Study on the effect of velocity and drag coefficient on Drag Force using Matlab

AIM : To study the effect velocity and drag coefficient on the drag force experienced by an object.

INTRODUCTION:

A drag force is the resistance caused by the motion of a body through a fluid like air or water. It acts opposite to the direction of the flow velocity. Just like friction, drag force opposes motion of a body.

The drag force experienced by an object is given by the formula:

`F=1/2*rho*A*V^2*Cd`

where:

`rho` = density of the fluid through which body is moving

A = frontal area or projected cross-sectional area of the body perpendicular to the flow direction

V = velocity of the body relative to the fluid

Cd = drag coefficient of the body

It is always desirable to have the drag force as minimal as possible. Ships, aircrafts, moving vehicles, cooling towers and all other structures are designed in such a way to have minimum amount of drag force.

ASSUMPTIONS:

For this study, the following assumptions are made:

• The bicycle and cyclist are considered as one system
• The density of air is assumed to be constant (1.225 kg/m3)
• Frontal area remains constant (0.2 m^2)

PROCESS:

The program is split into 3 parts:

Part 1: Variation of drag force w.r.t. velocity

Velocity is assumed to vary from 0.5 to 50m/s for a constant deag coefficent of 0.8.

Part 2: Variation of drag force w.r.t. drag coefficient:

The drag coefficient of various objects having the same frontal area is considered. The velocity is assumed to be constant (5 m/s)

Cd for flat plate = 1.28
Cd for prism = 1.14
Cd for bullet = 0.295
Cd for airfoil = 0.045
Cd of sphere = 0.47
The above values are taken from https://wright.nasa.gov/airplane/shaped.html

Part 3: Variation of drag force w.r.t. drag coefficient and velocity:

In this case, both velocity and drag coefficient are assumed to be varying. Their combined effect on drag force is studied.

CODE:

%To calculate drag force and study the effect of velocity and discharge coefficient on drag force
%For this study, different shapes having same frontal area is considered to calculate the drag force experienced.
%Cd for flat plate = 1.28
%cd for prism = 1.14
%Cd for bullet = 0.295
%Cd for airfoil = 0.045
%Cd of sphere = 0.47
%the above values are taken from https://wright.nasa.gov/airplane/shaped.html
%Drag force = 0.5*density*area*velocity*velocity*drag coefficient
%where area refers to the frontal area of the object

clear all
close all
clc

%Inputs (assumptions)
Area=0.2 %in m^2
Density=1.225  %in kg/m^3 for air

%Part 1 : Variation of drag force w.r.t. velocity
%Assuming velocity varying from 0.5 to 50m/s
v=linspace(0.5,50,200)
drag_coeff=0.8
leng=length(v)

for i=1:length(v)
  DragForce(i)=0.5*Density*Area*drag_coeff.*(v(i).^2)
end
figure(1)
subplot(2,1,1)
plot(v,DragForce)
xlabel('Velocity in m/s')
ylabel('Drag force in N')
title('Variation of Drag force w.r.t velocity')

%Part 2: Variation of Drag force w.r.t Drag coefficient
%Assuming velocity to be constant 5m/s
Cd=[1.28 1.14 0.295 0.045 0.47]
V_cons=5
for j=1:length(Cd)
  Drag_force(j)=0.5*Density*Area*(V_cons^2).*Cd(j)
end
subplot(2,1,2)
plot(Cd,Drag_force)
hold on
plot(Cd,Drag_force,'o')
xlabel('Drag Coefficient')
ylabel('Drag force in N')
title('Variation of Drag force w.r.t. drag coefficient')

%Part 3: Variation of Drag force w.r.t varying Drag coefficient and velocity
%Assuming velocity varying from 0.5 to 80m/s
%Assuming drag coefficient to vary from 0.01 to 1.42
C_d=linspace(0.01,1.42,100)
V=linspace(0.5,80,100)
[C V]=meshgrid(C_d,V)
for k=1:length(V)
  DragForce=0.5*Density*Area.*(V.^2).*C
end
figure(2)
surf(V,C,DragForce)
xlabel('Velocity m/s')
ylabel('Drag coeff')
zlabel('Drag force in N')

RESULTS:

DISCUSSION:

• From the above graphs, is evident that both velocity and drag coefficient directly affect the drag force
• Variation of drag force wr.t. drag coefficient is linear.
• Variation of drag force wr.t. velocity is parabolic i.e. drag force is proportioanl to square of velocity.
• Thus velocity changes have a biggert impact on drag force than drag coefficient.
• In order to reduce the magnitude of drag force, automobiles are aerodynamically designed as reducing the drag would drastically improve the milage. Similarly ships are designed to be streamlined for the same reason.