12V voltage recovery curve used by battery testers? Probably not.

I was pondering how the little battery testers determine SOH and thought it might have something to do with how the battery voltage recovers once the load is removed. So I measured the voltages and fit them with the tool at mycurvefit.com. This battery is 4 years old and has seen better days. It was driven for about an hour the day before, sat overnight with the hood unlatched and the battery voltage before doing anything was 12.64 V. Before the measurements were started the following operation was performed by a helper (I was measuring at the jump point under the hood).

Push unlock on remote 2 times.
Open passenger side front door and enter, leaving door open.
Put fob in ignition.
Press Power twice with foot off brake
Put all 4 windows down an inch. (voltages as low as 11.8 V observed here)
Power off
Exit car
Lock car

Immediately start taking measurements (minutes,volts):

0 12.56
1 12.59
2 12.60
3 12.61
4 12.62
5 12.62
6 12.62
40 12.64

This data was graphed and curve fitted (I picked the equation)



A few problems are evident. The voltmeter only has 2 digits to the right of the decimal place so it ends up quantizing values in the flat part of the curve - to make an accurate curve this way one would have to measure more accurately, but these devices display a battery voltage which looks like these values, so they probably don't have the extra accuracy needed. As a corollary the curve fit needed to take this accuracy limit into account, and it doesn't, so the curve it fit misses the last point. Finally, It takes a long time for the voltage to fully recover, so finding the value in the exponent (-0.3367459) requires a much longer test than these devices apply.

Anyway, the equation's "a" is just the %SOC as a voltage, "b" is the starting voltage as an offset from "a", and "c" is the interesting part, describing how fast the battery recovers (the value here is in inverse minutes). "b" could be set anywhere on the curve, it doesn't tell us anything about the battery, it tells us about the experiment. Presumably a bad battery recovers slower than a good one and the "c" value would reflect that. I suppose that it's possible the devices make a bunch of fast measurements on the rapidly rising part of the curve, but fitting all 3 values with the limited accuracy that way would be tricky.