# Fore and Aft Cp -- unresolved questions

Discussion in 'Boat Design' started by Paddlelite, Feb 19, 2013.

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I'm picking up on a two-year old thread at http://www.boatdesign.net/forums/bo...ntial-cp-foreward-aft-37842-2.html#post615673,
where Phil explained, in reference to human powered craft, that "regarding the merits of a different fore and aft Cp [with dividing point at the max sectional area]. . . if you envision two hulls, one consisting of the fore section mirrored front to back and the other consisting of the aft section mirrored front to back, you can look up the ideal Cp of each [hull] based on length for each and the design speed."

My first question is the extent to which this analysis should be employed or disregarded. For instance, I've attached pictures of two recently designed "race style" paddleboards of 12.5 ft length x 29" beam each, one designed by NA's Melvin & Morelli and the other by Tim Kernan Yachts, the first with max beam around 63% and the latter with max beam about 61.5%. Both are meant to maintain speeds around their theortical hull speeds with strong paddlers.

But if I use the suggested analysis, the stern section of either hull, along with with its mirror image, together comprising a virtual hull with its own hydrostatics, would be so short that it would be driven far above its "hull speed" and be holding back the more favorable bow.

So what's going on here? Is the stern section Cp far less relevant because it operates in turbulence and its wave is not as big as the bow's? It seems silly to totally disregard the fore and aft Cp as separate quantities, but equally silly to treat them as though they reflected identical functions in identical conditions. Are there accepted proportions for bow and stern Cp for small craft near hull speed? Or maybe some much broader or higher range for the stern? Need to know because I'm designing a paddleboard similar to those described, with max beam about 60% aft, decent Cp for the bow, but way high for the stern at .65 and pushing the stern (as a "mirrored hull") way above its hull speed. Any insights at all, please.

Secondly, notice the asymmety of these hulls, as well as the extreme asymmetry of Matt Broze's Mariner kayak, picture attached. I read Leo's paper on kayak hull asymmetry, squat, and resistance, generally favoring symmetry. So, how do these asymmetrical designs comport with Phil's suggestion of separate analysis for bow and stern Cp and hydrostatics, or Leo's work on kayak hull assymetry?

And thirdly, I'm seeing widely different sets of S/L to Cp figures. For S/L = 1.3, for instance, I see one suggested figure on this board of Cp = .62, but others as low as Cp = .57. Have these disparities been resolved over time, or is there really that much range depending on what reference source is used?

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### DCockeySenior Member

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### Remmlingerengineer

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### philSweetSenior Member

I vaguely remember that thread. I was being a bit of a devil's advocate at the time and hoping the discussion would continue on, but it kind of died out. IIRC, the main things I was hoping for was to recognize the sensitivity of locating the center from which to base the measurements- you'd need a VERY accurate maxarea location- and also the insensitivity to speed. Basically, there is a fairly sizable design space with a flattish total predicted drag. Whether or not my idea of matching fore and aft Cp to their respective Froude numbers is optimal- I don't know. I think it went uncommented on at the time. Maybe this time around the discussion will continue.

My other concern is that I'm beginning to suspect that conventional Cp data is better at optimising drag for boats that are deeper draft than a typical highspeed kayak.

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Here's some interesting data on kayaks FWIW.

Greg Barton's Epic 18' (fast tour style) has Cp .58 (very high for kayaks) and LCB at .51, presumably as located from bow as a percentage of LOA. I have one, and it's reasonably fast, though maybe could be better for 18'.

The popular all-around great handler, the Tempest 16.5' has Cp .49 and LCB at .50. I have one, and it's not at all fast -- sort of a tub with pointy ends.

The quick and somewhat tippy little Sonoma 13.5' has Cp .52 and LCB at .53. I have one, and it keeps up with any other boat to 4 kts.

Playing around with KAPER, it tells me the optimal Cp for my 12.5' x 26" paddleboard would be .55-.56 for 4 kts and .59-.60 for 4.5 kts.

Something screwy with KAPER though -- the further back you put your LCB, even all the way to the stern, the lower resistance it gives. It almost has as much effect on resistance as Cp. If LCB location, within a reasonable range, is really that critical, then a discussion of asymmetry is all the more relevant to design.

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### Leo LazauskasSenior Member

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### Leo LazauskasSenior Member

I'm not which one you are talking about, but one of the Epic surk-ski range
won a Molokai and many others were in the top 12 positions. They were all
designed using Michlet/Godzilla back then.

KAPER is not an analytical tool as such. It is more of an empirical formula
based on some fairly rough measurements, i.e. not tank tested under strict
protocols, IIRC. I'm not saying it's not useful, just to be wary of it as an
"optimisation" method.

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Oh, you're pointing out that the "mirrored hull" analysis can't hold up, at least here, because if you pretend that the fat short stern and its mirror image is a hull, it's no longer a slender ship to which any of these rules apply. At least I think that's the implication. Thanks, and now we're left with no rules (other than the study on squat and resistance with shifted LCB.)

The Epic 18 was basically a sea kayak, as depicted. I've been on the Epic skis as well, and they are definitely faster, but designed for very strong paddlers with excellent balance. Greg Barton once came out to our club, and our fastest member trained with him. He reports that he was able to keep side by side with Greg at 6 mph, until Greg said, "well, I'm warmed up now. I'm going to take off."

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### Leo LazauskasSenior Member

No, I was replying to David regarding his comment that the previous discussion was inconclusive.

Thin-ship theory is fine for the hulls we are discussing.

Over what distance? The Molokai is quite a long event.

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That event was unrelated to the Molokai, which has such varying sea conditions that it's hard to draw conclusions from the times or speeds. But when Epic first came out with the 18' sea kayak before the surf skis, Greg was able to show it off by paddling the 20 mile Blackburn Challenge with an 8 mph average speed.

Years later, I saw him and Oscar training for the Molokai with their V10 surf skis. They were paddling side by side, doing laps around a shallow lake in Charleston, SC at a kayak expo and demo event. When they would zoom by, their wake was so huge that people doing kayak demos would tip over.

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### DCockeySenior Member

I'll expand on Leo's comments. KAPER is based on a regression of measured drag of some sea kayaks and a number of parameters based on the physical characteristics of the sea kayaks. KAPER is not directly physics based. Regressions can be very useful, particularly when the physics involved are complex. However regressions can also be misleading, particularly when used to extrapolate beyond the range of the data used to create the regression.

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OK, I'll accept those limitations. But why is it that in the 500 years since Da Vinci drew this study of water flowing past objects, we've advanced technology in so many unimaginable ways, we still don't seem to understand the behavior of the most abundant large-molecule substance we see, touch, and consume every day? Maybe that's the attraction to hydrodynamics.

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### Leo LazauskasSenior Member

Different aspects of hydro fascinate different people. Turbulence is still one
of the great mysteries in physics. Remember too that the very existence of
boundary layers and their importance to drag were only discovered fairly
recently, at about the same time as Einstein proposed the laws of special
and general relativity. Coles noticed the behaviour of the outer "wake" of
boundary layers in the 1950's and these had escaped the attention of von
Karman and brilliant experimentalists like G.I. Taylor. Hairpin vortices and
other fluid structures in wall-bounded flows have only been found very
recently. There just hasn't been enough time and effort thrown at the
problem yet.
That is all just my off-the-cuff personal take on it; others will, no doubt,
have other opinions.

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### Ad HocNaval Architect

I know a couple of the Profs at Osaka Uni quite well, since i occasionally lecture there too. One of them mentioned to me a few years ago now in passing, so my memory has faded at bit, that they have discovered that in the boundary layer the water is behaving like light; 2 states. In that it can be either a wave or a particle.

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