Flow over Bicycle using Python

AIM

• Write a Python program to calculate drag force against a cyclist.
• Write a program to plot Velocity vs Drag force.(25 points)
• Write a program to plot Drag Co-efficient vs Drag force.(25 points)

THEORY

A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is the relative velocity between the body and the fluid.

Any object moving through a fluid experiences drag - the net force in the direction of flow due to pressure and shear stress forces on the surface of the object.

The drag force can be expressed as:

F_d = c_d 1/2 ρ v² A

Where,

F_d = drag force (N)

Cd = drag coefficient

ρ = density of fluid (1.2 kg/m³ for air at NTP)

v = flow velocity (m/s)

A = characteristic frontal area of the body (m²)

The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach number and Roughness of the Surface.

The characteristic frontal area - A - depends on the body.

Objects drag coefficients are mostly results of experiments. The drag coefficients for some common bodies are indicated below:

Type of Object	Drag Coefficient - cd -	Frontal Area
Laminar flat plate (Re=106)	0.001
Dolphin	0.0036	wetted area
Turbulent flat plate (Re=106)	0.005
Subsonic Transport Aircraft	0.012
Supersonic Fighter,M=2.5	0.016
Streamlined body	0.04	π / 4 d2
Airplane wing, normal position	0.05
Sreamlined half-body	0.09
Long stream-lined body	0.1
Airplane wing, stalled	0.15
Modern car like a Tesla model 3 or model Y	0.23
Toyota Prius, Tesla model S	0.24	frontal area
Tesla model X
Sports car, sloping rear	0.2 - 0.3	frontal area
Common car like Opel Vectra (class C)	0.29	frontal area
Hollow semi-sphere facing stream	0.38
Bird	0.4	frontal area
Solid Hemisphere	0.42	π / 4 d2
Sphere	0.5
Saloon Car, stepped rear	0.4 - 0.5	frontal area
Convertible, open top	0.6 - 0.7	frontal area
Bus	0.6 - 0.8	frontal area
Old Car like a T-ford	0.7 - 0.9	frontal area
Cube	0.8	s2
Bike racing	0.88	3.9
Bicycle	0.9
Tractor Trailed Truck	0.96	frontal area
Truck	0.8 - 1.0	frontal area
Person standing	1.0 – 1.3
Bicycle Upright Commuter	1.1	5.5
Thin Disk	1.1	π / 4 d2
Solid Hemisphere flow normal to flat side	1.17	π / 4 d2
Squared flat plate at 90 deg	1.17
Wires and cables	1.0 - 1.3
Person (upright position)	1.0 - 1.3
Hollow semi-cylinder opposite stream	1.2
Ski jumper	1.2 - 1.3
Hollow semi-sphere opposite stream	1.42
Passenger Train	1.8	frontal area
Motorcycle and rider	1.8	frontal area
Long flat plate at 90 deg	1.98
Rectangular box	2.1

PROCEDURE

• Initially we are going to ‘import the matplotlib.pyplot’ library to get the plots, we name it as plt.
• After that we just give the input values are velocity, density of air, drag co-efficient and frontal area.
• Then we are going to calculate the drag force for different velocity values.
• And then calculate the drag force for drag co-efficient values.
• Append command is used to add the values and for drag force value we can use ‘print’ command to get the answer.
• Then using plt.plot(), plt.title and plt.xlable commands to get the graph, title and lables.

PROGRAM

#program to calculate the Drag force
#by sallavoddin

import matplotlib.pyplot as plt

#inputs

#drag co-efficient
c_d=0.8
c_ds=[0.1,0.15,0.23,0.24,0.2,0.29,0.38,0.4,0.42,0.5,0.45,0.6,0.7,0.8,0.88,0.9,0.96,0.8,1.1,1.1,1.17,1.3,1.2,1.42]
drag_forces_cd=[]

#Frontal area m2
A=0.1

#Density (kg/m3)
rho=1.2
#bicycle velocity
velocities=[1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
drag_forces=[]

for velocity in velocities:
	drag_forces.append(0.5*c_d*rho*A*velocity*velocity)

print(drag_forces)

plt.plot(velocities,drag_forces)
plt.title('Velocity vs Drag force')
plt.xlabel('Velocity [m/sec]')
plt.ylabel('Drag force [N]')
plt.show()

for c_d in c_ds:
	drag_forces_cd.append(0.5*c_d*rho*A*velocity*velocity)

print(drag_forces_cd)
plt.plot(c_ds,drag_forces_cd)
plt.title('Darg co-efficient vs Drag force')
plt.xlabel('Drag co-efficient')
plt.ylabel('drag force [N]')
plt.show()

RESULTS

for different velocities

[0.048, 0.192, 0.43200000000000005, 0.768, 1.2, 1.7280000000000002, 3.072, 3.888, 4.8, 5.808, 6.912000000000001, 8.112, 9.408000000000001, 10.799999999999999, 12.288, 13.872000000000002, 15.552, 17.328, 19.2, 21.168, 23.232, 25.392000000000003, 27.648000000000003, 30.0]

for different Drag co-efficients

[3.75, 5.624999999999999, 8.625, 9.0, 7.5, 10.874999999999998, 14.250000000000002, 15.0, 15.75, 18.75, 16.875, 22.499999999999996, 26.25, 30.0, 33.0, 33.75, 36.0, 30.0, 41.25, 41.25, 43.875, 48.75000000000001, 44.99999999999999, 53.25]

PLOTS

Drag force vs Velocity

Drag force vs Drag co-efficient

CONCLUSION

• We can see that in figure1 velocity vs drag force, drag force is increases non-linearly with velocity.
• In the figure2 we can see that drag force is directly proportional to drag co-efficient. if we change the value of drag co-efficient then also there is no variation in straight line.

REFFERENCES

• https://www.engineeringtoolbox.com/drag-coefficient-d_627.html
• https://www.real-world-physics-problems.com/drag-force.html#:~:text=A%20drag%20force%20is%20the,the%20body%20and%20the%20fluid.