Flow Over A Bicycle

PROJECT NAME – FLOW OVER A BICYCLE

AIM -

1. To find out relationship between drag force and velocity by considering area of the cyclist and change in the speed of riding a bicycle with respect to incoming velocity.
2. write a programme to plot Drag Co-efficient vs Drag force and find out relationship between them.

OBJECTIVES –

1. To determine relationship between wind velocity and the speed of riding a bicycle.
2. To run a programme in MATLAB and doing Paramatrix study formula for drag force.

FORMULA TO CALCULATE DRAG FORCE-

F_{D =} ½* ξ * A * V² * C_D

Where,

F_D = Drag force in kg.m/s².

ξ = Density in kg/m³.

A = Area in m².

V = Velocity in m²/s².

C_D = Drag Coefficient (Unitless).

If you compare all these units from Left hand side to Right hand side you will get,

kg.m/s² = kg/m³ * m² * m²/s².

After you perform all mathematical operation on above variables you will get,

kg.m/s² = kg.m/s² * C_D.

When cyclists tries to move ahead we know he will face some amount of resistance what we are going to do is to run the programme and study the behaviour of drag force with respect to frontal area of cyclist. Most Important aspect in above formula is the area which is nothing but, Frontal area.

Now when the cyclists change their position while cycling is because he continuously changes its area and this area changing reduces air resistance faced by cyclists to move faster.

Fig. (1) – cyclist facing the drag force

Image from Chegg study

Fig (2) – Frontal area of cyclist

Now open MATLAB and start programming by opening new script file

Always remember to start programme with close all, clear all, clc which clears and erases all the old unnecessary plots, command window data, and other data.

Always start programing with comments because comments clarify the purpose of why and about what we are writing in the programme i.e. it is like a headline.

figure shows the programming done for Flow over a bicycle.

Now for clear understanding of the graph we will be adding some extra commands to show grids on the graph so that results will be clearly visible to the viewer and can be understood better also we will name x axis as velocity and y axis as drag coefficient.

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

%inputs
%drag coefficient 
c_d = 0.8

% Area m^2 
A = 0.362

% Density kg/m^3
rho = 1.2

% Velocity
v = [2:40];

% formula to calculate drag force
drag_force = rho*A*v.^2*c_d*0.5;

plot(v,drag_force)
grid on 
xlabel('velocity')
ylabel('drag force')

Fig (3) More enhanced plot after adding grids, labels to the axes.

Instead of using seperate elements of velocity like [1 2 3 4], if we use range operator [:] we can plot the range of v = [2:40] it means that you are using 40 values of v and after executing this you will see 40 values in your graph with much better and smoother curve.

CONCLUSION-

From above experiment we can conclude that as you increase velocity your drag force increases by the square of velocity that means if the velocity becomes twice the drag force will become four times. In simpler words we can say that drag force and velocity is twice propotional to each other because as velocity is increasing the drag force is also increasing by twice.

With respect to aerodynamics when you are driving cars or aeroplane if you increase your velocity you will experience two times drag force so your fuel economy will drop proportional to your drag force which is bad, that is why supersonic flights are really small because that reduces the frontal area and also the drag coefficient so the drag force will be kept as small as possible.

Now we will write a programme to plot Drag Co-efficient vs Drag force.

As we know that, for the same frontal area the drag coefficient varies for different shapes and we have to plot relationship between them so we will be taking different shapes having different frontal areas and we will see effect of that shape on drag coefficient.

Fig (4) – Values of different drag coefficients

% A program to find relationship between drag force and drag coefficient
clear all
close all
clc

%inputs
%drag coefficient for different shapes

% drag coefficient for sphere
c_d_s = 0.47;

% drag coefficient for halfsphere
c_d_h = 0.42;

% drag coefficient for cone
c_d_c = 0.50;

% drag coefficient for cube
c_d_cu = 1.05;

%drag coefficient for angled cube
c_d_a = 0.80;

% drag coefficient for shorter cyliender
c_d_sc = 1.15;

%drag coefficient for cyliender
c_d_cy = 0.82;

% drag coefficient for streamlined body 
c_d_st = 0.04;

%drag coefficient for streamlined half body
c_d_shb = 0.09;

c_d = [c_d_s, c_d_h, c_d_c, c_d_cu, c_d_a, c_d_sc, c_d_cy, c_d_st, c_d_shb];

% Area m^2 
A = 0.362

% Density kg/m^3
rho = 1.2

% Velocity
v = 4;

% formula to calculate relationship between drag force and drag coefficient
drag_force = rho*A*v^2.*c_d*0.5;

plot(c_d,drag_force)

grid on 

xlabel('drag coefficient')
ylabel('drag force')

Fig (5)– Plot between drag force and drag coefficient.

CONCLUSION-

As graph shows the straight nature and having linear relationship between drag coefficient and drag force we can say that as drag coefficient increases drag force also increases so, if we try to lessen the value of drag coefficient or if we use streamlined bodies rather than having sharp shaped we can definitely reduce the drag coefficient and can improve fuel economy.