Betz limit with regards to sailing

[EdParenteau]

 I was wondering how the Betz limit applied to sailboats, etc. if it did.  If not, does anyone know how much power a sailboat can put out relative to its "wind swept area"?

Thanks,

Ed

[Ungrounded Lightning Rod]

I was wondering how the Betz limit applied to sailboats, etc. if it did.

When I think about the swept area of a boat with a 30 foot mast sailing from, say, San Francisco Bay to Japan at 5 1/2 knotts, the amount of energy involved at even a tiny fraction of the Betz limit makes my head hurt.

A sailboat is an N-blade linear turbine.  Because you leave the used air behind you, you don't have to sweat it interfering with the slug of air involved in the next pass of a set of rotary blades.  So the conditions from which the Betz limit was derived don't apply.

No dobut there's some OTHER limit, which might be derived in a related way.  But I don't know what it is.

And since I just sail one occasionally, rather than racing it and making decisions about sails to get the last ounce from the air while coming in under the rules, the Rolls Royce horsepower answer is good enough for me:

Shopper:  "How much horsepower does this car's engine have?"

Rolls Salesman:  "Adequate."

[Dutch]

Of coarse the Betz limit appies to sailingboats. If all the energy of the wind is extracted the speed of the wind will be zero. That is impossible. However, there are some more things to say over the sailingboat.

At first, the amount of energy extracted from the wind depends on the course of the boat in relation to the wind.

Imagine, the wind comes from behind. The boat is speeding up, but when speed increases, the pressure of the wind in the sails decreases. If the speed of the boat is the same as windspeed the pressure in the sails is zero. That will never happen. There will arise an equilibrium between the force of the wind and the drag of the boat in the water. The speed of the boat will be always LESS than windspeed.

Imagine the wind comes from the side in an angle of 90 degrees. The boat is speeding up, but the pressure on the sails remains the same! There will arise again an equilibrium. But, depending on the shape of the hull, it's possible that the speed of the boat is HIGHER than windspeed.

What can we say with this in mind about drag based and lift based VAWT's:

Drag based turbines like the Savonius behave poorly even with the windward side shielded!!! The blades will never move at a speed more than windspeed. The TSR will never be more then one!!!

Lift based turbines like the Darrieus will possibly move with a speed more than windspeed. TSR > 1.