What is world's biggest planning hull boat and how fast?

It's current location seems to be a mystery.

 

I think, as Mr E suggests, there are several cube/square limits. The first is dynamic lift generated by momentum transfer to the water. The vertical component being lift, and limited by the surface area of the bottom- a square function, carrying load of the structure above- a cubic function.
The second limit is the power to weight ratio. The best number I've read is from a long time ago: Crouch reckoned a sea sled could plane at a 100 pounds per horsepower. For a battleship that's around a million horsepower. And power is force times distance over time. Force is limited by piston surface area, while the weight of the engine goes up with overall volume.

 

Most powerful engine is that Wärtsilä, making 46hp per ton. Our hypothetical planing BB would be half engines, by weight.

 

The most powerful boats have gas turbines that make considerably more hp/lb than any reciprocating piston engine. Its just their specific fuel consumption that is not the best.... If heat exchangers and recuperators were added like are used for stationary (utility) applications, it improves the efficiency at the expense of more weight and volume. The stationary turbines are probably a lot less maintenance intensive than any recip engine, but of course very expensive and still thirstier...
An example of a mid range utility grade gas turbine is the GE LM6000 General Electric LM6000 - Wikipedia https://en.wikipedia.org/wiki/General_Electric_LM6000
54 000 shp with a specific fuel consumption on par with competing recip engines (0.329 lb/hp hr)
Weighs in at 17 300 lb, shaft speed 3600rpm. 200" long, 85" wide and 80" high. 40% thermal efficiency.

A great powerplant if one needs it and can afford it.....

 

If one can find a system to actually convert that power to actual propulsion. Destreiro had 3 LM1600 turbines at 20,000shp each driving a waterjets....I see Kongsberg (ex KaMeWa) has some listed as almost big enough to absorb that power...I’m sure for the right fee they could stretch the design a bit.

 

"so how do you describe a nuclear sub doing 30 knts under water. its past hull speed so its not displacement. it is under water so it is not planing."

Hull speed is entirely based on the concepts surrounding "Free Surface Flow" where the interface between the high density fluid (water) and the low density fluid (air) has dynamic interactions, making waves, and for practical purposes this limits speed of displacement boats. For a fully deep submerged machine, hull speed has no meaning, and there is virtually no wave making with a deep submerged submarine hull. For submarines, submerged speed is simply a cubic function of applied propulsive power, all the way up to very high speeds. Cavitation also does not exist for all practical purposes when the local absolute pressure is around 90 atmospheres.

 

In the inner-war years (between WWI & WWII) torpedo designs were developed, but not fully tested under actual sea conditions. This led to various failed designs entering WWII. One interesting development was a British torpedo that had a 10,000 horsepower power plant, and was said to be capable of 100 knots. Quite an accomplishment to cram such a power plant into torpedo dimensions, however controlling such a beast was challenging in calm water, and virtually impossible at sea. The machine controls would try to compensate and maintain set depth, but a small control input would send the torpedo out of the water, and it would then very rapidly overspeed to destruction, sending pieces of the power plant in all directions.

 

Oh, we're talking crazy torpedos? How about 200 kts?

VA-111 Shkval - Wikipedia https://en.wikipedia.org/wiki/VA-111_Shkval

 

She's laid up at the Lürssen shipyard in Lemwerder, Germany, for some years now (I think since 2009), in quite pitiful condition:


Photograph source: Shots Magazine

 

That's a sad sight. She was quite a technical marvel. The designer is a friend of mine and we did some work supporting various aspects of the control of the vessel. I attended at least two of his technical presentations given soon after the vessel made her cross-Atlantic run. The original plan was to then outfit the vessel as a mega yacht. That obviously fell through at some point. The Freedom-class LCS hull design was based heavily on the Destriero, at least in the beginning, for the first of class.

 

Thjse dimensions are for the turbine only. Actual installation with ducting, intercoolers etc probably 10 times larger. Your point is well taken though. Even at ten times the volume, it's still significantly smaller and lighter. It is not however, correct that the most powerful vessels use gas turbines. Not in absolute numbers.

 

Here's another cube square test of our limiting case. Disk area of prop. Prop power is strictly limited by swept area. Our hypothetical planing BB would have 10,000 square feet of prop.

 

The largest recip engine listed in the BSFC wiki page that I found was a 46k hp engine "MAN Diesel G95ME-C9"
By contrast, if one looks at semi submersible oil platforms like the Thunder Horse PDQ - Wikipedia https://en.wikipedia.org/wiki/Thunder_Horse_PDQ one finds that they have installed turbine powerplants of 90Mw or 120k hp. Now clearly the semi submersible is not going to plane or win any race, but both are ocean going vessels....

 

Indeed. But the most powerful engine is the 107000hp Wartsila, as an individual engine. Thunderhorses slightly higher power is a powerplant. But it gives an excellent idea of available power, so thanks.

Really, I think the OPs question has been bracketed: even with an infinite budget, you could not build a planing battleship sized craft. Cube square relationships make it impossible.