Catamaran drag rise at less than hull speed

[sundancer]

In 2010, I designed and launched a 20' pontoon catamaran with a 100% solar powered electric propulsion system. The boat was operated last summer for over 50 hours without ever needing an electric outlet. The speed performance of the boat was pretty much as expected, but the top speed was less than predicted. This shortfall was caused by an unanticipated drag rise, which is the subject of this post. My performance data, and my quest for some answers is given below.

The 2 pontoon hulls are a 2 dimensional prismatic design, with long bow and stern tapers to minimize low speed drag. These tapers approximate the shape of a Wigley hull at the waterline in 3 straight line segments. However the width below the waterline is constant because the hulls are 2D for ease of manufacture. This results in flat bottomed hulls (pontoons).

Being electric powered, it is relatively easy to infer the drag vs speed from input power. I had also performed some measurements earlier on a 12' kayak powered by 2 different electric trolling motors, to get some idea of drag vs speed characteristics. These measured characteristics were Froude scaled for length, and also adjusted for weight, to get a speed vs power performance prediction for the 20' boat. The 20' boat was also measured after launch. All the results agree very well up to a Froude number of about 0.28. Above this number the pontoon boat has a drag rise significantly steeper than that of the kayak. Since the pontoons are slender like the kayak hull (fineness ratio of ~10:1), I am puzzled about what is happening. The discussion below develops some more details based on the attached chart. Anyone willing to submit some comments or ideas??

See 2010 Real Performance.pdf attached

The chart shows that the power vs speed trend is pretty close to a cubic equation, with no linear or quadratic terms. The kayak data shows this cubic trend up to the maximum speed measured F=0.37. This comes quite close to the calculated hull speed which corresponds to F=0.4. (Having read the forums on the subject of hull speed, I realize that it is only a reference speed that equals the speed of a regular, transverse surface wave whose length = LWL; not some absolute speed barrier). The 20' pontoon boat follows cubic trend almost exactly, up to F=0.28, above which it exceeds the cubic rise rate significantly. The literature that I have read generally states that a significant drag rise does indeed occur in diplacement hulls above F~0.35, and levels off at F>0.5.

There is one other qualitative fact which may have some bearing on the drag rise. In the water, I have observed a small but noticeable smooth transverse wave developing behind the boat at F>0.29. If one cuts power abruptly, this wave passes underneath the boat at constant speed, almost undisturbed by the hulls. Its visually observed wavelength is shorter than the boat, which would be consistent with the wave dispersion equation. Is this wave the power sink? Can it be reduced? Are there other possible, correctable suspects?

I'm looking for possible ideas to improve things above F=0.28

Hope this catches some interest out there.
Thanks from a new member.

[Ad Hoc]

Can you post the lines plan of each...hard to say for sure without looking at the hull shape for each.

[baeckmo]

Yes, and also a reasonably correct value on displacement, since the main non-linearities in a displacement catamaran manifests themselves through the slenderness ratio and hull transverse separation ratio.

[Alik]

...
I'm looking for possible ideas to improve things above F=0.28
...


There could be significant increase of drag around Fn=0.4 due to small horizontal clearance. What is BWL of hulls, and BCL?

[oldsailor7]

For min drag your hulls should have a a semi-circular underwater section, a prismatic of 67%, an L/B ratio of not less tha 12:1 and lightly loaded. :D

[Alik]

For min drag your hulls should have a a semi-circular section, a prismatic of 67%, an L/B ratio of not less tha 12:1 and lightly loaded. :D

This advice on L/B ratio and CP is very questionable; it is consumer's approach inspired by reading 'Multihull' magazine :) One has to look at all other parameters of boat before giving such numbers.

[oldsailor7]

Not so Alik.
All that information came from the research efflorts of the late Edmond Bruce using the British govts water test tanks in the early 1960's.
Lock Crowther studied Bruces findings very closely, which accounts for the success of his sailing multihulls, both racing and cruising.

[Alik]

Not so Alik.
All that information came from the research efflorts of the late Edmond Bruce using the British govts water test tanks in the early 1960's.
Lock Crowther studied Bruces findings very closely, which accounts for the success of his sailing multihulls, both racing and cruising.

The first issue should be horizontal clearance that can change drag by 40%. Other parameters like CP, L/B are of second order of importance. I don't see the reason why L/B should be 12:1, not 10:1 for particular displacement and required immersion.

[sundancer]

Can you post the lines plan of each...hard to say for sure without looking at the hull shape for each.

Don't have the lines for the kayak, but they are fairly typical for a recreational open water kayak (12' lwl, 2.5' max beam) The pontoon design is a simple rectangular cross section with the following footprint for each hull
X/L from 0 to 0.3, B/L = 0.27 X/L
X/L from 0.3 to 0.7, B/L = 0.09 L
X/L from 0.7 to 0.95, Complement of 0 to 0.3, A small blunt stern on each accomodates the motor mount

The hull centerline spacing is about 0.3 L

Hope this helps
sundancer

[sundancer]

There could be significant increase of drag around Fn=0.4 due to small horizontal clearance. What is BWL of hulls, and BCL?

BWL = 22" for 0.3<X/L<0.7, with linear beam tapers beyond those limits, (X=0 at bow)

BCL (hull C/L spacing?) = 74", L = 240"

Would like to achieve Fn ~ 0.35 for same power, greater is not of interest
Thanks

[sundancer]

The first issue should be horizontal clearance that can change drag by 40%. Other parameters like CP, L/B are of second order of importance. I don't see the reason why L/B should be 12:1, not 10:1 for particular displacement and required immersion.

Horizontal clearance certainly affects the bow & displacement wave interference between the hulls, and that is one of my main suspects. Unfortunately, highway transportability limits this separation (don't want to get a permit or an escort every time I move this boat).

A little can be done to increase fineness ratio, possibly 25% or so without a serious penalty. Certainly, a semicircular bottom would minimize skin frictional drag, relative to my rectangular crossection for a given hull displacement. But I suspect that the big increase at Fn>0.28 is not skin friction driven, but rather bow wake interference driven.

I have considered longer pontoons to increase the fineness ratio, but this choice would only decrease the separation ratio, and possibly make things worse.

Comments??

[oldsailor7]

[Quote.] "But I suspect that the big increase at Fn>0.28 is not skin friction driven, but rather bow wake interference driven. [Quote.]

Sorry Sundancer ---i didn't think your separation distance was so close,
But, at that distance all the considerations Alik and I were talking about are irrevelent. Interference drag will be large, especially with a rectangular stern section.

Edmond Bruce found that a L/B ratios of 12 or more don't make any "Bow Waves".
But displaced water has to go somewhere, so there is still an "interference". Perhaps it's just the blunt transom drag.

With a shape and configuration like yours I don't think it lends it'self to mathematical calculations.

More a situation of "Suck it and See". Widen it some more and try again. The legal trailing limit is 8' 2" afterall.

Just my 2c worth. Paddy.

[Gary Baigent]

I'm with Paddy, cat needs all the length you can get and be spaced to the maximum, what about 16 or 18 x 8 feet? One question: why bother with the inflatable hulls; why not make the hulls out of conventional boatbuilding materials, foam/glass/carbon or strip planked light woods etc. - because then you can shape the hulls to lowest wetted surface areas plus have a sweet hydrodynamic profile; also you can get a mirror polish surface - and achieve far better performance than what is possible with the somewhat crude, fat, inflatable straights. For low powered propulsion you need everything else to be as near perfect as you can get.

[sundancer]

Seems to be some confusion about the hull configuration, spacing & material. Sorry about that. The material is welded aluminum from sheet stock.

The attachment contains a hull planform sketch for the subject boat, and one alternate configuration that I have considered. With everything that is on top of the hulls, the width is very close to the highway limit of 102". The 52" minimum spacing could be increased by making the hulls thinner and deeper, but at the expense of increased wetted surface & softness in roll response.

The alternate clearly has a little larger spacing, but has a long tunnel. I think the bottom would have to have an outboard deadrise of 20-30 degrees to bias the flow of displaced water away from the tunnel, possibly minimizing interference drag. But this hull is a little more complicated to build, and probably has more drag at Fn<0.25 because of bigger turning angles - hence the selection of the symmetric hulls.

Comments on this, and what would be the spacing needed to minimize interference drag?

Thanks for your comments so far.
RWT

[cavalier mk2]

For my 2 cents I think the rectangular sections could be generating vortexes off the chines as well as the wake interference.

[Ad Hoc]

... I think the bottom would have to have an outboard deadrise of 20-30 degrees to bias the flow of displaced water away from the tunnel, possibly minimizing interference drag. But this hull is a little more complicated to build, and probably has more drag at Fn<0.25 because of bigger turning angles - hence the selection of the symmetric hulls.


It is rather difficult to comment when you have alerady come up with the solution/answer. Not sure how you arrived at these conclusions in the absnce of any hard data or the SOR.

If you want objective comments, you need to post the body plan, profile and also more hard data on the boat.

Otherwise all you're asking is for "other people" to agree with your hunches or guesses of what to do.

[Alik]

If boat is in alloy, probably it is too heavy and first thing to do is try reduce weight.

[sundancer]

I didn't consider chine vortex shedding as a possible candidate. Thanks:)

[sundancer]

It is rather difficult to comment when you have alerady come up with the solution/answer. Not sure how you arrived at these conclusions in the absnce of any hard data or the SOR.

If you want objective comments, you need to post the body plan, profile and also more hard data on the boat.

Otherwise all you're asking is for "other people" to agree with your hunches or guesses of what to do.

Noted: I think all I seeking was a comment, based on any research someone might be aware of, on whether a straight tunnel configuration had any clear benefit over two symmetric hull with regard to the phenomena illustrated in the graph posted earlier.

[Manfred.pech]

Hi Sundancer, you will find a lot of research about Wigley Hulls with Google, mostly academic and very interesting. If you really want to get hulls with optimized hydrodynamics you have to look for the flow of water around your hulls. May be it is helpful for you to get some photos from another boat to analyze the vortices and waves around and under your catamaran. May be I am wrong, but from my experience I would avoid too much gradient of curvature and reduce the wetted surface as much as possible. This can be done by slight hydrodynamic lift from an optimized water flow.

[sundancer]

Hi Sundancer, you will find a lot of research about Wigley Hulls with Google, mostly academic and very interesting. If you really want to get hulls with optimized hydrodynamics you have to look for the flow of water around your hulls. May be it is helpful for you to get some photos from another boat to analyze the vortices and waves around and under your catamaran. May be I am wrong, but from my experience I would avoid too much gradient of curvature and reduce the wetted surface as much as possible. This can be done by slight hydrodynamic lift from an optimized water flow.

When the boat goes back in the water later this coming spring, I plan to do a photo & video survey around and under the boat to check out the various suggestions I've received. I will search Google to see if there is anything about Wigley hulled catamarans, and hull spacing.
Thanks and Tschüß

[sundancer]

Thanks to Manfred.Pech's suggestion to Google Wigley hulls, I came across a paper published in Ocean Engineering by Moraes, et. al. in 2004 (vol 31, pp 2253-2282) To my pleasant surprise, they studied the wave drag of chine hull catamarans as well as the Wigley hulls as a function of their separation distances. With the help of the data in this paper, I was able to establish that Sundancer's drag rise behavior is entirely consistent with this class of catamarans, and not something odd. The details follow. Thanks again!

Sundancer's hulls fall well within the ranges analyzed except for the block coefficient, since Sundancer's deadrise is 0 degrees (flat bottom). Sundancer has following parameters:
L/b = 10.6
b/T ~ 2.5
S/L = 0.32
Entrance/exit = 0.31L
Block coefficient = 0.755

Although the focus of the Moraes paper was on high speeds (Fn > 0.3) they did include data points at Fn = 0.2 & 0.3. Of particular interest was the non-dimensional form of the wave drag, C*, given in figures 31,33 & 35, based on the 'Shipflow' 3D analysis code. Albeit a little hard to read accurately, these figures show ~ 45% drag rise in this neighborhood, with only a slight dependence on hull separation distance (S/L). The rise is very significant above 0.3, with a significant dependence on hull separation between Fn = 0.4 and Fn = 0.6. Since Sundancer's low power limits its speed to ~ 0.33, I concentrated on trying to read the Fn = 0.2 & 0.3 data point values as accurately as possible by enlarging the charts.

Acknowledging that propeller and motor efficiency vary over the speed range, Sundancer's drag trends can still be roughly inferred from the motor input power, After removing known constant overhead power, I divided out the cubic speed dependency on power (quadratic drag from the definition of a fluid drag coefficient). I then superimposed C* values from the Moraes paper rescaled to my 'funny units', and achieved a very reasonable match as shown in the attached chart.

I appreciate all the comments that I've received, and have certainly learned about some improvements that could reduce power consumption at lower speeds if and when another hull is built. However, it is very clear that no great improvements will occur in top speed with < 3kW of motor power. Thanks again to all the contributors for the help.