FLOW OVER BICYCLE

AIM : To calculate drag force against a cyclist using MATLAB

GOVERNING EQUATION :

`F_D=1/2.ρ.A.v^2.c_d`

`F_D`: Drag force (N)

`ρ` : Density of fluid (air) (`(kg)/m^3`)

`A` : Frontal area of cyclist and bicycle (`m^2`)

`v` : Velocity of the cyclist (`m/s`)

`c_d` : Coefficient of drag

Drag force : A drag force is the resistance force caused by the motion of the body through a fluid, such as water or air. It acts opposite to the direction of the oncoming flow velocity. In this case the cyclist is experiencing a drag force as he is cycling against the wind.

OBJECTIVE :

1. To plot a graph between Velocity vs Drag force.
2. To plot a graph between Drag coefficient vs Drag force.

PROCEDURE :

1. PLOTTING VELOCITY vs DRAG FORCE

• It is better to start programming in MATLAB with these three commands as through these all the previous calculations is erased.

1. clear : This command clear all the data stored in the workspace previously.
2. close all : This command closes all the previous figures and plots.
3. clc : This command clears the command window.

• Now, create all the variables required and assign appropriate value to it.

1. c_d (coefficient of drag) = 0.8
2. A (frontal area) = 0.1
3. rho (density) = 1.2
4. v (velocity) = range from 1 to 10

• Then write the formula through which drag force can be calculated. Use semicolon (;) to suppress unwanted results.

drag_force = 0.5*rho*v.^2*A*c_d

• Now, use the plot command to plot a graph between velocity and drag force. If you want mention the color and the style of the plotting line and also the pointer mark style.

  plot(v,drag_force,”r-*”)

• Now label the x-axis as "Velocity" using ‘xlabel’ command and y-axis as "Drag force" using ‘ylabel’ command.

  xlabel(“Velocity”)

  ylabel(“Drag force”)

• To enable the grid lines use ‘grid on’ command.

CODE :

% A program to calculate the drag force on a cyclist
clear 
close all
clc
% Inputs
% Drag coefficient
c_d = 0.8;

%Area m^2
A = 0.1;

%Density kg/m^3
rho = 1.2;

%Velocity m/s
v = (1:10)

%Drag force N
drag_force = 0.5*rho*v.^2*A*c_d

plot(v,drag_force,"r*-")
xlabel("Velocity")
ylabel('Drag force')
grid on

RESULTS:

PLOT :

II. PLOTTING DRAG COEFFICIENT vs DRAG FORCE

• It is better to start programming in MATLAB with these three commands as through this all the previous calculations is erased.

1. clear : This command clear all the data stored in the workspace previously.

2. close all : This command closes all the previous figures and plots.

3. clc : This command clears the command window.

• Now, create all the variables required and assign appropriate value to it.

1. A (frontal area) = 0.1

2. rho (density) = 1.2

3. v (velocity) = 10

4. For drag coefficient (c_d) we have different values according to the shape of the body.

SHAPE	DRAG COEFFICIENT
Sphere	0.47
Half sphere	0.42
Cone	0.50
Cube	1.05
Angled cube	0.80
Long cylinder	0.82
Short cylinder	1.15
Streamlined body	0.04
Streamlined half body	0.09

• Then write the formula through which drag force can be calculated. Use semicolon (;) to suppress unwanted results.

drag_force = 0.5*rho*v.^2*A*c_d

• Now, use the plot command to plot a graph between drag coefficient and drag force. If you want mention the color and the style of the plotting line and also the pointer mark style.

  plot(c_d,drag_force,”b-*”)

• Now label the x-axis as "Drag coefficient" using ‘xlabel’ command and y-axis as "Drag force" using ‘ylabel’ command.

  xlabel(“Drag coefficient”)

  ylabel(“Drag force”)

• To enable the grid lines use ‘grid on’ command.

CODE :

% A program to calculate the drag force on a cyclist
clear 
close all
clc
% Inputs
% Drag coefficients
c_d = [0.47 0.42 0.50 1.05 0.80 0.82 1.15 0.04 0.09]

%Area m^2
A = 0.1;

%Density kg/m^3
rho = 1.2;

%Velocity m/s
v = 10;

%Drag force N
drag_force = 0.5*rho*v.^2*A*c_d

plot(c_d,drag_force,"b*-")
xlabel("Drag coefficient")
ylabel('Drag force')
grid on

RESULTS :

PLOT :

CONCLUSION :

• From plot between Velocity and Drag force, we can see that there is a non linear relation in them, or in other words if we increase the velocity two times, then the drag force is increased by four times.

• From plot between Drag coefficient and Drag force, we can see that there is a linear relation in them, or in other words as the value of Drag coefficient decreases, the value of Drag force also decreases linearly.