# How to determine Genoa Size



## EJO (Jan 10, 2010)

We all know that the jenny is expressed in percentage of size over the regular jib. i.e. 110%, 130% etc. (I think)
The question here is how do you determine what you jenny percentage is when you don't know the standard jib size and only have a storm jib (reduced size jib) and a couple of different size genoas.
Or is the size based on the passing point aft of the mast. How would I know if I have a 135%, 130%, 140% etc. without being able to lay the sail down and measure its sides to determine its area.
Any ideas? 
what size is this








Thanks,
E-J 
s/v Sailmates, 1973 Irwin 32 Classic.


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## Faster (Sep 13, 2005)

The rating is how the sail's LP compares to the boat's J measurement.

The J is the horizontal distance from the forestay tang to the face of the mast.. on your boat probably around 12 feet.

The LP of the sail is measured by taking a line through the clew, intersecting the luff at 90 degrees (LP = Luff perpendicular).. so if that measurement on your sail is 12 feet, it's a 100%; 18 feet, it's a 150% etc....

The sail in your picture looks to be maybe a 120 or 130 at this angle.


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## Zanshin (Aug 27, 2006)

A 100% genoa would extend back to the mast. 

Measure the part that overlaps from the mast to the clew (O).
Get the sails "J" value 

Percentage Genoa = (J + O)/J*100


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## EJO (Jan 10, 2010)

Faster & Zanshin
Thank you gentlemen asked and answered. [The LP of the sail is measured by taking a line through the clew, intersecting the luff at 90 degrees (LP = Luff perpendicular).. so if that measurement on your sail is 12 feet, it's a 100%; 18 feet, it's a 150% etc....][(J + O)/J*100]
I have a 130, which is what I thought now only if I could afford a new 150.


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## QuickMick (Oct 15, 2009)

IRWIN 32 Sailboat details on sailboatdata.com


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## svHyLyte (Nov 13, 2008)

Faster said:


> The rating is how the sail's LP compares to the boat's J measurement.
> 
> The J is the horizontal distance from the forestay tang to the face of the mast.. on your boat probably around 12 feet.
> 
> ...


Exactly correct.

Area= (LP x J x Luff/2)


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## tap (Apr 1, 2009)

Area = LP x Luff / 2

Assuming the sails are full hoist, i.e. the luff length is the same, and the sails are triangles, then percent LP is the same thing as percent area.

LP x Luff x J would give you cubic feet, obviously that can't be right.


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## svHyLyte (Nov 13, 2008)

tap said:


> Area = LP x Luff / 2
> 
> Assuming the sails are full hoist, i.e. the luff length is the same, and the sails are triangles, then percent LP is the same thing as percent area.
> 
> LP x Luff x J would give you cubic feet, obviously that can't be right.


You are correct, my earlier formula posting appeared incorrectly. The P in (my) LP shoiuld have been a subscript to indicate the percentage overlap of the sail. That x the J measurement to yield the actual LP in feet multiplied by the luff divided by 2 to yield area (1/2 of the height multiplied by the base of a triangle). I did not realize that subscripts and superscripts would be eliminated when one copies and pasts from a Word file. Dumb me, eh?


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## blt2ski (May 5, 2005)

Area will equal (luff x LP)/2. BUT< this will not always equal (IxLP)/2. As I is smaller than the luff! So just because you have a 130, does not mean it is 130% of the fore triangle! If you have a full luff pull, you may in reality be 132-133% of the fore triangle! My 155 genoa, turned out to me 157% of the foretriangle, which cost me some time, as the sail maker went by LP to size it, not area which my local PHRF uses!

Marty


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## rstafford (Oct 8, 2016)

It is just convention or tradition in the sailing community to express a genoa's size as the percentage of the boat's J measurement represented by the genoa's LP measurement? Because it seems wrong mathematically. A 100% jib and a genoa share a common side: the luff. Let that be the base of each triangle in the area formula base*height/2, and the LP of each sail is the height in the area formula. So the ratio of the genoa's area to the jib's area is the same as the ratio of the genoa's LP to the jib's *LP*, not the boat's J measurement (which equals the jib's foot measurement). In other words Ag / Aj = LPg / LPj. But Ag / Aj <> LPg / J.

The math also works out if you let the boat's I dimension represent the height of each sail's triangle. Then Aj = J*I/2, and Ag = (J+O)*I/2, where O is the length of the genoa's foot aft of the mast. In other words the ratio of genoa to jib areas is the same as the ratio of genoa to jib foot measurements.

And yet it seems conventional to divide a genoa's LP by the boat's J to get the genoa's size as a percentage of the foretriangle, even though the math is wrong. Why is that?

Cheers,
Randy Stafford
S/V Grenadine
C&C 30-1 #7
Ken Caryl, CO


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## RichH (Jul 10, 2000)

rstafford said:


> ..................
> And yet it seems conventional to divide a genoa's LP by the boat's J to get the genoa's size as a percentage of the foretriangle, even though the math is wrong. Why is that?


The LP is the perpendicular from the luff to the clew. 
In determining (precise) Sail Area, one _should_ be calculating the TWO triangles contained in that jib/genoa, etc. - the triangular area 'above' the LP; plus, the triangular area 'below' the LP. The LP is perpendicular (90°) to the luff

Calculating with the J dimension, does not take into account 'how high' the clew is located - so calculating using the "J" dimension is just a 'rough ratio approximation'; ............ but a good enough approximation for 'government work'.


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## chip (Oct 23, 2008)

RichH said:


> The LP is the perpendicular from the luff to the clew.
> In determining (precise) Sail Area, one _should_ be calculating the TWO triangles contained in that jib/genoa, etc. - the triangular area 'above' the LP; plus, the triangular area 'below' the LP. The LP is perpendicular (90°) to the luff


I don't think you need to do that, right? You can, but it's no more precise than a=1/2 bh (area equals one-half base times height) where h=the LP and the b=the luff.

That's the most common formula for area of a triangle:
Wolfram|Alpha Widgets: "Area of Triangle (1/2)bh" - Free Mathematics Widget

The last time I tried to buy a used jib, I got tired of running the numbers by hand and made this to do it more quickly:

Jib Overlap Calculator

My methodology is explained at the bottom.


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## chip (Oct 23, 2008)

rstafford said:


> It is just convention or tradition in the sailing community to express a genoa's size as the percentage of the boat's J measurement represented by the genoa's LP measurement? Because it seems wrong mathematically. A 100% jib and a genoa share a common side: the luff. Let that be the base of each triangle in the area formula base*height/2, and the LP of each sail is the height in the area formula. So the ratio of the genoa's area to the jib's area is the same as the ratio of the genoa's LP to the jib's *LP*, not the boat's J measurement (which equals the jib's foot measurement). In other words Ag / Aj = LPg / LPj. But Ag / Aj LPg / J.
> 
> The math also works out if you let the boat's I dimension represent the height of each sail's triangle. Then Aj = J*I/2, and Ag = (J+O)*I/2, where O is the length of the genoa's foot aft of the mast. In other words the ratio of genoa to jib areas is the same as the ratio of genoa to jib foot measurements.
> 
> And yet it seems conventional to divide a genoa's LP by the boat's J to get the genoa's size as a percentage of the foretriangle, even though the math is wrong. Why is that?


I think it's just a matter of defining terms. It sounds like you're assuming that the definition of a standard (100) jib is that the foot=J, or, later, that "100" means "100% of the area of the foretriangle." I don't think it means either of those.

In the numeric notation, I think it's defined the other way around: the number is just LP/J*100, and there's no other implication. Even on a 100 jib, the foot may or may not match the J, depending on the cut of the sail and the geometry of the rig, and the jib may have overlap or not.

For an extreme example, imagine the same sail flown upside down...this "100" sail (let's say...I didn't measure) has no overlap when flown rightside up, but tons of overlap when flow upside down. In neither configuration does the foot match the J, and the sail area doesn't equal to the full area of the foretriangle. But it's still a 100.









(Upside down sail idea courtesy Rimas M.)

So I think this means that the number should be taken with a grain of salt, since it doesn't define a whole lot about the shape of the headsail, but it's convenient for imagining the relative size of different sails of a similar cut.


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## JimsCAL (May 23, 2007)

RichH said:


> Calculating with the J dimension, does not take into account 'how high' the clew is located - so calculating using the "J" dimension is just a 'rough ratio approximation'; ............ but a good enough approximation for 'government work'.


Actually, any sail with the same luff and the same LP will have the same area. The clew height doesn't matter.


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## Jeff_H (Feb 26, 2000)

I am not sure that the above discussion has it right when it comes to racing rule sail measurements. Doing this from memory, which is never a good idea anymore, I think that racing rules use the'I' of the sail (the vertical dimension from the point where the forestay hits the mast to the point where that line hits the side deck.) And J (the point where the forestay intersects the deck to the point where I hits the deck. These are multiplied together and divided by two to get 100℅ fore triangle. 

Then the actual luff length of the sail in question times the length perpendicular of that sail are multiplied and then divided by two to get the sail area. That is divided by the 100 ℅ fore triangle to get the % of that jib.

In other words it is not just the LP or overlap that determines the % of the sail.

Jeff


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## rstafford (Oct 8, 2016)

Thank you Chip and Jeff_H for the insightful replies. Very nice jib overlap calculator, Chip, I learned things e.g. Heron's formula, and I'm a math major 

So I can accept that it's just a definition or convention that genoa size, as a percentage, is defined as 100*LP/J. Trying to understand the mathematical reason for that only led to cognitive dissonance.

Jeff_H - if you can refer me to any written definition of "racing rule sail measurements", I would really appreciate it. To me it makes perfect sense that 100% of the foretriangle is defined by I*J/2, and that a 100% jib would have exactly that area, and that a genoa's size would be expressed as a percentage of that area.

Meanwhile I'll assume the apparent conventional definition of genoa size, 100*LP/J.

Cheers,
Randy


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## RichH (Jul 10, 2000)

Salimakers use the LP dimension vs. luff length in calculating actual sail area. Using LP divides the sail into TWO distinct triangles which adds to total sail area. 
The reason why LP is used is because the geometry formula of 1/2 base times height ...... is *ONLY* VALID for 'right' (at least one internal angle is 90°) triangles.

Using a graphical solution, and arbitrarily using J at 1.20 'units' and 'scaling all the rest of the dimensions of the OP's 'pic' .... 
If one calculates SA by using J then the sail area becomes 2.49 'units' (INVALID) as such includes the missing area below the clew, etc. 
If one calculates SA with an upside down sail and by using an increased J dimension as the base, the sail area becomes 4.02 (INVALID)
If one uses the correct LP as the base and luff (which is perpendicular to the base/LP) then the TWO parts of the areas equal to the TOTAL area .... and which is VALID for RIGHT triangles = 2.03 'units' total sail area.

2.49 is not equal to 4.09 which is not equal to 2.03 units. 2.03 by using LP as the base of the TWO 'RIGHT' triangle is the _correct_ solution.

Rx: alway use the LP when calculating SA .... and then add the two triangular areas. 1/2 height • times • base is ONLY valid for 'right' (90°) triangles; LP divides any triangle into TWO 'right' triangles.


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## chip (Oct 23, 2008)

RichH said:


> The reason why LP is used is because the geometry formula of 1/2 base times height ...... is *ONLY* VALID for 'right' (at least one internal angle is 90°) triangles.


I think I get what you're trying to say, but just to be clear, 1/2 base times height definitely works for any triangle.

Here's the mathematical proof (it starts with a right triangle, then shows how it works for any arbitrary triangle): 
Proof of the Area of a Triangle

You're correct that sailmakers use the LP to calculate area, because that is the "height" in 1/2 base times height--the J is not a part of the triangle at all and is therefore not part of the area calculation. But you don't need a right triangle for 1/2 bh to work, and the "sail overlap" is still LP/J*100.


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## chip (Oct 23, 2008)

Jeff_H said:


> I am not sure that the above discussion has it right when it comes to racing rule sail measurements. Doing this from memory, which is never a good idea anymore, I think that racing rules use the'I' of the sail (the vertical dimension from the point where the forestay hits the mast to the point where that line hits the side deck.) And J (the point where the forestay intersects the deck to the point where I hits the deck. These are multiplied together and divided by two to get 100℅ fore triangle.
> 
> Then the actual luff length of the sail in question times the length perpendicular of that sail are multiplied and then divided by two to get the sail area. That is divided by the 100 ℅ fore triangle to get the % of that jib.
> 
> ...


Ah, using the fore triangle calculated like that would actually make more sense.

When I did the original research for my calculator, I was using sources like this:

http://thesailwarehouse.com/cgi-bin/web_store_TSW.cgi?page=sailbuyingtips.html

_Overlap - Working jibs normally fall between 90% and 115% overlap. This means the jib's L/P dimension is between 90% - 115% of the distance from the bow of the boat to the mast (known as the "J" dimension)._

But using the actual fore triangle made of the I, J, and luff seems like it would be more logical. I wonder where the definitive answer is? I may need to re-do my calculator!


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## GeorgeB (Dec 30, 2004)

Ah! You can tell that it’s a change in the seasons (and boats are beginning to be put away) when the discussions turn towards the nuance. In a past life I was the national measurer for my class. I measured a lot of jibs. I also spent a pretty penny to maximize my own jibs under the class rules. Everybody uses LP/”J” to describe the size of a jib. Now for the nuance. How do you guys calculate the area lost to hollow (negative) roach? If I have a leach of 39’ 2”, and a LP of 17’ 7” with a hollow roach of 10”. How much area am I giving up? Can you provide a formula so I can calculate the benefit of battens? (this would decrease the “hollowness” by 5”. This involves calculus which I’m not too good at but I would like to put the formula on an excel spreadsheet.


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## RichH (Jul 10, 2000)

chip said:


> I think I get what you're trying to say, but just to be clear, 1/2 base times height definitely works for any triangle.
> 
> Here's the mathematical proof (it starts with a right triangle, then shows how it works for any arbitrary triangle):
> Proof of the Area of a Triangle


NOPE, I don't think you're getting what Im stating at all. You are MISQUOTING the fundamental (simplified) equation for the area of triangles: 1/2 base 'times' height. You're mistakenly using the WRONG 'height' where 'height' (h) MUST be at 90° to the base (b). You are using the WRONG 'height'. ;-)

Here's a 'development'/illustration of a*VALID* proof:

Look at the diagrams in: Area of a Triangle 
To find the area of a triangle, multiply the base by the (CORRECT) 'height', and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, the area of each triangle is equal to one-half the area of the parallelogram.
Since the area of a parallelogram is A = b x h, the area of a triangle must be one-half the area of a parallelogram.

*The base and height of a triangle must be perpendicular to each other* when using 1/2b•h. 
In each of the examples in the above URL, the base is a side of the triangle. However, depending on the triangle, the height *may or may not be a side of the triangle*. For sail area calculation its the LP line which is 'h'. 
For example, in the right triangle in Example 2 (see URL), the height is a side of the triangle since it is perpendicular to the base. 
In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height ...... and where that dotted line is the 'h' = LP of a sail.

Rx: in calculating triangular area by 1/2b•h, _the 'height' MUST *always* be 90° perpendicular to the 'base'_ ..... or in "sailmaker-speak": 1/2 luff 'times' LP, _nothing_ else.

Of course one can always use the 'double angle formula' to find the area of 'any' triangle ... and its not: base 'times' height !!!!!!!!


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## rstafford (Oct 8, 2016)

Rich I must disagree. Given any triangle, choose its longest side as the base (for an equilateral triangle it doesn't matter which side you choose). Then draw a line from the opposite vertex to that base, intersecting that base at a right angle (e.g. a luff perpendicular). The length of that line is the height of the triangle, and the area of the triangle is the product of that base and that height divided by two. That works for any triangle.

Cheers,
Randy


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## rstafford (Oct 8, 2016)

chip said:


> Ah, using the fore triangle calculated like that would actually make more sense.
> 
> When I did the original research for my calculator, I was using sources like this:
> 
> ...


That's what I'm talking about! If the area of the foretriangle is I*J/2, then it seems logical that a 155% genoa would have 55% more area than the foretriangle or a 100% jib!

And note that for a 100% jib, the length of its LP will be less than J. In fact I think for any headsail the length of its LP will always be less than the length of its foot.

So why do we say that the size of a genoa is 100*LP/J? It should be 100*LPg/LPj or 100*(J+O)/J, depending on whether you're measuring the LP or the foot of the sails.

Cheers,
Randy


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## chip (Oct 23, 2008)

RichH said:


> NOPE, I don't think you're getting what Im stating at all. You are MISQUOTING the fundamental (simplified) equation for the area of triangles: 1/2 base 'times' height. You're mistakenly using the WRONG 'height' where 'height' (h) MUST be at 90° to the base (b). You are using the WRONG 'height'. ;-)


No, I'm not, but I think I've exceeded my tolerance for discussing 9th grade geometry online.


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## chip (Oct 23, 2008)

rstafford said:


> So why do we say that the size of a genoa is 100*LP/J? It should be 100*LPg/LPj or 100*(J+O)/J, depending on whether you're measuring the LP or the foot of the sails.


Yeah, I understand better now what you were getting at the other day. I think it's still convention to do it the way I originally described, but it leaves a lot of unanswered questions about why that is the convention.


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## Jeff_H (Feb 26, 2000)

I only mentioned the race rating rule measurements since referring to sails using percentages derives from the rating rules. Here is an explanation of sail measurements under used for PHRF but similar to other racing rule methods.definitions of measurements - from PHRF of the Chesapeake, Inc.
http://www.phrfchesbay.org/SOMD/defn9901.htm

Jeff


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## Faster (Sep 13, 2005)

You guys were making my head hurt.. and on a Saturday morning!!

But, using the longest side (Luff) as the 'base' and and LP it (i.e. 0.5bh) does indeed work for the 'whole triangle'.


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## rstafford (Oct 8, 2016)

Chip - agreed. If you ever find that definitive answer you mentioned in a earlier reply, please do post it 

Cheers,
Randy


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## rstafford (Oct 8, 2016)

Thanks Jeff, I see where it defines LP% as Luff Perpendicular percent of J.

The PRHF rules for my regional sailing association also base adjustments on LP percentage of J: PHRF Rules for 2014 | Sailing Association of Intermountain Lakes (SAIL)

I guess it must just be a convention, but it doesn't make a hell of a lot of sense mathematically.

Cheers,
Randy


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## blt2ski (May 5, 2005)

My post 9 many years ago, basically said what Jeff is saying. For racing rules, the jib/genoa is based on the (I*J)/2 or 100% sq footage. BUT, your max head sail is based on (luff x lp)/2 So if your max % is 150, better not get an LP of 150, as that will put you over the 150% amount. Penalty time when it comes to racing rules. At the time, I did not use formulas. 

George,
TO get a hollow figured out, you would have to include a mid girth and maybe a 1/4 and 3/4 girth, Along with luff, leach and actual foot lengths,so you can turn the sail into 4 different trapezoidal parts. Probably similar to how a main sail is calculated to figure out roach square footage. 

Marty


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