# Looking for an article/book suggestion that talks up scaling up and down designs

Discussion in 'Boat Design' started by fpjeepy05, Dec 14, 2012.

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### fpjeepy05Senior Member

Sorry if there is a thread already covering this a couldn't find it.

Basically, I'm looking to do some reading about the scaling of designs. I'd like to know if there are some simple generalizations and equations that can be used for design development.

For Example, Proportionalities

If a boat is increased in length by say 20% assuming the boat takes the same shape beam, draft, and construction would increase by the same. So displacement might increase by say 1.2^3-1= 78%
But, as boats get larger or smaller people stay the same size so amenities might not change. For example there would be no reason for ceiling height, on the previous example, to increase by 20%
Also in the small boat range many boats get stuck on the 8'6" beam for trailering purposes so those may not increase.
Engines are a portion of weight and determine speed. As engines scale up max rpm traditionally goes down. (I understand this is a over generalization but a 50cc scooter engine can turn at 12,000 rpm and a Wartsila-Sulzer RTA96-C turns at 102 rpm) With this hp/weight ratio generally goes down, driving displacement up.
There is also the question of speed verses length. It may not be comfortable to travel the same speed in a boat that is 50% smaller and it may not be economical to travel the same speed in a boat that is 50% larger.

Can things be simplified? Or does everything have to be addressed individually for each design? Where do designers start? Designing for a HP, designing for a displacement, or designing for a length?

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No.....

Yes.....

At the beginning........It all comes down to the requirements....write them out in order of importance, then you'll have a point to start from. For powerboats, "How big and how fast?" are the usual starting points. But it may be "how many passengers?", or "how many dollars?".

I lied up above....things can be simplified, I make ballpark guesses all the time. But they are tempered with 30 years experience of what is really possible.

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### fpjeepy05Senior Member

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### Mik the stickSenior Member

Again I'll say I know more about designing aircraft than boats I have formula for scaling up engines Jet/ IC and V's I don't know if you would get sensible answers if you used boat dimensions. Its late, I'm tired, off to bed. I'll post formula when I dig out the books tomorrow.

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### PARYacht Designer/Builder

Fpjeep, in spite of what seems a fairly simple request and one that is often asked of designers, Tad is correct, there isn't any simple formula, method or scaling factor that will help. It's really just physics, but most don't have a grasp on it at this level.

This said, there are some elemental rules you can follow, in regard to changing a boat's length, up or down, that will result in a safe compromise. Note that I said length, not wholesale scaling up or down. The easy method to gain or decrease length is to respace station molds, up to as much as 15% of the previous length. This keeps beam and draft the same, but provides the longitudinal elbow room you might desire. Simply put, if you have a boat that is 20' on deck, but need a 23' boat, respace the station molds with this 15% increase in distance between them.

Once you step over this line (15%) a whole world of unforeseen issues will crop up, affecting stability, hull volume, weight, drag, amount of power for propulsion, etc., etc., etc.

How much of a change do you have in mind? If you have a 20' boat and want to make it a 30' boat, you're in for a world of hurt, design wise. The same is true in reverse. On the other hand, if you have a 30' design and want to make it a 25' 6" boat, then station mold spacing can solve this problem easily.

Over the years many attempts at scaling factors have been tried, most with very limited ranges of success, again because of the physics involved. To get a better grasp of what happens when you make scaling changes to an object, look up "mechanical similitude".

A quick overview is:

Linear dimensions (such as beam and draft) vary proportionally to length (L).

Areas will vary as the length squared (L2). This includes wetted surface area and sail area. Resistance varies with wetted surface area.

Speed varies as the square root of length (√L).

Weight, displacement, and volume vary as length cubed (L3). Corollary: Cost varies with the displacement and therefore as the length cubed (L3).

What does this mean? Well an example of a boat that is twice as long as another boat will be:

It'll have twice the beam and twice the draft.
It'll have four times the sail and wetted surface area.
It'll travel √2 or 1.4 times faster (displacement hull speed)
It'll displace eight times as much.
It'll cost eight times as much!

So, again, what are you trying to do with your "scaling" project?

6. ### outside the boxPrevious Member

Boat Design Forums > Design > Boat Design
Can you resize a design without complications? Can you resize a design without complications?

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### fpjeepy05Senior Member

I agree. I think I'm pretty understanding of the physics. I guess small scaling will be more accurate than larger scaling. I guess what I am trying to do is "large scaling" taking a design to its extreme. Like looking at a 60ft cc or a 16ft flybridge and seeing why neither is produced.
What I've done so far is taken all 14 current Viking Convertible models and put length, beam, displacement, base hp, and speed in an excel chart to develop some ratios and regressions. The most interesting that I have found is that length to beam ratio decreases as length increases. lb/hp is highest at the ends of the spectrum (the largest and smallest boats). As hp increases operating rpm decreases. And lastly the best fit proportionality between displacement and length/beam seems to be as follows Disp. (L*B)^1.75 [R^2=0.988]
I guess I have a target speed, and mpg, Which can give you a target hp, lb/hp, and displacement, and length, beam, draft, deadrise, etc can be fitted from that. Just was looking for some related reading. Couldn't find anything in any of my books.

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FPJ, a good square one book for this subject is: The Nature Of Boats..... by Dave Gerr. The author does provide a lot of conversion figures. There are not any direct conversion figures that can simplify the scaling up/down problem. There is enough discussion about all sorts of variables. You can probably combine some of them to get a ballpark solution.

The book does not make you an NA or even a boat designer, nor does it intend to, but it is a good start.

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### PARYacht Designer/Builder

Geer's (or anyone else for that matter) conversion factors will not make an 80' PT hull viable at 40'. Simply put, a 50% scale down size isn't possible, without huge loses and a boat that will likely just capsize come launch day.

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### fpjeepy05Senior Member

Thanks

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### fpjeepy05Senior Member

50% less length, beam, draft, height. 125% less wetted area. 238% less displacement, hp, fuel, other weight. I'm not too sure it would capsize, but also wouldn't function properly.

12. ### outside the boxPrevious Member

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I did suggest that Gerrs book was a "square one" reference, not a treatise on similitude. I hasten to agree that an 80 footer can not be scaled down to produce a suitably functional 40 footer. Also that a15 percent, or less, change in size is about all that might be tolerated.

People keep doing big size changes, usually resulting in disappointment. There is a guy not far from here who has scaled a 15 footer up to about 24 feet. Not only that : the small one was a sailboat while the larger one is a power boat. Result is that it floats but maybe not in the manner that was hoped for. That is a continuing project that will see some modifications, but I dont think he will be able to unring that bell.

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### fpjeepy05Senior Member

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### PARYacht Designer/Builder

Mechanical similitude applies to everything: coffee tables, elevators, birdhouses and even powerboats.

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