# Harmonizing Multihull Rules?

A recent remark by Erik Lerouge inspires me to try to recapitulate how far we have come and how far we need to come in harmonizing existing multihull rules. To harmonize systems all the details have to be considered. Subject for subject, line for line, all methods of measuring and calculating, have to be studied and discussed. After that process decisions have to be made about which method for each detail is found out to be the best to be used in the one final system. Is that what we really want? Is this what we need? One world rule completely equal in all details? Can different rules be not more flexible and far more easily adaptable?. Less bureaucratic? Could a rule for each country or continent be more than enough? I tend to believe this is worth considering..

## 1. Short introduction on multihull racing, using rating numbers

If you want to determine who is the best crew, you must organize sailing races in the way as for instance swimming contests are organized.. All start practically at the same moment. He or she who finishes first wins. If you need to compare their results with the races of others over the same distance, you can measure the times used, for each race, as they do now, even in parts of seconds. Or you may decide to use a simple points system.

An equivalent way of organizing sailing races needs the use of strictly one-design boats, like a Laser. Even a multihull class as the formula 18, a two men open catamaran, is not strictly one design. Different designs have been developed within the limits given in the class rules. Mainly limits for length, sail area and weight.

All this does not mean that for racing purposes it is useless to try to find rating numbers, that do not more than approximate the relative performance for a range of different designs. These numbers can be used for racing indeed. But we must understand that the results of the races then too, have not more than a relative meaning, Apart from that, like with the specifications about cars, rating numbers give owners of the designs a good idea of what they can expect of their boats. A rating number is a value worth knowing .

## 2. The basis formula

The general structure of this formula is MR (TCF) = c * rl ^ p * rsa ^ q / rw ^ r.

rl being the rated length, rsa the rated sail area and rw the rated weight. And c is a constant number to give all rating numbers a desired level .

There are three widely practised rules now that use this power formula with the same exponents. c = 1; p = 0.3; q = 0.4; and r = 0.325.

They are the TR (Texel Rating) rule in the Netherlands for cabin multihulls used too in many countries in Europe, since 1984, the Australian OMR (Offshore Multihull Rule), used too in parts of eastern Asia and the French Multi2000 Rating rule used in France. OMR and Multi2000 started in 1997. In the TR rule the exponent for rw has been lowered to 0.3 in 2002, but returned to the power of 0.325 in 2010, using the constant 1, like in the two other rules. For the open cats the TR rule still has kept the constant c at 1.15, to keep the final numbers at about the same level as the numbers produced by the ISAF rule for open cats, published under the name of SCHRS. (Small Catamaran Handicap Rating System),

Conclusion: The elements in the basic rating formula are harmonized now.

Both TR rules and the SCHRS do not use a TCF for a rating but the reverse values (100/ TCF for the TR and 1 /TCF for the SCHRS). In the TR rating lists for cabin multihulls TR numbers as well as their reverse TCF numbers are published.. This gives a choice for racing organizations.. Crews tend to like the integer numbers which show the relative time used. TCF numbers represent relative speeds.

To complete the picture, the English Mocra rule needs to be mentioned. That rule uses from around 1996 a basic formula of the same structure, but with different values for the constant and the three exponents. The background of their values has not been revealed so far..

The Mocra formula is: TCF = 1.74 * rl ^ 0.2814 * rsa ^ 0.3546 / rw ^ 0.3124

The MYCQ, the Multihull Yacht Club Queensland, started with the OMR power formula in 1997. They wanted to stop using the IOMR rule developed in 1968 with its complicated details and chose the TR formula.

One set from a total of four of the old IOMR rule is used in the SCHRS rule mentioned above..

## 3. What to measure and weigh?

To measure the area of the mainsail, the TR as well as the Multi2000 rule uses the Simpson rule. By dividing the sail in 4 parallel bands of equal width. The Mocra does the same, but uses a separate system to determine the area of the upper ¼ band of the mainsail, In the TR method a simple top correction is available, when sails show a heavily rounded top, without being a complete flat top. In the TR system It has not been necessary to use this extra facility in many cases.

The OMR uses an older quite usual method to measure the main by dividing that sail in two triangles and adding one relatively large segment near the leech, calculated with a simple formula as one big area with one rounded side. The area of this segment can be less accurate in extreme cases. Roundings in luff and foot of the sail are added too. For the open cats in the TR mainsails are measured in a way comparable to the OMR method, but with many more triangles, if needed and one or more relatively small segments. This may be the most accurate method of measuring mainsails. A comparison with the Simpson rule results does not show substantial differences.

For the open cats rules not many sails have to be measured, as class organizations now often define maximum sail areas allowed. If that is the case the class rules determine the areas to be used. In the calculations.

Jibs and genoas in the OMR are measured as triangles, including all rounding's and hollows in the sides. The same procedure is followed in the TR rule for open cats and in the SCHRS system. In the TR rule for cabin multihulls and the M2000 rule only a positive rounding in the leech of these triangle sails will be added. There is no deduction for hollows there or in one of the other sides. If the sail makers include a hollow they generally will not do that to reduce the area, for a rating advantage, but to make the handling of sails easier.

The same happens when screachers are made. Hollows in the leeches in these triangle sails sometimes make the ratio smg (midgirth) divided by sf, (foot length) a bit less than 0.50. For that reason it makes sense to define a screacher as a sail with a smg/sf ratio of less than 0.75. No mention of a lower limit. In the few cases such a sail indeed shows a ratio slightly below 0.50. In the OMR such a sail is considered then not to be legal..

In the MOCRA rule only the foot rounding of a jib in included in its measured area. Finally the jib area then is compared to FTA, the area of the fore triangle, the area formed by mast and forestay. (the well-known dimensions I and J).

## 4. How to calculate rated sail areas from measured areas?

From independent reviews in the committees of the OMR and TR on how to rate sails, methods have been developed In 2009 to determine a new aspect ratio. The old method to calculate the aspect ratio by dividing the square of the height of main, or jib, by its area, gives pinheaded mainsails an advantage above the actually more efficient popular flathead mainsails. In the Multi2000 rule, this same aspect ratio formula is used but then for the rig as a whole (main plus jib). A flattop mainsail being more effective than a pinheaded one, then may be found back in an acceptable way in the final result.

The new aspect ratio formula for the mainsail in the TR rule is calculated in this way. arm = area mainsail divided by e ^2.

The dimension e generally being the length of the sail alongside the boom. Some sails, mainly without a boom show a different form in the leech. Then the largest width of the sail must be used in the formula, not e.

In the OMR e is not used in its formula, but the dimension lpm. This is the (measured) perpendicular from the tack to the line connecting the top of the sail on the mast with the clew. arm = area mainsail divided by lpm ^2

As lpm easily can be calculated from the dimensions e and p of the main,

(lpm =p * sin(arc tan(e/p)), and because the ratio lpm / e is not a constant, It can be sensible, to consider adapting the OMR aspect ratio method in the TR rule. Then the formula for the main can be exactly the same in both rules.

For the jib (genoa) OMR and TR already use the same aspect ratio formula. This is: arg = area jib divided by lpg ^2.

The final formulas for calculating the rated areas in both rules now.

RSAM OMR = 0.65 * (area /lpm^2) ^0.298 * msam +. Area mast, if rotating

RSAM TR = 0.67 * (area / e ^2) ^ 0.3 * msam + Area mast if rotating

Because lpm always is shorter than e, the constant in the TR formula had to be a bit higher than 0.65 to get about the same results..

RSAG OMR = 0.72 * (area/lpg^2) ^ 0.298 * msag

RSAG TR = 0.72 * (area/lpg^2) ^ 0.3 * msag

The OMR uses the power of 0.298, the TR simplified this by using 0.3.

Following the KISS principle (Dick Newick).. This could easily be done considering the margins in the measuring of sails.

The limits in the accuracy may be around 1 % plus or minus for ail areas measured. When we have to use class limits the accuracy is absolute indeed.

## 5. How to calculate the rated length

In 2011 the OMR simplified the rated length definition by taking the length overall.. For trimarans the longer length of the outrigger, if that is the case.. Until the January 1, 2015, for boats designed and launched before january 1, 1985, FOC may be deducted. The TR rule is a bit more refined. The forward overhang component (FOC) is calculated at a height of 2 % of the loa above the waterline, without crew on board and deducted from loa. The OMR changed is for practical reasons. Many modern designs have a vertical stem, even a reverse stem. (longer below the waterline than above).. .

For designs with a lot of overhang, (these designs do still exist), the measurer might be given the freedom to determine the length used when sailing, as he or she thinks to be right .To use 1985 may be not flexible enough.

Multi2000 still defines the length at half way the freeboard, generally a bit longer with older designs than the TR method. Actually most cabin multihulls racing seriously have vertical ends. In practice there are no problems then..

Mocra defines length in a bit different way, but tries to find the real waterline length.

## 6. How to calculate the rated weight. (weight boat plus crew)?

In all the rules the weight of the boat has to be determined by actual weighing. This always proves the element in the rating process with the highest uncertainty in the results. An accuracy here of + or – 1 % may be fine.

Both OMR and TR provide a list with the equipment on board which has to be filled in and checked. It proves to be difficult to have these lists complete and accurate enough for each individual design, for each race. The consequence is always an extra margin of uncertainty in the basic boat weight.

Then there is the problem of adding an allowance for the crew, to approach the weight of the boat when racing. All rules so far use a type of formula.

The TR started with a very simple formula crew = 40 *rl -70. (This to give 18 feet cats a weight of 150 kg). This rule penalized small racers in the OMR too much. They used more crew weight than the formula gave them. On the other hand big boats got more crew allowance then they used sometimes.

In 2011 this TR formula (adopted in 2010 by the OMR) has been refined. Crew = 70 * rl ^0.78 – 60. For 2012 the TR formula will not be changed.

The OMR suggested for 2012 a formula based on rl as well as rsa (rated sail area), but after recent crew complaints needs to develop new (or old) ideas to find ways to give any design the crew number that actually races the boat. May be no formula at all.

Multi2000 as well as the Mocra use formulas with an upper limit.

## 7. Extra elements in the rules.

### 7.1 Propeller(s) correction (P factor)

Most rules contain small constants, giving a factor P. It will not give many problems to harmonize the methods. For the TR rule the factors used are >1, because the TR number is a divisor. For the rules using a TCF values, all correcting factors are < 1. In most cases they are the exact reverse of each other.

### 7.2 Catamarans correction (K factor) .

In the TR and Multi2000 rules a correction K is included for catamarans which are considered to have a disadvantage compared to trimarans. Motivated a.o. by more wetted area and slower tacking. The formulas used are more or less comparable. In Multi2000 a factor is calculated for trimarans as well as catamarans. In the TR rule all trimarans are given the factor 1, All catamarans get a correction >1 up to about 1.05 for the heavy slow cruising catamarans.

The TR formula is: K = max (1 / (0.19*rsa^0.4/rw ^ 0.36 + 0.91):1). That means if >1, use the value of the formula, else the factor is 1. The final effects are comparable to the Multi2000 ones. An analysis is available as an Excel file.

The OMR committee members decided that there was no need to include a catamaran correction in the rule. Erik Lerouge explained that this correction was one of the most important ones in the Multi2000 rule. May be the catamaran designs that seriously race In the Queensland race area are of a different type than the catamarans that race here, in France and elsewhere in Europe. The design elements of the bigger more cruising oriented catamarans even made the Danish designer Lars Oudrup decide to start in 2011 organizing races for these type of designs using the old IOMR rule (from 1968) again.

He himself races a Lagoon 380 now..

### 7.3 Keel corrections (Q factor)

In the OMR all yachts not having an effective keel or centreboard get an allowance of 2 % (In their TCF system a multiplier of 0.98). The Mocra does it in a comparable way under the name of hull factor. Not always exactly 0.98.

In Multi2000 a rather complicated second degree polynomial formula using as input draft en rl calculates a correction factor for boats not having a dagger board or pivoting centreboard.

In the TR rule for open cats all boats not having a dagger board or centreboard get an allowance of 4 % (multiplier 1.04). For cabin multihulls the correction factor is found by the formula K = 0.94 / (draft/rl) ^ 0.037

### 7.4 Other elements in the rating.

Multi2000 includes elements in the rating which have to do with the dimensions of the cabins. The fast designs like the Firebird get a small correction. The maximum correction is about1 % for a formula 40 design multihull.

In the OMR and the TR rule these elements are not included. The idea in the TR committee is that the accuracy in say the weight of the boat makes such corrections irrelevant. This accuracy may be guessed to be about plus or minus 1 % as mentioned before for the sails. A boat actually weighing 2000 kg easily can be given a weight of 1980 or 2020 kg, following this idea. The difference in a rating caused by this margin may be far beyond the refinement of a correction based on cabin dimensions..

Most rule elements in Multi2000 and OMR, even those of the Mocra, have been compared with the TR equivalent. The solutions with the more simple formulas given in the TR rule only very slightly divert from the output given by the other Rules.

The Mocra introduced in 2011 a so-called age correction, for older designs.

A maximum age of 20 years is accepted. In that case the correction factor is 0.987 (a multiplier in that TCF system).

## 8. Final aspects

To decide on changes in the rule calculations, the OMR uses statistics of race results. For that purpose the dimensionless ratio 'coefficient of variation' is used.(standard deviation divided by the average corrected time), The idea is that a perfect rule, combined with perfect crews will make the CV % equal to 0. All corrected times will be equal then. A fantasy.. But the lower the cv % the better the rule methods, is the philosophy behind it.

Actually something strange can be observed. As an example the results of a race ;like the round the isle of Texel can be taken. In all years a class like the formula 18, more or less one design, is the biggest class with from 50 to more than 100 finishers each year, depending on the weather.

Calculating the cv % for each number of finishers of that class
shows that the cv % rises from a low number for the best of the class
(and the world), say the nrs 1 to 5 (5.3 %), to around 12.4 % for all
50 finishers.(results for 2011). The last finisher in that year took 55
% more time to finish than nr. 1. With other classes the picture it is
not much different. The higher the number of finishers the higher the
cv %. Expressing the corrected times in a graph shows that these times
generally can very well be described by a straight line. For the
formula 18 in 2011 this linear equation gave a high correlation with R
^{2} > 0.98. This best sailed formula 18 class crews show
relatively lower cv %'s, than other classes when comparing an equal
number of boats..(Excel analysis sheets are available).

The conclusion could be that crew quality is such a high factor in the results, that a low cv % is not more than an indication that the rating numbers calculated are relatively correct.