Calculation of drag force on a bicycle using Matlab

AIM: Calculating the drag force over a bicycle by the flow of air and

To plot the relation between the velocity of the bicycle and drag force and

To plot the relation between drag coefficient and the drag force.

%Air flow over a Bicycle

clear all
close all
clc

%input parameters

%drag co-efficient
c_d= [0.9:1.1]; %dimensionless

%frontal area
a= 0.45; %m/s^2

%density
rho= 1.225; %kg/m^3

%velocity
v= [1:15]; %m/s

%drag_force
drag_force = rho*a*c_d*v.^2*0.5;  %N

%plotting
%plot1
figure(1)
plot(v,drag_force);
xlabel('velocity');
ylabel('drag force');
grid on

the above code is for plotting velocity and drag force

%Air flow over a Bicycle

clear all
close all
clc

%input parameters

%drag co-efficient
c_d= [0.9 1 1.1]; %dimensionless

%frontal area
a= 0.45; %m/s^2

%density
rho= 1.225; %kg/m^3

%velocity
v= 5.5; %m/s

%drag_force
drag_force = rho*a*c_d.*v.^2*0.5;  %N

%plotting
%plot1
figure(1)
plot(c_d,drag_force);
xlabel('drag coefficient');
ylabel('drag force');
grid on

the second code is for plotting drag coefficient and drag force.

ASSUMPTIONS:

the drag cofficient for constant front area but different shapes i.e. for different cycling positions was obtained from the following source and was found to be mainly in the range of 0.9 to 1.1

https://www.engineeringtoolbox.com/drag-coefficient-d_627.html

the frontal area is assumed to be 0.45 m^2.

it is an average of various positions of bicycling as given in the below reference. https://www.cyclingpowerlab.com/CyclingAerodynamics.aspx

the density of air is taken as 1.225 kg/m^3

for the first code, the velocity is assumed in the range of 0 to 15 m/s i.e. 50 kmph.

for the second code, the velocity is assumed to be 20 kmph i.e. 5.55 m/s.

PROCEDURE:

1. the constant values such as frontal area, density of air, drag coefficient, velocity are given in the code.

2. theoretically, the formula for drag force is given by

`F_d= 0.5*a*rho*v^2*c_d`

where F_d is drag force (in newtons)

3. hence, the formula for drag force is written and the element wise operator is included for velocity as it varies form 0 to 15.

4. the plot operator is used to plot the required relations.

5. the 'xlabel', 'ylabel' operators are used to name the x and y axis respectively.

6.the 'grid on' function is used.

7. the 'figure' function can be used to include 2 plots in the same code but the element wise operator must be used appropriately for required variables in the drag force formula

8.the program is run and the 2 plots are obtained.

RESULTS:

from the plots, we can infer that

1. the drag force is directly proportional to the square of velocity. hence, for a slight increase in velocity, there will be a huge increase in drag force.

2. the drag force is almost directly proportional to drag coefficient.

from these, we can conclude that for attaining high speeds with little resistance, one must reduce the frontal area, i.e. make the object/vehicle more aerodynamic and choose shape with low drag coefficient.