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How long did it take a US fleet submarine running on the surface to recharge its battery fully for maximum duration submergence?

I realize that the answer depends on how many engines were being used for recharging, versus propulsion — I imagine that in a really tight situation that anticipated an imminent need for long submergence, all four diesels would be thrown into recharging, as fast as possible.

In Edward L. Beach's novel Run Silent, Run Deep, at one point the protagonist/narrator Lt. Cmdr. Richardson indicates that with two of his four engines recharging the battery, every 10 minutes gives them another hour of submergence, if that becomes necessary. But 10 minutes for an hour submerged running time, even at only 2 knots, seems very optimistic. Or am I wrong?

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    +1 for the question being interesting, and FYI there's a Physics Stack Exchange in the (unlikely) event this question gets closed as off topic for a reason or another. – Denis de Bernardy Mar 30 at 19:44
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    Electrical Engineering SE has a batteries tag. – Rodrigo de Azevedo Mar 31 at 8:29
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Run silent, run deep is about a WW1 S-class submarine. Looking at their specifications they all have 2 diesels, not 4.

Using a Group 1 sub as an example:

Propulsion: 2 × New London Ship and Engine Company (NELSECO) diesels, 600 hp (448 kW) each; 2 × electric motors, 750 horsepower (560 kW) each; 120 cell Exide battery; two shafts

Speed: 14.5 knots (27 km/h) surfaced; 11 knots (20 km/h) submerged

So with 2 diesels dedicated to charging, they put 900 kW into the batteries. 10 minutes gives 9000 kW.min or 150 kWh, enough to run one motor at 1/4 load for an hour. (yes, I ignored charging losses. I've no idea how efficient 1914-era electric systems were). 1/4 on one motor should be enough to get to 2 kts (drag increases with the square of speed).

The big question is what the non-propulsion loads were. If we take 30 kW (a little under 1 kW/person for the 40-man crew) that gives 5 hours of endurance if you're sitting still.

The later groups have more diesel power. For a Group 1 boat it really depends on the non-propulsion load, but the later groups should be able to do it.

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