Calculating Sail Power

Hi I need to know the power of an international moth sail for a physics project i am doing. The sail is 8 m2. Is there an 'easy' way of calculating this?

 

If I tell you the formula, it wouldn't be a project, would it?

 

Though I’m pretty sure the subtlety of this will be lost, but sail size comes from a power requirement, not the other way around.

..."The proof is left to the student'...

 

Now I am also wondering about this. I have always chosen the amount of sail area by a comparison to other similar boats or by comparing stability to heeling moment using the standard method described in the texts. How much horsepower does a sail generate?

 

Power = force x velocity

Power is not a terribly useful concept for a sailboat because the faster it goes, the more power it has available! Power boats have a fixed amount of power available, so you get the performance from the point where power required = power available. With a sailboat, it's only after you already know the performance that you can go back and figure out what the power is.

Instead, it's much more straightforward to look at the balance of forces and moments. A sailboat has maximum heeling and pitching moments, or a maximum force available from the sail in a given wind, so you can work to those.

 

C.A. Marchaj, an authority of considerable stature, gives us a little bit of information about this subject. He is mainly interested in the overturnig force of the sail, a matter of considerable importance. His equation is pretty simple really. It does not tell you what the driving force is but it will give you some clues.

F= 0.0034*A*V^2 Where F=force, A= sail area in square feet, V= wind velocity in knots. It is easy to see that the big factor is wind velocity squared.

The Moth you describe has about 80 square feet of sail. (The Moth I sailed about a hundred years ago had only 72 sq. ft.) You can see that 80 sq. ft. might be manageable in a 10 knot breeze but pretty iffy in a 20 knot blow. The force is 4 times greater on account of the mean little exponent. You do the math.

I hope this helps.

 

See Larsson - "Principles of Yacht Design" pages 148/149.

Larsson details the major parts of Hazen's aerodynamic model. Have a read, it will all become clear.

Tim B.

 

See Dave Gerr's "Nature of Boats" this reference will give a simple explanation and rough method for calculating what your talking about.

 

Something to keep in mind when you're using such formulae to analyze sails. Remember that these are only approximations! There are a great many factors that affect the power one can extract from a sail- to account for shape and curvature, for instance, involves a mind-numbingly long process of iterating nasty multiple integrals. So boatbuilders develop simple algebraic formulae that give reasonable approximations in most conditions. Not all formulae apply to all boats, so make sure you read up a bit before you start plugging numbers in.

 

I once asked a similar question of my NA, response was to work back from the speed of that hull & the power required to overcome its resistance-etc-etc-etc & that an accurate HP per sq metre was "hard to define" due to variable opperating modes of sails camber etc etc.Some times I've heard TV commentators quote rig HP numbers- I wonder where they get them from?. regards from Jeff.

 

Thanks for all your replys. Your much more helpful than my physics teacher was. I might actualy finish my project now!