STUDY OF DRAG FORCE

THE STUDY OF DRAG FORCE VARIATION WITH RESPECT TO VELOCITY AND WITH RESPECT TO CHANGE IN DRAG-COEFFICIENT(CHANGE OF SHAPE)

INTRODUCTION

Here I am intending to write a Matlab program to calculate drag force against a cyclist and to plot the variation of drag force with respect to the velocity of the bicycle while he pedals it and to plot the variation of dragforce with respect to drag coefficient of various shapes at a constant velocity

The factors involved are Velocity,Drag coefficient,Frontal Area,Density of air.

BACKGROUND

Program to plot Velocity vs Drag force.

Here we calculate the variation of drag force with respect to the velocity of a bicycle.The frontal area is assumed to be 0.1 sq.m.The drag force is calculated according to the formula

`Fd = frac{1}{2}xxCd xxrho xx A xx V^2`

Program to plot Drag Co-efficient vs Drag force.

For the same frontal area, the coefficient of drag varies for different shapes. Here we obtained drag coefficient for various shapes namely Aerofoil,Sphere,bullet,prism and flat plate from NASA website and then plot the variation of drag force with respect to drag coefficient of the above mentioned shapes at a constant velocity of say 50 m/s.

MATLAB CODE:

%Program to calculate drag force against a cyclist
clear all
close all
clc

%Inputs
%Drag coefficient
c_d=0.8;

%Density Kg/m^3
rho=1.2;

%Frontal area m^2
A=0.1;

%velocity
v=[1:50];

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

%Plotting
plot(v,drag_force)
xlabel('Velocity')
ylabel('Drag Force')

grid on

%Calculating variation of drag force w.r.t drag coefficient

%Drag coeeficients of a Aerofoil,Sphere,Bullet,Prism,flat plate in the
%ascending order as per data from NASA website
%Drag coefficient
c_d1=[0.045,0.07,0.295,0.5,1.14,1.28];

%Velocity constant at 50 m/s
v_c=50;

drag_force_cd=0.5*c_d1*rho*A*v_c^2;

%Plotting
plot(c_d1, drag_force_cd)
xlabel('drag coefficient')
ylabel('Drag Force')
grid on

OUTPUT:

The outputs of the code are as presented here as plots of variation of Drag Force with respect to velocity of the cyclist and with respect to drag coefficient of various shapes at a constant velocity

Here I have calculated the drag force using the equation for drag force .I have folllowed the instructions in the video for this program. I had plotted Drag force against velocity for the same frontal area. We can observe that the plot is parabolic because , the other parameters remaining constant and if we consider the equation for drag force it follows the equation of a parabola, as drag force varies as per square of velocity (y=ax^2)

Here I have calculated the drag force using the equation for drag force .I have obtained the values by the instructions given in the hint. From the data for different shapes.After which I had plotted Drag force against drag coefficient for different shapes for the same frontal area. We can observe that the plot is a straight line because , the other parameters remaining constant and if we consider the equation for drag force it follows the euation of a straight line (y=mx)