To calculate the Drag Force experienced by a cyclist during motion and establish relation between Velocity and Drag Force, Drag co-efficient and Drag Force to study the parameters which increase or decrease drag.

AIM

To calculate the Drag Force experienced by a cyclist during motion taking into consideration variable velocities and drag-coefficients for similar frontal areas and plot the relation between velocity and drag force as well as drag co-efficient and drag force.

GOVERNING EQUATIONS

The equation for the drag force experienced is given by:

`Df = 1/2*rho*V^2*C`

Where,

D_f = Drag Force in Newtons

`rho`= Density of air (usually taken as a standard value of 1.225 kg/m³)

V= Velocity at which the cyclist moves in m/s

C = Drag co=efficient which is a dimensionless quantity

OBJECTIVES

The main objective of the project is to try to figure out the drag force experienced by the cyclist so that we can understand the parameters that increase the drag force, thereby enabling us to limit those factors in practical applications to ensure smoother riding. We also try to understand the relation between velocity and drag force as well as drag co-efficient and drag force which further helps us understand the importance of these variable quantities on drag force (Density of air is usually a constant value).

The workflow of the project is explained below for better understanding:

• The constant parameters are input and set at a particular value.
• For the first plot, the variable parameter (In this case, it is velocity) is given a range of values while all other parameters are set at a constant value and the plot is obtained.
• A similar procedure as the above one is followed to obtain the other plot as well and all results are tabulated and studied in detail for further conclusions.

  PLOTS AND INFERENCES

  The above graph gives the relation between Drag co-efficient and Drag force when velocity is given a single value. We can observe that there is a linear positive relation between the two parameters. We can hence conclude that objects having lesser drag co-efficient produce lesser drag force and hence enable smooth movement. Drag co-efficient is directly proportional to the frontal area, a small frontal area gives lesser drag. This is the exact reason why aeroplanes have streamline shape to avoid drag.

  The above graph gives the relation between velocity and drag force, when drag co-efficient value is kept constant. We can observe a parabolic variation of drag force as velocity increases. We can hence say that both parameters are dependant parabolically.

The above screenshot is that of the coomand window displaying the results of drag force once the tabulation and calculation takes places under both conditions.

BODY OF THE CONTENT

The above question can be solved using octave or Matlab.

This program is written in Octave.

% Calculation of drag force acting on a cyclist
% For shapes having the same frontal area, the drag coefficients of various shapes are given below
%Drag_coeff of cube=1.05;cone=0.5;sphere=0.47;hemisphere=0.42;streamline body=0.04;half steamline=0.09;flat plate=1.28;bullet=0.295;aerofoil=0.45

%  Constant Inputs

D=1.225    % 'D' is the density of air which is a standard value of 1.225 kg/m^3
A =0.1     % 'A' is the frontal area in m^2 which is exposed to air resistance which produces drag


%Plotting with Variable Inputs

figure(1)
V=linspace(1,10,8); % 'V' is the velocity of motion which is considered progressively increasing between 1 and 10m/s in this case
Drag_coeff = 0.6  % Considering drag co-efficient a constant here for the plot of velocity vs drag force
Drag_force= 0.5*D*A*V.^2.*Drag_coeff;  % Dimensionless quantity - Drag Co=efficient
plot(V,Drag_force,'linewidth',2,'color','b');  % Plotting velocity vs drag force
title(' Velocity vs Drag Force');
xlabel(' Velocity ');   
ylabel('  Drag force');

figure(2)
V=2  % Keeping velocity a constant value for the plot of drag co-efficient and drag force
Drag_coeff = [ 1.05 0.50 0.47 0.42  1.28 0.295 0.45 0.04 0.09] 
Drag_force= 0.5*D*A*V.^2.*Drag_coeff % Dimensionless quantity - Drag Co=efficient
plot(Drag_coeff,Drag_force,'linewidth',2,'color','r')   % Plotting drag co=efficient vs drag force
title(' Drag Co-efficient vs Drag Force');
xlabel('Drag Co-efficient');
ylabel(' Drag Force');