bicycle = varying between 8 to 15 m/s

As we can see in the above graph, Velocity varies proportionaly with drag force. And as velocity increases drag force also increases.

2. Drag Co-efficient vs Drag force.

Here, we wrote a program to drag coefficient vs drag force. The above image is the output of the program.

Assumptions made were,

Frontal area = 0.1 m² .

Density = 1.2 Kg/m³ .

Coefficient of drag = varying between 0.4 to 0.8. (sphere=0.47, cone=0.5, angles cube=0.8, etc)

Velocity of bicycle = 10 m/s

As we can see in the above graph, drag coefficient varies linearly with drag force. And as drag coefficient increases drag force also increases.

Conclusion:-

From the program we found the variation of drag force with velocity and drag coefficient respectively.