Multi speed/length relationship?

Thank You!

First things first, if indeed the potential speed (on a random leg course) is higher at 90ft LWL than at 45ft LWL then other things need to be considered. As j mentioned not everything scales at the same rate. Loads are 4th power? At some point I suspect the course racing multi will have loads so high it prohibits keeping the weight low enough to maintain performance or the number of crew required to sail the beast and their extra weight become a stumbling block.

I've been looking for some ideas of what these loads will be on 90ft LWL multis and got to wondering if given the HP per pound of human crew that something smaller than 90ft LWL might prove to be a better solution to the fastest course racing boat with LWL between 44 and 90 ft.

I'll stick a bunch of numbers into the spread sheet and see if anything jumps out at me.

Thanks again!

 

I got bitten by the multi bug this year. I raced on a Corsair Sprint 750R. We got the boat rated 36 sec/mile and nearly corrected out ahead of a 45 ft cat, we sailed through the fleet that started 6 minutes ahead of us and finished ahead of a 60 ft cat on the water in two races.

Very impressive for a 24ft boat with a pick-up crew in our first regatta.

The down side of course is that as a 24 ft weekend cruiser the Corsair is a joke, a Cal 20 has better accommodation.

When you look at 30-40 foot boats they start to have enough living space that my last mate might be interested. The Cross 45R "Defiance" is a VERY pretty boat. I like the F-39 also.

 

http://www.boatdesign.net/forums/showthread.php?p=181976&highlight=speed record#post181976
And this mono beats all

 

Double post deleted

 

I felt that a well prepared Stiletto 23 cat could have won that race against the big mono. It wouldn't have been the same 'drubbing', and there were some possibilities she could have gotten locked up in wind shadows of the bigger boat.

 

Ok ... to save the next person that asks the too simple question ...

What effect does LWL have on a Multihull's speed potential?

Short answer:
The difference in speed in knots is equal to the difference in LWL^.1992
LWL = 45
LWL^.1992 = 2.1346

LWL = 90
LWL^.1992 = 2.4506

1-(90^.1992/45^.1992) = 14.8%

Long answer (how I got to the short answer)

The Texel Rating system:

TR = 100 / (.99 x RL^.3 x RSA^.4/RW^.3)
Where RL = Rated Length (approx equal to LWL) in meters
and RSA = Rated Sail Area (approx equal to Main + Mast + 100% Fore Triangle) in sq meters
and RW = Weight as raced (boat + rig + crew) in kg

Smaller TR numbers = faster boat

I plugged in the numbers for Alinghi's Lake Rule Cat (modified to fit the AC rule):
RL = 13.7 m
RSA = 183 m^2
RW = 1390 kg
TR = 50.24
Bruce # = 3.07
SA-D = 150
D/L = 15

I know that big ocean tris can be built to D/L = 15 so that is a believable number. The 1390 kg is only 40 kg more than the stated weight of Alinghi's Cat and the SA is about right for the Main, Mast, and Jib.

The AC 90ft Multi has these numbers:
RL = 27.4 m
RSA = 732 m^2
RW = 11134 kg
TR = 43.76
Bruce # = 3.07
SA-D = 150
D/L = 15

The TR rating converts to a Time Correction thus: 100/TR = TCF
The 45 foot boat TCF = 1.990
The 90 foot boat TCF = 2.285

Over a 60 minute race the 90 footer owes the 45 footer just under 9 minutes.

The TR can also be used to estimate the Average Boat Speed for a given wind strength by: Vb = 164 x VTW^.666/TR
Where:
Vb = avg speed in knots
VTW = True Wind Velocity in knots
TR = Texel Rating

In 12 knots of breeze the 45 foot boat should avg 17.1 knots (1.2 x Wind Speed), the 90 foot boat should average 19.6 knots (1.6 x Wind Speed).

The AC courses these boats will sail are 40 miles, the 90ft boat should take 122.4 minutes for a corrected time of about 280 minutes, to save her time the 45ft boat must finish within about 18 minutes of the 90 ft boat in a 2 hour race.

Yes, I made a bunch of assumptions. No, I'm not betting that the actual performance of a 90ft AC Multi will be exactly what this estimate says it will be. What I will conclude is that longer is faster in multihulls just as it is in monos. That a 45 ft LWL multi has little chance to beat a 90 ft LWL multi on the water.

I suspected there was a relationship between length and speed and that longer = faster (in general, same type boat, same power/weight ratios).

Interestingly enough at 12 knots VTW the TR formula says 45 foot boat should average S/L ratio of 2.55, while at the same wind speed the 90 foot boat is only doing S/L = 2.07. I've always thought that higher S/L ratios required higher power/weight ratios. Yet the TR formula that has been used to rate multi's since 1984 does not reflect that. For the same wind speed and power/weight ratio the smaller boat has a higher S/L average than the larger boat with the same power ratios. Hmmm?

As an aside, the TR rating formula and other multihull rating systems that I've stumbled into all consider two main factors; Length and SA-D

Thanks again for the link and spreadsheet, I had looked at the Texel Rating system a couple of years ago and didn't realize how simple it is whilst giving results that racers seem to be happy with.

After bit of reverse engineering to calculate the effect of LWL between two multihulls of the same Bruce number and same D/L use LWL^.1992

If you take double the LWL (keeping D/L and SA-D the same) you get an estimated speed increase of 14.806 % using the Texel Rating formula. To get the same 14.806 % all you have to do is compare LWL^.1992 from one boat to another. NOTE: this only works if the D/L and SA-D are exactly the same.
Better to use the whole formula.

 

For the top speed of a catamran, you can try this empical formula, specifically for catamarans:

v = (1.7*L^0.5*SA^0.353)/(D^0.253)

where
v is speed in knots
L is waterline length in feet
SA is sail area in square feet
D is displacement in pounds

I'm afraid I've lost the reference for this equation, but an internet search might find it for you, or someone here may know it.

Edit: Having plugged in your numbers, that gives a max speed of 21.8kts for the 45' cat and 29.7kts for the 90' cat. The 45' seems a little low to me.

 

When this formula is used, the number for the 45' boat is close to the Texel Rating prediction of average speed in 18 knots of true wind (22.4). For the 90' boat, 29.7 knots is close to the TR prediction at 22 knots true wind (29.4).

The formula must be assuming some wind strength? As a maximum speed predictor neither formula gives a believeable result. 60 foot tris hit maximums over 40 knots with some regularity but do not average that speed around a course.



What both formulas agree on is that the 90' boat will be (should be?) faster than the 45' boat. Exactly how fast or exactly how much faster is a big ask for any simple formula.

What weight to give length in speed potential comparisions is a bag of snakes, and as je pointed out, there are hull types that will not fit the rule. I suspect the Texel system that was created to rate beach cats would not handle YPE very well at all. I think it is probably safe to use it to get a broad idea of the speed potential of two or more designs that are close to a standard beach cat in design. I'm certainly not going to bet money on the accuracy of either formula.

 

Here is one document to read and two spreadsheets to play with.

Terho

 

Thanks, very interesting read.

I see that you have gone the next step and used the Texel Rating formula for speed estimates using maximum no reef wind speed. I was just starting to go that direction myself!

I was going to use the RPI:

RPI = (Beam/Height of CE)^.5 x (Displacement/1000)^.1666


Where:

RPI = Real Performance Index h = height from DWL to center of effort of sailplan, with 100% foretriangle, ft.

Real Performance Index (RPI) gives the Bruce Number (the power-to-weight ratio in Bruce Number form) that the boat can handle in mid force-7 winds (30.7 knots).

To get to a maximum no reef wind speed and go from there.

I'll spend some more time looking at your numbers to see how you got there.

Thanks again.

R

 

Faster hull speeds for narrow hulls - how to calculate

The 'k factor' is a number that is substituted for the standard 1.35 x the DWL sq. root. It gives a larger multiplier for the DWL sq. root that compensates for the faster speed that is available for very narrow hulls. See: http://www.southwindssailing.com/articles/multihulls/CruiseMulti.shtml

 

Made some calculations by Michlet. The hull length is 7.5 m and displacement is 800 kg. The propotional speed is Fn = 0.6, similar to 10 knots with LWL 7.5 m. The lowest resistance appears when beam/draft ratio is about 1.0 and length/beam ratio is 15.5. These plots are only valid with this size of a hull, but surely the phenomenon is general.

Terho

 

AMAZING. You have just about described the hulls of Richard Woods Gwahir.
No wonder it is so fast.

 

Gwahir's hulls are 15 to 1? That's unusually fine for a cruiser, isn't it?

Ray

 

It is indeed fine for a cruiser, but the Gwahir is a very fast race boat with accommodation.

The problem with hulls that are too fine is that the WSA is proprtionately higher than a fuller hulled boat. So this means that in light winds performance suffers.

In very light winds my similar looking Strider design is a faster boat, but it is limited to about 18 knots top speed in flat water, whereas the Gwahir will go quite a bit quicker. My Merlin design (which I currently sail) is a compromise.

I don't think it is a good idea to have a cruising boat that has a L/B ratio finer than about 12:1

For several reasons.

You don't sail fast enough, often enough, to benefit and will be slower at normal cruising speeds compared to a fuller hull.

Load carrying will suffer

Seakindliness probably won't be as good. In part because finer hulls by implication have to have less rocker and flatter sections so they tend to pound

Hope these quick notes about a very complex subject help the discussion. There is much more on hull shapes on my website.

Richard Woods of Woods Designs

www.sailingcatamarans.com