Centre of effort - gaff

[SaintAustell]

Can someone tell me how to calculate the centre of effort of a gaff sail?

[DerekW]

If you'll settle for the centre of sail area then that's straightforward:

Divide your foursided shape into two triangles: peak to tack or throat to clew, it doesn't matter. Actually , if you want a confidence check you could do both - the answer should come out the same in either case.

Mark the centre of area for each of the two triangles in the usual way, then calculate their respective areas.

Now draw a straight line connecting the two centres. The overall centre of area for the foursided sail lies somewhere on that line.

This next bit is really simple, but I might not word it as clearly as I'd like...

Let's imagine that you ended up with areas for your upper and lower triangles of 30 and 40 units respectively: a Three to Four [3:4] ratio.Now measure the length of the line connecting the triangles centers. Let us pretend it is exactly 7 units long.

The aggregate center of area for the foursided sail is at a position on the connecting line at a distance from each of the triangle centers in inverse ratio to the ratio of the areas.

In our imaginary example, the center would be three units from the center of the 40 unit triangle, 4 units from the center of the 30 unit triangle.

Of course in real life the units never work out that neatly, but the 'Inverse ratio' holds true.

cheers
Derek

[P.I. Stazzer-Newt]

Yup, that will work.

Now the easy method, finding the center of area for a lamina is the same as finding the "center of gravity".

You will need:
</font> Pencil </font> Piece of string </font> Ruler </font> Some sheet material.
Cardboard, Ply or whatever comes to hand </font> One thumb tack or nail </font> One Medium sized Nut (3/8" to 3/4" ish) </font>Tie the string to the nut, tie a small loop in the other end of the string - congratulations you have just built a "Plumb Bob".
Using the pencil and the ruler, mark out a scale drawing of the sail on the sheet stuff.
Cut out your "Sail".

Drill (small) holes in the four corners of the "Sail".

For each hole: </font> Hang the "Sail" from the nail/thumb-tack. </font> Hang the Plumb Bob from the Nail/Tack </font> Mark the vertical line using the ruler/pencil. </font>Where the four lines cross is the "Center of Gravity" and the "Center of Area/Effort".
Good project if you've got a surplus ten year-old.
Edited for speeling

[ 08-29-2005, 01:04 PM: Message edited by: P.I. Stazzer-Newt ]