AFAIK, altitude data from our recreational GPSes is not real accurate. If you're going to go to this extra effort, I'd make sure I had better data.

A method I'm aware of is using SportTracks training software to download the GPS track from your ride. Use the elevation correction plugin. This will download elevation data for your ride track from SRTM (Shuttle Radar Topography Mission). Then you can examine your track in detail in SportTracks to see the change in elevation between different points on your ride.

I'm sure there are other applications to accomplish the same thing: overlaying your two-dimensional ride track with elevation data from far more accurate measurements than those provided by the phone or bike GPSes we're using today.