# Gerr's Math on Hull Speed

Discussion in 'Hydrodynamics and Aerodynamics' started by Brian Alsum, Dec 2, 2018.

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### Brian AlsumJunior Member

Im trying to learn the math of calculating hull speed. I bought Dave Gears: Propeller Handbook. In the book he talks about his new way of calculating hull speed.

In other parts of the inter webs I found a chart that talks about looking at the D/L Ratio to determining if a boat is light, heavy, stupid heavy.... So the boat I'm messing around with the math on is a 30T 54' LWL Catamaran.

How does the Twin Hulls effect (affect?) the math?

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The Propeller book describes the displacement speed ratio on page 13 To use that equation be sure to use long tons as the D dimension. The resulting quotient does not indicate the speed of the vessel but it does categorize the boat sufficiently to make an educated guess. In your case the 30 ton figure, if converted to long tons is 26.78.....and the calculation yields a D/L of about 170 which is pretty heavy and will surely limit your achievable speed. Really fast displacement boats have D/L in the 40s or 50s. It might be helpful to think of it as something similar to power to weight ratio.

There are a mess of variables that play into the speed potential of the boat. Gerr discusses one of the several variables on page 12 and thirteen. That particular subject is quarter beam buttock angle. Elsewhere in the book, there is length beam ratio which matters.

The math is pretty much the same for multihulls. Long skinny hulls, as with most cats, are usually faster than fatter boats unless the hulls are overloaded which yours almost surely is. If the design elements of your boat accommodate 30 tons then previously mentioned quarter beam buttocks will need to be steeper than optimum. If so that will affect your speed potential negatively. The run angle could be kept smaller if the length to beam ratio was a smaller number ( like 6 or 7 more or less) but if that is the case then the boat will probably be slower. Hot rod cats have L/B of 12 or more.

Here is the bottom line Brian. A boat design, cat or mono, consists of a whole gaggle of compromises where one factor influences the next factor, and the next, and the next. If you put enough power on a 54 foot WL displacement boat you can persuade it to go about 10 knots per hour more or less.. If it is a planing boat and you provide it with a huge horsepower out put you can force it to go a lot faster than that. In either case it will be pulling an impressive wave train.

I am fully aware that I have not answered your question. I only mean to give you some really basic information about the variables in boat design and how they might affect performance predictions.

Hang in here. Some of the other members may provide more useful information.

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### Ad HocNaval Architect

Well, firstly, the term 'hull speed' is a misnomer. It is not correct.
You may find a more appropriate understanding of shape of hull speed and length given here.

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### sandhammaren05Senior Member

Gerr merely uses Crouch's formula, which is wrong. It cannot be derived from hydrodynamics.
Furthermore, Crocuh's formula was not derived from empirical data analysis, nor can it be s0-derived. The correct scaling law has been derived from hydrodynamics and is in the attached paper. I correctly accounts for all of the APBA OPC kilo records analyzed in the paper.

#### Attached Files:

• ###### scaling_for_speed.pdf
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5.8 MB
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600
Last edited: Jan 22, 2019
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### sandhammaren05Senior Member

Here's an update, also on my paper. In a correct speed-weight-power formula catamarans form a single class. V-bottoms form another class, pad-Vs yet another. Flat bottoms, hydros, etc form different classes. Crouch and other similar stabs in the dark have no empirical basis. Crouch claimed that U/(P/w)^1/2=constant.
If tht is true then plotting that ratio for empirical data must produce scatter about a flat line. No such result follows. Try it and you'll see. the formula is wrong.

In the correct speed-power-weight scaling (see the attachment) the classes are defined by drag coefficient of both hull and gearcase. New in the paper is the discussion of the limitations on high and low gear ratios in the context of the p/D ratio (pitch/diameter). The standard advice of naval architect to 'swing as large a diameter as slowly as possible' is not only wrong, it's not stated as a dimensionless rule. Correct is: we expect, given the inadequate data on prop efficiencies, that for the range 1<p/D<2 peak efficiency increases with p/D. This means that, given the shaft hp, a good p/D can only be achieved via gear ratio. That's the advice for high performance boats. For pushing loads at low speeds smaller p/D provides higher efficiency (at advance ratios below that where the efficiency peaks). This is the correct advice for naval architects.

My speed-power-weight formula is compared with empirical data in this updated attachment.

#### Attached Files:

• ###### scaling_for_speed.pdf
File size:
5.8 MB
Views:
522
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### sandhammaren05Senior Member

If you know how to use a GPS or a radar gun then hull speed should be clear to you. Speed/hull length is a meaningless concept for planing hull. It is of no use whatsoever. See my posted paper for the correct Froude nr.

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### sandhammaren05Senior Member

The formula you're advocating is empirically wrong, mess of variables or not. If you rewrite the prediction as a ratio equal to a constant and plot it aginst empirical data then you will not obtain scatter about a constant!

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