FLOW OVER A BICYCLE

DRAG FORCE AGAINST A CYCLIST

1.AIM:

To calculate drag force on a cyclist

2.INTRODUCTION:

When a body is in motion it is going to face a set of resistances which includes friction,gravitational force ,drag force and some other reactve forces . As previously mentioned ,drag force is one of the resistance forces that caused by motion of a body through a fluid such as water or air . In some cases it is also termed as air resistance or fluid resistance . It acts oppposite to the relative motion of any object with surrounding fluid.

The drag force F_d exerted on a body travelling through a fluid is given by F_d =rho*A*v.^2*c_d*0.5

typically the drag force depends on the properties of the fluid and on the size shape and speed of the object

where

F_d = drag force (in kg*m/s^2)

rho = density of fluid through which the body is moving (in kg/m^3)

v = velocity of the body relative to the fluid (m/s)

c_d = drag coefficient which can varry along with the speed of body (for fluidds like water and air it willbe 0.4 to 1.0) (unitless )

A = projected cross sectional area of the body perpendicular to the flow direction(m^2) i.e, perpendicular to v

3.PRINCIPLE :

As already mentioned the dragforce depends on velocity ,size and shape of the body. For respec-tive drag areas the drag force and velocity are going to be altered. Depending on the value of drag coefficient and drag force cyclist have to monitior kinetic energy. In order to perform motion, the cyclist has to overcome this dragforce . To overcome this drag force cyclists focuses in the major factors that affects drag force i.e, shape . Aerodynamically the cyclist is going to experiance several drag forces according to his position on bicycle as well . In Each and every position, frontal area or drag area is going to varry and different values of drag force are going to be existed. ( "This kind of analysis is majorly done by using CFD simulation techniques where we can explore different parameters regarding the drag force ") . Typically there are 15 cyclist positions which cyclists follows in general can be devided into 3 sets . Frontal area , drag coefficient and drag area for those major cyclist positions along with diagram are also given below .

Photographs, side views and perspective views of first, second and third set of cyclists positions and Frontal area is indicated below picture :-

Frontal area, drag coefficient and drag area for the 15 cyclist positions:

RANKING OF 11 ROAD RACE POSITIONES FROM FASTEST TO LOWEST:

4. OBJECTIVE OF THE PROJECT :

1. To calculate the drag force

2. To plot velocity v/s drag force

3. To plot drag coefficient v/s drag force

5. CODE :

*CODE FOR VARIATION OF VELOCITY AND DRAG FORCE IN GENERAL CASE :

% A program to calculate drag force on a bicycle in 
clear all 
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 = [1:50];

drag_force = rho*A*v.^2*c_d*0.5;
plot(v,drag_force)
xlabel('Velocity')
ylabel('Drag force')

OUT PUT :

c_d =

    0.8000


A =

    0.1000


rho =

    1.2000

>> drag_force

drag_force =

  Columns 1 through 11

    0.0480    0.1920    0.4320    0.7680    1.2000    1.7280    2.3520    3.0720    3.8880    4.8000    5.8080

  Columns 12 through 22

    6.9120    8.1120    9.4080   10.8000   12.2880   13.8720   15.5520   17.3280   19.2000   21.1680   23.2320

  Columns 23 through 33

   25.3920   27.6480   30.0000   32.4480   34.9920   37.6320   40.3680   43.2000   46.1280   49.1520   52.2720

  Columns 34 through 44

   55.4880   58.8000   62.2080   65.7120   69.3120   73.0080   76.8000   80.6880   84.6720   88.7520   92.9280

  Columns 45 through 50

   97.2000  101.5680  106.0320  110.5920  115.2480  120.0000

>> 

PLOT :

*CODE FOR VARIATION OF VELOCITY AND DRAG FORCE FOR 15 CYCLISTS POSITIONS :

% Inputs 
% drag coefficient
c_d= [0.568,0.588,0.604,0.611,0.615,0.618,0.638,0.641,0.641,0.644,0.655,0.655,0.677,0.677,0.679];

% Area m^2
A = [0.244,0.331,0.333,0.334,0.339,0.343,0.344,0.345,0.355,0.370,0.370,0.371,0.374,0.381,0.423];

% Density kg/m^3 
rho =1.2

% Velocity m/s 
v = [1:15]

drag_force = rho.*A.*v.^2.*c_d.*0.5;
plot(v,drag_force)
xlabel('velocity')
ylabel('Drag force')

OUTPUT

rho =

    1.2000


v =

     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15

>> drag_force

drag_force =

  Columns 1 through 11

    0.0832    0.4671    1.0861    1.9591    3.1273    4.5786    6.4525    8.4920   11.0592   14.2968   17.5946

  Columns 12 through 15

   20.9956   25.6743   30.3334   38.7743

>> 

PLOT:-

**CODE FOR VARIATION OF C_d AND DRAG FORCE IN GENERAL CASE :-

% A program to calculate drag force on a bicycle 
clear all 
close all
clc

% Inputs 
% drag coefficient
c_d= linspace (0.8,1.8,50)

% Area m^2
A = 0.1

% Density kg/m^3 
rho =1.2

% Velocity m/s 
v = 15

drag_force = rho*A*v.^2*c_d*0.5;
plot(c_d,drag_force)
xlabel('c_d')
ylabel('Drag force')

OUTPUT:

c_d =

  Columns 1 through 11

    0.8000    0.8204    0.8408    0.8612    0.8816    0.9020    0.9224    0.9429    0.9633    0.9837    1.0041

  Columns 12 through 22

    1.0245    1.0449    1.0653    1.0857    1.1061    1.1265    1.1469    1.1673    1.1878    1.2082    1.2286

  Columns 23 through 33

    1.2490    1.2694    1.2898    1.3102    1.3306    1.3510    1.3714    1.3918    1.4122    1.4327    1.4531

  Columns 34 through 44

    1.4735    1.4939    1.5143    1.5347    1.5551    1.5755    1.5959    1.6163    1.6367    1.6571    1.6776

  Columns 45 through 50

    1.6980    1.7184    1.7388    1.7592    1.7796    1.8000


A =

    0.1000


rho =

    1.2000


v =

    15

>> drag_force

drag_force =

  Columns 1 through 11

   10.8000   11.0755   11.3510   11.6265   11.9020   12.1776   12.4531   12.7286   13.0041   13.2796   13.5551

  Columns 12 through 22

   13.8306   14.1061   14.3816   14.6571   14.9327   15.2082   15.4837   15.7592   16.0347   16.3102   16.5857

  Columns 23 through 33

   16.8612   17.1367   17.4122   17.6878   17.9633   18.2388   18.5143   18.7898   19.0653   19.3408   19.6163

  Columns 34 through 44

   19.8918   20.1673   20.4429   20.7184   20.9939   21.2694   21.5449   21.8204   22.0959   22.3714   22.6469

  Columns 45 through 50

   22.9224   23.1980   23.4735   23.7490   24.0245   24.3000

PLOT :

**CODE FOR VARIATION OF C_d AND DRAG FORCE FOR 15 CYCLISTS POSITIONS :

% A program to calculate drag force on a bicycle 
clear all 
close all
clc

% Inputs 
% drag coefficient
c_d= [0.568,0.588,0.604,0.611,0.615,0.618,0.638,0.641,0.641,0.644,0.655,0.655,0.677,0.677,0.679];

% Area m^2
A = [0.244,0.331,0.333,0.334,0.339,0.343,0.344,0.345,0.355,0.370,0.370,0.371,0.374,0.381,0.423];

% Density kg/m^3 
rho =1.2;

% Velocity m/s 
v = 15;

drag_force = rho.*A.*v.^2.*c_d.*0.5;
plot(c_d,drag_force)
xlabel('c_d')
ylabel('Drag force')

OUTPUT:-

drag_force =

  Columns 1 through 11

   18.7099   26.2748   27.1528   27.5500   28.1455   28.6165   29.6287   29.8546   30.7199   32.1678   32.7172

  Columns 12 through 15

   32.8057   34.1817   34.8215   38.7743

>> 

PLOT:-

6.EXPLANATION OF THE CODE :

1. In first case values of density ,frontal area and varying velocity are given initialised

2. Inputs executed according to the given formula of drag force

3.By the obtained value of drag force and velocity graph is plotted between them

4.In second case values of density ,frontal area, velocity ,varying c_d are given and initialized

5.Inputs executed according to the given formula of drag force

6.By the obtained value of drag force and velocity graph is plotted between them

7. OBSERVATIONS

1. Variation of drag force and velocity is parabolic

2.Variation of drag force and drag coefficient is linear

8. CONCLUSION:

1.Calculated drag force for different frontal areas of different cyclist positions.

2.Variation of drag force with Velocity and drag coefficient is studied .

3. Ranked different cyclist positions from fastest to lowest according to drag area