Flow over a bicycle using Matlab

Aim: - To Calculate Drag Force over a cyclist

Objective:-

1) To plot Velocity vs Drag Force

2) To plot Drag coefficient vs Drag Force

Introduction:-

Drag force is the resistive force experienced by a body in a fluid film which resist the relative motion between both.

Frontal Area is the area in contact with the incoming fluid and on which the drag force acts.

Drag coefficient which quantify the drag that will be faced by the body. Lesser the coefficient lesser is the drag. It is based on skin friction and form drag as in our case we are considering drag due to the form of the body .

Drag force is expressed as:-

F_d = ρ * 0.5 * A * V² *c_d

Where;

F_d = Drag Force (N);

ρ = Density of the fluid in which motion of body is taking place (kg/m³);

A = Frontal area which is in contact with the incoming fluid (m²);

V = velocity of the body (m/s);

c_d = coefficient of drag

Program :-

Case 1:-Velocity vs Drag Force

Parameters assumed:-

Frontal Area (A):-1m²

Coefficient of Drag (c_d):-0.8

Velocity is varying from 1 to 50 m/s

rho (ρ)=1.2kg/m³(Air is assumed to be the medium)

%A program to calculate drag force
clc
clear all
close all
%Inputs
%Drag_coefficient
c_d= 0.8;
%Area m^2
A=0.1;
%Density kg/m^3
rho=1.2;
%Velocity
V=[0:50];
drag_force=rho*A*V.^2*c_d*0.5;
plot(V,drag_force,'color','r','linewidth',3)
xlabel('Velocity(m/s)')
ylabel('Drag force(N)')
grid on

Fig 1.Velocity vs Drag Force

Conclusion: - Drag force is increasing to square of the velocity .As the velocity of the cyclist increases the drag force increases.

Case 2:-Drag coefficient vs Drag force

Parameters assumed:-

Frontal Area (A):-1m²

Coefficient of Drag (c_d) is varying from 0.04 to 1.05

Velocity (V) = 1 m/s

rho (ρ)=1.2kg/m³(Air is assumed to be the medium)

%A program to calculate drag force
clc
clear all
close all
%Inputs
%Drag_coefficient
c_d=[0.47 0.42 1.05 0.80 0.82 0.04 0.09];
%Area m^2
A=0.1;
%Density kg/m^3
rho=1.2;
%Velocity
V=1;
drag_force=rho*A*V^2*c_d.*0.5;
plot(c_d,drag_force)
xlabel('Coefficient of drag')
ylabel('Drag force(N)')
grid on

Fig 2. Coefficient of drag vs Drag Force

Conclusion: - Drag force is in linear relationship w.r.t coefficient of drag.

Case study:-

Considering a case in which a cyclist is drafting behind another cyclist; calculating the drag force experienced by both the cyclist and the reduction in drag force of the following cyclist.

Fig 3. Various drag coefficients over different shapes

Fig 4 .Effect of Drag Force when a cyclist is following another cyclist

Case 3:-Velocity vs Drag Force for two cyclist

Parameters assumed:-

1) For Leading Cyclist

Frontal Area (A1):-1m²

Coefficient of Drag (c_d) considering streamline body from (fig 3):-0.04

Velocity (V1):-1m/s

rho (ρ)=1.2kg/m³(Air is assumed to be the medium)

2) For the Following Cyclist

Assuming frontal area of the following cyclist to be 10% of frontal area of leading cyclist

Frontal Area for the leading cyclist (A2):-0.1* A1

(A2):-0.1 m²

Coefficient of Drag (c_d) considering half streamline body from (fig 3):-0.09

Velocity of following bike is assumed to same as first bike otherwise it will lead to following bike crashing into leading bike (V2):-1 m/s

rho (ρ)=1.2kg/m³(Air is assumed to be the medium)

%A program to calculate drag force for two cyclist 
clc
clear all
close all
%Inputs
%Drag_coefficient
c_d1=0.04;
c_d2=0.09;
%Area m^2
A1=1;
A2=0.1;
%Density kg/m^3
rho=1.2;
%Velocity
V=[0:50];
drag_force1=rho*A1*V.^2*c_d1*0.5;
drag_force2=rho*A2*V.^2*c_d2*0.5;
plot(V,drag_force1,'color','b','linewidth',3)
hold on;
plot(V,drag_force2,'color','r','linewidth',3)
xlabel('Velocity(m/s)')
ylabel('Drag force(N)')
grid on

Fig 5.Difference in Drag force between two cyclists over range of the velocity

Conclusion: - There is subsequent decrease in drag force between the leading cyclist (shown in blue colour) and following cyclist(shown in red colour).