MATLAB project : To calculate the Drag force experienced by the cyclist and plot the various graphs.

1.AIM :

To calculate the drag force experienced by the cyclist.
To plot a graph between Velocity of cycle(v) to the drag experienced by the cyclist (Fd).
To plot a graph between Drag Coefficient (Cd ) and Drag force(Fd).

2.Governoring Equation

Fd = 0.5 *Cd*v*v*𝞀

Where,

Fd = Drag force

Cd = Coefficient of drag

v = Velocity of the cyclist

𝞀 = Density of the air

3.Objective of the project

To write a MATLAB code that will help visualise the graph as mentioned above.

4.Procedure

When a cyclist moves in a direction it experiences a resistive or friction force.
In fact, there are a lot of forces which may act on the cyclist during his run, like friction forces between road and tyres of the bicycle,force of friction between chain and sprocket etc.
But for our consideration we are taking into account the force which is experienced by the cyclist due to air,which is also known as Drag Force.
Why do cyclists experience such force ?
Well, it is explained by Newton’s 3rd Law of Motion, Which states that for any action there is an equal and opposite reaction.
To calculate the drag force we will use the following relation

Fd = 0.5 *Cd*v*v*𝞀.

Different position of the cyclist affects the drag force.

: www.princeton.edu

fig. 1 showing different positions of cyclist

2. As we can see from the above figure that how Cd changes as the cyclist changes its position. Moreover we can say that Drag Coefficient is not entirely dependent upon the area of cyclist.

3.We can see in the streamlined position case in respect to the above figure, In this case the cyclist has adjusted himself in aerodynamic position, so that he can minimise the drag.

Conversion of area from ft to m^2.

Upright commuter 5.5 ft^2 = 0.511m^2
Racing 3.9 ft^2 = 0.362m^2
Drafting 3.9 ft^2 = 0.362m^2
Streamlined 5 ft^2 = 0.464m^2

Coding part of the project begins.

1st Program

%To plot a graph between Velocity and Drag Force for upright commuter
%Language used is MATLAB


% Defining variables and constants as per the equation



cd = 1.1;  %it is the coefficient of drag,it is a unit less quantity



rho = 1.2;  %density of fluid in Kg/M^3



a = 0.511;     %Area under drag in M^2 area here is the front area of cyclist in the direction of motion



v = [1:100]; %velocity of the cyclist in  m/sec



drag_force=0.5*rho*v.^2*cd; %drag force is in newton(N)



plot(v,drag_force,'linewidth',4) % To plot the graph between velocity and drag force



xlabel('velocity') % To mark ‘x’ axis as velocity



ylabel('drag_coefficient') % To mark ‘y’ axis as drag coefficient

2nd Program

%To plot a graph between Drag Coefficient (Cd ) and Drag force(Fd).
%Language used is MATLAB



% Defining variables and constants as per the equation

Cd = 1.1

cd = linspace(1.1,1.1,100);

%it is the coefficient of drag, it is a unit less quantity



rho = 1.2;  %density of fluid in Kg/M^3



a = 0.511;     %Area under drag in M^2 area here is the front area of cyclist in the direction of motion



v = [1:100]; %velocity of the cyclist in  m/sec



drag_force=0.5*rho*v.^2*Cd; %drag force is in newton(N)



plot(cd,drag_force,'linewidth',4) % To plot the graph between velocity and drag force

xlabel('cd') % To mark ‘x’ axis as Cd  drag coefficient

ylabel('drag Force') % To mark ‘y’ axis as Drag Force

5.Explanation of the commands used

Plot : It is used to generate a 2-d graph from the defined variables.
Linewidth : It is used to adjust the thickness of the graph line.
linspace : It is used to genereate a matrix in which user defines the range and number of outputs.

6. Error encountered during program 2

When I tried to plot a graph between Drag Coefficient (Cd ) and Drag force(Fd).The graph came blank like this
To fix this error i needed a matrix of cd with 1 row and 100 columns, then i used linspace command as the value of cd = 1.1, then syntax will be

linspace(1.1,1.1,100)

It will generate me a matrix with 1.1

3. I needed this because drag force has a 100 values to plot a graph, I needed 100 values of cd (coefficient of drag) as well.

4.In my 2nd Program i have used cd and Cd, both actually hold same value, only difference is,

cd = holds value in 1 row and 100 columns, It is used for ploting purpose.

Cd = holds value in 1 row and 1 column, it is used in equation of drag force for calculation purpose.

Outcomes of the program 1 are as follow :

Case 1 :

Cd = 1.1 and A = 0.511m^2