Calculating sq ft for marconi and gaff sails?

[Thorne]

So I'm an idiot at math -- but how do you calculate the sq ft of triangular sails?

And for gaff sails -- the latter with this info:

Luff = 12', Leech = 17', Foot = 9', Gaff = 7'8"

[Keith Wilson]

The area of a triangle is (base*height)/2, with the base and height dimensins perpendicular, so if the boom is more or less at right angles to the mast (luff*foot)/2 will be pretty close. If there's a lot of roach, that adds a little.

The gaff sail you described, assuming an 85-degree angle between the boom and mast, has 108.5 sq ft.

[ 11-18-2005, 06:14 PM: Message edited by: Keith Wilson ]

[Bruce Hooke]

As Keith noted, the standard way to calculate the area of a triangle is to multiple a base (which can be any side) times the height, which is the distance from that side to the far corner, perpendicular to the base and then divide by 2. The illustration below, from this web page (http://www.luminet.net/~bkuhl/imprvperf.htm), illustrates the idea:

http://www.luminet.net/~bkuhl/AreaTriangle.gif

Gaff sails are harder. You need to know the length of one of the diagonals to figure the area (or lay it out using the angle of the gaff). Once you know the length of one of the diagonals you can treat it as two triangles and calculate the area the same as with a triangular sail, but to get the heights you will probably want to draw the sale to scale, BUT

It is possible to calculate the area of a triangle when all you know is the lengths of the three sides (which we will abbreviate a, b, and c):

First calculate "S":

S = 1/2 (a + b + c)

Then use that to calculate the area:

A = square root of [S*(S-a)*(S-b)*(S-c)]

[ 11-18-2005, 06:37 PM: Message edited by: Bruce Hooke ]

[Thorne]

Thanks!

You are talking to someone who took algebra 1 three different times...

;- (

But I think I understand -- for most marconi sails you can calculate the sq ft fairly easily.

But for a gaff or spritsail, you either have to physically measure the angle to make two triangles, or have the maker's specs. Just having the 4 edge measurements doesn't give anything but a vague guess at the actual size.

[ 11-18-2005, 07:59 PM: Message edited by: Thorne ]

[Todd Bradshaw]

In sailmaker lingo, that perpendicular measurement used to calculate three-sided area is known as the Luff Perpendicular, or "LP". Line "B" on this drawing shows the LP of this jib.

http://www.imagestation.com/picture/sraid117/p8a7c241520f2e5d92b954ba4194333a7/f89cbadd.jpg

If a 3-sided mainsail has a mast-to-boom angle pretty close to 90 degrees you can get a quick and dirty measurement by just multiplying the luff times the foot, but if you really want an accurate figure and the boom angle is more or less than 90 degrees, find the LP and do your calculations with that. Roach isn't generally counted as sail area in most cases, due to the ways that racing rules have been set up. Class rules will give you the basic triangle and then may specify how much roach you're allowed to add-on and where. For recreational sailing (non-class racing) unless the roach is really huge (like on a bat-wing sail where it can nearly double the sail's area) there isn't much reason to figure out the roach area for anything other than estimating fabric yardage for building the sail - and that's usually done with fairly simple guestimates. The same is true for foot round. It may or may not be regulated by racing rules or even on the plan, but it isn't generally calculated or added to the sail area figures.

Likewise, if a sail has no leech battens it will need to have the leech cut in a slightly hollow curve (typically 1" of hollow per every 6' of leech length) to prevent the leech from flapping. This is a given and that little sliver of missing fabric is not subtracted from the sail's area. The finished sail measurement is figured as though there was no hollow, even though there really is some. It also often won't be shown on the designer's sailplan.

As the guys mentioned, the four-sided sail is simply divided to yield two triangles and the LP method is used (even though the long leg may be the luff, or it actually may be the leech or a diagonal - whichever works best). In this drawing, for example, B&D are the perpendiculars but the leech length and clew-to-throat measurements are being used for the long sides of the two triangles rather than the luff length. You could even do it by using the diagonal "A" as the long side for both triangles. In that case the perpendicular for the top half "D" would run from the diagonal "A" to the sail's peak corner".

http://www.imagestation.com/picture/sraid117/pce24dfa4f8ab2f0c1e76b39359b1bcfc/f89cbaf0.jpg

Always be sure to get at least one diagonal measurement on a four-sided sail. Without one, the sail could have numerous profile shape variations, even with the same edge measurements.

[ 11-18-2005, 09:28 PM: Message edited by: Todd Bradshaw ]

[merlinron]

i've always wondered just how accurate you need to be with measurement. some roaches are pretty big on the plans i've looked at and can add several feet to the square area. do need to add that to the standard equation? iknow it is considered that the roach doesn't matter, but in some cases i wonder, it is sail area, afterall. how big does the luff have to be before you should consider adding it to sail area for center of effort calculation? is there a situation where not adding a big roach roach ( on a more or less conventionally shaped marconi sail) to the calculation might take the center of effort outside the ability to tune the rig by changing mast rake after it's up and sailing?

[Bruce Hooke]

The basic rule on this sort of thing (whether to measure the roach) is "what are you comparing with?" As an example, when you hear discussions about how much "lead" is required between the Center of Effort and the Center of Lateral Resistance, this is based on what seems to work well for similar boats, not on some "absolute" math about hydro- and aerodynamics, so what matters is what the person who came up with that lead measured (i.e., did they include the roach). Of course most sources for this sort of information may well not go into that sort of detail, but I think it is safe to say that IF the roach is fairly normal then it usually will not have been included in the sail area and thus not included in the calculation of the CE and the lead. It is then up to you, the designer, to determine whether you are dealing with an exceptional amount of roach and factor that into your calculations. One way to approach this would be to first re-figure the recommended lead based on including a typical roach, and then adjust your lead with the real roach figured in, to match that new figure. Of course there could also be subtler factors that mean that the roach has more or less impact on the balance of the boat...and in those sort of subtlties lies the art of the matter!