Flow Over An Everyday Commuting Bicycle
AIM:
To analyse the variations of drag force over a bicycle with respect to both changes in its velocity as well as when considering different bicycle body shapes.
OBJECTIVES:
- To create a program to understand how the drag force over a bicycle changes when travelling at varying velocities as well as when employing different bicycle body shapes.
- To plot the results obtained depicting how the drag force over a bicycle is affected by changes in travel velocity.
- To plot the results obtained depicting how different body shapes vary the drag force experienced by the bicycle.
MATHEMATICAL MODEL:
The main equation governing the drag force experienced by a body is given by:
Where,
- FD = Drag Force Experienced, kg.m/s^2
- = Density of the considered medium, kg/m^3
- u^2 = Velocity of Bicycle Squared, (m/s)^2
- CD = Drag Coefficient, Dimensionless (varies with bicycle body shape)
- A = Frontal Area of Bicycle, m^2
MATLAB PROGRAM:
In order to proceed with the MATLAB program, a number of assumptions had to be made, such as:
- (da), taken as 1.225 kg/m^3, as the medium through which the bicycle travelled through in this case was air.
- u (v), an array was created to initially analyse how drag forces varried along the bicycle for velcities ranging between 1 and 10 m/s. For the second part of the program, velocity was assumed to be a mean value of 5 m/s to see how drag forces were affected by varying drag coefficients due to different bicycle body shapes.
- CD (cd), initially taken as 1.1 for standard everyday commuting bikes. For the latter part, however, this value is made to be varied between 0.09 and 1.15 through the use of an array in order to assess how drag forces vary according to different bicycle body shapes.
- A (fa), taken as 0.55 m^2 indicating the frontal area of a normal commuting bike.
fa=0.55; %Frontal Area of Normal Commuting Bike (in m^2)
cd= 1.1; %For bikes
v = linspace(1,10,9); %9 Velocity increments taken for bike travelling between 1 and
%10 m/s
da = 1.225; %Density of air taken in kg/m^3
FD = 0.5*da*(v.*v)*cd*fa %Calculates drag force in Newtons for first case
figure(1)
plot(v,FD,'color','b')%To create first plot of velocity vs.drag force
xlabel('Velocity')
ylabel('Drag Force')
grid on
cdall=linspace(0.09,1.15,9);%Drag Coefficient for different bike bodies
%vary between 0.09 to 1.15
vbike=5; %Velocity assumed to be 5 m/s in this case
FD = 0.5*da*vbike*cdall*fa %Calculates drag force in Newtons for second
%case
figure(2)
plot(cdall,FD,'color','r') %To create second plot of drag coefficient vs.
%drag force
xlabel('Drag Coefficient')
ylabel('Drag Force')
grid onPLOT 1: Drag Force (kg.m/s^2) vs. Velocity (m/s)
PLOT 2: Drag Force (kg.m/s^2) vs. Drag Coefficient
CONCLUSION
- In the first case, the graph obtained from studying the variations of drag force with velocity indicates a direct correlation with the two. Drag experienced increases drastically with the increase in velocity of the bicycle. This is an undesirable effect as measures are mostly taken to reduce drag as much as possible in any situation. This can be countered, however, by reducing the frontal area of the bicycle considered as well as employing a more streamlined bicycle body.
- In the second case, the graph obtained shows a direct proportionality between the drag coefficient and the drag force, therefore reiterating the latter point made in the previous case where a body with a lesser drag coefficient would allow for lesser drag to be felt on the bicycle body.
REFERENCES
- Drag Coefficients Obtained:
https://en.wikipedia.org/wiki/Drag_coefficient
- Drag Equation Used:
https://en.wikipedia.org/wiki/Drag_equation
- Bicycle Frontal Area Value Employed: