Hull Asymmetry and Minimum Wave Drag

It wasn't a quote, just a generic example of a statement, ergo "such as".

Oh sure. You originally wanted to know about LCB because some empirical testing shows that not having it in the middle is better in some instances. I agree it is an interesting question and have been following the thread since the OP. It appears that, even for thinnish hulls, sinkage and trim have to be included in calculations. Since basic thin ship theory doesn't include them, a more complex model is required if what's wanted is an explanation of why having the LCB aft of midhsips might be better at times.

 

This has been done ad infinitum by many, including us, see below. Here is a plot of various hull shapes, all with the same length-displacement ratio. The length was fixed, the displacement was fixed, just the XSA is changed to provide a variation of hull forms, from a hull that has zero transom immersion, to a semi-circular to a canoe right through to a square block of wood with a “pointy” end, as the extreme.



As can be seen, each has an “Oooohh..ohhh..me..me..me” moment. At varying speed (Fn) each hull has a very slight advantage over the others, but barely. They are all so close to be considered ostensibly the same. Save for the Crude hull, which is interesting in itself, a square block of wood, with a pointy end, one would consider to be very very draggy, yet evidence is contrary to intuition.

As I noted right way way back, the reason being the key to understanding all this, as simple as it sounds (because it is), is the length displacement ratio effects with residuary resistance. Again, the variation of residuary resistance with Fn is clear. You can either read nothing into this or endless “possible” reasons.



As has been noted by several here, an “optimal” hull is often for reasons other than minimising residuary resistance. Yet to use that hull for justification of a premise/hypothesis for LCB/LCF link is wide of the mark.

In other words looking at one or two parameters , LCB and LCF in isolation to determine if there is a link between these two just misses the whole point of hull design. Since all evidence (empirical or otherwise) indicates that there is either no link (in a practical sense – see below on “Wave”) or as Daiquiri succinctly put it….why does it matter?

The hull coefficients/parameters that we naval architects use to define a hull more often than not have a symbiotic relationship, some have an influence and some do not. Just because there is a link does not automatically suggest that it has influence despite the fact the link can me mathematically expressed. The LCB dictates where the LCF ends up being longitudinally on a hull. Yet the LCB can vary greatly with no change in LCF. But to change the LCF and keep the LCB constant results in a most peculiar (un-ship shape) variants, or one ends up using surface piercing struts only, just like a SWATH. And that is the point, the LCB is the influencing factor, the LCF is well, what it is. And the location of LCB depends, upon the Fn or range the hull is designed for. Hulls may trim about the LCF, but their equilibrium is dictated by the LCB, not the LCF.

If you want to read up more on shapes of waterplanes or correctly waterlines, may I suggest you look at the boat called “Wave” designed by J.Scott Russel in 1834. He devised the lines of the boat to be taken from a “curve of sines”. It kind of worked at certain speeds when compares to others of that time. But, and here is thing about hull design…which also relates to my question before about have you designed a hull before. Since what was later found (after advances in hydrodynamics) that cutting down the angle of entrance and hollowing the waterline fwd resulted in an increase of the waterline slope in a way of and aft of that point. This had the negative effect of resulting in greater curvature at the fwd point to bring the “slope” back to zero at or near midships. “Which in turn created a greater pressure disturbance and an increase in amplitude of the wave system that originates from that point”. He summarised:

“…as the hollowness and fineness of the waterlines are increased, the wave making disturbance decreases to a minimum, after which if the lines are made still finer and hollower, the wave-making disturbance again increases…” [SNAME 1909]

It is not always so easy to mathematically define a “compromise”, as one finds in hull design.

 

As I've said several times previously, this thread is not about general optimization of a hull shape or about hull design. It's about a more specific topic, a question about hydrodynamics and the effect of particular hull characteristics on resistance.

The charts Ad Hoc recently posted do not address the question I had which he quoted: "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." Does anyone know of any charts which are relevant to that questionas opposed to variation of resistance with cross-sectional shape, effects of slenderness ratio on resistance at various Fv, or design lanes for Cp and displacementlength ratio. Of course these are important considerations if designing a hull but that's not the topic here.

I'm not disputing that "the length displacement ratio effects with residuary resistance" or that residuary resistance varies with Fn. I think everyone here will agree with that.

If my questions don't matter to you, please ignore them.

 

I have to ask a question here. How do you change LCB position alone on a transom-stern (immersed transom) hull?

 

Obviously you would have to change the lines, but you would be able to do it without changing some of the common measurements.

 

But would you be able to do it without altering, for example, Cp and at the same time without altering the nature and purpose of that transom-stern hull?

 

Within limits, you could do it without changing C_p. Nature and purpose? That's getting trickier. You'd have to be more specific I think.

 

Probably by changing the forward half of the hull. Depends on what else you're willing to change and what you want to hold constant. I'm somewhat skeptical of using the published resistance change vs LCB location charts developed for vessels without immersed transoms for vessels with transoms.

 

I was hoping for a discussion about why shifting volume fore/aft as characterized by LCB changes drag, and why the changes differ depending on Froude number, not design direction.

LCB is only one parameter to be considered in making vessel design decisions and tradeoffs, though as previously pointed out it is frequently a major one. Depending on the purpose/mission of the vessel and other considerations there may or may not be the ability to shifting hull volume in the pursuit of drag reduction. And shifting hull volume will probably affect other parameters.

There have been numerous plots published by a variety of authors showing resistance vs LCB, LCB for lowest drag as a function of Fn, etc with recommendations for design. Considering everything I said in the previous paragraph these curves and recommendations may or may not be relevant for a particular design.

 

I've been trying to figure out a polite way to imply futility; but so far not having any luck. Instead, I'll try for an analogy.

Suppose you have a computer and it executes a code and this inspires you to wonder about the inner nature of the CPUs at the heart of it all. You figure you have all you need right in front of you. You collect the code objects,decompile the code into development code, decompile again and again until you're looking and at 1s and 0s microcode. Now all you have to do is correlate how the microcode relates to the observed performance of the upper level program and you're good. Totally futile. The microcode you are looking at is 99.99% determined by the decompilers. There are millions of congruent codes of the same length that will produce exactly the same observable performance. On the otherhand, if you start with a clean sheet of paper and draft a flowchart of what you see the program doing and then design a CPU and Microcode to execute the flowchart, you will damn sure understand how at least one CPU works.

LCB is the result of the way that a thousand little decisions all influence one another. Even in the rarefied world of parametric hull studies, it would take a huge effort using carefully constructed multivariable runs (I've yet to see Sobol Distributions used for constructing hull series and test runs) to demonstrate that there is any real correlation. You basically want to demonstrate that given a set of samples, even the worst possible subset shows some positive correlation if the sample size is big enough, and that the distribution of the subsets' correlation is as predicted by the sampling method used. That's how you tease out dependence from a busy set of variables.

If you combed through all the hull studies done since the beginning, you wouldn't be able to assemble a set that meets the analytic criteria that is even 1 percent big enough. Go though the process of designing the study which would satisfy your inquiry and you will see what I mean.

 

Ok, maybe this is a better way of approaching it. Say you have a basic hull with parabolic waterlines and a rectangular keel profile. Whatever midship section shape you like. Midship section is smack in the middle of the hull, which of course means LCB is too. You run it at (pulling an example out of nowhere) Fn=0.4 and get residuary resistance of X.

You then make a second hull with the midship section at 60% aft. This means LCB moves aft to, say, 54% from the bow but displacement, prismatic, and several other things don't change. You run this hull and get R_r of 0.95X.

What causes the reduction?

 

Not so fast, sonny!

From a discussion at the 15th IWWWFB ...

Formally squat is of second order in thinness of the ship and its effect should be small. If it is not small, it may still be acceptable to include it, but perhaps then there might be other second-order effects which should also be included.
http://www.iwwwfb.org/Abstracts/iwwwfb15/iwwwfb15_discussions.pdf

See p. 18.

 

Why do you have to go and confuse things with damnable facts?

Ok, how about my last question? It might seem like a silly question, but what I'm getting at is that from some of the hull series tests I've seen, it appears that when the blokes writing it up talk about "moving the LCB aft" and this "giving lower or higher wave drag at Fn=whatever", what they are talking about is a situation in which the midship section of the base hull has been moved either aft or for'd.

Now obviously this does not change only the LCB, but it gets presented that way when talking about it. I think this is the sort of thing that DCockey is thinking of too.


So, in that sort of situation, what factor or combination of factors is causing the residuary resistance to change?

 

I am total agreement there are limits to how much can be understood by just looking at plots of integrated items resistance vs LCB, and that it may not be possible to go much further without bringing in some other knowledge. I was hoping someone might have ideas about the physics of what's going on, or at least know of some other information (such as how the near-field waves change as hull volume is shifted) which might shed a glimmer of light on the subject. Based on some very limited information, the apparent contradiction between a simplified theory and experimental data it seems trim might help with the understanding. But that might be a dead end.

Perhaps a somewhat analagous situation is the resistance of hulls with wetted transoms and how it changes as a function of vessel speed. By looking at the flow past transoms with different static immersion depths and systematic experiments a body of knowledge has been assembled which says that a Froude number based on static immersion depth appears to be a good parameter to use rather than the usual Froude number based on static waterline length or similar, and there are several different flow regimes which can be associated with different values of the Froude number based on immersed depth. Rules for predicting the associated drag are less well developed, and there are also very open questions about how to model the flow past an immersed transom, at least with less than full RANS model.

I have an interest in understanding the hydrodynamics of boats which goes beyond that which has immediate, direct application to design. Perhaps few here share that interest. It appears that some folks can not comprehend such an interest.

 

My version of Adobe Reader won't go beyond page 5 of the attachment.

I haven't seen anything suggesting changes in drag due to shift in volume distribution are fundamentally different for "thin ships" than for not so thin ships. But the mention of Thin Ship theory in the first post may have caused some folks to think this was about thin ships.

I think there is still an open question of why Leo's kayak models showed an opposite trend for drag with a shift of volume resulting in a 9% LCB change compared to the published curves for small changes of LCB. Perhaps there are other second order effects which should be included. To me it's an interesting question. To others it may just demonstrate the deficiencies of thin ship theory as a design tool.