A part of the problem with any discussion of range is that no one who was there ever seems to give actual ranges. Without going into a detailed discussion of hydrodynamic drag it can be simply said that drag increases as the cube of the speed. It takes 1000 times as much horsepower for any ship to make 10 knots as it does to make 1 knot. At 15 knots you're using 3375 as much power as you were at 1 knot. That's more than 3 times the horsepower required to cruise at 15 knots than at 10 knots. does that equate to 3 times the fuel consumption and 1/3 the range? I don't know, and I admit it does sound extreme.
By that calculation a ship is using 9261 times as much power at 21 knots as it was at 1 knot. If a Gato class submarine makes 21 knots at 5400 horsepower then it only needs 1970 horsepower to cruise at 15 knots and 580 horsepower to cruise at 10 knots, again just over 3 times the power. On the other hand Dick O'Kane says that they cruised at 80% power, which would be 4320 hp, which by the relative drag calculation would give 16.3 knots.
But there's another problem. The Gato's range is listed variously as 11,000 nm, 11,800 nm and 12,000 nm at 10 knots. Even at the 12,000 mile range that makes for a patrol of 50 days, and the Gato is also listed as carrying fuel for 75-day patrols. At 10 knots that's 18,000 nm, not 12,000. Even if 15 knots required twice the fuel that would still give a 9000-mile range.
Without actual reports of how fast they cruised it's impossible to know what the reality was.
What is the game reality? Go different speeds and check the estimated range at those speeds.
If you have the patience here is an old discussion on the subject which I found informative and enlightening, even if in the end there is still nothing truly conclusive.
http://warships1discussionboards.yuk...-Type-IX-Range