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Yes, it’s the B2 algorithm on a SN80. I programmed the first version of plot track for B1 that Gordon then added to the gps recorder app and it used exactly the equirectangular approximation you have suggested for the Run app. I have just checked and the current version still uses it so the distance should be accurate as I did check its accuracy at the time.
Just to be clear are you saying you are using the B2 algorithm on a SN80 and getting these results ? If so that is really encouraging.
Its an ok approximation method providing you work out the stride distance or have a setting for stride distance. You will know it will be different for each person depending on height. I know for me that 2000 steps (on a pavement) is 1 mile. But walking on tracks, grass, mud etc etc, stride length changes a lot.
I have not tested how accurate the Recorder calculation of distance is using the GPS trace. It may suffer from the bug I just fixed in the RUN app where the distance between two lat/lon's was not an accurate calculation. The 0.03 of RUN app should be good now.
I would definitely recommend you take a look at the RUN App. You can use it with GPS on / off. One option would be to add a stride length and when the GPS is off to estimate PACE and distance based on steps*stride length. Would save a lot of battery.