Optimising Marblehead Sail Area

We all know that a Marblehead has a maximum sail area of 516100 mm2.  Well it does and it doesn’t.  It is true that the ‘certified’ sail area of a Marblehead is 516100 mm2 but, thanks to the rather arcane way in which the sail area is measured, the actual plan projected area is about 40% bigger than the quoted figure (assuming I’ve got my maths right).   To put it another way, if you were to measure a set of Marblehead sails using the 10R rules, then the answer you would get would be about 722500 mm2 (which goes some way to explaining why 10Rs don’t beat Ms as easily as you might first think they should). The attached sketch explains why.

For a mainsail (jibs are similar), the red area is measured as a triangle defined by the length of the luff and the perpendicular foot length (A and B in the measurement rules).  If the cross-widths exceed a given limit then the orange area is also measured, however the white areas are always ‘free’ and account for a significant area of the sail. 

Does this matter? Again the answer is yes and no.  If the certified area was always the same proportion of the actual area then it wouldn’t really matter, however a quick look at the measurement rules suggests strongly that this isn’t going to be the case and two sails with the same certified area could have different actual sail areas.  To para-phrase George Orwell, ‘All Marblehead sails are equal but some are more equal than others’.

By remembering my ‘O’ level trigonometry (that dates me!) I’ve managed to calculate a pretty good approximation of the actual sail area for a given set of measurements (i.e. A,B, X,Y & Z for a mainsail).  It uses 8 triangles and three sectors in a spreadsheet with 70 columns so I won’t detail it here, I’ll just summarise the results.

There are three basic parameters you can alter when designing a Marblehead sail, namely the length of the luff, the X,Y & Z dimensions and the height of the clew relative to the foot.  The foot length would then be determined by your choice of the other parameters.  Taking each of these parameters in turn.

Luff Length

The luff length has a fairly strong effect of the ratio of actual area to certified area, the longer the luff the greater the actual sail area.  According to my calculations, a sail with a luff length of 1700mm has about 5% less actual sail area than a sail with a luff length 0f 2120mm (for the same certified area of course).   For mainsails this isn’t a major concern as aerodynamic considerations would push you towards the longest luff anyway (a higher aspect ratio sail can produce the same amount of lift for less induced drag), however it does suggest that tall narrow jibs might have a small advantage over shorter wider ones. 

An interesting side effect occurs with reduced rigs.  For example, if you wanted to create a B rig with a 10% reduction in actual sail are and a Luff length of 1700mm then you should only reduce the certified area by 5%.

Clew Height

The rules take no account of clew height and most swing rigs are made with the clew higher than the foot to try to prevent it hitting the water surface.  Unfortunately raising the clew does incur a penalty in actual sail area.  I calculate that having the clew 80mm higher than the foot incurs a penalty of about 1%.  Not huge but just about significant.

X,Y,Z Dimensions

These measurements are what started this whole analysis off.  They are often referred to as penalty areas, implying that you have to suffer a reduction in sail area if you use them. As I couldn’t see how the formula was derived (I’ve since learned it is based on Simpson’s Rule) I decided to try to calculate the effect for myself.  The motivation being that (to my mind at least), modern Marblehead sails are too narrow in the upper part of the sail and one would like to make a sail that has a largish Z dimension, but does this cost you sail area and what should you make the X & Y dimensions?  The answer is that, although I have a few problems with it, (see the thread on this subject) the formula in the rules is surprisingly accurate for reasonable values of X, Y & Z : less than 0.5% even in the worst case.  For a typical max luff mainsail, there seems to be a peak at X = Y = Z = 16mm but it is only 0.04% above X = Y = Z = 0.  Having Y greater than X & Z incurs a small penalty of 0.5% but you probably wouldn’t want a sail this shape anyway.  My advice would be to make the sail the shape you want and not worry about the X, Y & Z dimensions.

Caveats

There are a couple of major caveats to my conclusions. Firstly, I could easily have got the maths wrong.  It’s quite a tortuous calculation.  Secondly, I’m only talking about maximising the plan area not aerodynamic efficiency.  Just because a sail is slightly bigger it doesn’t mean the boat will go faster.

I realise this sort of analysis is not for everyone but I thought the conclusions were interesting enough to post.  If anyone wants more detail then I’m happy to give it.

Conclusion

I've never been a fan of the way Marblehead sails are measured as I believe it is error prone and doesn't measure the actual area.  I think I've now proved that it is also unfair in relation to certain sail shapes.  I would much prefer to use a method similar to the 10R rules as this would be much closer to the real area and allow much more freedom in sail shape. In my view laying a sail over a grid and measuring along the grid lines is much more accurate than trying to find equidistant points and then judging the minimum distance between it and the luff. This would however be a rather radical change and would also involve our American cousins calling it a 50/1120, so I can't see that happening anytime soon.