Multi speed/length relationship?

I should have come down on the first off-topic post in my thread. My error.

We don't need lessons in debate, if we do, we know who to ask.

The five words you keep trying to hide behind are:

"Anyway, of course it's nonsense, ..."

That statement refers to "By that token, one could make an equally illfounded argument, that an unballasted multihull is like a top-heavy tricycle, or that a multihull is like a tall man trying to stay balanced on two slow water skis towed sideways."

When Mr. Aldridge questioned your statement "Why do you believe this?" you could have responded, "It was nonsense, like post #53", but you chose to feed the fire with, "What makes you think otherwise, I may ask?".

It seems that you desired to provocate emotional response and you succeeded. Other posters may not be as protective of their threads as I am, and these antics may be tolerated there. However, as I said I don't appreciate it in my thread.

I don't want to make an enemy. Once again, I invite you to start a thread based on your opinion "But a multihull seems to have a bigger risk at capsizing than a monohull has for sinking." I'm sure you will have fun with it.

 

The answer - depends on the conditions.

At slower speeds the larger boat will do better. In the middle range for the 90 footer and higher end for the 45 footer the smaller boat will do better. At the very top end the bigger boat will claw its way back - not sure if it actually gets better. Refer attached chart for a 4T 45 footer versus 32T 90 footer.

There are two principal factors that come into play.

1. The friction factor on a hull reduces for rising Re# so the 90 footer enjoys an advantage in viscous drag. This dominates at slower speed.

2. The celerity of the transverse waves plays a significant role as speed builds. The celerity of a wave train in deep water is calculated as:
V=sqrt(g x Wavelength / (2 PI)) (g is gravitational constant 9.8m/s/s)
As the vessel speed approaches the celerity of its lateral wave train where wavelength equals LWL the wave drag builds and then levels out once the vessel speed exceeds the celerity at that wavelength. For a 45ft wavelength the celerity is 9kts. For a 90ft wavelength it is 12.7kts. The larger boat gains a large advantage when the wave drag is building on the smaller boat. The table is turned as the larger boat gets into the rising wave drag. By this time the wave drag on the smaller boat has leveled out.

I did not go beyond 20kts in the analysis as I felt this was a practical limit.

I know a complex answer to a simple question but if I responded with a simple yes or no I could be both wrong and right. May be why there has been so much dancing on this topic.

Rick W.

 

Rick, is this the correct chart? How does one read it??

Regards

Alan

 

The given conditions were for catamarans of 45ft and 90ft. I just took a stab at displacements of 4T for the smaller one so the 90 footer ends up at 32T - I am not worried about the practicalities of this as it is an example based exactly on the question.

The SA-D was given as 100 for both. So the sail power is 4 times for the 90 footer compared with the 45 footer. The condition I considered was both hulls equally loaded so lets say a broad reach and crew ballast set to equalise hull loading for both vessels.

The red line in the chart is the sail drive component and is taken to be constant at a ratio of 4 times; bigger boat to little boat. There will be slight difference in drive because the lift coefficient on the sails is a weak function of Reynolds number but is a small variation for the wind speed of interest.

The blue line is the hull drag ratio; bigger to smaller. For the boats to perform identically the drag ratio needs to be 4, the same as the sail drive ratio. When the blue line is lower than 4 the bigger boat goes faster and slower when the blue line exceeds 4.

Rick W.

 

Thanks for the explanation Rick! Funny that the smaller boat is faster at higher would have thought the opposite.

Regards

Alan

 

The above analysis assumes smooth water. So would be meaningful in protected waters. In unprotected waters the larger boat would be affected less by the heavy seas associated with the wind required to do 14+ knots. On the other hand a smaller boat might be pushed closer to the limit.

You do see examples of small cats doing well against larger cats in ocean races though.

Rick W.

 

In our multihull sailing club (no beach cats), there is Saturday racing throughout the year. Boats vary from 23' to 45'. The 28R Corsairs and Farriers routinely dominate the finish line.

 

Hi Everybody,
Just to mention a reference that I didn't find on this very interesting thread:
Serie 64 from the David Taylor Institute, I don't remenber exactly the reference, but I guess it is a classic among multihull architects
It deals mainly with L/B ratios and related displacement, and it seems that the heavier the boat the smaller beam/draft will perform better at hight speeds

 

Maybe I'm getting a bit thick in my old age---but I can't work out exactly what you mean by that. You are mixing Length/Beam ratios with Beam/Draft ratios and throwing Weight in for good measure.

 

Sorry for poor precision

As far as I remenber, in order to compare apple with apple, the drag was related to displacement (x Newtons drag/ 1 ton ).

All hulls have the same lenghts but different displacement and therefore different Beam:draft ratio for different displacement lenght ratios

Drag was mesured between 1 and 5 of a Froude related ratio.

And for high speeds it appears that heavy hulls with small beam/draft ratio show less drag per ton than larger one.

The original text would be better, unfortunatly I do not get the paper anymore.

Hope it is a bit clearer

Regards

 

Sorry Erwan, that comparison only works with the Series 64 forebodies, afterbodies, and PMB. Using Series 64 data as a reference to L/D ratios only applies to decreases in drag per ton due to volumeteric considerations, i.e. a geosim with twice the tonnage only has 1/2 the wetted surface....see my earlier post on geosims.

 

Hi, Terho - Over here in the US, we do things so differently that I am a little lost when I look at your numbers. For example, here a very light D/L ratio for a cruising cat would be 60, and a heavy one might be 150. Are you saying that a heavy cat should have a hull draft equal to its hull beam at the dwl? But that can't be, because it would either be impossibly heavy or impossibly narrow. My BigCat design has a d/l ratio in the mid 70s, loaded, and even though it is a shallow 'v' hull, the hull draft is 1.5' and the hull beam at the dwl is 5, so there are 3.3 hull depths per hull beam at the dwl. If I sink the same hull down a foot by adding 30,000 pounds or so, there are still 2.7 times the hull draft to equal the dwl beam, with 12 dwl beams for the overall length. The d/l ratio would then be 122, as we calculate it. See: http://www.sailingusa.info/cal__dl_ratio.htm

 

As I wrote, in practice, heavy catamarans can't be optimum. Well, they are slow anyway, so few percent addition in resistanse is nothing.
In my calculation the hulls were round bottom ones. My light cat has DLR 56, average 80 and heavy 120.

 

Yeh, Hugh Y. H.,
"Series 64 Resistance Experiments on High-Speed Displacement Forms"
Marine Technology, July 1965, pp. 248-271.

 

Thanks for exact reference

Thank you Léo for posting the exact reference.

Sorry Jehardiman, I cannot keep up, as I dont remenber exactly, and there are brighter persons than me on these forums to address smartly these issues.

Considering Terho remark about square main section, I could mention that the Hobie Tiger designer has currently a "TigerII" design called ALADO II,
only a few of them have been sailing locally, since a few years with "amateur" crews.
One of them was at the F18 World last month. The only boat with horizontal panels dacron-mainsail of the fleet. She ranks about 30.

The boat is thinner than the HC Tiger and deeper, a perfect square.
As a result she can be pushed harder in strong wind with the kite, the
main drawback, it is a bit more difficult to tack.

It is the opposite philosophy of the new Nacra infusion's wide hulls.