# a startling discovery on required power.

Discussion in 'Boat Design' started by Mik the stick, Sep 17, 2015.

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### Mik the stickSenior Member

I have long been obsessed with accuracy in maths. Applying maths to power prediction and you come up with Wymans formula, Gerr's formula and Kieth's formula. It is the latter i want to talk about. If you search the net for "repowering Tortuga" you will find a very interesting article on these three formulas, how and why the owner chose his engine. His maths more or less proves that the power required for a speed on a flat calm times 1.36 gives the power for average conditions, and times 2.5 give the requirement for rough water. Now I know rough water for the Bismarck would keep Tortuga in harbour but: I decided Kieth's formula seemed to predict flat water conditions so I applied it to boats from "Voyaging under power". I then multiplied the result by 1.36 and got results very close to the installed power. If you apply the formula to WW2 destroyers and multiply by 2.5 you get very close to the installed power.

Little Sinbad 9.2kts 150hp predicted 151 hp
Nordhaven 46 8.75kts 101hp predicted 107.6hp
Diesel Duck 38 9kts 80hp predicted 85hp
Neville 39 9.1kts 105hp predicted 101hp
Neville 48 10kts 200hp predicted 193.7hp
Seaton 256 9.8kts 195hp predicted 180.7hp
Willard 40 10.5kts 130hp predicted 140hp

It looks like these 6 designers used Kieth's formula for power and added 36% then fitted an available power unit as close to that number as they could fit in their engine space.

Mik

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### Mr EfficiencySenior Member

Obviously "average" and "rough" are very hard to quantify, and if you want to employ formulae reliably, you must have accurately defined, quantified input, rather than a qualitative one. Or so it seems to me. Empirical observation is probably the best guide, looking at boats in-service in a particular area, especially commercial boats that go out in less than ideal conditions, tells you something.

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### DCockeySenior Member

Remember that those formulas and coefficients, no matter how much math is used in their derivation, are all based on empiricism and curve fits, not on first principals.

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### Mik the stickSenior Member

It seems to me that Kieth's curve fit is better than the others. The large number of complicated calculations hardly seem worth the effort for example the formula gives a speed of 34.14kts in rough water on 50,000shp for Dunlap launched in 1936. Her trial speed was 36.5kts. Fletcher (1942) was about 600 tons heavier and 25ft longer so I think most people would guess a 10% increase in power would be the minimum required to maintain a speed of 36.5kts. The formula predicts 35.28kts on Fletcher's 60,000shp in reality 37kts was Fletcher's top speed. I don't know when Kieth's formula was published but there could have been other rule of thumb methods available in 1936.

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### Mik the stickSenior Member

The author Robert Beebe officer in the USN in 1933. Some time ago I asked if anyone knew the formula for his power prediction aigorythm. The graghs in his book are limited to 95 tons and SL 1.65. which is great for small boats. It looks like he used Kieth's Formula and added about 15% as a weather allowance. this seems seasonable to me, after all when 15% extra power is absorbed by wind and waves and weather worsens full speed cannot be maintained in a small boat. The boat is probably far more capable of withstanding bad weather than the crew.
I liked everything I read in Beebe's book especially his algorythm and was disappointed I could not apply it to larger ships. I think I may have answered my own question.
mik

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### RurudyneSenior Member

One nice thing about that, though, is the math is a lot easier for getting you in the ballpark. Can you imagine what the math might be like if someone really did figure it all out?

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### DCockeySenior Member

Simpler regression models can be very useful, particularly as input to the early design process, provided the limitations of accuracy and applicability are understood.

Donald MacPherson may be closest to "really figuring it out". No need to do the math, just buy the software. http://hydrocompinc.com/software/navcad

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### Mik the stickSenior Member

I downloaded the Demo, not impressed. There are so many required inputs I suppose I should have expected that but the result for the Diesel Duck was 34hp in a force 4. 35Hp is the required power in flat calm water, I think I saw it on the designers site. I changed conditions to a force 9 and the result did not change. The problem with software is the same as a calculator you can't trust it unless you can already do the maths. For example Hitting a 2 instead of a 5 in a long calculation can give a result 100 times more than the correct result. Sorry about the rant

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### DCockeySenior Member

So you don't trust any software which does calculations which you can't do by "hand"?

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### DMacPhersonSenior Member

David:

Thanks for the endorsement, but like anything, you do something long enough and things begin to take shape. I've always found hydrodynamic puzzles to be particularly fun to solve. I guess I'm wired to "find the signal in the noise"...

Regarding the use of the demo, I am not surprised at all that it did not give a useful (or realistic) prediction for a duck boat. The demo is limited to one prediction method (Holtrop), which as you rightly pointed out, was developed from empirical sources. There is a scope to the method, and NavCad's "Method Export" would show you that this method is particularly unsuitable for this type of hull. A bit like using Savitsky for a tanker - not really useful. (There are other methods in the commercial version that do handle these hulls.) Likewise, the environmental predictions (wind, waves, shallow water) are not enabled in the demo. (It is a demo, after all.) The switches to turn on the seas prediction are also not enabled (and pop up a demo message), so I'm surprised that it was not clear. (We will look at this, and try to be sure that users are advised more clearly about the scope of the prediction methods when using the demo.)

Yes, there are many hull form inputs required for NavCad. Our brand is about quantitative accuracy. The fewer the inputs, the less precise (i.e., more averaged) you get. For a common length and displacement, one can fit a canoe shape or a barge shape or anything in between. A simple method with two parameters and a coefficient is limited to a very rough average through the scatter. Tweaking the coefficient to suit a hull type requires prior experience to correlate coefficients to hull forms, and still it only goes so far. Be careful about having too high expectations for these simple (yet certainly still useful) prediction models.

Don MacPherson
HydroComp, Inc.

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### Mik the stickSenior Member

I like software to give me results close to published figures which this software did not. I think I would like the full version but could not justify buying it. My problem with software is like Freeship although I'm hopeless at tech drawing Freeship could probably do it all for me. However I just cant seem to teach myself how to use it. The effort I put into learning is not nearly matched by the results I get.
mik.

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