Plotting Drag Forces vs (Velocities and Drag Coeff) Over A Moving Body in Python

This program code in python helps to visualise the effect of the drag forces on a moving body at different speeds and at different drag coefficients. 

 Drag Force

The drag force is a type of fluid friction or resistance which is experienced by a body moving inside a fluid medium. Depending upon the type of the flow, the drag can be laminar, where it is proportional to the velocity of flow, or turbulent, where it is proportional to the squared velocity.

The drag force depends upon factors like object geometry (size and shape), fluid properties (density) and the speed of motion. 

The formula for Drag Force is given by the drag equation:

`F_{D}=frac {1}{2}rho v^{2}C_{D}A`

where:`F_D` is the drag force

         `rho` is the density of the fluid medium

         `v` is the velocity of the moving body, and

         `C_D` is the drag coefficient which depends upon the shape of the object and Reynold's number

         `A` is the frontal area which experiences the drag head on.

 Python Program

Python can be used effectively to plot the drag forces that a body experiences when its velocity or the drag coefficient is varied. 

I order to understand the code, I will explain some basic functions used in the code.

1) import:

This command is used to get access to a particular Module in python. Thus 'import' function is one of the ways of invoking a module. 

2) matplotlib:

 Matlplotlib.plot is a collection of command style functions that make matplotlib, a Python 2D plotting library, work like MATLAB

3) append

append command is used when we want to add or concatenate successive values in a single array. This command concatenates the entries in a single array (check the Line_Space Program below for syntax).

4) range()

range(start,end,division) is an inbuilt function in Python where equally spaced integers. However, this command only creates integer values

To create equally spaced float numbers, we can use a for loop with the range() command as shown in the program below. In this program, we need the starting value, increment and the number of desired elements.

#Line_Space Program

#pre-defining/allocating

'''
To create an equally spaced numbers, we need the starting number, the last number and the no of elements.'''

start = 0
increment= .1
number = 11

'''start is the first element, increment is the increment and number is the no. of elemets required'''


#Generating Numbers
array =[]

 
for i in range(number):
	array.append(start + increment*i)

''' the values in array are [0.0, 0.1, 0.2, 0.3, 0.40, .50, .60, .70, .80, .9, 10]'''

5) numpy:

Numpy is a package for Python used in scientific computing. This includes N-dimensional array objects, linear algebra, Fourier transform, and random number generation.

5) linspace()

linspace(start,end,number) command, integrated with Numpy, creates a line space of equally spaced values. e.g., linspace(0,1,11) creates an array of 10 values equally spaced between 0 and 9 i.e., [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]

Programs

I provide two separate codes for velocities and drag coefficients variations.

A) Drag Force Vs Velocity 

#Program to Calculate the Drag force on A Moving Body And Plot Drag Force vs Velocities Graph

import matplotlib.pyplot as plot_var 
import numpy as np

'''
'Import' grants access to code from another module by importing the file/function.
Here, I stored the function in a variable named 'plot_var' using 'as' command. 
'''

# A:  Inputs

 # 1) Drag-Coefficient
cd = 0.8

 # 2) Density of the medium, air (kg/m^2)
rho = 1.2

 # 3) Frontal Area (m^2)
A = 0.1

# 4) Vehicle Velocity (m/s)
v_array = np.linspace(0,20,21)

''' Here, the velocity range is from 0 to 20 m/s with an interval of 1m/s'''


#B) Plotting
 
constant = 0.5*rho*A*cd '''this part remains constant in the equation'''
drag = [] '''defining/preallocating'''

for vel in v_array:
	drag.append(vel*vel*constant)

plot_var.plot(v_array,drag)       
plot_var.xlabel("Velocity (m/s)")            
plot_var.ylabel('Drag Force (N)')
plot_var.title('''Drag Forces vs Velocities''')
plot_var.show()

Note: While labelling we can use single, double, or even three quotation marks. The plot,xlabel,ylabel and title commands are used to plot, add axes labels and the titile of the plot similar to MatLab.

Output:

Clearly, the drag force can be seen as proportional to the square of the velocity.

A) Drag Force Vs Drag Coefficients

From the equation of the drag force, it is seen that the drag is directly proportional to the drag coefficient. Hence, a plot between drag forces and the drag coefficients (all other factors remaining constant) should furnish a straight curve.  (I am varying the coefficients from 0.1 to 1 with 20 data points).

The program is given below:

Program to Calculate the Drag force on A Moving Body With Varying Drag Coefficients

import matplotlib.pyplot as plot_var 
import numpy as np

rho = 1.2
A = 0.1
v = 5

cd = np.linspace(.1,1,20)
dragc =[]
constant  = 0.5*rho*A*v*v

for vel in cd:
	dragc.append(constant*vel) 


plot_var.plot(cd,dragc)
plot_var.xlabel("Drag Coefficient")
plot_var.ylabel('Drag Force (N)')
plot_var.title(''''Drag Force Vs Drag Coefficients (v=5)''')
plot_var.show()

Output: 

Clearly, drag force varies linearly with drag Coefficient.

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