Flow Over Bicycle using Matlab

A program to calculate Aerodynamic Drag Force for Study of Flow over Bicycle using Matlab.

Aim : To write a Matlab program to calculate Aerodynamic Drag Force against a bicycle and study the relation between –

• Velocity and Drag Force
• Drag Co-efficient and Drag Force

Objective :

• To calculate the drag force on a bicycle at varying speeds.
• A program to plot Velocity vs Drag force.
• A program to plot Drag Co-efficient vs Drag force.

Keywords : Frontal Area, Drag Force, Drag Co-efficient, Velocity.

Introduction :

The rider along with the bicycle contributes a majority of the aerodynamic drag of the entire bicycle and rider system. In fact, a rider’s body typically contributes 70% of the total aerodynamic drag of the system. The general shape of a rider along with the bicycle is not streamlined and there are many pockets where air can be trapped and increase the drag. A simple study of drag force on a cyclist can be illustrated using Matlab.

Theory :

• Drag Force – The force related to the resistance of an object as it moves through a fluid is called as drag force. A drag forceacts opposite to the direction of the oncoming flow velocity. The magnitude of drag force mainly depends on -

1. The type of surrounding fluid.
2. The shape of the object.
3. Velocity of the object.

The expression of Drag force `F_D` is :

`F_D= 1/2 ρAV^2 C_d`

Where,
`rho` = Density of fluid;

A = Frontal Area;

V = Velocity of object;

C_d = Drag Co-efficient;

• Frontal Area – Frontal Area is the area of the object which is subjected to fluid force. This area is considered as 2D geometry. The total resistance offered by the vehicle is the product of frontal areaand drag coefficient. Following are some of the positions of rider and the corresponding values of Frontal Area associated with the particular position of the cyclist.

Fig. 1] Frontal Area for different positions of cyclist

• Drag Co-efficient – The drag co-efficient is used to quantify the drag or resistance of an object in a fluid environment. It is a dimensionless quantity. It has different values for different shapes. Drag Co-efficient mainly depends on Frontal Area and other factors which include density of fluid, velocity of object, etc.

Matlab Program :

1] Program to calculate Drag Force on bicycle and study relation between Velocity and Drag Force by plotting graph :

Here the values of Frontal Area and Co-efficient of drag are considered to be constant and the value of Velocity is considered to be in the range of 1 m/s to 35 m/s.

Editor Window -

%Program to calculate the drag force of a bicycle and plot Velocity vs Drag Force
close all
clear all
clc

%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(1,35,10);

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

%Plotting: Velocity vs Drag Force
plot(v,F_d,'linewidth',2);
xlabel('Velocity (m/s)');
ylabel('Drag Force (N)');
title('Velocity vs Drag Force')
grid on;

Output –

Graph of Velocity vs Drag Force –

Result based on graph –

As the velocity increases, the drag force increases with V². At higher velocities, the drag coefficient increases upto 4 times.

2] Program to calculate Drag Force on bicycle and study relation between Drag Co-efficient and Drag Force by plotting graph :

Here velocity is considered as constant whereas the values of Frontal Area and Drag Co-efficient are taken from the following table (for positions mentioned in Fig 1.) –

Fig. 2] Drag Co-efficient(`C_d`) Values

Editor Window –

%Program to calculate the drag force of a bicycle and plot Drag Coefficient vs Drag Force.
close all
clear all
clc

%Inputs
%Drag coefficient 
C_d = [0.626 0.638 0.655 0.655 0.670]; 

%Frontal Area (m^2)
A = [0.374 0.370 0.339 0.423 0.460];

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

%Velocity (m/s)
v = 7;

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

%Plotting: Drag Co-efficient(with respect to area) vs Drag Force
plot(A.*C_d,F_d,'color','r','linewidth',2);
xlabel('Drag Co-efficient w.r.t Area');
ylabel('Drag Force (N)');
title('Drag Co-efficient w.r.t Area vs Drag Force')
grid on;

Output –

Graph of Drag Co-efficient vs Drag Force –

Result based on graph –

Drag Force increases linearly with Drag Co-efficient. Every value of Drag Co-efficient is associated with a particular value of Frontal Area.

Conclusion :

• From Velocity vs Drag Force Graph, we can conclude that as the speed of the cyclist increases, the drag force increases in an exponential manner and varies with V².
• From Drag Co-efficient vs Drag Force Graph, we can conclude that larger the frontal area, more the drag co-efficient which in turn increases the drag force. Hence in order to reduce the drag force, the frontal area must be as low as possible. So we can find that in some bicycles the frame of the bicycle is made oval instead of circular shape. Also the cyclist prefer back down position due to which better aerodynamics can be achieved.

References :

• Aerodynamic Analysis and Drag Co-efficient evaluation of time-trial bicycle riders, https://dc.uwm.edu/cgi/viewcontent.cgi?article=1031&context=etd
• CFD analysis of an exceptional cyclist sprint position,https://www.researchgate.net/publication/331366310_CFD_analysis_of_an_exceptional_cyclist_sprint_position