Scaling a design?

[Mhall]

I have been desiging RC model planes for years and scaling does not always work without some changes to the design. Are boats the same way or can you take a very well designed model boat and build it on a larger scale?

Thanks
Mike

[Tad]

Mike,

The law of Mechanical Similitude applies to boats as well as to airplanes. So no, you cannot just scale in 3D equally and get the same characteristics.

[Mhall]

Figured so. Are there any plans out there for a boat like the Alpha Z but around 25ft long? I just need a good fast hull design and I can change around the rest to look how I want it to.

Thanks
Mike

[Trevlyns]

Have a look at the bottom of this page for "similar threads" There has been quite a lot of discussion on the subject.

Best!

[bobg3723]

This is the first I've heard of this law so for my own edification I did some searching and found this at this link that discusses this law as it relates to scaling up boats.
http://www.answers.com/topic/enlarging-plans

Bob

[messabout]

The homespun explanations in the Answers.com link are good enough. There is one statement that I take issue with. The author states that a vessel whose size is doubled, will have 16 times more stability. I think that we can wrestle the math around to agree with that, but there are too many other variables in a boat to accept such a profound statement as a useful one.

[marshmat]

Definitely, messabout, there are too many other variables.

If all of that practical nonsense is ignored, though, and we look purely at a simple scaling of a floating body of homogeneous density:

Length, draught, beam, etc. increase linearly (1st power)
Surface area of hull, sails, deck, etc. increases quadratically (2nd power)
Volume, mass, etc. increase cubically (3rd power)
Stability increases quartically (4th power)

You can see why it is difficult to scale a boat at all, and virtually impossible to do a direct scaling if there is a significant difference in size. The displacement, stability and sail area would no longer match up.

Thanks to H. M. Barkla of the University of St. Andrews (Scotland), the approximate proportionality factors to scale a boat and end up with something in a similar performance family are known. They end up being decimal exponents; ie. adjusting sail area by the 1.85 power of length. Larsson & Eliasson, Principles of Yacht Design has a good summary of this in chapter 2. Do note, though, that this scaling only gives you the general proportions of a similar craft at different scale; the scaled boat must still be engineered as if it were a completely new design.

[BHOFM]

Having built RC airplanes and boats for many years, airplanes
are more likely to work in real scale than boats!!

Some of the classic aircraft work as well in reduced scale as
the full size version,, Piper J-3, DC-3, Stearman for a few.

Model sail boats need more center board, and ballast than
their full size cousins! I don't know the formula if there is
one?

Power boats are less affected by the difference!

Remember, when you double the size of a boat, aircraft,
you square the weight! That why 747s weight a million
pounds! Not quite,, 875,000lbs!

[messabout]

BHOFM

I believe that you will find the diplacement increasing/decreasing as a function of the cube of the scale, not the square of the scale. Model boats may or may not need proportionately more board area or ballast weight. Depends on several other factors like sail height, area, hull section shape etc.

[ancient kayaker]

Most scale models of aircraft require extra stabilizer area to fly adequately if scaled down by a factor of 10 or more, which is typical. Even in non-scale models there is a noticable difference in the proportions of small (05. m span) and large (3+m) designs. As BHOFM noted, rigorous scaling of sailboats doesn't work too well either.

Things work better if the scaling factor is less extreme but a half scale of the Cutty Sark is not entirely practical and a quarter scale racing dinghy would still be over-sailed even with a midget to hike out in a crosswind.

There are examples of series of boats that have been scaled, but that is the first step towards what is essentially a new design as things like cabin height get adjusted to accommodate stubbornly non-scalable humans. A straight scale might work for someone at the outer limits of human size but the boat would be difficult to sell it when no longer required!

[Earl Boebert]

As always, there are exceptions. Since the Universal Rule, in the smaller sizes, led to undercanvassed boats, R Class designs at 1/8 or 1/2 size sail very well.

Cheers,

Earl

[diwebb]

In the days of sailing cargo boats owners would quite often lengthen boats with no change to cross sections, simply sawing the boat in half and then inserting a piece in the middle. The length was often increased by a quarter and sometimes up to a third and usually worked out ok. The rig was usually modified by adding a mast in the new section, or increasing the boom length if fore and aft rigged. If the desire is to modify a design by up to 25% in lenth then I have found that if the beam is increased by 50% of the length increase and the depth by 25% of the length increase and rig linear dimensions fore and aft proportional to lenth, but height no more then 50% of the percentage length increase, then a reasonable result is achieved. As stated by previous contributors any changes constitute a new design and must be reviewed thoroughly before proceeding with construction.

[dcstrng]

Originally Posted by Mhall

I have been desiging RC model planes for years and scaling does not always work...

Widely disparate Reynolds numbers are often the culprit when attempting to scale full-sized aircraft to their unpiloted cousins… As I recall, in boating the Gimcrack coefficients, and their progeny from the towing tank, were the designers’ attempt to quantify the scaling effect, among others…