Study of Drag force against a Cyclist with respect to Relative Velocity & Effect of Drag coefficient for various shapes using PYTHON.

Introduction:

The Drag Force is the resistance offered due to an object moving with relative velocity with respect to surrounding Fluid. Drag Force is calculated by formulae shown below

`F_d = 0.5 ρ a v^2 C_d`

In this Scenario, the Cyclist travelling with some velocity experiences drag force with surrounding air being the fluid. Our Study includes using PYTHON programming as listed below

• Program to plot Velocity vs. Drag force for cyclist traveling with different velocities.
• Program to plot Drag Co-efficient vs. Drag force for constant velocity for different drag coefficients with different shapes having the same frontal area.

"""
Challenge#03 Program to calculate Drag Force Experienced by Cyclist
by Pradeep
"""
import math
import matplotlib.pyplot as plt 

# Inputs

# Drag coefficient
c_d = 0.8

# Frontal Area (m^2)
A = 0.1

# Density (Kg/m^2)
Density = 1.225

# Bicycle Velocity (m/s)
Velocities = [1,2,3,4,5,6,7,8,9,10]

Drag_Forces = []

#Plot 1 : Velocity vs Drag force

for Velocity in Velocities:
	Drag_Force = 0.5*Density*A*Velocity*Velocity*c_d
	Drag_Forces.append(Drag_Force)
print(Drag_Forces)
plt.figure(1)
plt.plot(Drag_Forces,Velocities)
plt.xlabel('Drag Force (N)')
plt.ylabel('Velocity (m/s)')
plt.title('Velocity VS Drag Force')

#Plot 2 : Drag Co-efficient vs Drag force

# Coefficient of Drag for Different Shapes
Cd_StreamlinedBody	=	0.04
Cd_StreamlinedHalfBody	=	0.09
Cd_HalfSphere	=	0.42
Cd_Sphere	=	0.47
Cd_Cone	=	0.50
Cd_AngCube	=	0.80
Cd_LongCylinder	=	0.82
Cd_Cube	=	1.05
Cd_ShortCylinder	=	1.15

coeff_drags = [Cd_StreamlinedBody, Cd_StreamlinedHalfBody, Cd_HalfSphere, Cd_Sphere, Cd_Cone, Cd_AngCube, Cd_LongCylinder, Cd_Cube, Cd_ShortCylinder]

# Constant Velocity (10 m/s)
V = 10
Drag_Forces_cds = []

for coeff_drag in coeff_drags:
	Drag_Force_cd = 0.5*Density*A*V*V*coeff_drag
	Drag_Forces_cds.append(Drag_Force_cd)
print(Drag_Forces_cds)
plt.figure(2)
plt.plot(Drag_Forces_cds,coeff_drags)
plt.xlabel('Drag Force (N)')
plt.ylabel('Drag Coefficient')
plt.title('Drag Coefficient of Different Shapes vs Drag Force(N)')

colors = ['c','m','r','g','y','k']

print(Drag_Forces_cds)
print(coeff_drags)

print(Drag_Forces_cds[0])

cd_1 = plt.scatter(Drag_Forces_cds[0],coeff_drags[0], marker='x', color=colors[0])
cd_2 = plt.scatter(Drag_Forces_cds[1],coeff_drags[1], marker='x', color=colors[1])
cd_3 = plt.scatter(Drag_Forces_cds[2],coeff_drags[2], marker='o', color=colors[2])
cd_4 = plt.scatter(Drag_Forces_cds[3],coeff_drags[3], marker='o', color=colors[3])
cd_5 = plt.scatter(Drag_Forces_cds[4],coeff_drags[4], marker='x', color=colors[4])
cd_6 = plt.scatter(Drag_Forces_cds[5],coeff_drags[5], marker='x', color=colors[5])
cd_7 = plt.scatter(Drag_Forces_cds[6],coeff_drags[6], marker='x', color=colors[1])
cd_8 = plt.scatter(Drag_Forces_cds[7],coeff_drags[7], marker='x', color=colors[3])
cd_9 = plt.scatter(Drag_Forces_cds[8],coeff_drags[8], marker='o', color=colors[4])

plt.legend((cd_1, cd_2, cd_3, cd_4, cd_5, cd_6, cd_7,cd_8,cd_9),
           ('Cd_StreamlinedBody', 'Cd_StreamlinedHalfBody', 'Cd_HalfSphere', 'Cd_Sphere', 'Cd_Cone', 'Cd_AngCube', 'Cd_LongCylinder', 'Cd_Cube', 'Cd_ShortCylinder'),
           scatterpoints=1,
           loc='upper left',
           ncol=1,
           fontsize=8)

plt.show()

Graph 1: Velocity vs. Drag force for cyclist travelling with different velocities

Graph 2: Drag Co-efficient vs. Drag force for constant velocity for different drag coefficients with different shapes having same frontal area.

Conclusion

1. Drag Force increases with increases in velocity by a factor of square of velocity.

2. Drag Force is less for Stream line body as it has less drag coefficient, while more for short cylinder.