Flow over Bicycle (MATLAB)

Aim: To calculate drag force against a cyclist using MATLAB

GOVERNING EQUATION :

                                               $F_D=\frac{1}{2}.\rho .A.v^2.c_d$

$F_D$: Drag force (N)

  $\rho$  : Density of fluid (air) ($\frac{kg}{m^3}$) 

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

  $v$  : Velocity of the cyclist ($\frac{m}{s}$)

$c_d$ : 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.

• 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 the 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 the 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.