# Parabolizing lines of existing hulls

Discussion in 'Software' started by Leo Lazauskas, Nov 15, 2009.

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### Leo LazauskasSenior Member

Here is a link to an unusual study done on "parabolizing" the
lines of vessels with extensive parallel middle bodies.

http://www.journalofoceantechnology...terlineParabol.pdf&article=True&vol=4&issue=3

If that link is too long, the article is in the latest edition
of the Journal of Ocean Technology. See:
http://www.journalofoceantechnology.com/CurrentIssue.asp

I really don't know what to make of the claims made in the paper. In my (mostly theoretical) optimisation work I have found that parabolic waterlines are often "optimal" from a total resistance aspect unless there are severe constraints on length, beam or draft for a given displacement.

When would it make economic sense to make such changes to existing vessels?

Is it really feasible to retrofit such changes on anything except small craft?

All the best,
Leo.

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### yipsterdesigner

they mention 15% optimising is possible but compared to what?
parabolising fluid dynamics helps but again, from to what?
awhile ago we discussed such an optimal hullform here
on ships i think the straight sides are worth something too
article mentions Michlet was used so guess you know best

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Had a scan through. The authors may have studied naval architecture, but clearly do not practiced it.

Their model #3, is running in a hump, (n=3) of the resistance curve. As such any modification would be beneficial.

But the main parameter for design, length displacement ratio, is shockingly low. If they changed the L/D ratio they would get significantly better results.

Their conclusion #2 and 3 is nothing new, just repeating what is well known in the 'faster vessel' naval architecture field. These two factors are beneficial whether one is using parabolic lines or not.

It says they used Michlet for their results. Correct me if I am wrong Leo, but Michlet is not for such low L/D ratio hulls shapes, nor transom style sterns. It surprises me they would used Michelt, knowing such limitations.

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### daiquiriEngineering and Design

I understand that the paper talks about the experimental work on parent hulls in towing-tank (pages 63-67). Michlet was used for preliminary calculations before the realization of the final optimized model (pages 67-69). The Authors claim that Michlet has indicated a possible resistance reduction of about 25%, which then turned out to be 20% during the tests (page 68), which is not bad (imho), considering that uncertainity of measurements in repeated tests was about 3%.

This hull form at first appears not to be very suitable for analysis with Michlet, because the waterlines of the rear part of underwater hull are blunt-shaped and because of the wet transom, but maybe it is not really so. After having read the paper "The Wave-Resistance of a Ship" by J.H. Michell, I believe that Michlet software's applicability is not so much related to the general geometrical parameters of the hull, as it is to the form of the flow streamlines around it. If the angle between streamlines and the undisturbed flow is sufficiently small in every point of the computational domain, the error produced should be small, or at least acceptable. The error should be proportional, among other things, to the number of points (or to the extension of areas) which do not follow this rule.

In this particular case (hull lines at the page 71), the critical areas appear to be at the bow and at the transom. The angle of entrance at the bow should be considered in the horizontal plane, and it doesn't appear to be high (just don't ask me to define "high" and "low"... I don't know, it is a matter of feeling in this case ). It is a pretty fine bow actually. At the rear portion of the hull, though the waterlines are blunt the streamlines will get curved mainly in the vertical plane imho, and if you look at them from that perpective they again appear to be sufficiently flat relative to the undisturbed flow.
Remains the problem of the wet transom, which is another story. I would like Leo to confirm or deny this intuitive consideration of mine.

And Ad Hoc, thank you very much for the very informative papers you have sent me yesterday. You have a pretty impressive library of technical papers over there.

Cheers!

S.

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Hi D.

I see what they have done and what they 'appear' to be saying (although I've only scanned it quickly). My point is, that have changed the hull form, rather than just changing the line curvatures.

Since in their table 7, the original hull has a Cb of 0.6, whereas B11p has 0.54. Keeping all 'things' the same; the length is the same, the draft is the same and the displacement is the same, but the beam has increased, the ratio of Cb's to maintain constant displacement, the Cb must be reduced.

So the form factors are different. It is not a case of just creating parabolic hull lines and hey presto. The parabolic lines created a new form factor. If they used curves lines or straigher lines etc, with the same form factors as a result, rather than parabolic, they would get the same result!

Hope you enjoy the read....i have some 1500~2000 tech papers scattered about in my library and on CD, so i have a few, half of which, i have forgotten i have them!

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### daiquiriEngineering and Design

Yes, I see your point and it does seem very reasonable.
It would be really interesting to hear what would Authors have to reply on that valid objection, if only they had left some address for contacting them...

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D
All they have really done, is what any naval architect all ready knows, or should know. That changing form factors has an effect....but they have gone, "wow", look what happens when you do this, as if no one knows. Only because they don't design. All naval architects understand this manipulation of form factors, since it establishes trends, that is all a NA does, looks to see what 'factors' have an effect and in what way. They just seem surprised...!!

As such, yes, would be interesting to hear what they have to say!

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### Leo LazauskasSenior Member

1. Yes, Yipster, parallel middles have some advantages: for a start, they are probably cheaper to fabricate, especially if more than one vessel is being built.

The possible 15% optimisation mentioned in the paper is relative to their unmodified baseline hull.

2. Calisal is a very experienced experimentalist and has used Michell's integral for over 30 years. He would be well aware of its limitations.

That said, I personally wouldn't trust absolute predictions of the wave resistance for such low L/D ratios, but I would be fairly confident of relative rankings predicted by Michlet.

On the other hand, as Daiquiri mentioned, the experimental confirmation of the estimated potential improvement is reasonable, but a bit of a fluke, IMO.

3. I agree that there is nothing really new in the observation regarding parallel middle body. If a hull has extensive parallel regions, it often has a less sharp bow and stern and it is well known that "shoulders" in the hull can kick up large waves. I seem to recall that this issue was even mentioned in early editions of PONA.

Incidentally, the energy lost by these "shoulders" should be evident in the free-wave spectrum. It is a very useful exercise to see at what wave propagation angles most energy is lost, and to modify the hull shape accordingly to reduce peaks in the spectrum. It's not easy to do manually, but Godzilla can be set up to do a lot of the work.

3. Prediction of the drag of transom sterns is very difficult. Daiquiri is correct that Michell's integral can be used for hulls with transom sterns, but care needs to be exercised.

Michell's integral depends on the longitudinal slope of the hull. If this is small (in most regions), then predictions should be reasonable.

What is small? A good measure is if the sine of the slope is less
than the slope in radians, i.e. sin(alpha) < alpha.

So, yes, Daiquiri, you could also say that the streamlines should be smooth, and their longitudinal slope should be small.

Michlet uses the offsets of the hull rather than the slope (as in Michell's paper) because inputting slopes is less intuitive and small errors in slope specification can produce large errors.

In early versions of Michlet I allowed users to choose a variety of transom stern resistance models but I removed nearly all of the choices because they are inconsistent. In their mathematical models, Couser et al, and Doctors and Day add small extensions behind the transom to simulate the effects of the hollow cavity behind the stern. They claim better agreement with experiments, but I would add, "sometimes". Sometimes they agree better, and sometimes they don't. In other words, they are not consistent.

I am completely unconvinced by those methods, as I have said a few times on this forum. I cannot see how a cavity ventilated to atmospheric can sustain a transverse pressure. It can't create waves in the same way as a solid body.

Wet transoms are even more problematic.

A blunt wet transom can be modelled, but it would be very inaccurate at low Froude numbers. I have seen several papers that use the "wet transom" formulation of the integral, but I sometimes suspect that the authors were either too lazy, or couldn't do the required (slightly tricky) integration
by parts to get the infinite hollow formulation of Michell's integral. On the other hand, at high Froude numbers the difference between the "wet" transom results and those using the "infinite hollow" results are not large. Maybe some people figure that the extra drag predicted by the wet
transom formulation accounts for some otherwise unexplained non-linear effects.

In recent versions of Michlet, the transom is assumed to be completely wet at rest. I also define a Froude number based on the draft at the stern, Frt, and a (user-specified) critical transom depth Froude number, Frtcrit.
Frtcrit = 2.23 corresponds to the only theoretical result available at present.

In my model, if Frt >= Frtcrit then the transom is presumed to be running completely dry; if Frt < Frtcrit, it is partly wet and partly dry. A linear interpolation is used to estimate how much of the transom is wet. The wave resistance of the wet portion is estimated using the "wet" formulation. An infinitely long parallel-sided hollow (which makes no waves) is assumed to trail behind the dry portion.

In other words, it's a complete hack!

Michlet also includes the so-called transom stern hydrostatic resistance which is due to the loss of pressure on the dry portion of the transom.

Personally, I prefer using the infinite hollow method plus the hydrostatic resistance. If there are significant differences with experiments then I assume that they are due to a variety of effects that Michlet cannot hope to predict, such as wave-breaking, splash and spray, and boundary layer separation.

4. And now a question for you "practical" types...

When a heavily-laden planing hull with a big transom accelerates from rest, it
often creates a very large wave behind it. Is this primarily due to the wet
transom? Is it more to do with the wake created by the props? Or is it
because the vessel is in shallow water when it starts?

All the best,
Leo.

All typos and errors are due to loss of sleep during the hottest November
in Adelaide on record. And 41C for the next couple of days!

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### Leo LazauskasSenior Member

Calisal was last at the University of British Columbia (after stints at Berkeley and the US Naval Academy). Goren and some others were from Turkey.

I've attached an example of some of their other work.

Personally, I have no real interest in clarifying the points in their paper. I'll leave that to you "practical types". I have mathematical hierogyphics to play with

Cheers,
Leo.

Last edited: Aug 12, 2015
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Leo
"..When a heavily-laden planing hull with a big transom accelerates from rest, it often creates a very large wave behind it. Is this primarily due to the wet transom? Is it more to do with the wake created by the props? Or is it
because the vessel is in shallow water when it starts?.."

Hmmm...when you say heavily laden, does this imply too heavy to climb over the hump, or just a 'colourful' turn of phrase? (ie just a low L/D ratio)
Monohull...what L/B ratios are you thinking..since this influences the answer
Are you only considering props?...such as surface props or submerged props?
Are you assuming the 'wave' system is from the stern only..or are you trying to separate each wave system?
When you saying the transom is wet at the beginning, you imply this is not because it is at rest, but already moving?

11. ### Guest625101138Previous Member

Leo
I doubt if there is any merit beyond relatively small craft. Larger cargo vessels are essentially a box with somewhat streamline ends.

Loading and unloading terminals are gradually increasing in size of vessel that they can handle as there are savings associated with economy of scale however the increasing size is gradual. (Melbourne has recently endured the pain of dredging Port Phillip to maintain its ability to handle modern cargo vessels)

The cost of dredging berth pockets and channels to accept deeper vessels is a factor that limits draft.

The reach of loaders and unloaders is a factor as increasing reach requires heavier machines, which, in turn, require heavier wharf structures. Hence there is significant cost associated with increasing beam. It would be wasteful to have one short section of the vessel setting the reach of machines rather than most of the full length. Also think of what would need to be done to the quay line to accept vessels of varying length and curvature. The fenders on exposed water berths would need to have significant adjustment so breasting loads could be distributed.

Other major factor is the canals. I know there is talk of widening the Panama Canal but even if it does happen there will still be a desire to maximise the volume within the available dimensional limits.

So I do not see any merit in considering the lower drag lines for anything but relatively small vessels. Certainly not up into the size of the smaller bulk carriers and upwards. Oil tankers could be an exception as these can have more adaptable loading and unloading set ups - but is the benefit going to be noticeable in their operating regime!

Actually it is interesting that you bring this question up because I was recently asked to determine the best hull shape for an origami pedal boat with parallel sides - so reverse of the topic in question. Aim is to do an infusion layup in one go for the entire hull as a single flat panel with four folding lines and taped ends. I can get drag within 10% of a hull with parabolic lines so speed difference of 3%.

Rick W

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### baeckmoHydrodynamics

Leo, on your accelerating boat: Without diving into the math of it, I think it is mainly a result of the transient state. We have an analogy in pipe flow. Here we see pressure waves set up by a change of state; f.i. a valve closing generates a positive pressure pulse travelling upstream and a negative going downstream, both propagating with the respective speeds of sound in the fluid.

If the rate of change is faster than the time for the wave to reach a substantial area change, being reflected there (positive or negative, depending on status of reflecting point), and back to its origin, then it will produce its maximum pressure peak amplitude [pmax=density*(speed change)*(speed of sound)]. A "slower" change of speed, ie taking longer time than the critical travelling time, will result in a lower pressure wave.

With gravity waves, as you guys are working with, the surface amplitude is a manifestation of static energy, just as pressure will be in a closed system. There is also a typical length factor; WL length, so the necessary determining ingredients are certainly present. The difference is that the critical propagation velocity within a pipe is varying with sqr(elasticity/density), while the surface waves change with a length factor.

If the hull is accelerating at, or above the critical rate, it will be "locked" into the solitary wave's max amplitude until the rate of speed increase is levelling off as it reaches its final speed.

You also said "highly loaded"....If that means that the forward hull sections are full and buttocks increasingly convex, there will be a negative pressure on the hull surface, pulling it "nose down", increasing the total amplitudes. We have a fleet of planing pilot vessels in this region, all characterized by high bottom loading. They all show this nose-down attitude at about 8 to 10 knots. We studied this phenomenon long ago when looking into an accident where one of these vessels was trapped within the wave system of a bigger vessel, when separating after having picked up the pilot. The crew was not aware of the attraction forces and applied the wrong departing procedure, resulting in the loss of one crew member.

A slight off topic (?) note BTW: Speed of sound in clean water is ~1500 m/s, but even a small mix of free gas will reduce this speed substantially. 2 % free volume (as recorded from oceans, will result in a propagation speed of 110 m/s if the bubbles contain air, and 69 m/s if they contain a mix of air and water vapour, as in the state of incipient cavitation. With 10 % by volume, as when ocean water is accelerated into a propeller or water jet, the speeds are 53 and 33 m/s respectively. This means that the machine is partially operating in a high subsonic or transsonic state, where compressibility effects have to be dealt with. Simple numerical calculation methods will fail due to this, their basic application range beeing below Mach 0,5.

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### daiquiriEngineering and Design

Damn!
I feel like a *******. I have never thought of such an obvious thing. Knowing (from readings on ecology) how important ocean waves are for the aeration of sea water and for the support of sea-life, it becomes pretty obvious that the considerations you have done are very important when treating both slamming loads on hull and flow around prop blades in rough seas. Yet, I've never thought of it, dammit...
I'm an ignorant. It is such a great and priviledged condition - lets me learn so many new things every day. Guess that's the beauty of life!

The figure n.1 in this work looks impressive:
http://www.iahr.org/publications/assets/jhr38-5/Zhao_Li.pdf

P.S.: "You must spread some Reputation around before giving it to baeckmo (or Leo L.) again." is very unfair.

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### baeckmoHydrodynamics

Calma, calma per favore!! The beauty of life is the intelligent interaction that makes 1+1=3!

When talking about slamming, there is some russian research on the consequenses of free gas on bottom slamming, sorry I lost the guy's name, it began with a K.... . I'll see if I can find the writer for you if you are into the subject.

As an example, we have managed to modify the inverted V hull in order to reduce slamming, by deliberately introducing forward hull lines that produced a liberal volume of foaming spray into the tunnel section.

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### baeckmoHydrodynamics

Aah, D, I think the name is Korobkin. I'm in a rush right now, but will search more later.

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