Aero Magic

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Virtual Elevation: Does Rotational Inertia Play a Role?

The method of Virtual Elevation and all its variants are derived from Newton’s 2nd Law for linear motion, neglecting rotational inertia terms.   Do those additional terms play a significant role in elevation-matching? Can we accurately measure the moment of inertia (MOI)? In this post, I’ll describe the terms and provide a [...]

VE: A Test of the Small-Angle Approximation

A recent discussion on the Wattage Training Forum got me to hack the VE code to quantify the difference between the exact and small-angle version of the VE calculation.

The columns of the resulting CSV file are as follows:

SAMPLE #: row index
SLOPE_EXACT,SLOPE_SA: exact and small-angle slope
DELTA_EXACT,DELTA_SA: delta-elevation, exact and small-angle
ELEV_EXACT,ELEV_SA: cumulative elevation, exact and small-angle

The final [...]

VE Update: Improved Stability and Convergence

I was looking at the convergence of the first version of VE and thinking, “this can’t be right…”. When it’s coded right, Newton-Raphson typically converges extremely well, or not at all.

So looking at the code I realized I made a beginner mistake and used a one-sided numerical differentiation scheme:

sub fy
{

my $x [...]

VE - A Perl Script for Virtual Elevation Calculations

In trying to create a prototype for Golden Cheetah, I put together this perl script that I submit for your perusal.   The script comes with the sample data used by Robert Chung in his recent post to the Wattage Forum, so it may look familiar to many of you.

My aim was to match a known [...]