Scaling the Single-handed Schooner

I decided to use the study plans in my copy of Boats with an Open Mind as the depature point for my design. This was in lieu of ordering the plans from Dynamite Payson because I planned on changing them so much. I also wanted the challenge of starting with study plans and developing a design myself. For anyone building the stock boats, Payson's plans are well worth the price.

According to BWAOM , the singlehander schooner is 19 feet 6 inches long with 50 inches maximum beam. To make it fit comfortably into my garage, it had to be less than 18 and a half feet long (apologies to the metric world, but the plans are in feet and inches). A scaling factor of 94% would make the boat short enough to fit. The results of applying this scaling factor are:

Bolger's Design
94% Scaled Design
19 feet 6 inches
18 feet 4 inches
17 feet 9.25 inches
16 feet 8.5 inches
Max Beam
4 feet 2 inches
3 feet 11 inches
Sail Area
126 square feet
111 square feet
0.78 or 1.2 (see discussion below)

So we lose 14 inches of overall length, 12 3/4 inches of waterline length and 3 inches of beam. The hull shape stays the same. If the two designs were side by side 30 feet away, it'd be hard to see the difference.

A few of the numbers need further explanation. First, the weight decrease is not as much as straight scaling should produce. This is because of using standard dimensioned wood. The panels and other lumber are reduced in 2 dimensions, only. That is, while the hull panels are 6% shorter and 6% narrower, they are still 1/4 inch thick. The result is that the weight of the wood is only reduced by a factor of 88%.

The payload is reduced by 22% because while the hull's volume (and therefore its displacement) is reduced by 17%, its weight is only reduced by 12%. To keep the DWL at the same relative position on the hull, the payload must be reduced by 22% compared to the original design.

The acceleration comes from the ratio of the sail area to the weight. Because we are scaling down, it could have been expected that the boat would have been brisker, but since the weight changed in the same proportion as the sail area, there's no difference. The ultimate speed is slightly higher because of the reduced wetted area (which causes drag) relative to the sail area. Some will want to throw the wave equation at me right about now, pointing out that the LWL is shorter so the scaled boat should be slower. That will not be the case because of the hull shape picked by Bolger. When either boat is heeled, it slices through the water, rather than plowing through it. Neither generates a displacement wave. Kayak rules apply rather than displacement rules. The performance should be approximately the same as the original design.

The stability number comes from the rule of thumb that for an unballasted hull the stability is proportional to the 4th power of the scaling factor. That is, make the boat twice the size and it's 16 times as stable. That formula is based on an an analysis that models the boat as a dumbell balanced on a point in the middle. It's a good first approximation, but not necessarily the whole story since it ignores ballast and form stability.

Bolger gave his boat a ballasted drop keel. The ballast makes up 67 to 75% of the total weight of the empty boat. That can't be ignored when calculating stability. Using a model that accounts for hull form, the ballasted drop keel, the reduced sail area and the reduced moment arms results in a stability of 1, the same as the original design. Leaving the ballast weight and keel depth unscaled actually makes the scaled boat more stable than the original.

There will still be some nuisances caused by the scaling, compared to the original boat. The balance of the scaled boat will be more sensitive to loading. The cockpit & hold will be smaller and potentially less comfortable. There will be less space between the edge of the deck and the coaming, with the greater potential for water coming aboard when heeled.

Against these disadvantages, the boat will be lighter and easier to handle. It will require less material to build. A smaller trailer can be used. It fits in the length of a standard garage, allowing stowage out of the weather and out of the view of the homeowners' association . In some states, such as Maryland, the reduction in length is enough to remove the legal requirement to register the boat (saving the titling fee, the 10% excise tax, the annual registration fee and the effort of collecting all the documentation required to prove that state sales tax was paid on every component of the boat). For me, at least, smaller is better.

Copyright © 2011-2013 László I. Mórocz. All Rights Reserved.
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