cycle-path

MATLAB functions to estimate increase in bicycle path length due to lateral bicycle sway

Author(s)	Brief Description	Intended Uses and Known Limitations	Included Material	Updated
Ross Wilkinson, Ph.D.	Uses numerical integration within MATLAB to calculate the increase in the path length travelled by a bicycle due to lean angle.	Investigate the effect of bicycle lean angle on the travel path of a bicycle at specific combinations of ground velocity and cadence. Assumes a sinusoidal travel path with an amplitude proportional to bicycle lean angle.	MATLAB function	April 19, 2021

Description

function [pd, L, v, dT] = analyzeCyclePath(c1,c2,c3,cad,A,D)
    %ANALYZECYCLEPATH Analyze effect of bicycle lean on travel path
    %distance by integrating sine wave function with respect to 
    %distance covered.
    %   Inputs:
    %       c1  - Tyre circumference (m)
    %       c2  - Front-chainring circumference (teeth)
    %       c3  - Rear-sprocket circumference (teeth)
    %       cad - Cadence (rpm)
    %       A   - Amplitude of path due to lean (m)
    %       D   - Straight-line distance from point A to B (m)
    %   Outputs:
    %       pd  - Percentage diff. between new path length and D
    %       L   - New path length (m)
    %       v   - Velocity travelled (m/s)
    %       dT  - Time penalty compared to D (s)
    
    % calculate gain and wave length
    gain = c2/c3;
    lambda = c1*gain;
    
    % calculate period with respect to distance along x-axis
    k = 2*pi/lambda;
    
    % solve sine-wave function to find new path length
    syms x
    L = vpaintegral((A.^2*k.^2*cos(k.*x).^2 + 1)^(1/2),x,0,D);
    
    % calculate increase in path length, ground velocity, and time
    pd = (L/D - 1)*100;    
    v = lambda/(60/cad);
    dT = (L-D)/v;
    
end