Aero Magic

raam-055 2010-05-14-18-45-47 2010-05-14-18-42-52

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 elevation numbers are as follows:

SAMPLE # ELEV_EXACT ELEV_SA
2978 8.51942653497284 8.55456417534516

Conclusion: The cumulative error on the final elevation of the ride is on the order of about 0.4% error.

Downloadable results and code are here.

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