I had experimented with Kokam LiPo 85Ah and they sag for cca 8% at 225A when charged to 4V/cell, which is the max i dare to load them. I think that is quite good for such a small cell!You're right, you can get 1200A out of the average battery pack. The issue with that is twofold. One, the battery has some effective resistance itself and this will cause the pack to sag when you draw a lot of power. And two, its not particularly good on the battery to draw it too heavily (chemical and mechanical damage may result). I've seen plenty of graphs of the Tesla battery pack when doing hard accelerations. They sag that pack pretty heavily when drawing 1000A. So, I wonder what your "most of a volt pack" does when you draw 1200A. There's no way I'd believe you're still seeing 340V when you do that. It's pretty likely it sags by many 10's of volts. I wouldn't even doubt it if you said it sags to 280V or less. To some extent that's OK. Like I said, Tesla packs sag *heavily* when you draw on them hard. It isn't as heavy a sag as you see with lead acid batteries but lithium cells certainly do sag.
I'd be interested to hear how those volt cells hold up in the long run. It's always a bit of a gamble but maybe they'll do fine and I'll be surprised.
Also i have made one cell of 48P1S panasonic NCR18650PF. So some 134Ah cell in effect. They show 13% voltage drop at same load. I put it in my car in series with kokams. Liions have more Ri and it shows with load. When i remove my foot however they bounce back to 3.9V/cell without significant effect. No significant temp increase too. They are just softer...
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