sail area for a new design

K Reinke "Yachtbau". 198X edition .

As explained by the author, stability to carry sail is mainly determined by waterline beam. Than a statistical analysis revealed above mentioned result.
According to time of publication, and author's preferences, seen in his designs, this is applicable to masthead rigs with large foretriangle of that time.
I do not have more recent editions at hand and do not know if the formula was updated for more modern designs.
From my observations, 2.4 number is about adequate for boats with really large main and small fore triangle, like late IOR era designs.
Again for multimasted vessel the number could be larger, as heeling lever is shorter.
When you intuitively see the boat as over-canvassed, the formula usually reveal the ratio closer to 3.0 or 2.8. When she is obviously under-canvassed,
you find the ratio way below 2.0.
I devoted some time to test the formula, did find it adequate and use for my work since.

 

Michael Kasten in one of his articles mentions this formula too, but he uses the wetted hull surface (WS) instead of LWL*Beam. His formula is: SA = WS * (2.2 - 2.4)
Evidently, the only rule is - there's no firm rules.

 

using this formula SA=(LWL*beam on WL)*(2.0 ... 2.4) I get 150 to 168sq.ft. for my boat. It looks like I could and maybe should increase the sail area to at least 150sq.ft.

 

There is always reefing! If you size it with the idea of putting your first reef in at about 12kts you have some good size for ghosting. With 3 rows of reefs and a final reefed sail area around 40% of the full unreefed area you should have a nice wide sailing range.

 

Thanks for the reply! Any idea of what range of boat sizes and types it was derived from and is applicable for? If it was derived from data on 1970's IOR "racer/cruisers" only I'd be skeptical about applying it to small, unballasted boats with occupant weight a large fraction of the total displacment.

 

This ratio is important for light airs speed, when stability is largely irrelevant, and hull drag consist almost exclusively from skin friction.
And, yes, this ratio end up at about the same number for most "moderate" sailboats.
Just go over the boats you know and check the ratio of nominal SA against LWL*BWL; you will be surprised how little scatter you will find.

 

The author do not describe in detail his database.
His designs generally are close to 2.0 as far as I remember.
_________

Just take an Optimist:

3.5m2/(2.13m(LWL)*1.0 (BWL))=1.64.

It is undercanvassed, intentionally so as kid's first boat.

 

calcualtion for bending moment (using 1 lb/sf sail area): 132 lb x 120.5"= 15,906 in-lb

bending stress on 3.7" dia mast; I= (piex 3.7^4)/64 = 9.20 in4

Fb = (15,906 x (3.7/2))/9.20= 3,198 PSI

For clear hand selected Sitka Spruce w/ less than 15 percent grain run-out and 6 or more grain per inch it should be good for 3,750 PSI for transient loading. So you should be good with the 3.7 in dia cantalevered mast. The max stress occurs where you have it pass through the deck beam or fitting when it is cantilevered.

So for most sailing conditions you should be good!

 

Pressure on sail is determined by maximum righting moment at sailing heel angles. From there the pressure for all the other calcs is derived.

 

In a small boat crew weight and location can have a major influence on righting moment, or even be the primary factor. The maximum crew weight and how far to windward including being outboard (hiking, trapeze, etc) needs to be considered.

I also wonder if a quasi-static righting moment analysis is sufficient for small boats, and if inertia effects should also be considered. A reasonable approximation may be a factor which increases the effective righting moment. Perhaps this is done implicitly in some analysis.

 

Yeah, well - they are all components of the righting moment... What's the news there?

Safety factors and coefficients are also commonly in use and an inevitable part of any scantling process. Also called coefficients of ignorance.

 

No news to those who recognize it.
-BUT-
Could be significant to those who have learned from most design books which are oriented towards larger boat design, such as Principles of Yacht Design or Skene's Elements of Yacht Design, which only discuss righting moment in terms of a fixed center of mass located on the centerplane of the boat. There is also the possibility that a designer with only "big boat" experience may over look how significant and even dominant crew weight and location can be to righting moment on a small boat.

 

Just check some boats around you for this (SA/(LWL*BWL)) criteria. You will find little scatter in data.

 

Umm, what does that formula have to do with a comment about righting moment, not sail area?

 

It has to do that without extremes in design like 49-er, hiking or trapezing do not cahnge righting moment so much as to render WL beam factor out of the dominant position.
that is about selection of sail area, which is closely related to stability of boat.

As to pressure, we either:
a) know the exact righting moment to be developed, and appply normal engineering routine with safety factors, or
b) go with old rules of thumb, developed for boats with "normal" proportions; they already (indirectly) contain stability, sail loads, as result of stability and sail type, safety factor for dynamics, for imperfection and deterioration of materials.

Mixing of those two approaches is not so productive, because nobody ever knows where to draw a line and say "strong enough".