Week 1 - Flow over Bicycle

Introduction

Drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid in this case air. To calculate drag force velocity, drag coefficient, frontal area, density of air are required to be known.

The formula used to calculate Drag Force `D = 0.5*Cd * A *ρ * v^2`

where,

`Cd=`Coefficient of drag

`A=`Frontal Area

`ρ=`Density of Air

`v=`Velocity

Inputs

Coefficient of Drag is taken from internet for different shapes-

1. Streamlined Body : 0.04
2. Streamlined Half-Body : 0.09
3. Half-Sphere : 0.42
4. Sphere : 0.47
5. Cone : 0.5
6. Angled Cube : 0.8
7. Long Cylinder : 0.82
8. Cube : 1.05
9. Short Cylinder : 1.15

Area and Density are taken inputs from the user in this case `0.1 m^2` and `1.2 kg*m^-3`. Velocity is entered as a row matrix 1 to 50. Two variables m and n are input as 1.

Code

1. Inputs are entered for drag force to be calculated.
2. First for loop is used to calculate drag force and plot drag force vs velocity for coefficient of drag of different shapes.
3. Second for loop is used to calculate drag force and plot coefficient of drag vs drag force for velocity equal to `5, 10, 15, 20, 25, 30, 35, 40, 45 and 50 m/s`.
4. Every plot is saved in the current directory.

% A program to calculate the drag force on a cyclictclose allclear allclc% Inputs% Drag coefficients of different shapescd=[0.04 0.09 0.42 0.47 0.5 0.8 0.82 1.05 1.15];% Displaying Drag Coefficients for different shapesdisp('Streamlined Body : 0.04');disp('Streamlined Half-Body : 0.09');disp('Half-Sphere : 0.42');disp('Sphere : 0.47');disp('Cone : 0.5');disp('Angled Cube : 0.8');disp('Long Cylinder : 0.82');disp('Cube : 1.05');disp('Short Cylinder : 1.15');% Area of the cyclict m^2A=input('Enter the area of the cyclist : ');% Density kg/m^3rho=input('Enter density of the Air : ');% Velocity m/sv=[1:50];% Variables = 1 for sprintfn=m=1;% Plotting drag force vs velocity for every value of cdfor i=1:length(cd)  drag_Force=rho*A*v.^2*cd(i)*0.5;    plot(v, drag_Force);  xlabel('Velocity (m/s)');  ylabel('Drag Force (N)');  grid on  file_plot=sprintf('Velocity_vs_Drag_Force_%d.png',n);  saveas (gca, file_plot);  n=n+1;end% Plotting cd vs drag force for velocity = 5,10,15,20,25,30,35,40,45,50for j=1:length(v)/5  v1=v(j*5);  drag_Force_1=rho*A*v1^2*cd*0.5;    plot(drag_Force_1,cd);  ylabel('Coefficient of Drag');  xlabel('Drag Force (N)');  grid on  file_plot1=sprintf('Drag_Force_vs_cd_%d.png',m);  saveas (gca, file_plot1);  m=m+1;end

Errors

Instead of using v1 in calculating drag force v was used which is a higher order matrix.

Output

The plots for drag force vs velocity-

Streamlined Body : 0.04

Streamlined Half-Body : 0.09

Half-Sphere : 0.42

Sphere : 0.47

Cone : 0.5

Angled Cube : 0.8

Long Cylinder : 0.82

Cube : 1.05

Short Cylinder : 1.15

Plots of coefficient of drag vs drag force for velocity equal to `5, 10, 15, 20, 25, 30, 35, 40, 45 and 50 m/s`-

Velocity : `5ms^-1`

Velocity : `10ms^-1`

Velocity : `15ms^-1`

Velocity : `20ms^-1`

Velocity : `25ms^-1`

Velocity : `30ms^-1`

Velocity : `35ms^-1`

Velocity : `40ms^-1`

Velocity : `45ms^-1`

Velocity : `50ms^-1`