lift mode sail's power formula

oops-that's me [the O.p ] again!

I didn't succseed to write here in the power of,so I just wrote it as v*v*v but I didn't put it in brackets!

so the wind power formula is 0.5[v*v*v]p per sq.meter.

The thrust vectors resulting from a sail can be gotten out one of best books on the subject. "The Theory of Wing Sections" by Ira Herbert Abbott.

Unlike an aircraft, the camber of a sail is constantly changing as is the angle of attack.

The book will get you close.

L.J.

Hi, Laughing Jaguar!

Although the camber of a sail is constantly changing, the point of calculation for lift is not. It is the center of the sail and its maximum billow line. The variable is wind velocity which dictates the pressure on the sail that sucks the boat along; and how much advantage can be taken from that depends upon the skill of the skipper.

However, a chart could be derived for a specific boat with a skipper patient enough to take the time, for maximum pull vs wind speed per sail (potentially additive); and even potentially incorporating a z axis denoting angle of heel.

Of course there are other variables such as hull design, lwl, and sailing location etc., which factor in to a boat's upper speed limits. Factor these variables into a reefing control computer hooked up to a gyro sensor of some kind, a wind vane and an anemometer, and potentially, one could option for a best course at top speed automatically.

I think for that, one would want either a center cockpit or ketch design to stay out of the way of swinging booms.

I betcha some groovy nerdy yacht architect dude/dudette has already gone a long way to developing a program like this, maybe even one that just lets you fill in the blanks with your own boat/sail specs.

Mark

Hi Mark,

Although the camber of a sail is constantly changing, the point of calculation for lift is not. It is the center of the sail and its maximum billow line. The variable is wind velocity which dictates the pressure on the sail that sucks the boat along;

This is actually an oversimplification. The coefficient of lift of a sail varies in the same way (and for roughly the same reasons) as that of an airplane wing. As a result, sails that are trimmed flat (by pulling on a lot of downhaul, outhaul, and easing the traveler, etc) will, for a given angle of attack, generate less lift (and less drag) than a sail trimmed full. (A full sail is the rough equivalent of an airplane wing with flaps extended, although the actual Cl is lower.) The angle of attack of the sail with the apparent wind has a large effect on Cl, also, so that a flat sail with small angle of attack will have a Cl of perhaps .3, whereas a full (more highly cambered) sail with a higher angle of attack will have a Cl of 1 or higher. Drag varies roughly in proportion to lift, so that highly cambered sails also create a lot of drag (as do highly-cambered and flapped wings).

The point at which a sail's lift acts on the boat changes with sail trim. When the sail is eased, the center of effort moves both out and forward, so that many boats will develop weather helm (tend to steer themselves into the wind) on a beam reach because the forward vector of the lift is not centered on the boat.

There are dudes and perhaps dudettes who have designed automatic sail management systems, although they are not widely accepted, nor do many see the need for them in recreational sailing. It is a subject of interest to me, however, because I built a rigid wing powered boat, and the feasibility of automatic management is much better in such craft. One huge advantage is the ability to let the wing weathervane, under which condition it will create less drag than the "bare poles" (sails taken down) of a traditional sailboat. Sailing with a low coefficient of lift is simple, whereas with soft sails it can be difficult: in sailboat racing, there always comes a time when, after having flattened the sail as much as possible, you need to reef or put up a smaller sail, which is something hard to automate.

I built a full scale wing-powered boat with manual control for the purpose of going very fast. But I also built an RC model in which wing angle of attack was controlled by a trim wing, which was in turn controlled by a servo. The boat was remarkably easy to sail, and the arrangement allowed for going from forward thrust to reverse thrust, more or less instantly. The boat could be easily sailed in reverse, something which can be done on a small dinghy, but which is difficult on a larger boat.

Walker (of Walker Wingsail) arranged his boat for essentially automatic sailing: he had a thrust control that looked just like the throttle lever on a motor boat. He went out of business, and his business methods were controversial, but his boat worked pretty well. This page show his boats (http://www.geocities.com/CptinRn/strange.html - sorry, link no longer available) (all the way at the end of the page) and also mine (the Windrocket, two above his). He apparently went through a few gales on ocean crossings and the wings behaved well. At a sailboat show, I met a guy who had sailed on one of his boats, and who was very well impressed.

However, a chart could be derived for a specific boat with a skipper patient enough to take the time, for maximum pull vs wind speed per sail (potentially additive); and even potentially incorporating a z axis denoting angle of heel.

I raced J-24s for a while, and a lot of us had charts like this, with settings for downhaul, outhaul, cunningham, traveler, mast bend, etc, as well as sail selections for various wind speeds. These boats were always sailed at 5 degrees heal, never more never less, if sailed well. I never sailed mine well.

Cheers, Ken

Hi, ken_fry!

WoahHo! The man designs more than wheelies! Every time I read you, you get better and better!

Well, Ken, I am suitably sweetened by your experience, and (obviously) not just because you agreed with my recitation (can't take credit for developing it) of the calculation basics. The complications/variations are also calculable and interesting, but the basics for a cloth sail remain the same, while the rest (the part that makes sailing as fascinating a pursuit as it is) takes place between zero and max.

BTW, next time I'm hiking wayyyy out in my son's dinghy, I intend to pay no attention at all to your 5^o of heel!

Mark

"I betcha some groovy nerdy yacht architect dude/dudette has already gone a long way to developing a program like this. . . . ,"

Charley Morgan, former America Cup racer and naval architect used to keep my dizzy with stories about draw tanks, Beta waves hull optimization and such.

Charley is semi retired in Florida now and as far as I know has also stopped toying with aircraft designs ( a natural side step for a man with his talents and curiosity)

If anyone can do that sort of thing he can, assuming of course he is still interested.

"Groovy"? Absolutely!

"Nerdy?" Not!!

Rascal? You betcha!

L.J.

The standard formula for calculating lift is the same as that for calculating drag (only the coefficient changes, and the reference area can change depending upon what you are trying to do: for example for measuring drag on an automobile body,the reference area is the frontal area. For measuring drag on a wing, the reference area is wing area, roughly perpendicular to frontal area.)

In any case, the formula for lift is:

1/2 x rho x V2 x area x Cl

rho is the mass density of air

If p in your formula means rho, then your formula appears to lack a factor for area and for Cl. (or Cd) Of course, to go from lift or drag (forces) to power, you would , as you did, put in V as a factor one more time.

A Laughing Jaguar said, Abbott and Doenhoff is the classic text, and well worth reading.

"Obviously, the second part of this sentence is false, but at least the first part true."

Ken I had to read it three times, slowly, before I was sure that I "grocked" it!

When I did, I could not stop laughing.

Thanks!

L.J.