# Cat hull resistance change with heel?

Discussion in 'Hydrodynamics and Aerodynamics' started by DennisRB, Mar 1, 2016.

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### DennisRBSenior Member

When looking at say a catamaran. The length to displacement ratio is divided by 2 due to the 2 hulls sharing the displacement. This gives an impressive figure. But it would seem this would only apply to a motor cat or a sailing cat sailing DDW.

When sailing the hulls will not be loaded at 50% each. Up to the point of flying a hull where one hull carries all the displacement, and possibly even more than 100% thanks to the dynamic forces of the sails. In this situation its obvious the displacement to length ratio can not be divided by 2.

Now as displacement reduces on one hull and increases on the other, one hull will have a lot less resistance and the other a lot more. What typically happens to the total hull resistance as the cat heels? Does it go up with heel until a hull flies?

All the parameters like cp, bt etc etc all seem to be given at optimal figures for sailing cats but these seem to be calculated with equal hull loading. I am yet to see any literature regarding the changes to these paramaters as the hull heels. Are the implications of this usually taken into consideration when compared to a motor cat?

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### Mr EfficiencySenior Member

Wetted area goes down, though ?

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### DennisRBSenior Member

Yeah it has to go down once the hull is flying! But what about before that? And how much does the wetted area change make a difference compared to the displacement changes? I seem to remember (perhaps wrongly) that on a slender hull doubling the displacement more that doubled the resistance. So heeling could give an over all resistance increase?

I am thinking of performance cruising cats which could, but usually would not fly a hull, but they would sail with one hull much more lightly loaded than the other.

I have seen a graph comparing a tri with a cat as they heel. There was a big difference in the resistance at various points of heel. But the graph was just to show the difference between a can and a tri and was not very detailed. I can't seem to find it and I forgot the results. Perhaps it was on the Shuttleworth site.

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### bjnSenior Member

Based on Michlet simulations of long slender hulls, I've done the following conclusions:

Residual (~ Wave) drag is about proportional to displacement. Flying a hull will not change this drag much, since the displacement will not change, only move it to either hull.

Skin friction drag is about proportional to the square root of displacement. Flying a hull will decrease drag about 40% compared to sharing the displacement evenly. But only shifting the displacement a bit will also help. With 3/4 of the displacement in one hull, the drag should be about 20% less than evenly sharing (motoring).

In a light catamaran, skin friction drag dominates residual drag, so flying a hull should decrease drag with up to 40% compared to motoring.

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### Mr EfficiencySenior Member

Flying the hull of a cruising cat would qualify as suicidal behaviour anyway. You wouldn't grow old doing that for a hobby !

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### StumbleSenior Member

In small cats there is also the advantage of getting the foils out of the water. Though they make up almost zero displacement they have a lot of surface area, and worse frontal area relative to the rest of the boat. So getting up on one hull helps reduce drag out of proportion to just display meant shifting.

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### Ad HocNaval Architect

And that is incorrect too. The LD ratio is the length over the total displacement, regardless how many hulls are being used. not per hull. Thus when comparing LD ratios, it must be like for like, since monohull LD ratios of residuary resistance are different to those of catamarans, for the same LD ratio.

It is only affected by abrupt changes in section which creates drag/eddies/vortex from the said appentadge. If the transom depth ratio changes this may also affect the resistance, but marginally, since the depth cannot change that must anyway if in a constant mode. So the resistance is basically the same.

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### patzefranpatzefran

Ad Hoc, I don't understand / agree with your statement :

"And that is incorrect too. The LD ratio is the length over the total displacement, regardless how many hulls are being used. not per hull. Thus when comparing LD ratios, it must be like for like, since monohull LD ratios of residuary resistance are different to those of catamarans, for the same LD ratio"
This may be true for the definition, but practically, to determine the total wave drag of the non heeled cat (Neglecting interference drag) we have to use the L/D (e.g. using Series 64 high speed semi displacement tables) of each individual hull and multiply the individual drag by two, so half the total displacement per hull. I used this method in my VPP program wich proved to be accurately predicting A class cat performance (non foiling !).
I Agree about drastic reduction of wetted area dividing the total hull friction drag by about 1.41 flying a hull, and even more considering the appendages. It is why it is so interesting for racing cats to fly a hull. Flying hull downwind was used first by Mitch booth (Tornado) and widely used on non foiling A cats since the 80.

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### Ad HocNaval Architect

Sorry, incorrect.

You can't use the LD rtaio of a single hull and multiply it by 2 for 2 hulls. Since the interference effects vary with speed, transom immersion and hull spacing considerably, from 1.05 - 1.60 thus a wide variance.

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### patzefranpatzefran

From what I read about interference effect, it becomes small or negligible when the width of the catamaran is of the order of half hull length or more. It seems many people have used this approximation before me. Please give your reference for the range you mention, i;e; 1.05, 1.6

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### Ad HocNaval Architect

This paper by Prof Molland and many others by him, on the same subject, have a series of LD ratios and their effects.

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### Richard WoodsWoods Designs

The test tank project I did in 1978 as a student (under Tony Molland) showed that drag from wave interactions could be as high as 20%. But I was only allotted time for a limited number of tests and of course was only a student. But the trend was obvious

I doubt if flying a hull increases speed by 40% - or does it? Sail at 10 knots, fly a hull and speed jumps to 14??

Certainly, once you have got a hull out of the water, then going higher slows the boat down, but it does point higher to windward. So there are more performance factors at stake than just flying a hull

Richard Woods of Woods Designs

www.sailingcatamarans.com

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### StumbleSenior Member

I can promise you on the A-Cat that there isn't an immediate speed gain just from flying a hull. Because typically the hull doesn't just go from normally loaded to out of the water, instead the windward hull progressively unloads as theboat heels over. In other words I am not even sure how to quantify this.

As the boat heels the drag goes down, which allows higher speed, this higher speed creates more apparent breeze which heels the boat more, so drag goes down... And round and round we go.

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### patzefranpatzefran

Richard, I never said velocity increased 40%, but only wetted area decreased, and accordingly friction drag. A class cat flyng hull downwind are consistently faster and deeper than flat one, it is a well established fact. Semi foiling or foiling A cats are faster dpending on wind range but the velocity gain is much smaller than Moth, some knots only not ten or more.

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### patzefranpatzefran

Captain Rubin, obviously the velociy increase is not immediate, this is a matter of acceleration and they are low on water. But it seems you never sailed or looked at racing A cats(I got my first one in 1985 and raced them up to now). The windward hull don't move progressively, in no time you are swimming into the water. Complete A cat weight 75 kg, the power to weight is very high.

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