To calculate a drag force against the cyclist using matlab

Introduction:

In this project i am going to calculate the different forces that are acting on the bicycle when it\'s in dynamic motion ,we account all the forces to the Ftot.

The forces that we accompained are:

The force resisting the motion of the bicycle Ftotal consists of the sum of rolling friction (Froll), aerodynamic drag (Fwind), the force needed to accelerate (Faccel), the upward slope resistance (Fslope), bearing friction resistance and loss due to the drive train efficiency factor η [Greek letter eta]. Unlike the other quantities, acceleration and upward slope resistance can also be negative - usually a positive thing for the cyclist - propelling rather than retarding the bicycle. Naturally, The drive train losses apply only, if the cyclist is pedalling,Bearing friction, such as friction in the hubs, is usually combined with rolling friction. similarly, the bearing friction forces in the drivetrain, specifically, pedals, bottom bracket, freewheel and partially also the hubs (the additional forces on the hub due to chain tension) are calculated as they affect the drive efficiency η. Thus one arrives at the formula:

Ftotal = (Froll + Fslope + Faccel + Fwind)/η

here η is the Drive train efficiency.

calculation:

To calculate the Ftot in matlab, the program are:

% program to calculate the drag force of bycycle
clear all
close all
clc
%inputs to calculate ftotal=(Froll+Fslope+Facc+Fwind)/n(efficiency)

%calculating rolling resistance
cr=0.015;
m=70;
g=9.81;
Froll=cr*m*g;

%calculating Fslope
%here \\\'s\\\' is the slope
%take slope as 10% i.e the road raises over 10m height over 100m 
%i.e to calculate the slope sind(theta)=0.1,so s=0.1
s=0.1;
Fslope=s*m*g;

%calculation of Faccleration
%here \\\'a\\\' is acceleration
%here a is in m/s^2
a=0.0023;
Facc=a*m;


%calculating of Fwind 
%r is density of air in kg/m^3
%cw is the coefficeient of wind ressistance
%\\\'A\\\' is the frontal area in m^2
%\\\'vwind\\\' is the velocity of the wind m/s 
r=1.2;
cw=[0.45;0.7;1.14;1.28;2.95];
A=1;
v=(1:10);
Fwind=(r*cw*A*v.^2)/2;

%calculating Ftot
n=0.95
Ftot=(Froll+Fslope+Facc+Fwind)/n

%ploting the graph between velocity and Fwind
%to plot the graph between cw and Fwind\\\"simply replace the v with cw\\\"
plot(v,Fwind,\'linewidth\',3)
grid on
xlabel(\'velocity\');
ylabel(\'drag_force\');

Results: In this graph we can see that the increase in the velocity the drag force is increasing,it means it increases exponentially.