Flow over Bicycle

Flow over the bicyle or any other shape

Here the main factor in drag force, which is calculated as a function of velocity, frontal area, density of the flow medium and the co-efficient of drag.

`Fd=1/2*rho*A*v^2*c_d`; where

Fd- drag force (kg.m/s)

`rho`- density (kg/m^3)

A- frontal area (m^2), area which is exposed to the flow is called as the frontal area.

v- velocity (m/s)

c_d - co-efficient of drag (unitlless)

-To plot velocity v/s drag force variation using MATLAB.

Initially the inputs like density, frontal area of the body, velocity and drag co-efficient are to be given.

Here as the velocity varaition is to studied the input values leaving the velocity are constant i.e. do not change, but the input value for velocity is given as an array in order to have different values of the velocity and respective drag force variation.

From the above equation as all the parameters are constant, on comparing the drag force and velocity it is observed that the drag force is directly proportional to the square of the velocity i.e. the variation of drag force with respect to velocity is quadratic there by the plot obtained would be non-linear.

Following is the code for plotting the variation of velocity and drag force.

clear all
close all
clc

%inputs
%drag coeeff
c_d=0.8;

%area m^2
a=0.1;

%density kg/m^3
rho= 1.2;

%velocity
v=[1:10];

drag_force=0.5*rho*a*v.^2*c_d;
figure(1)
plot(v,drag_force,'*')
line(v,drag_force)
xlabel 'velocity'
ylabel 'drag force'

On implementation of the code the following plot is obtained

Here in the plot x axis is the velocity in m/s and y axis is the drag force in kg.m/sec.

it is observed from the plot that the variation is non-linear and the the drag force increases by 4 times if the velocity increases by 2 times when the area, drag co-efficient and density are constant.

-To plot Drag Co-efficient vs Drag force variation using MATLAB

Inputs like velocity, frontal area, density are given as a single value inputs and the drag co-efficients is an array of various shapes and their drag co-efficients having the same area.

here veocity is taken as 20m/s and the following are the shapes considered with drag co-efficients with the same area.

Shape	Drag Coefficient
Sphere	0.47
Half-sphere	0.42
cone	0.5
cube	1.05
angled cube	0.85
long cylinder	0.82
Short cylinder	1.15
Streamlined body	0.04
Streamlined half-body	0.09
flat plat	1.24
Bullet	0.29

considering the above shapes cd is an array consisting of all the above values and used one at time using the dot operator as it is a vector. Following is the code for plotting the variation of the drag co-efficient.

clear all
close all
clc

%inputs
%area m^2
a=0.1;

%density kg/m^3
rho= 1.2;

%drag coefficients for different shapes with same area
%1.Sphere cd=0.47
%2.Half-sphere cd=0.42
%3.cone cd=0.5
%4.cube cd=1.05
%5.angled cube cd=0.85
%6.long cylinder cd=0.82
%7.Short cylinder cd=1.15
%8.streamlined body cd=0.04
%9.streamlined half-body cd=0.09
%10.flat plat cd=1.24
%11.Bullet cd=0.29

%cd is the array of drag coeff for different shapes of same area
cd=[0.47 0.42 0.5 1.05 0.85 0.82 1.15 0.04 0.09 1.24 0.29];

%v1 is the velocity
v1=20;

%fd is the drag force to be calculated 
fd=rho*a*v1^2*cd.*0.5;

figure(2)
plot(cd,fd,'x')
line(cd,fd)
xlabel 'drag coeff'
ylabel 'drag force'

The plot obtained for the above code is

here in the plot x axis is drag co-efficient and y axis is the drag force of units kg.m/sec.

when the velocity, area and density are constant, the variation of the drag force with respect to the dragco-efficient is linear as both are directly proportional to each other.