TL;DR: that is difficult to say. Mainly due to technological limitations and fluid dynamics, and as such there is a correlation between output of the engines (or reactors) and the current speed of the vessel. In other words: time to ramp the power plant to max output is THE time ship needs to accelerate to flank/emergency speed. For USS Iowa it will be about 45 min to emergency speed (assuming 15 kt comfy maneuvering speed), about 120 min during peace time for flank (from same 15kt). The difference between flank speed and emergency speed is in the time to get there, as the latter is wartime.
Full answer:
In fact, you should ask about time to flank speed, as this would be your only measure of maximum output shaft horsepower (on all shafts). The power delivered to the shafts is just enough to propel ship at desired speed, and a bit more if ship is accelerating, and the power output is increased in increments as long as the target speed is not achieved. And this is where we start getting into trouble with said physics and fluid dynamics.
For example, HMS Canada
could cruise at 14 knots using less than 18% of nominal power, yet reaching 22 knots required her full (nominal) power of over 38k shp (303 RPM). And during trials she exceeded 24 knots, at 52.6k shp (and propeller shaft RPM exceeded 335).
See "British Battleships of World War One: New Revised Edition" for more details.
So you see, the problem at some point is the water... Because at those speeds water is... well, hard would be one way of putting it. Another is: when one goes that fast it's not a lubricant anymore...
Another problem is cavitation, which was recognized well after 1960s, and which reduces the efficiency of powertrain.
And last but not least... With the exception of nuclear-powered ships designed from keel as such, ships' designs are optimized for cruising speed (which is not the max speed), and those designs are not efficient at high speeds. There are ways to alleviate that, but obviously older designs would be deficient in that regard too, sometimes greatly. This has to do with fuel consumption, which is not a concern for nuclear-powered vessels. So while it's not in your question, I would recommend to do any comparison on era-by-era basis.
To illustrate the difference of the hull optimization: USS Iowa
was rated for power output of 158MW. That's slightly more than 80% of the Nimitz Class CV
s 194MW. Both are rated at 30+ kts max speed, so it shows the problems, limitations, general approach and specific solutions used: battleship with a full load displacement of a bit more than half of the Nimitz Class CV
's (58kt vs 102kt) has that much power and is just a smidge faster than a CV. The only real difference is that Iowa
is rated for 10000 nautical miles of range, Nimitz's
range is 25 years and fuel for all his aircraft.
So. By now you should see the problem with your question...
Typically battleships of that size (25-30k tons displacement) required about 50-60 min to reach maximum speed. They could reach maximum power only during max-speed runs, as power produced by the engines must be dumped somewhere, and you literally can't run ship's propeller shaft from start to 225-335 RPM immediately. If that would happen, the propeller shaft would overheat and warp in seconds, most probably, and the propeller itself would break off (big ship = big propeller, which is HEAVY), quite probably before the warping.
USS Iowa
, when on her trials, reached contracted 32.5 knots, and that required about 212k shp. And she was running light for that (so no full bunkers, no full ammo load, no full crew), as well as it was a shallow water run.
And one must not forget that USS Iowa
was built with designed overload of 20%, so we don't really know how fast really she could go. Same thing would apply to most WWII-era ships.
According to an article I found USS Iowa
requires superheat condition on her boilers if the required speed is above 22 kts. Going from "no superheat" to "full superheat" requires 30 min. Only then she can hit her top speed of 27 kts. If we assume the 205 RPM of the propeller shaft to be at her max speed - that is the 32 kts - then to reach that speed, during trials, required increasing the shaft RPM by 10 RPM every 10 min. So it gives you simple calculation that it requires 220 mins to reach flank speed from rest. From Class trials in 1985 (i think, when reactivated) we know that it takes about 25 shaft RPms to add 4kt, but that same 4kt require doubling the engine output (and these go at about 4200 RPM at 202 shaft RPMs), which cannot happen instantaneously.
However, from the description of the "Close the barn doors" stopping maneuver (done once by USS Wisconsin), it is necessary to go all back full from all ahead full, and this happens within 700 feet (so in less than a minute), mclearly requiring the dump of all power to shafts in under one minute, basically immediately (with obvious all stop somewhere in the middle).
Bottom lining the answer: USS Iowa
will hit it's not disclosed emergency speed (though fastest of the class reached 35+ kts) in about 45 mins: 30 min to reach superheated status on boilers and max speed of 22 kts, then about 15 min to ramp it up all the way up to emergency
speed, 2 min or so for every 10 RPM from 130 to 225.