Week 3.1 - Flow over Bicycle

Aim: To write a Matlab program to calculate drag force against a cyclist.

Objective:

1. Write a program to plot Velocity vs Drag force.

2. Write a program to plot Drag Co-efficient vs Drag force.

FACTORS ENTAILED:

• Velocity: It is defined as the displacement of the object in unit time.
• Drag coefficient: The drag coefficient, which has no dimensions, evaluates an object's resistance to motion in a fluid environment like air or water.
• Frontal Area: The front surface of a vehicle that presents an obstruction to the airflow past the vehicle at speed. Used in conjunction with the coefficient of drag to determine the aerodynamic efficiency of a vehicle.
• The density of air: The density of air though is calculated on the basis of mass and volume, it also depends on many other factors and can vary in different places. It can change with significant changes in the level of temperature, relative humidity, pressure, and altitude. The greek letter ρ (rho) is usually used to denote the density of air. It measures the mass of the air per unit volume.

- The expression for Drag force:

FD=CDAρV22FD=CDAρV22

Where,

is the drag force

is the drag coefficient

is the reference area

is the density of the fluid

is the flow velocity relative the object.

- Different Positions of cyclists:

MATLAB PROGRAM:

1) Program to plot Velocity VS Drag force:

The values for the Frontal Area and Co-efficient of drag are considered to be CONSTANT and the values of Velocity to be in the range of 10 m/s to 50 m/s.

Program:

%Program to calculate the drag force of a cyclist and plot Velocity VS Drag force.

%Inputs

%Drag coefficient

C_d = 0.6;

%Frontal Area (m^2)

A = 0.4;

%Density (kg/m^2)

rho = 1.2;

%velocity (m/s)

v = linspace(1.5,40.5,10);

%drag force (N)

F_d = rho*A*v.^2*C_d*0.5

%Plotting: Velocity VS Drag Force

plot(v,F_d,'linewidth',1.5);

xlable('velocity (m/s)');

ylable('Drag Force (N)');

title('Velocity VS Drag Force')

grid on;

Output:

Graph:

Result:

• Drag force increases as the flow rate increases.

• The drag force is considerably high in the case of high-speed objects, this effect may be negligible in the case of low-velocity objects. whereas high drag force is high fuel consumption.

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2) Program to plot. Drag Co-efficient VS Drag force:

Here velocity is considered as the constant whereas the values of Frontal area and Drag Coefficient are taken from the following table

Position	A (m^2)	C_d	Velocity (m/s)
UP	0.41	0.67	10
DP	0.37	0.62	15
TPP	0.34	0.65	20

UP - UPPER POSITION

DP - DROPPED POSITION

TPP - TIME TRAIL POSITION.

Program:

%program to calculate the drag force of a bicycle and plot Drag Coefficient

close all
clear all
clc

%inputs
%drag coefficient
C_d = [0.67 0.62 0.65];

%Frontal Area (m^2)
A = [0.34 0.37 0.37];

%Density (kg/m^2)
rho = 1.2;

%velocity (m/s)
v = 5

%Drag Force (N)
F_d =  0.5*rho*A.*C_d*v^2

%Plotting: Drag Co-efficient( in reference to the area) VS Drag Force
plot(A.*C_d,F_d,'color','g','linewidth',2.5);
xlable('Drag Co-efficient i.r.t Area');
ylable('Drag Force (N)');
title('Drag Co-efficient i.r.t Area VS Drag Force')
grid on;

Output:

Graph:

Result:

• The drag coefficient then expresses the ratio of the drag force to the force produced by the dynamic pressure times the area.
• C_d varies with the respective function of flow direction, flow speed, object position, and object size.

Conclusion:

• From the Velocity VS Drag Force Graph, We can state that the drag force increases exponentially and varies with v^2 as the cyclist's speed increases.
• From the Drag Co-efficient VS Drag Force graph, We can assert that a larger frontal area results in a higher drag coefficient, which raises the drag force.
• Therefore, a Matlab program was created to determine the drag force against a cyclist.

References:

- Aerodynamic study of different cyclist positions: CFD analysis and full-scale wind-tunnel tests.

https://www.sciencedirect.com/science/article/abs/pii/S002192901000059X