This is one question up my ally.
I will give answering it my best shot before I begin I would like to underline one very important thing. More efficient does not always equal being faste. For one great story on this please read the Miss Nylex C-class article at :
http://wwwstaff.murdoch.edu.au/~tlamont/miss_nylex/page2.htmIt is more efficient in rig design and sorts but it still lost to US build Aquarius because Miss Nylex was more efficient in the wrong set of condtions, the races turned out to be in light winds. But also very much because going conservative allowed Aquarius to be some 90 kg's lighter. And that is a weight advantage that must first be corrected out over before and gain is made, no matter how more efficient the new technology was.
>> Sloops with big jibs are great for reaching,
And therefor great for distance races which often have significant portions of (shy) reaching and in them.
>>but much of cat racing is on windward-leeward course, so reaching speed alone is not that important.
Just like the designers of miss nylex discovered. Mind you guys there is a limit to plaining craft like the ventilo here. These may have great top speeds but how will that translate into "round the bouys" speed ?
>>Which rig is most efficient upwind, considering VMG?
And this is the difficult question. Okay lets say that the design with the highest VMG upwind is more efficient. Can we answer your question now ? No, we can't. Why, because Efficiency times the amount over which the efficiency is taken is the determining factor. Lets look at a practical example:
Say a uni-rig has a sail area of 20 sq.mtr. and is able to fly that without depowering. This system has, lets say, an efficiency of 95 %. Ergo is effectively has an active area of 19 sq. mtr.
Now the sloop. The sloop has a main of say 18 sq. mtr. with an efficiency of 85 % = effective area of 15,3. Noticably less than the uni rig. But because it's heeling moment is alot less as a result of this shorter rig with less mainsail area, this boat can fit a noticably large jib before it arrives at the same heeling moment as the uni-rig. Lest say 5 sq.mtr. with the efficiency of 75 %. This will lead to an effective jib area of 5 * 0,75 = 3,75. With this the total effective area becomes 15,3 + 4,25 = 19,05 sq. mtr. effective area = more than the 19 sq. mtr. of the uni rig. So despite the fact that both the main and jib have much worse efficiency the sloop can expect to be just as fast or faster depending based on these named %'s
But ofcourse when the jib has an efficiency of 70 % than the sloop has just less total effecive area tha the uni-rig.
So one can not simply say that one rig is better than another, it dependents on the way the other rig is designed and even then because the example above is still too simple. Because it is a well know fact that sloops may point a little lower than unis upwind but also that they broad reach (downwind) alot better. Depending on the individual design the one outweights the other and visa versa. The spi goes a long way of negating this.
>>Which rig is most efficient downwind?
Without a spi the sloop is faster downwind, not more efficient.
>>If you had 2 rigs of equal total sail area, which would be more advantageous?
And here you get to the core of the problem. When two rigs are of equal size than the advantage moves a significant way towards the uni-rig setup. When looking at upwind -downwind courses. With increasing shy reaches and shy broad reaches the advantage shifts back to sloops again. Mind you a windshift on a windward-downwind course could be enough to shift the balance significantly.
But even this question is more complex than it seems. Which one of the two will determine what the "equal area" is ? The Tornado features 18 + 5 sq.mtr. of sailarea = 23 sq.mtr. of area. What will happen if you fit that area to a uni-rig. In order to get a significant aspect ratio which is needed for a high efficiency % the masts needs to be tall. Some 10,5 to 11 mtr.. It was said in the F18HT class tha F18HT's went down to 10 mtr. mast because 10,5 mtr. wasn't faster. Overpowered? Or will the most efficient area of a uni-rig be used to limit the sloop area, in this situation is actually holding back the sloop as that craft will than be underpowered. Neither of this hypothetical situations is fair to one of the two rigs and therefor such a comparison is usefull to extend understanding but is not a practical methode of comparing rigs.
In effect, the F16's can never feature a 18,5 sq. mtr. uni rig and be faster, the platform won't be able to harnass the power. But the 18,5 sq.mtr in the sloop configuration does make the craft alot faster than the jibless F16 setup with a 14,85 sq.mtr. main even though overall efficiency may be less in that setup. So more efficient but slower and less efficient but faster. It's a strange world and than we aren't even discussing the dynamics of different windstrenghts.
And ofcourse we are talking aerodynamic efficiency here. And than there is that other thing about aerodynamic efficiency. Surely high lift to drag ratios at small angle of attacks is important upwind. So there the uni rig is aerodynamic more efficient than a sloop. But what about non-upwind courses where the angle of attack is often alot greater and the drag of rig has alot less impact on the overall drag of a craft ? Typically sloop rig can operate efficiently over a wider span of angles of attack. This makes sloop rigs more aerodynamic efficient on non-upwind courses.
And there is the boat speed devided by windspeed ratio. Below a certain ratio large angles of attack are encountered and sloops are aerodynamic more efficient even when pointing high (mono's) and above a certain ratio only uni rigs are efficient enough to achieve these speeds (ice-yachts). Where is this ratio and on what side of that ration do catamarans as we know them lie ?
Some have argued that because ice-yachts with speeds typically 3 times the windspeed use uni-rigs that it means that catamarans with typically speeds of 1 to 1,5 times the windspeed are better off with a uni-rig too.
I say this difference between 3 and 1-1.5 times the windspeed is the same as the speed difference between WW2 prop aircraft and supersonic jet figters. Clearly a big stretch to base comparisons on, lets not forget that those WW2 props were very efficient in their operational conditions !
>>I realize there are a lot of variables here, like mast height, heeling moment, high vs low aspect sails, etc. But surely some science has been done on this.
Like I said read the Miss Nylex article and notice how it failed to defend the little america's cup title.
And please notice that a regatta is won by having the best average results over multiple races under different conditions. Surely Miss Nylex is a better design in the top windspeed ranges and Aquarius is better in the ligter conditions but this doesn't give an outright advantage to either of them. It is totally dependent on the conditions and even the spread of conditions of who wins the regatta.
Another example (analogue this time) : what if a foiling craft is alot faster in winds over 12 knots but slow under those 12 knots. it will win all 12 knots and over races with a non foiling craft coming second. Now the first race below 12 knots the foiling craft will bump out and come in say 10th while number 2 of the other races comes in 1st. The chances of the foiling craft of winning the regatta are now pretty much nullified.
So next to being fast and efficient as good regatta boat has one other requirement and that is to minimize its maximum speed difference to the average of the fleet. A craft can be ver fast but if that is achieved by sacrificizing alot of speed under a different of conditions then it will still not be a winning design. In regatta's often the craft that does best on average without being exceptional end ups high on the list or on the first spot.
>>Yes, I've read Bethwaithe. He only really talks about sloop rigs, and I didn't really understand everything anyway.
To bad because that book is really something. And you should read it again and again and again. As often it's nuances are only understood after several times of reading and meditating. It is all there but it is indeed an excersize of letting go of preconceptions and analysing the data in teh book.
>>So I'd like to learn here. Not about boat handling--sloops definitely have a lot of advantages there--I'm interested in speed and efficiency.
I hope I've helped you in this respect by this post.
Regards,
Wouter