Flow Over Bicycle

AIM:

Write a program to calculate the drag force against a cyclist giving a plot of velocity vs drag force and coefficient of drag vs drag force

THEORY:

Drag Force is calculated by the equation

FD = 1/2*CD*rho*A*V^2

Where,

FD = Drag Force (kgm/s^2 or N)

CD = Coefficient of drag

rho = Density of air (kg/m^3)

A = Frontal Area (m^2)

V = velocity (m/s)

PROCEDURE:

1. First the new editor window is opened, the commands "clear all", "close all" and "clc" are used to clear the command window and the previously done programs
2. The aim of the program is commented using the "%" symbol on the top of the editor window
3. The program written is saved using the extension ".m"
4. The velocity, area and coefficient values are stored in the form of array
5. After this the program is saved and run to achieve the results

POGRAMS:

PROGRAM TO CALCULATE DRAG FORCE AND PLOT GRAPH OF "VELOCITY VS DRAG FORCE"

%Program to calculate the drag force of flow over the bicycle
clear all 
close all 
clc

%Inputs
%Frontal area m^2
A = [82.50; 66; 54.45]; %positions considered = [@upright position, @drops position, @top tube position]

%Velocity m/s^2
V = [1:20];          

%Density kg/m^3
rho = 1.225;

%Coefficient of drag (dimensionless)
c_d = [0.82; 0.50; 0.47]; %positions considered = [@upright_position, @drops_position, @top_tube_position]

%Calculation of drag force
drag_force = 0.5*rho*c_d.*V.^2.*A

%plotting of graph of velocity vs drag force
plot(V, drag_force)

xlabel('Velocity (m/s)')
ylabel('Drag Force (kgm/sec^2)')

grid on

PROGRAM TO CALCULATE DRAG FORCE AND PLOT GRAPH OF "COEFFICIENT OF DRAG VS DRAG FORCE"

%Program to calculate the drag force of flow over the bicycle
clear all 
close all 
clc

%Inputs
%Frontal area m^2
A = [82.50; 66; 54.45]; %positions considered = [@upright position, @drops position, @top tube position]

%Velocity m/s^2
V = [1:20];          

%Density kg/m^3
rho = 1.225;

%Coefficient of drag (dimensionless)
c_d = [0.82; 0.50; 0.47]; %positions considered = [@upright_position, @drops_position, @top_tube_position]

%Calculation of drag force
drag_force = 0.5*rho*c_d.*V.^2.*A

%plotting of graph of velocity vs drag force
plot(c_d, drag_force)

xlabel('Coefficient of drag')
ylabel('Drag Force (kgm/sec^2)')

grid on

EXPLANATION:

• Considering three different frontal area conditions at three different position -

a) Upright position b) Drops position c) Top Tube position

• Assuming them to take nearly the shape of long cylinder, a cone and sphere respectively, the values of coefficient of drag varies from 0.80 to 0.47
• Hereby, getting the different values of drag force

RESULT:

drag_force =

Columns 1 through 8

41.436 165.74 372.92 662.97 1035.9 1491.7 2030.3 2651.9
20.213 80.85 181.91 323.4 505.31 727.65 990.41 1293.6
15.675 62.699 141.07 250.8 391.87 564.29 768.06 1003.2

Columns 9 through 16

3356.3 4143.6 5013.7 5966.7 7002.6 8121.4 9323 10608
1637.2 2021.3 2445.7 2910.6 3415.9 3961.7 4547.8 5174.4
1269.7 1567.5 1896.7 2257.2 2649 3072.3 3526.8 4012.7

Columns 17 through 20

11975 13425 14958 16574
5841.4 6548.9 7296.7 8085
4530 5078.6 5658.6 6269.9

The graphs of "Velocity vs Drag Force" and "Coefficient of Drag vs Drag Force" are plotted and give characteristic curves as in the graphs attached above.