Created : 20 july 2001
Last updated : 14 november 2001
Classification : Mathematical analysis
Copyright : Restricted shareware
Status : Completely rewritten, Finished.
Comments : This is an educated but still rough comparison. The tendencies discovered here must be compared to real life experiences too. To date these have confirmed the results of this analysis
2,5 mtr
14,50 sq. mtr
8,30 mtr.
13,00 sq. mtr.
3,50 sq. mtr.
5,00 mtr.
3,30 sq.mtr.
100 kg
150 kg
17,5 sq. mtr.
7,50 mtr.
250 kg
2,6 mtr
17 sq. mtr
8,50 mtr.
14,83 sq. mtr.
4,15 sq. mtr.
5,50 mtr.
3,96 sq. mtr.
180 kg
150 kg
21 sq. mtr.
8,27 mtr.
330 kg
Width
Mainsail area
Mainsail luff
Rated main area
Jib area
Jib luff
Rated jib area
Weight
Weight crew
Genaker size
Hoist height -
from deck
Total weight
Width
Mainsail area
Mainsail luff
Rated main area
Jib area
Jib luff
Rated jib area
Weight
Weight crew
Genaker size
Hoist height - from deck
Total weight
The values given for the F18 class are all fixed and found in the F18 rules; the values given for the F16HP however represent just one possible implementation of the F16 HP 2-up rule. Nethertheless, all important values, apart from the actual sailarea's and sail luff lengths, will remain unchanged as they are given; this includes the Texel handicap number. Both ISAF handicap numbers may change a bit with different dimensions of boards as this is unregulated in the F16HP and only mildly regulated in the F18 class. We've used extremes in both cases in this comparison. Under ISAF the F16HP is calculated with a carbon mast while the F18 number is calculated with an aluminium mast as is regulated by F18 rules.
The values given for the actual sail areas and luff lengths represent a setup that is expected to be a general optimum for the Formula 16 HP class. It gives the values encountered on a craft with a small, high aspect jib that can easily be made to be selftacking or is sheeted of the forebeam. Fitted with a mainsail that has a higher aspect ratio than a F18 mainsail but fitted on a equally high 9 mtr. mast. The mainsail is "just" 8,3 mtr. so the boom is positioned high above the trampoline. These aspects improve handlebility while retaining good light air performance and getting a normal sized crew of 150 kg's double trapped in the stronger winds. The F16 HP is not intended to be a "youth boat" as some might call it solely based on it's length. (without disrespect to youth classes or other 16 ft classes in general)
The F16 HP board dimensions, needed to calculate the ISAF handicap rating, are inspired by the Stealth R design which did so well in the UK 2001 beach catamaran championship. Taipans and Bim 16's are slightly smaller in area and have a lower aspect ratio too. So the values used can be assumed to be at the maximum dimensions.
Anyways, the crew will have to work hard at the higher wind ranges with this "high heeling moment" rig but than we don't call this class HP (High or Hyper Performance) for nothing, do we ?
* wetted surface area determines the total amount of hull drag at low speeds, meaning in light winds.
* that prismatic ratio determined by (displacement / length) determines the total amount of hull drag at
high speeds, which are only reached in heavy air. Ofcourse a sizeable contribution of the wetted
surface area is now neglected, however this approach will favour the longer boats and therefor give a
carefull estimate of F16HP actual high speed drag.
* both boats have equally tall, sophisticated and optimized sail rigs, with the same level of control.
* both boats can transform the full sail power potential into thrust without capsizing or pitchpoling.
* both boats have similar hull shapes to such a degree that the small differences that exist can be
neglected.
* Both crews weight 150 kg's and are equally tall. In general, both crews are the same in every respect.
Measured ratios
Total Weight F16HP / F18 = (150+100) / (150+180) = 0,7575 = 76 %
Length hulls F16HP / F18 = 5 / 5,52 = 0,9058 = 91 %
Width platform F16HP / F18 = 2,5 / 2,6 = 0,9615 = 96 %
Mast leverage (mast heights) F16HP / F18 = about 100 % in this F16HP implementation
Mainsail area F16HP / F18 = 14,50 / 17 = 0,8529 = 85 %
Rated mainsail area F16HP / F18 = 13,00 / 14,83 = 0,8766 = 88 %
Luff lengths F16HP / F18 = 8,3 / 8,5 = 0,9765 = 98 %
Mainsail aspect ratio F16HP / F18 = ((8,3)^2 / 14,50) / ((8,5)^2 / 17) = 1,1179 = 112 %
Jib area F16HP / F18 = 3,50 / 4,15 = 0,8434 = 84 %
Rated jib area F16HP / F18 = 3,33 / 3,96 = 0,8409 = 84 %
Jib aspect ratio F16HP / F18 = ((5,0)^2 / 3,50) / ((5,5)^2 / 4,15) = 0,9799 = 98 %
Genaker area F16HP / F18 = 17,5 / 21 = 0,83333 = 83 %
Genaker luff (hoist height) F16HP / F18 = about (7,50 / 8,27) = 0,9069 = 91 %
Genaker aspect ratio F16HP / F18 = ((7,50)^2 / 17,5) / ((8,27)^2 / 21) = 0,9869 = 99 %
Calculated Ratios
Wetted surface area est. F16HP / F18 = sq.rt. (Ratio weight * Ratio length) = 0,8283 = 83 %
Prismatic drag ratio est. F16HP / F18 = Ratio weight / Ratio Length = 0,8363 = 84 %
Sailpower sloop no genaker est. F16HP / F18 = (2 * ratio Rat. main + 1 * ratio Rat. jib) / 3) = 86 %
Sailpower genaker est. F16HP / F18 = (2 * ratio genaker area + 1 * ratio sloop) / 3) = 84 %
Max. righting moments crew (150 * (2,5 + 1) + 100 * 2,5 *0,5) / (150 (2,6 + 1) + 180 * 2,6 * 0,5) =
= 650 kgm / 774 kgm = 0,8398 = 84 %
Performance Ratios
(light to medium air performance)
Sailpower to wetted surf. upwind F16HP / F18 = 86 % / 83 % = 1,0361 = 104 %
Sailpower to wetted surf. downwind F16HP / F18 = 84 % / 83 % = 1,0120 = 101 %
(medium to heavy air performance)
Sailpower to prism. drag upwind F16HP / F18 = 86 % / 84 % = 1,0238 = 102 %
Sailpower to prism. drag downwind F16HP / F18 = 84 % / 84 % = 1,0000 = 100 %
(indicator ability to keep rig under full power)
Max.Righting to heeling moment upwind F16HP / F18= 84 % / (86 % *100 %)= 1,0120= 98 %
Max.Righting to heeling moment downwind F16HP / F18= 84 % / (84 % *100%)= 1,0000= 100 %
Accelleration (sailpower to weight) upwind F16HP / F18 = 86 % / 76 % = 113 %
Accelleration (sailpower to weight) downwind F16HP / F18 = 84 % / 76 % = 111 %
Bear in mind that the calculated ratio's must be considered with a margin of several %. An offset of 1% or 2 % can be considered to indicate equality because these offsets can well be caused by the used mathematical approximation methodes instead of the laws of physics.
Before we begin our analysis I would like to bring two ratio's back into memory :
First the aspect ratios of the sails, often seen as indicators of effectiveness, respectively Main = 112 %, jib = 106 % and genaker = 99 %. I can be concluded that the F16HP sails are either just as effective as the sails of the F18 or more efficient. (6 % and 12 % offsets are more than what can be considered as inside an inaccuracy margin.)
Secondly the mastheight ratio. This one is not given in numbers but was part of the assumptions. This means that equal sailarea's harnessed by equal righting moments produce as good as equal pitch- and heeling moments (within a margin of 1 to 2 %). So when the sailarea of our F16HP implementation is about 86 % than it's moments are about 86 % too.
Compare this number for the moments to the max.righting moment of 84 %, ergo 86 % / 84 % = 102 %. The F16HP has about the same ratio as the F18 has between heeling moment and the crews ability to keep the platform level in the stronger winds. Or, when this difference can not be explained by the inaccuracy margin, the F16 HP is slightly more overpowered at heavy winds than the F18 class. Still, 2 % is not a huge amount and can be "downhauled out" of the rig easily. Or the designer can trade of the 104 % light air performance to improve this heavy air performance indicator of 98 % by lowering the mast or moving main sailarea to the jib. But this is tweaking comparable to deciding how much diamond wire tension and mast prebend you want. This setup may well favour heavier than 150 kg's crews.
All the performance ratios seem to be very much equal to those of the F18's; otherwise they would not produce ratios around 100 % when they are compared to eachother. The only true exception are the accelleration ratio's. The concept of reducing weight in order to boost performance and to correct out over the performance hits caused by going smaller have worked quite well to keep things equal to the F18's. But is left one aspect out which accelleration and decelleration. This characteristic is governed by fixed laws of physics that can never be manipulated enough, without sacrificing the other ratios of about 100%, so that it too reflect equality by given a ratio of about 100 %. This is just fundamentally impossible.
Accelleration and decelleration also include the dependency between reserved volume and decelleration moments produced by the rig (pitchpole). The F16 HP needs a lighter rig to make the pitchpole tendency comparable to that of the F18's. This can be done. F18 doesn't allow carbon masts, F16 HP does. Ofcourse trimming the sails will be slightly different between the two designs but that is not really something that will hold a crew and craft back with respect to a design from the other class. Mind you, really light aluminium masts have been succesfully used in Australia for years. So going Carbon, as they say, will definately do the trick but may not have to be compulsary. The smaller sail will also weight less and therefor help for example.
Is this inequality bad ? I would say :"Not really", The main allout performance is equal and that was the main goal. The fact that the different crafts have a slightly different character while achieving this allout performance is not really that important.
That still leaves us the accelleration and decelleration of the craft as a whole, we also can't alter this for the overall weight is already fixed by the necessity to have equal power to drag ratios. Experiences with the foundation boats indicate that the advantage of faster accelleration outweights the disadvantage of quicker decelleration. Well that is than just the advantage of the F16HP class. Under most conditions it will probably only produce gains of a few seconds.
From this comparison we will conclude that nor the F18 or the F16 HP has a clear and decisive advantage over the other on allout performance. A few smaller differences (accelleration, pitchpoling) will be encountered but their related effects will be much smaller than what can be contributed to good or poor helmsmanship or just luck. It could be possible to get some of the performance ratios right on 100 % or inside a 1 % margin around 100 % by tweaking the sailarea's and luff / mast lengths a bit but this is left to the catamaran designers out there. We have shown in this comparison that the two classes as layed down in the rules are virtually equal in performance as is reflected by the equal Texel and ISAF handicap numbers for both classes. Now when we have proved this both theoretically as well as emperically to your satisfaction than I'm sure that we've convinced you, the reader, of the merits of the Formula 16 High Performance class.
On the whole it is quite an extraordinary result considering the absolute differences between the two classes. Even more so when one considers that other extraordinary phenomenon that the same F16HP without the jib is a very capable solo craft. (for which a comparison with the A-cat class will be made)
Last question
Is this as fast as a 16,4 footer can potentially go ? No, and this might well be the best thing that can be said from this comparison. Remember we had to downsize both the genaker and jib areas to perfect the equality to the F18 class, which is one of the two most important design goals of the F16HP. The foundation boats fly bigger jibs for example and the 17,5 sq.mtr. genaker could be entlarged.
So a good designer could still sqeaze out a few percent here and there, but he will than leave the concept of Equal Performance Classes by doing so. This was another important design goal of the F16HP class. That is unless he is able to boost the 16,4 ft cat performance to that of the NEXT Equal Performance class of the iF20 !!!