Parameter Estimation with Virtual Elevation

Note: This post has been migrated from my old WanderTech blog. The original post contained various screenshots of the Virtual Elevation software which are currently missing. I’ll update this post if I can track down the original images.

Virtual Elevation is a parameter estimation tool used to estimate constants associated with any dynamic system. Using Monte Carlo Methods and some proprietary optimization techniques, any two fully de-coupled parameters can be simultaneously estimated quickly and accurately.

These methods have been successfully applied to bicycles (estimating CdA and Crr), and cars (estimating Cx and Crr). In both cases the results were not only accurate (between 2%-10% of true value), but also repeatable and quick.

Bike VE

Bike VE is a prototype desktop application to estimate CdA and Crr from Garmin .TCX files. It has been developed and tested with fantastic results. The application works on Windows 7 and requires just a few inputs:

Required inputs:

  • Total mass (including bike, rider, equipment)
  • Air density (in kg/m³)

Optional inputs:

  • Lap number for analysis
  • Wind speed (in m/s)
  • Wind direction (in radians or compass directions like ‘N’, ‘NE’, ‘NNE’)

The analysis process:

  1. Import any Garmin .TCX file containing power data
  2. Fill in the required mass and air density values
  3. Add optional wind and lap information if available
  4. Click Calculate to run the analysis (typically takes 60-120 seconds for an hour-long file)
  5. Review the Virtual Elevation plot comparing actual vs. calculated elevation profiles
  6. Find output files in the ‘files’ directory, including converted .csv and results

The Virtual Elevation plot provides a quick visual assessment of fit quality - the calculated virtual elevation (green) should closely match the actual elevation profile (blue). Deviations often indicate sections with braking or other non-steady-state riding that weren’t part of the designed test protocol.