DRAG FORCE EXPERIENCED BY A BICYCLIST(USING PYTHON)

AIM:

To determine the drag force experienced by a cyclist on the road.

OBJECTIVES:

• To understand and know about the relationship between drag force and its parameters namely
  • The velocity of the vehicle
  • The frontal area of the vehicle
  • The density of the medium through which the vehicle passes
  • The drag coefficient
• To plot velocity vs drag force graph and analyze their relationship
• To plot drag coefficient vs drag force (keeping frontal area constant) for varying shapes and analyze their relationship

INTRODUCTION:

The drag force or the air resistance (in more general) is the amount of resistive force applied by the medium (i.e. the air) on a specific automobile. This is one of the key concepts of designing an automobile as it affects the overall performance and passenger comfort which are two basic components of vehicle designing. The calculation of drag force can be done as follows:

`F = 1/2rhoAv^2c_d`

where F = amount of drag force

`rho` = density of the medium

A = frontal area of the automobile

`v` = velocity of the automobile

c_d = drag coefficient of the vehicle

Hence, looking at these parameters, designers can alter only the frontal area and drag coefficient of the vehicle which are really important. Drag force has always hindered the performance of the vehicle and passenger comfort for which more aerodynamic shapes are being preferred over boxy figures and etc.

KEY WORDS:

• Drag coefficient:

It is a dimensionless quantity which quantifies how well the automobile can resist the movement of the medium passing through it. It is an important characteristic of a vehicle as it allows us to know how aerodynamic and how well-performed can an automobile be. The drag coefficient for same frontal area for some shapes are as follows:

• Frontal area:

The projected area of the vehicle in the front. This is another important aspect as smaller the frontal area, smaller is the drag force, greater is the performance and comfort.

PROCEDURE OF EXPLANATION:

Here, we have taken an example of a simple cyclist who is driving on the road and calculating the amount of drag force acting on him/her.

Here, we have used scipy module to smoothen the curve and numpy module to use numerical arrays instead of lists so that doing mathematical operations will be easier.

Below is the attached program:

# PROGRAM TO FIND DRAG FORCE EXPERIENCED BY A BICYCLIST
# THE DRAG FORCE DEPENDS ON THE FOLLOWING FOUR FACTORS:
#                   1. DENSITY OF THE MEDIUM
#                   2. VELOCITY OF THE BICYCLIST
#                   3. FRONTAL AREA
#                   4. DRAG COEFFICIENT

# IMPORTING NECESSARY MODULES
# Plotting
import matplotlib.pyplot as plt
# Smoothing
from scipy.interpolate import make_interp_spline
# Mathematical operations
import numpy as np

# INITIALIZATION OF PARAMETERS
# Density(kg/m^3)
rho = 1.225
# Frontal Area(in m^2)
A = 0.983
# Drag coefficient
cd = 0.7
# Velocity(in  m/s)
v = np.array([1.108, 3.252, 5.502, 6.72, 8.83, 9.92])

# CALCULATION
df = []
for element in v:
    df.append(0.5*rho*A*pow(element, 2)*cd)

# SMOOTHING THE CURVE
x = np.linspace(v.min(), v.max(), 300)
spl = make_interp_spline(df, v, k=2)
power_smooth = spl(x)

# PLOTTING
plt.figure(1)
plt.plot(power_smooth, x)
plt.xlabel('Drag Force(in N)')
plt.ylabel('Velocity(in m/s)')
plt.title('Drag Force vs velocity')
plt.grid()
plt.show()

# KEEPING VELOCITY CONSTANT AND CHANGING THE DRAG COEFFICIENT
v1 = 5.502
cd1 = np.array([0.04, 0.09, 0.42, 0.47, 0.50, 0.80, 0.82, 1.05, 1.15])
df1 = []
for c in cd1:
    df1.append(0.5*rho*A*pow(v1, 2)*c)

# PLOTTING
plt.figure(2)
plt.plot(df1, cd1)
plt.xlabel('Drag Force(in N)')
plt.ylabel('Drag coefficient')
plt.title('Drag force vs Drag coefficient')
plt.grid()
plt.show()

OBSERVATIONS:

As in the formula velocity is squared, a parabolical graph occurs.

Keeping velocity and frontal area constant, we see that the drag force is directly proportional to that of drag coefficient.

CONCLUSION:

Drag force can sometimes be helpful but in most of the cases it has been a hindrance for the automobile industry as it results in poor mileage, poor performance and poor passenger comfort. Hence, industries tend to design more aerodynamic shapes like that of in a F1 car or hyper cars and sports cars which do provide lot of downforce and offer very little drag force due to their low frontal area and drag coefficient. Hence, while designing an automobile these two parameters should always be considered.