703A at 7.86V is around 5.5kW. What is the kW rating of the starter? I think my MB diesel starters are around 1.7-1.9kW, and my Cummins 5.9L is 2.6kW or something like that.
Ive seen claims that standard motors have a locked rotor inrush of 600-650% nameplate, while "low inrush" variants are more like 400-450%. If those numbers are correct, it certainly is feasible that for an infinitesimally small period of time, that sort of a peak output was achieved. It seems like it is in the ballpark.
In reality I wouldnt much worry about it. The reality is that if the battery and cabling ESR is around 6.8mOhm, then the battery can source around 1700A in a short circuit condition (I=V/R = 12/0.0068 = 1764.7A). Even a degraded battery can source pretty substantial short circuit current for a very small amount of time, because in a lead acid battery, there is a ready supply of ions in the electrolyte ready to rapidly move. The other reality is that the actual cranking voltage is much lower, for a longer (still short) period of time. That's more of what you need to be concerned about, since that's where the sustained current is high, stuff gets hot, battery conduction voltages drop fast, etc. The reality is that I barely saw a dip below 10V, so while I think a new battery at some point might be smart, its not bad enough to condemn. Its the longer timeframe where batteries that are going to polarize and drop will, and where the sustained high current will heat and bake things.
What was your sampling rate to get those data? Its interesting to see that little blip over 15V. There isnt a significant dI/dt, nor do I think this is that hugely inductive of a system (inductance with a rapid change in current vs time results in a voltage).
Id shop for a battery before the next winter if it was taken here. For you? Maybe a year if it makes you feel good, maybe longer if you test like this again.
