Hull Asymmetry and Minimum Wave Drag

A theory is a supposition (or “system”) of ideas that explains “something”. That ‘something’ has to be observed. If the theory proposed elegantly and consistently described the observation and then one can extrapolate and manipulate the theory for predications, that also turn out to also be correct based upon future observations, everyone is happy.

There is a happy marriage between science and engineering.

When the two are at invariance with each other, who is right and who is wrong?

If the current state of theories cannot prediction simple observation correctly 100% of the time for all conditions and parameters one can describe, such as squat or transom ventilation, or even how to 'model' friction of a hull etc then is that the fault of the observation?

To assist the observation requires measurements. Such measurements can be good or bad, but without them, for most cases it is somewhat more difficult to state categorically the theory proposed is correct. That is basic Physics and metrology not naval architecture.

So where does that leave resistance/power predications?

I have tremendous sympathy for scientists those like Leo, whom spend endless hours trying to square this circle yet consistently come up against poor data to enable him (and others) to describe with a beautiful elegant theory expressed mathematically of what is being observed. As I noted before, this occurred to us where the tank test data was incorrect by a very wide margin and had to be rerun in another tank (2 more in fact) to establish why.

So, this leaves with:

This “experience” is where the NA diverges from the thinking of the scientist.

Why, because the naval architect has one more observation at their disposal that allows them to at least be more “confident” than scientists to state with a high degree of certainty; despite such flaws present in the “system”.

Sea trials.

On sea trails, the draught marks are taken accurately (after the hull has been built accurately via NC cut parts), so the displacement is known with a high degree of accuracy and consistently so. The only real “error bar” as such, is the method of measurement (there we go again). The engine power is known when running at full chat and at progressive rpms through the range, this is taken from strain gauging the shaft. Again, the “error bars” are to be consistent, the "independent" check is to be compared with the test bed data (since this can be one of the biggest sources of arguments when on sea trails). The speed of the vessel, at said rpms, is taken via several methods, timed measured runs of a fixed distance and also many use GPS when doing a very long run. Both provide consistently quantitative results to say with a high degree of accuracy what the speed attained actually is.

Thus, from all the tank test results the results are plotted and compared to see how close the two are of the sea trial data and tank test predications.

The more sea trials the naval architect performs and the more referencing back to tank test data, the more confident the NA becomes in future predictions. The NA knows all the parameters of their hull and design. The NA knows what true actual speeds were obtained. The NA may have an enquiry for a similar design with a slight modification..once eventually taken on trails, again knows the result. The more and more this is performed, trends appear and become very self evident. These trends indicate what at least based upon observations and knowing what has actually changed, indicate what factors really have an effect on the results.

So long as the trends are consistent time and time again, no matter whether there is any reasonable theory to indicate why, the NA shall always use, as noted here by PhilSweet, experience. The absolute is not necessary, that is the realm for scientist. If a trend can predict future events with a high degree of accuracy a speed/power (for a NA ie less than 5-10% can be considered acceptable), that is generally sufficient. Since the more data set for trends, and the more sea trails these ‘trends’ themselves become more accurate. But, here is the point, the NA is constantly juggling with the known variables at hand, from a design perspective, that alters these variables based upon their observations on sea trails. This is the difference between good design and poor design and is based upon experience.

In this instance, scientists and NAs shall never converge in their “what is most important” for power predications. Since one is focusing on the source data at its most fundamental level, the other upon the final result. The way each arrives at their conclusions is at variance with each other, for the aforementioned reasons above.

 

All of which is wonderful, but gives absolutely zero insight into the topic of the thread.

 

Any know of any observations from tests of the differences between hulls with volume shifted fore-aft but otherwise more or less similar? Do not need to be related to power prediction in any way.

 

Poor data and reliance on empirical claptrap was a major reason (my erstwhile colleague) E.O. Tuck gave up working on ship motions. Dreadful shame that as he, Salvesen and Faltinsen were real pioneers in their day.

Although I'm very critical of towing tank methods, I do think it would be worthwhile to conduct studies with some simple struts or modified Wigley hulls to assess the effect of LCB (and other parameters) on resistance.

The advantage of using mathematical hulls is that the geometry is easily reproducible by others, and some of the integrals can be done analytically. It also might be possible to isolate the effects of LCB from other parameters a little more easily. (That's a guess though!) L.J. Doctors' experiments with the "Lego Series" comes closest to what I have in mind, but most of the data and papers I have seen of his relate to transom sterns.

For those who don't know the "Lego Series" it is basically a Wigley hull with various lengths of parallel middle body. The aft half is made up of modular blocks that can be added to give different transom stern areas, including none. The shortest hull is a Wigley hull cut in half (i.e. with a huge transom stern). Drag and squat measurements are available for the series.

 

Since we seem to have arrived at a point where everyone agrees that longitudinal asymmetry can produce lower resistance under some circumstances, but that there appears to be no useful threoretical basis for explaining why the resistance is reduced, and therefore we have to rely solely on observations: what basis is there for assessing the reliability of observations from tank testing?

Note that here I am assuming that comparisons from sea trials are not available.

 

Here's a report using Doctors' Lego Series

 

Anyone else having problems opening the Doctors.pdf? I get a "could not be repaired" error. I'm using 8.1 reader.

 

Just checked...works ok for me.

 

No problems with it on my box. Mind you, I do keep my software updated. Reader 9.4.4 is the current version, and updates are free and automatic. So, why are you still on 8.1?

 

This discrepancy seems adequately explained by looking at the actual immersed curve of areas (including wave, trim, and squat effects) and the resulting LCB. If that curve of areas is formed to minimize wave resistance it will be for-aft symmetric.

If you take a hull that has been made to have fore-aft symmetry in it's immersed curve of areas at Fn = 0.25 it will have a fuller section ahead of the mid-section to make up for the wave hollow that occurs there for Fn = 0.25. The areas aft of the mid-section will be reduced to compensate for the wave peak that occurs there at this low Fn. Note that you have a fish-form, forward LCB hull.

Now if wave drag is minimized at Fn = 0.4 and the result is the fore-aft symmetric curve of areas at speed, the hull will have a less full hull forward to compensate for the higher and longer wave peak and then a fuller hull aft to compensate for the deeper wave trough aft of the mid-section. On this boat, taking the static curve of areas will give a swede form hull with LCB behind the mid-section.

So by taking the theroretical optimum and superimposing it onto the real world wave profile, trim, and squat; you can account for the apparent discrepancy.

 

The thin ship assumption is extremely restrictive in its application to fore-aft symmetry, even in theory. When the thin ship restriction is relaxed, we find shapes that clearly provide differing wave resistance going forward than going backward.

At Fn=.35, a hull that is deep and narrow between bow and midships, and wide and shallower between midships and stern (with beam at midships filling out the Kelvin angle) will have less wave resistance going forward. Note that such a shape can still have cross-sectional area that is fore-aft symmetric.

Likewise, a cruise ship is not thin relative to its cruising wavelength. In a typical modern design, the bulbous bow has destructive interference with the broad shoulders that fill in the hollow a half wavelength behind. A symmetric backward facing bulb would be a very poor shape for the stern (even ignoring flow separation), worse by far than a conventional transom.

 

Welcome to the forum, Richard!

Adding simple viscous effects (e.g. boundary layer displacement) also destroys the symmetry.

The idea of separating the total resistance into components is only useful up
to a point. There are many interactions that are routinely ignored, but can
be important for some applications. Once viscosity is included, even the
notion of wave resistance becomes a little muddy, and difficult to measure.

 

Are the thin ship assumptions necessary for same wave resistance when traveling in either direction? Or are "ideal" fluid" with irrotational flow, trim fixed, and a linearized free surface boundary condition sufficient? My recollection is that it's the latter but I don't have a reference readily available.

 

My understanding is that the thin ship assumption is necessary, even with pressure distributions. Leo, in his paper with Tuck http://www.cyberiad.net/library/pdf/tl01.pdf that he references earlier in this thread, asserts symmetry without proof, stating that "it can be shown" that optimality requires fore-aft symmetry. They then apply symmetry to pressure distributions with beam/length of .5, definitely not thin.

The same authors appear to contradict fore-aft symmetry in their studies of optimal configurations of trimaran hulls as part of http://www.cyberiad.net/library/multihulls/multipep/multipep.htm . The favored trimaran configurations have the center hull forward of the amas. While each of the hulls are assumed thin, the combination of the three falls outside of the thin ship assumption, and the result seems to come out asymmetric.

I would be astonished to see a valid proof of the optimality of fore-aft symmetry that did not require the thin ship assumption, under the most idealized of conditions, whether of pressure distributions or of underwater hull shape relative to the free surface under way. Of course, I have been astonished and wrong before, that's how I learn.

Wave propapagation, needlesss to say, is most decidedly asymmetric fore and aft. My intuition forces me to a preconception that optimal hull shapes, under idealized conditions, would require filling out substantial portions of the space within the Kelvin angle in order to acheive the greatest degrees of sought-after destructive wake interference. The commercial and military success of the bulbous bow, hollow waterline bow sections, and broad shoulders filling out the Kelvin angle at one half cruising speed wavelength from the bulb, tends to confirm my preconception (lots of innovation yet to be applied to the stern but it won't be hollow stern sections with a backwards bulb).

I am in no way trying to attack Leo here. I have learned much from reading his published works and his comments in this forum, and appreciate having effortless and free access to them.

 

Richard, there's no need to excuse yourself for questioning my
work. Unfortunately, I was only the mathematical monkey in my work
with Tuck - he was Australia's foremost applied mathematician,
and his untimely death shook many us to the core.

For proofs relating to fore-aft symmetry in Michell's Integral,
you should work through some chapters of:
Wehausen, J.V. and Laitone, E.V., "Surface Waves".
http://coe.berkeley.edu/SurfaceWaves/
(Thanks to those who put this magnificent work online for free!)
and then Wehausen's monograph:
"The Wave Resistance of Ships".
There's probably a way to use the calculus of variations (and
odd and even functions) to prove it too, but I haven't tried
that myself.

With pressure distributions, the equivalent of the thin-ship
assumption is that the pressures and waves are small, i.e.
the linearisation of the free-surface boundary condition is
justified. The length-to-beam ratio is not really all that relevant.
Incidentally, (inviscid) wave resistance predictions agree well
with experiments with travelling pressure distributions,
presumably because viscosity plays a very minor role.
We confirmed the optimality of fore-aft pressures in:
E.O. Tuck and L. Lazauskas
"Free-surface pressure distributions with minimum wave resistance",
ANZIAM Journal, Vol. 43, 2001,
http://www.cyberiad.net/library/pdf/tl01.pdf
(I believe you are already aware of that paper).

With multihulls, the individual hulls must be fore-aft symmetric.
Trimarans can have asymmetric fore-aft arrangements, e.g. in an
arrow formation, and they will have the same (Michell) wave
resistance travelling forwards as backwards.

Narita's towing tank tests confirmed this. It is
counter-intuitive, especially when you see that the vessel
makes different wave patterns when travelling forwards and
backwards. See:
Narita, S.,
"Some research on the wave resistance of a trimaran",
International seminar on Wave Resistance,
Kansai, Osaka, JAPAN, Feb. 9, 1976.

All the best,
Leo.