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For a typical capital warship (including aircraft carriers) of any navy circa 1920s-1960s I am looking for a rough power ramp up time for the power plant to go from min load to max load.

That is to say, if you are cruising at a dead slow speed making turns for only a few knots, with all boilers lit and cut in on the line, how long would it take the ship to respond to an engine order for flank speed?

I'm not looking for the actual time it takes the ship to accelerate to flank speed, only the amount of time for the power plant to ramp up to where it is producing maximum output shaft horsepower.

Anyone have any information on that?

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    40 years is a pretty long time. What would count as a "typical" capital ship over such a large range of time? I mean, it covers from HMS Neptune to USS Enterprise. – Semaphore Apr 30 '18 at 17:53
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    Maybe ask this in the Physics SE, since it largely depends on the ship's weight, engines, and (inasmuch as it determines the maximum speed as well as how much the vessel resists acceleration in water) streamlining? – Denis de Bernardy Apr 30 '18 at 19:24
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    Not a complete answer, but you have to separate the time to make steam for top speed from a cold start and the time to accelerate to top speed with all boilers being hot. – o.m. Apr 30 '18 at 22:18
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The answer to that is difficult. It has to do mainly with technological limitations and fluid dynamics.

In fact, you should ask about time to flank speed, as this would be your only measure of maximum output shaft horsepower (shafts, actually). The power delivered to the shaft is just enough to propel ship at desired speed. 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). At those speeds water is... hard would be one way of putting it. Another is: when one goes that fast it's not a lubricant anymore... See "British Battleships of World War One: New Revised Edition" for more details.

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 as efficient at high speeds. There are ways to alleviate that, but obviously older designs would be deficient in that regard, 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.

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 330RPM in no-time. It's same thing everywhere - when you want to burn tyres when accelerating in your car there are parts of the transmission system that would prevent engine from sending all it's power to the powertrain... There is a reason why new (that is new when they first unveiled the new generation) Nissan GTR had a caveat in warranty stating pressing "race mode" button voids it as it is likely to damage shaft.

And the above numbers are nothing. USS Iowa, when on her trials, reached contracted 32.5 knots, what requried about 212k shp. And she was running light for that. How long it took is nowhere to be found (those numbers are classified), but since she was larger than Canada or Hood (and heavier) it would be definintely longer. For some basic info on British ships see here, for stats on Iowa here. CVNs have on hand even more: Truman is rated for 31 knots at 280k shp from 8 nuclear reactors.

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.

To show you how much power we're talking about Queen Elizabeth 2 has, if I remember correctly, 2 power plants of output of 86MW each. I can barely imagine how much power that is, and yet it's most certainly not a patch on BB class. But even then this is a lot and even with modern designs one cannot use all that pile of power immediately.

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    Which meaning of "patch" is meant here? – Aaron Brick May 1 '18 at 16:10
  • @AaronBrick - not native english speaker, simple error. googled, corrected. Again. Thanks. – AcePL May 2 '18 at 7:52
  • what unit is k shp? – mart May 4 '18 at 6:22
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    @mart - after en.wikipedia.org/wiki/Horsepower: Shaft horsepower (shp) is the power delivered to a propeller shaft, a turbine shaft – or to an output shaft of an automotive transmission. This shaft horsepower can be measured with a torque (torsion) meter, or estimated from the horsepower at the crankshaft and a standard figure for the losses in the transmission (around 10%). Shaft horsepower is a common rating for jet engines, industrial turbines, and some marine applications. k stands for kilo, which is a prefix to a unit of measurement meaning one thousand. – AcePL May 4 '18 at 8:08
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A major limiting factor on rate of acceleration of an oil fired steam ship is how quickly the boilers can be brought to full pressure.

Large ships, such as battleships and aircraft carriers, have multiple boilers, and at cruising speed will only be operating some of them, as running all boilers at reduced heat is very inefficient. To achieve full power, all boilers have to be operating at their maximum pressure, and that means bringing cold boilers on line. This takes some time, as the boiler must be heated evenly and slowly, lest parts of it expand too quickly, which could result in a rupture, and a horrible death for anyone in the boiler room if that happens.

Here is a simple description for bringing a water tube boiler online. Fire for five minutes, wait 15 minutes, repeat until steam comes out of the bleed line instead of air (this usually takes eight or nine cycles), then slowly step it up to full pressure by firing for 30 minutes, and then waiting ten minutes. The whole process can take three to four hours, though it can be rushed a bit if the alternative is sinking, albeit while placing the machinery room crew at some risk of being boiled alive if a steam line ruptures.

If we assume the warship is operating under wartime conditions, and the crew has kept the inactive boilers at least partly heated in anticipation of a change of speed, all boilers could be brought online in around two to three hours.

So, to begin with, the battleship captain must allow a minimum of two to three hours just to get enough steam pressure on all boilers to even contemplate high speed. And then there is the matter of accelerating a mass of 30,000+ tons in water, after all boilers have achieved operating pressure.

This isn't as much of an issue with nuclear powered warships, as the heat is applied to the water in the boiler internally with a heating loop, not externally by first heating the boiler. The water itself acts as a thermal buffer for the boiler, so they can be heated more quickly without as much concern for uneven heating and thermal shock.

The US navy has abandoned oil fired steam plants entirely, replaced with either nuclear plants or gas turbines. The gas turbines are much lower maintenance, and can be brought to full power in a matter of seconds.

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