Finding the center of an elipetical sail

In considering different sail plans for my pipe dreams I often think of using an elipetical mainsail. I know that you can always draw the sail, cut it out and then balance it on a ruler or pin to find the center of area. But it would be easier if I could just somehow find the center on my computer. Maybe the cad programs will do this but I am cad program challenged. I found google sketchup much easier to use and it suits my needs for just about everything I draw. But it won't give me the center of an elipetical mainsail. So is there some formula for finding the center an elipetical mainsail? The closest that I have come is to first draw the sail, then draw another elipse using the boom length and 1/2 the luff length, and then draw another elipse using 1/2 the boom length and the luff length. The intersection of these two elipses comes within about 2 1/2 % of of the center found by balancing on a ruler. The true center is about 5" lower and 2.5" forward on the attached drawing. I would think that is close enough. The intersection of the dashed lines on the drawing is where I found the center of area by balancing on a ruler.

 

I hope this is useful.

 

The centroid of that flat shape is not the same as the center of effort in the sail. It will depend on the cut of the sail and how it is set. Are you trying to find how the boat will balance?

 

I will go with Gonzo on this one. The center of effort of a sail is not necessarily the center of area or centroid. Matter of fact if you mean to delve into the aerodynamics of fixed wings, then you find that lift or force centers are not at the centroid position .

 

As a rule you can ignore the roach on conventionally shaped Bermudan sails. This means a line starting at half the width of the base, intersects the head and another at half of the height of the hoist intersects the clew. This moves the CE slight forward and is more realistic in terms of figuring lead and balance. Once other sails are introduced into the equation, more rules of thumb are employed, such as the area of the fore triangle instead of the actual sail and/or half the area of the mizzen, instead of all of it, etc.

 

Some of you may recall from my other threads that I like cat ketches. They typical have 2 elipetical shaped sails. I know with a typical masthead sloop rig you disregard the roach on the mainsail and only use the fore triangle as Par posted to calculate the center of effort of the sail plan to compare to the center of lateral plane. But elipetical shaped sails have a much larger roach and a lot more sail area that a typical mainsail. It only makes sense to me to use the actual center of the sail. If you didn't use the actual center of an elipetical sail and just calculated the center as for a typical mainsail the center of effort would be several feet farther forward and none of the guidelines for balancing a rig would apply. At least that is my thought process and why I am looking for a way to determine the center of an elipetical sail on my computer. My method in the diagram I posted comes close and maybe it is good enough. But I don't know if it is.

 

https://en.wikipedia.org/wiki/Integral

 

Bingo Teddy. Chuck, the "Elliptical" sails you're seeing aren't any different than most conventionally proportioned Bermudian mainsails, so the same rules apply.

These thing tend to sort themselves out, which is how the rules of thumb come to be. After dozens of calculations on similarly shaped sails, you realize you don't need to do some things and still get a CE that's close enough. For example, when I design a sail plan I always (as sport) take a guess at the CE, placing a temporary mark, where I think it will be. After years of doing this, I'm never more than a few inches off, on a 200 sq. ft. sail plan. This is way more than close enough. The same is true of foot, luff and roach rounding, you just pretend the sail is really triangular and the CE is close enough. The only time this doesn't work well is square tops and these are treated like any quadrilateral sail, again kissing off any edge rounding.

If you want, take this to a simple test. Draw up a rounded roach (don't forget the luff and foot rounds), but with typical proportions. Next, subdivide the sail into smaller triangles, say two or three and calculate the centers, averaging them out in the end. Check this against using the full dimensions and see how far off it is. Yeah, you'll see some differences, but getting a sail cut within these differences will be challenging enough, let alone making an extra half a turn adjustment on the headstay turnbuckle, come rig tune up time, just doesn't justify the precision, you're looking to make a lead guess at.

This is part of the black magic of yacht design. You don't really think the latest America's Cup boats, came out of the barn with deadnuts (technical term) lead/CE relationships, that didn't need significant adjustment did you? Of course they did, eventually refining the placement. You can spend 10's of millions and still be just as "off" as the amount you'll spend on designing your rig. Your boat isn't going to be any different than Oracle, so an adjustable mast step or other way to make adjustments is a wise idea. The only other option is to build a boat with the CE/lead relationship you think is right, than launch and see how bad it is. You'll make adjustments and eventually "settle" (just like Oracle did). Subsequent versions of your sail plan, should include what you learned from the prototype, which of course isn't going to be where you figured it might be, when designing it up. Welcome to yacht design.

 

For what you need and the methods of calculation that you have, in my opinion, what you have done is enough. Try something else would complicate life with problems you, at the moment, can not solve.
In calculating mast and rigging, for example with the method of the NBS, they assume simplifications, as important or more than indentifying the sails center of efforts and the geometric center of their surfaces.

 

thanks for the replies. I'll stick with my method. It seems to be close enough to get me in the ball park.

 

One thing that I have found in using my method of finding the center of an elipetical sail is that on every sail that I have tried so far the center always comes out at 44.4% of the luff length above the boom and 44.4% of the boom length aft of the mast. Finding the center by balancing averages around 43% in both directions. This simple math calculation gives me the center of an elipetical sail which is close enough to suit my purposes.

 

Oooooo, 1.4% difference, hummmm, you can get it closer than that . . .

When working out the CE/lead relationship, add a percent to your prefered lead, to accommodate the geometry you've employed. Simply put, if you think 12% lead is what you need, make it 13.

 

I like that PAR, and bet your right too!. Not to mention they also had the option of moving and angling the foils too, just to make things more interesting...