# Crouch Constant

Discussion in 'Boat Design' started by Willallison, May 24, 2002.

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### WillallisonSenior Member

Crouch's formula is commonly used when determing the hp required to attain a given speed.
But determing what constant to use seems somewhat of a black art. It would be too much to hope for, I guess, that there is a list somewhere of boats and their Crouch Constants....?

2. ### GuestGuest

Crouch's formula for planing speed is

Vk = C / SQRT(Disp/SHP)

Where:
Vk = Speed in knots
C = Constant based on the type of vessel
Disp = Displacements in pounds
SHP = Shaft Horsepower

(See Dave Gerr's Propeller Handbook, pages 15-17)

Dave gives the following constants

150 - average runabouts, cruisers, passenger vessels
190 - high speed runabouts, very light high-speed cruisers
210 - race boat types
220 - three-point hydroplanes, stepped hydroplanes
230 - racing power catamarans and sea sleds

This is a very simple formula (perhaps too simple), but I remember in one Professional Boatbuilder article about how a racing boat designer used it very successfully. I assume that he already had already figured out a good value of C for his type of boat. I think he used the formula to figure out that the engines weren't performing up to spec.

How about calculating 'C' using existing boats

C = Vk * SQRT(DISP/SHP)

That way, you can use the 'C' value of the boat that most nearly matches the one you want to design. You can also figure out a bracket of the best and worst case values of 'C' for your design.

Does anyone out there wish to contribute the 'C' values for specific boats?

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### tom28571Senior Member

I used Crouch's constant in designing LIZ and it worked out very well. Working backward to derive the constant gives a number between 145 and 155 depending on which pitch prop is being used. I normally run with a prop that produces a top speed equivalent to a constant of 145 since the higher pitch prop that gives a number of 155 loads the engine too much. This might adversely affect the life of the engine so I accept the slower speed in favor of longer engine life.

In making this calculation, I assumed that the shaft horsepower is the same as the rated power of 50hp. I think this valid for outboards but not for inboard power.

Actually, the top speed of LIZ is also reduced by a design decision to make the boat stay in planing mode at lower speed and run more level at all speeds than other similar boats. Another example of the " no free lunch" axiom.

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### WillallisonSenior Member

I think that the idea of contributing to a list of constants for existing boats is a great suggestion.
It would need to be set up in such a way that the various aspects of the boat - its size, displacement, speed, power, general type and a description could be entered. That way viewers could get a good idea of how the various craft compare to their own. Other aspects of the boat could be incorporated as well - such as length/beam ratio etc.

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### tspeerSenior Member

I'd like to suggest a different use for the constant: reducing test data to standard conditions.

The power the engine puts out will vary with temperature, humidity, and atmospheric pressure because all these affect the air density. So if you want a consistent basis of comparison, you have to pick standard atmospheric conditions and correct the data you take on a given day to those conditions. This can be done using charts from the engine manufacturer. If you instrument your engine to measure the torque delivered to the shaft, you can get the actual power it's producing from Power = torque * rpm.

Likewise, the displacement of the boat will vary from test to test, and you need to establish a standard loading. This might be maximum displacement, or it might be half loaded.

To correct your test data to standard conditions, you'd plug in the actual power, displacement and speed corresponding to the test day conditions and calculate the Crouch constant. Once you have that, you can go the other way, this time using the power for standard day and the nominal displacement to calculate the speed you would have achieved had you run the test under the standard conditions.

Procedures very much like this are used to standardize aircraft flight test data to create the performance charts you'll find at the back of every aircraft flight manual.

Once you have standardized test results, you can detect more subtle changes in performance. For example, if you make a change to the boat, say, altering the bottom to change the running attitude, was the boat faster or slower because it was colder or hotter today, or did the change really work? Or was it because you had a different amount of fuel/water/stores/people on board last time? With standardized data, there's a lot less scatter in the results, so you can start to work out what's really important.

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### tom28571Senior Member

Tom,

I agree with you in principle, but in practice I find that other things make such accuracy hard to find. Water and air temperature are pretty consistent but wind, wave action, inaccuracy of speed and RPM measurement and difficulty of getting ANY specific information from manufacturers all work against you. My Yamaha tach and paddlewneel knotmeter both require a practiced eye to make a reasonable determination of speed and RPM. Yamaha does not have any avenue of direct communication with the user. They require all communication to go through the dealer and that is a poor method.

I record most of the things that you mention but find that they tend to get lost in the other variables. I suspect that the high quality of instrumentation and more steady state environment in aircraft testing make things easier there. Displacement is, of course, critical in any measurement.

Establishing constant conditions and obtaining accurate (read expensive) instrumentation is probably beyond our reasonable capabilities or our needs. Even on relatively short perfrmance runs, the speed probably varies more than the effect of the variables that you mention.

I'm not against your suggestion, just think it's beyond our needs.

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### WillallisonSenior Member

Tom must be then name given to those who will posess great wisdom........
Both of you make valid points - but for the most part gaining the level accuracy described by Tom S would require testing be done with the aim of gaining our particular set of data. It is certainly possible - but would be very expensive, time consuming and would result in relatively few different boats being analysed.
What I have in mind - and I think Tom L is suggesting - is that data taken from magazine tests, peoples own experiences and possibly even manufacturers claims could be entered into a spreadsheet by any number of partcipants. This could result in a large data base from which designers could make a more informed guestimate of what number(s) to choose when making their various calculations

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### WillallisonSenior Member

Speed in knots or mph?

The two texts to which I have referred in looking at Crouch's formula for estimating speed, both state that the formula gives the speed in statute miles per hour.
A web page I came across and Tom's usage of it both refer to the speed in knots.
Which is correct, or does ascertaining the speed in knots simply require the use of a slightly different constant?

Incidentally the constants suggested in my Westlawn text are (not surprisingly) similar to those quoted by Tom. They are:

Multi-step Hydros 190 - 205
Single-step Hydros around 210
Sea Sleds 220 to 270
Seagoing Monohulls to around 40' around 205
Seagoing Monohulls , 70' to 80' increasing to 230

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### Mike DSenior Member

Hello All

Does this help?

It comes from an old textbook so I would guess it pre-dates Crouch and the coefficients are probably for designs of around 1950-1960.

But the proportions for the various types should be reasonably accurate.
Michael

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### TimmSenior Member

The book Mike referred to in his post is Basic Naval Architecture by Kenneth C. Barnaby. Though out of print, you can find them through online used booksellers, such as http://www.abebooks.com/. This is a good book for those studying the subject who want more in depth discussion than what is in Skene's or some of the others.

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### Mike DSenior Member

That's the one, Timm.

Is it any use for planing craft? It is gold-mine for many things that aren't in most other text-books.

Michael

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### tom28571Senior Member

Occasionally the Gods smile on me. I had a book request on Abebooks for for Lindsay Lord's Naval Architecture of Planing Hulls for quite a while when in June they sent a reply that a copy of the '63 edition was available from CA. The guy wanted \$22.50 for it and I quickly sent off an acceptance. It is in very good condition too. Since then there have been two other copies listed, one '46 edition for \$250 and another \$225. Perhaps the older printings are worth more to collectors, but I'm still shocked that I got mine for so small a price.

I'm not sending it back.

I'm not at all familiar with the other book.

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### TimmSenior Member

Mike, I don't find it all that useful for planing hull design, but then again, there aren't any books I have found that are useful on that subject. Lord's book can be usseful, though is somewhat dated now. The company I work for also publishes nautical books, so I have a bit of an inside line on new books (not to mention buying at cost!). Daniel Savitsky has written a book regarding planing hulls that we have a copy of in the office. It was sent to us by Westlawn to get a quote on publishing it, but unfortunately has not yet been published. I will have to press my boss to come to an agreement with Westlawn so this book can become available.

Tom, I too was lucky in getting a copy of Lord's book. A co-worker of mine at Carver a number of years back had become so disillusioned with design after 20+ years that he left the business. He sold me all of his books and symposia reports for a whopping \$20! Included in the box of stuff was Lord's book, Marine Design Manual from Gibbs & Cox and the old Kaiser aluminum book on designing and building aluminum boats among others. I figure I got my \$20 out of the deal!

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### Mike DSenior Member

Timm

Thanks for the advice, I am curious about planing rather than "must have it". I had been considering doodling with various diagrams to produce a computerized method of resistance calculation.

Instead of writing programs in Visual Basic or C, nowadays I use the Excel spreadsheet with a few VBA routines making a lot of use of GoalSeeking and Solver. Fun, really.

I was looking for something to use, so I'll pay you \$25 + postage for that old load of junk your colleague maneuvered you into. Within 30 days of arrival I'll send you a cheque that is guaranteed.

Michael

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