Flow over Bicycle

CALCULATING DRAG FORCE OVER A BICYCLE USING MATLAB

AIM :To calculate the drag force over a bicycle and plot respective graphs using Matlab programming

OBJECTIVE : 1.drag force vs velocity graph

2.drag force vs drag coefficient graph

THEORY :

Any object moving through a fluid experiences drag - the net force in the direction of flow due to pressure and shear stress forces on the surface of the object.

The drag force can be expressed as:

F_d = c_d 1/2 ρ v² A

where

F_d = drag force (N)

c_d = drag coefficient(dimensionless)

ρ = density of fluid (1.2 kg/m³ for air at normal temperature and pressure)

v = flow velocity (m/s)

A = characteristic frontal area of the body (m²)

The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach Number and Roughness of the Surface.

The characteristic frontal area - A - depends on the body.

Objects drag coefficients are mostly results of experiments.

PROGRAM :

1. PLOTTING VELOCITY VS DRAG FORCE

%program to plot drag force vs velocity
clear all
close all
clc

%inputs

%drag coefficient(dimensionless)
C_d=0.8;
%density(kg/m^3)
rho=1.2;
%Area(m^2)
A=1;
%velocity(m/s)
v=[1:50];
%DRAG FORCE(N)
drag_f=0.5*rho*A*v.^2*C_d;
plot(v,drag_f)
xlabel('velocity')
ylabel('dragForce')
grid on

2. PLOTTING DRAG COEFFICIENT VS DRAG FORCE

%program to plot drag force vs drag coefficient
clear all
close all
clc

%inputs

%density(kg/m^3)
rho=1.2;

%Area(m^2)
A=1;

%constant velocity(m/s)
V_constant=1;

%varying drag coefficient(dimensionless)
%it is varying from 0.001 to 2.1 incrementing at 0.05
Cd_var=[0.001:0.05:2.1]

%DRAG FORCE(N)
drag_f=0.5*rho*A*V_constant^2*Cd_var;
plot(Cd_var,drag_f)
xlabel('drag coefficient')
ylabel('dragForce')
grid on

PLOTS

FIG 1 : velocity vs drag force

FIG 2 : drag coefficient vs drag force

RESULT AND CONCLUSION :

1. Figure 1 shows the parabolic variation of drag force with velocity ie if velocity gets doubled then the drag force gets quadrupled. This happens to be a major problem while designing an automobile. The design parameters required is dependent on the drag coefficient which is described in Figure 2. The design should be aerodynamic enough to reduce the drag coefficient.

2.Figure 2 shows directly proportional variation of drag force with drag coefficient. Different bodies have different drag coefficient depending upon their shapes.

Following data shows different drag coefficient for different shapes:

As seen above it is better to have a streamlined body to decrease drag coefficient while a rectangular box has a very high drag coefficient and hence high drag force.