Hull Asymmetry and Minimum Wave Drag

These are potential flow models which do not include viscous effects. There is also probably an assumption that the waves are not "too large". The Thin Ship theory which Michlet is based on also assumes longitudinal slope of the hull is sufficiently small, though I believe Thin Ship theory geometry assumptions are not required.

But there is another major difference between the models/analysis which show longitudinal symmetry produces minimum wave drag and real boats.

It's important to note that the models which show longitudinal symmetry produces minimum wave drag is the hull relative to the water does not change attitude. That means it does not sink or trim. The equivalent in a tow tank test would be a model which is constrained to not move relative to the carriage. Obviously this is not how real boats behave. Even a longitudinal symmertric real boat with the CG mid-ships will trim when moving, bow down at lower Froude numbers and bow up at higher Froude numbers (neglecting triming moments due to propulsion). The trim means that the real boat does not stay longitudinal symmetric relative to the water.

Leo's kayak models demonstrate this. When sinkage and trim were not considered the longitudinal symmetric model has minimum drag. When it is included one of the longitudinal asymmetric models has minimum drag.

This is what has me intrigued.

 

Since trim appears to be significant in understanding the link between longitudinal shifts in volume distribution and wave resistance, then perhaps LCF is as important a parameter as LCB. LCF provides better characterization of the changes in waterplane area as the volume is shifted than LCB.

But since LCF tends to track LCB, though not exactly, it's difficult to separate the effects of LCF from LCB.

 

This paper is available for download at http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD419990&Location=U2&doc=GetTRDoc.pdf

 

These fixed attitude tests introduce other problems, e.g. the model doesn't squat but the water surrounding the hull does.

Remember too...

First, Froude's method is only a hypothesis, although many NAs and engineers speak of it as though it as a fundamental law.

Second, the split into influences due purely to viscosity and those purely gravitational in nature has only been moderately successful. In some cases the discrepancies can be about 5%-10% which could make many tank tests insufficiently accurate to make a determination of whether LCB is a prime factor or whether other influences are as important.

Third, and most important, defining "wave resistance" in a viscous fluid is not as easy at it sounds. I haven't seen an entirely satisfactory one yet, but I'm happy to be enlightened

My wife is wandering around our apartment dressed in a lab coat and armed with a huge hypodermic she tells me is filled with blue "printer ink", so I better get on with other things for a while!

Leo.
(Dun Kvetchin')

 

I disagree with this, It's not that simple. Consider a fore-and-aft symmetrical hull, like a canoe-body with plumb bow and stern, or simply a rectangular barge. Now rotate the hull bow-up around the pitch axis. You will shift the LCB considerably aft (how much will depend on the fullness of the extreme sections), but the LCF will move only slightly.
Their relationship cannot be generalized because LCB depends on the longitudinal distribution of draft, whilst LCF doesn't.

 

Yeah, that's surely better than hanging around at BD.net.

 

I assume you're disagreeing with my last statement, the part about LCF and LCB tending to track together. I agree that they don't move the same and you provide some good counter-examples. Usually, though not always, if a hull shape is modified to move LCB aft then LCF also moves aft. I believe that's the trend in the systematic series which some of the statements about the effects of LCB are based on.

 

Correct

Since the LCF is the longitudinal second moment of area of a waterplane area, Aw. Whereas the LCB is the first moment of volume in the longitudinal plane with respect to the vertical ordinate of that waterplane. Thus, the volume is a function of the waterplane area integrated in the vertical plane. Hence the waterplane area Aw, when integrated can remain the same, ie LCF remains the same, but the lever, in the vertical plane changes. This is your prismatic box hull or the canoe hull when trimmed.

Not so. Changing the transom depth, for example (one of the most common changes in hull form), alters the LCB but not the LCF. Only the under water profile (volume distribution) has changed. It also depends whether one is attempting to decouple pitch and heave in response to excitations…but that is another thread

 

I have to correct myself. LCB depends on the longitudinal distribution of section areas, not directly on draft. I wanted to emhasize the 3-D nature of LCB vs. 2-D nature of LCF, but in haste have choosen the wrong words.

P.S.
Just saw that Ad Hoc wrote a note about the same thing in the above post...

 

Good points about LCF not necessarially moving with LCB.

It would be interesting to look at Series 60 and the various Delft Sailing Yacht systematic series and see how LCF changed relative to LCB for the varying models tested. Series 60 and Delft SY series are two of the sources of data used to establish relationships between hull volume distribution and resistance.

 

... but why?

 

I also wonder if the relationship of longitudinal volume shifts to resistance is different for hulls with immersed transoms and more traditional "displacement" hulls. Another way to express it would be hulls with an area curve which has a step at the stern vs those which have an area curve that goes to zero continuously and smoothly at the stern.

Also, a guess would be that planing Froude numbers where the hydrodynamic forces predominate is a somewhat different situation.

 

The test results from those series are the basis for some of for curves published of LCB vs resistance. If LCF tracks with the LCB changes for those series, then that would suggest to me anyway that their isn't any point in trying to deduce the significance of LCF vs LCB based on those series tests. B
ut if the variation of LCF is somewhat independent of LCB for those series then it might be possible to learn something about LCF vs LCB relative to shifts of volume affecting drag.

The Delft YS resistance formulas contain terms using LCB and LCF. My understanding is those formulas are based on regression, not fundamental physics. So how much could or should the Delft YS forumulas be used to establish whether the LCF and LCB have different effects? It would simple to generate a curve of change in resistance vs LCB as a function of Froude number from that series, and in fact I presume that is how the published curve was determined. Likewise it would simple to generate a similar curve for change of resistance vs LCF. But would it be independent of LCB?

 

Ok, so it appears that sinkage and trim are the answers if we are talking about thinnish hulls.

Seaway is another possibility. The Delft series was for offshore racing yeachts, and of course windward performance in a seaway is important to such yachts. I assume this scenario would have been tested for the Delft series but I'm not sure. If they did test upwind in waves and weighted their conclusions to include this then it would encourage fine bow sections and a fuller stern for "optiumum hull of least resistance".

Anyway, what I'm getting at here is that statements such as "theory predicts that longitudinally symmetrical hulls will have minimum wave drag" are not useful if they rely on the hull not changing attitude at any Fn. The theory in question is too simplified to generate realistic results. IF a guide to drafting real hulls is what is wanted (and hey, some people are funny like that) then we need a more complex and realistic model, even if it is not quite so conveniently tractable.

ETA: If more realistic results are desired from Michlet, what guides are there for correctly estimating sinkage and trim so that it can be included in the calculations?

 

The Delft Systematic Yacht Series resistance results discussed here are calm water and upright. They are also for the hull only without keel or rudder. I believe that's also true for the Series 60 tests and the other ones used by Larsson and Raven.

Resistance in waves is another, more complicated topic which hasn't been considered here.

Simple theory without understanding and interpertation is generally not a good guide to use for designing hulls. Frequently emperical models are better guides for design purposes. Of course they also can be misleading if not understood and properly interpreted.

Had a look for the quote you gave. The closest I could find in my posts was in the first sentence of post #1: "Leo explained in another thread that Michell's thin-ship theory predicts minimum wave drag occurs when a hull is fore-aft symmetric." I then went on to discuss how that experimental results do not agree with that particular theoretical result and raised the question of what is the reason for the difference between that bit of theory and test results. Not exactly a suggestion to use that bit of theory for design.

In post #63 I asked about the conditions necessary for the theoretical result of a symmetric hull having minimum wave drag. I provided a disclaimer at the top of the post: "(Disclaimer, this question is theoretical and does not concern the design of real boats.)" I also commented that for that particular theoretical result to hold: "Obviously the attitude of the hull would have to be invarient to direction of motion." I hope no one thought there was any suggestion in that post to use that particular theoretical result as the basis for design.

Maybe a large, bold letter warning is needed for threads like this letting folks know that not all the theory discussed is 100% directly transferable to designing boats.

Relative to emperical or analytical models to use to guide hull design, I have a direct interest in that for very small boats and will try to find time to start another thread about that. I hope this one doesn't get taken over by that topic.