# Hull Asymmetry and Minimum Wave Drag

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, May 28, 2011.

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Indeed. A naval architect requires trends not absolutes.

But, for your understanding that is insufficient, the theory and science side requires greater depth and understanding the limitations.

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### Leo LazauskasSenior Member

As Ad Hoc said, we could go in endless circles here.
I also agree with whoever said BL thickness isn't worth considering.

I offer the attached as something to point at while discussing
this topic.

In the note I looked at three 5.72m long, 100kg displacement kayaks with
different shapes.
"Symmetric" is fore-aft symmetric; "Swede" has the widest section
aft of centre, and "Fish" has its widest part forward of centre.
(Waterplanes are formed using parabolas.)

In the "Static" attitude, all hulls have the same skin-friction because
they are the same length and have the same surface area.
"Symmetric" has lowest wave drag. That's Michell's thin ship theory
at work. It's nice to see confirmation via calculation, though

In the graphs, squat is shown as the change in position of the bow and
stern. Positive values mean the bow (or) stern are higher than their
static (i.e. level) position.

Including squat has the following effects...
"Fish" has the lowest wave drag because it becomes more symmetric as it
squats. "Symmetric" loses its symmetry, and "Swede becomes even more
asymmetric than in its static attitude.

I'm not sure why a forward LCB might be "optimal" for one range of Froude
numbers and then a more aftward LCB might be better at others. However,
there are some crossovers in the graphs that could offer some clues.

I'm busy atm, but I'll stick my nose in again later.
Leo.

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### Leo LazauskasSenior Member

Attached are a few extra graphs that might be illuminating,
or they might muddy the waters further.

For those that prefer Froude numbers, a speed of 3m/s for the 5.72m long
kayaks corresponds to F=0.4; 3.75 m/s => F=0.5.

The first two plots show the shift of the LCB and LCF as speed (and squat)
increase. Note how "Fish" starts with LCB and LCF bowwards of centre and
ends up with both aft of centre.

The next two plots show the sinkage force and the trimming moment.
(Ad Hoc prefers to think of squat in terms of changes in buoyancy;
I prefer forces and moments, but we should end up with the same result).

As you can see, the sinkage force is essentially identical for all three
hulls. The trimming moment (about the hull centre) is significantly
different for speeds greater than about 3.5 m/s.

The last graph is the height of the wave at the stern.
The height is positive for speeds below 3 m/s, and increasingly negative
for higher speeds. The results coincide with Ad Hoc's view that the stern
"sinks" at higher Froude numbers. Viscosity would tend to damp out the
wave at the stern.

I do not agree with Larson's interpretation that the boundary layer
effectively lengthens the hull as far as wave-making is concerned.
A BL cannot sustain a pressure and therefore it should not be viewed as a
wave-maker. The BL, after it passes the stern, is not a rigid body with
clearly defined edges. Rather, it tends to diffuse and spread out as
distance from the stern increases.

Leo.

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• ###### more_kayak3.pdf
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### philSweetSenior Member

One way at this is to consider the different traditional fleet designs and how and where they were used.

There have been some interesting studies of traditional fleets of fish boats regarding this.
Historically, there were quite a few traditional "cod headed and mackerel tailed" types, but they have mostly been displaced by the CoB aft boats now. Someone analyzed the locations where the CoB fwd boats still competed and suggested they all had a common weather situation. (They all operated off a lee shore with regards to the dominant weather? I can't remember.)

If this is so, they would be returning loaded in the lee of land and presumably less of a seaway. Cod headed boats have always been regarded as easily driven. No idea where the study came from; It must have been 20 years ago when I read it.

And just because I like to look at things *** backwards, consider the following proposition-

The boats don't have an aft CoB so much as it has been found that extending the bow out to make it a bit finer has certain advantages. Take away the seaway or chop and you would probably shorten it up, as opposed to shift the CoB fwd.

The only steady state hydrodynamic consideration I can think of would be due to the propellers. The props certainly influence the wake of ships and can be designed to interfere in the most productive way.

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### DCockeySenior Member

Leo, how are you defining LCB? Presumably it's not the location through which the vertical resultant of the hydrodynamic forces pass if the it moves. Or are you constraining trim and then determining the corresponding LCB?

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### Leo LazauskasSenior Member

All calculations are relative to midships in the static position.
i.e. bow is at x = -L/2, stern at x= L/2 and midships at x=0.

The equations for the calculations can be found in the report at:

That might help you to see the interplay between LCF, LCB, waterplane area, and the longitudinal moment of inertia. (At least for thin ships with small values of trim).

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### DCockeySenior Member

In the initial post in this thread I used LCB in the usual sense, the longitudinal position of the center of the immersed volume of the boat determined using the static waterline. LCB is an indicator of the fore/aft distribution of the distribution of the immersed volume.

A fundamental principal of equilibrium of a boat is that at rest the LCB must be in the location as the CG. This is a result of the condition that the net moment about the CG must be zero.

When a vessel is moving the immersed volume changes because the free surface changes, ie waves form. Also the pressure distribution over the hull surface changes from simple hydrostatic; it is no longer simply proportional to the depth from either the undisturbed free surface or even the free surface of the waves. This difference can be considered as the hydrodynamic pressure.

Leo, on page 5 of http://www.cyberiad.net/library/pdf/tsl01a.pdf, gives the equilibrium conditions for a moving vessel. On page 6 he expands it for small amounts of sinkage and trim in terms of the center of the waterplane area, center of floatation, and moment of inertia of the waterplane area. From these equations for sinkage and trim in terms of the hydrodynamic vertical force and moment are derived. It should be noted that the hydrodynamic force and moment are defined only in terms of the vertical components. Also viscous forces are negelected.

On page 7 there's a comment that "the longitudinal centre of buoyancy (LCB) and vertical centre of buoyancy (VCB) are calculated for the hull in its static and squatted attitudes." No equations or definitions of LCB are given. Static is simple, the usual definition of LCB. Presumably the LCB in squatted attitude is the center of the immersed volume including the changes due to sinkage and trim, which would correspond to the location of the "hydrostatic" portion of the vertical force acting on the water. What isn't clear is whether this is the volume beneath the static freesurface, or the volume beneath the free surface including waves.

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### DCockeySenior Member

I'll emphasize that my original post was about wave drag and hull volume distribution, using static LCB as a way to characterize volume distribution, and the possibility that sinkage and trim account are contributors to different volume distributions providing reduced wave resistance at different Froude Numbers.

Last edited: May 29, 2011
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Well, in a way it is both. Easier to see in this sketch. Same hull 3 different wave profiles:-

First static…the hull is in equilibrium. The second, a wave generating a bow up trim, the third a bow down trim. All owing to the wave profile on the hull, and thus what buoyancy this profile produces. This is then the new LCB, in that condition with that wave profile. The couple between the LCG and LCB produces the trim.

No. The sinkage and trim arises from the fwd motion of the hull creating a pressure wave. The wave is created first. Without the wave, there is no change in attitude. The volume aspect only contributes to the slenderness ratio which affects the residuary resistance. The hull volume distribution is just the location of the LCB. The LCB does not affect the slenderness ratio. You can take the same hull and reverse it...same hull, same L/D ratio..but the LCB location has now changed.

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### DCockeySenior Member

Your sketch shows the vessel in the original, static attitude without sinkage or trim. Leo describes the LCB as "calculated for the hull in its static and squatted attitudes". So what he calculated is different than your sketches.

Not sure what the relevance is of whether the waves or the change in attitude comes first. They are synergetic and affect each other.

There was a mistake in my statement which I'll correct. Meant to say "using static LCB as a way to characterize volume distribution".

I didn't say or imply anything about slenderness ratio or L/D ratio, just the fore/aft distribution of volume as characterized by static LCB location.

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I’m not sure you’re reading the sketches correctly. I left the hull in the same attitude as the static, for each wave profile. Simply to demonstrate, prior to trim and sinkage, where and why it occurs. I could have drawn the other 2 images in their final attitudes with the combined sinkage and trim, the result is the same either way. So I can only interpret your statement as you’re still not clear on how this mechanism occurs.

Again, I think you’re missing the point.

Take a short fat hull, with the LCB at 5% aft midships. Take another hull, same displacement, but very long and slender, with the LCB at 5% aft of midship. Slenderness ratio is the key to understanding all this. But it appears you’re either dismissing it, or assuming some other mechanism is at play, or fail to appreciate its significance…im not sure?

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### DCockeySenior Member

You left the static waterline unchanged relative to the boat in your drawings. My question for Leo was whether he calculates the "moving" LCB by:
1) Integrating over the dynamic, hull surface of the boat in the new attitude with sinkage and trim below the surface with the waves.
-or-
2) Uses a linearizing, leading order assumption, and integrates over the hull surface in the new attitude with sinkage and trim but below the static free surface.

Either yields a "LCB" which will generally be different than the static LCB.

I can only interpret your statement as you are considerably underestimating what I do understand. I do understand the fundamentals of sinkage and trim. I did learn something in graduate school studying hydrodynamics.

I do not disagree with your statement. But it's not relevant to my original question.

My original question was about what are the mechanisms/reasons which cause a volume distribution with the static LCB not at mid-ships to generally have lower wave resistance than one with static LCB at mid-ships, with other paremeters such as displacement, L/B, L/D, Cp the same? In other word static LCB changes but L/B and displacment do not.

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### DCockeySenior Member

Attached is a sketch illustrating the two alternatives for calculating the "moving" LCB. Top is the static condition.
Other two rows are two different speeds.
Left is the calculation done using the the free surface with waves as the upper bound.
Right is the calculation done using the static waterline as the upper bound. This uses a a "leading order" assumption.
Both have the boat in the attitude corresponding to the speed.

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With respect, I don’t think you learnt as much as you perhaps think. You’re still either over thinking this or fail to grasp the simplicity

It really is very simple. Length-displacement ratio (slenderness ratio) and Fn. I really do mean Fn and not speed.

Take a box hull of dimensions say 10m long, 2m wide and 1m draft. With the LCB at midships. Tow the vessel long the longitudinal axis. You obtain a resistance of X.
Now rotate the hull (roll), so the draft is now 2 and beam 1.0m. Tow it, you get a resistance Y. This is similar to X.
Now rotate the hull about the midplane. So the hull length is now 1.0m, at 10m wide and 2.0m draft. The resistance is now Z.

The length displacement ratio for the first 2 are identical. The L/D ratio of the last is vastly different from the first two being towed. Same hull, same displacement, and same LCB. The resistance for the last is massively higher than the first two. The L/D ratio….nothing else has changed.

The simplicity of understanding appears to be lost when also comparing hulls at different Fns. What is true of one hull, call it A, at a low Fn, as being described as “optimal”, is no longer valid at a higher Fn, another hull shall be. That “new” hull, call it B, that is optimal at the higher Fn, is not “optimal” at lower Fn of the original hull A. So hull A and hull B are each “optimal”, but both at the same time. Why…this again goes to your understanding of the hull form and how it relates to residuary resistance across Froude range and the L/D ratio. Froude = waves!

So, let me throw this one back at you. Have you gone through the process of desiging a hull before??

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