sail area for a new design

is there a formula for calculating how much sail area a boat can handle?

 

Yes. Several. Not just for performance, but of course stability

A good start is here

http://www.sailingusa.info/design_winds.htm

 

Not a single formula as such, I'm afraid, but you have to find the equilibrium between heeling moment from the sail(s) and the boat's stability.

You have to guess a heeling angle, determine the centre of effort of the sailplan, the sailforce generated at a certain windspeed (unless you are dealing with something very special you can take the lift coefficients of the sails from Larsson and Eliasson's "Principles of Yacht Design", for example) and angle (I think it's clever to assume an upwind sailing situation) and calculate the heeling moment (don't forget to include the lateral force from the hull!).

If the righting moment of the boat at this angle of heel is larger, reduce the heeling angle for the next loop and vice versa, until you find the equilibrium angle that you can then decide to be acceptable or too large. In the latter case you have to reduce your sail area and if the equilibrium angle is small enough you can add some canvas.

All this assumes that the boat's structure is able to withstand the loads, of course.

 

Thanks. I was hoping there was a simple solution for a simple hull. Here's the boat I'm designing, a 15ft LOA open family daysailor. She will have built in floatation fore and aft and side benches. She's 14'2" LWL x 5'10" beam and I have it drawn with a 132 sq. ft. gaff rig for starters.

 

Nice little thing!

The sail area looks reasonable and well within the ballpark of comparable dinghies - nothing to worry about.

 

great! that's what I was wanting to hear.

 

any thoughts on if this rig could be free standing or one stay forward?

 

Spar dimensions will determine if she can be free standing or not. You don't really need a headstay on a cat boat of this size.

 

You can do a quick calculation based on about 1 lb of wind force for each square foot of sail (a reasonable number of max in sailing conditions). Than from the height of centroid of the area calculate the bending moment on the mast. From there you have to know how to calculate stress on the mast, this is a function of the cross sectional shape (if round than there are simple formulas for determining that), and the size. The max allowable stress is a matter of the type of wood and its quality.

If you do not know this stuff list your sail centroid height, sail area, your perferred type of lumber and someone can determine the dia of the mast you need.

There is no fixed sail size, large sails mean in low wind conditions you can still make reasonable headway. but large sails also mean you have to reef early than with smaller sails, or pull the large one down and raise a smaller one. There is always a point no matter how big or how small, where the wind is too large to maintain control of the boat, and it can put too much stress on the rigging if not reefed early.

On a small boat meant for beginners they will but less sail area so it is easier to handle, but it also means you will not be as fast with similar sized boats.

So it is more about design intent rather than "proper" sail area.

 

Dinghies have a larger variation than bigger boats. It depends largely on the expected weight of the crew, if they will hike out and if there are trapezes.

 

Often the crew will be just me and I'm not interested in winning races. The sail area is 132 sq.ft. and it's centroid is 10'-1/2" above the DWL. I would build the mast out of spruce. Using the formula in "Skene's Elements of Yacht Design" I come up with a diameter of 3.7"

 

Nice boat, Timothy!
The sail area looks about right, based on existing similar boats.

 

To start with:

SA=(LWL*beam on WL)*(2.0 ... 2.4)

here sail area is nominal -i.e. roach of main is not accounted for, overlap of genoa is not accounted for.

 

Source of the forumla? Any idea how it was derived and what assumptions and approximations were used?

 

This is a handy on-line sail calculator: http://www.wb-sails.fi/news/SailPowerCalc/SailPowerCalc.htm
Put zeros for jib measures (I, J), estimate the righting moment from your body weight, size and see what happens with varying mainsail dimensions and wind speeds.
Cheers!