pitching control

I am confused about what causes and prevents pitching in a sailing cruising catamaran. I see this excellent article: Optimising Hull Lines for Performance https://www.graingerdesigns.net/the-lab-library-02/optimising-hull-lines-for-performance/

Which talks about two factors that mitigate pitching; asymmetry in the waterplane (which I understand to mean a beamy/wide stern, and a narrow bow waterplane in this case), and a high prismatic coefficient (which I understand to be a waterplane that is relatively beamy at both ends).

I don't have a good mental image of what will dampen pitching, I am thinking that a bow needs deadrise to avoid slamming but then should progressively but firmly increase in buoyancy as it submerges, pushing the LCB forward and setting up a couple with the LCG to counter the nose-down pitch. However, modern designs seem to show little flare in the bow topsides and sometimes use tumblehome or a reverse axe shape, so is pitch control really only achieved by the shape of the stern ?

Then my whole mental image of this gets scrambled when I consider it from the point of view of the hull passing through a wave which initially lifts the bow (so now less buoyancy there means less pitching) and then passes under the stern (more buoyancy there will pitch the, now unsupported, bow down unless all the weight is in the stern, perhaps causing the boat to heave more than pitch)

If I do a hydrostatic analysis and pitch the boat from stern-down to bow down, what should I look for ? presumably maximum "pitch righting arm" for minimum change in bow buoyancy.

I'm trying to achieve a safe, comfortable, easy to sail, reasonably efficient ride for a cruising catamaran that is no more difficult to tack than the average cat. Is part of the answer to move the weight away from amidships and toward the stern, make the stern wider (and maybe deeper too) to compensate, and then retain freeboard and some flare and overhang in the bow for safety and dryness but otherwise keep the bow fine near the waterline ?

 

Interesting article on reverse bows and pitching: Wave-Piercing Bows | Catamaran Brokerage Long Island, NY http://www.aeroyacht.com/catamaran-learning-center-2/wave-piercing-bows/
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In my opinion, this is one of the best ways to reduce pitching. Unfortunately I don't know the designer :

 

Keeping weight away from the ends, helps. Asymmetry between bow and stern helps with damping the pendulum effect, and don't forget that narrower hulls tends to more pitching.

 

This part at the first page is the opposite of excellent:

Prismatic coefficient is defined as diplacement volume / (lwl * maximum cross-section area)
Thus it is not dependent on:
1) cross section shape in the middle of the boat
2) how much volume there is at the ends
3) how beamy the waterplane is at both ends (as you, not the content of the quoted link, suggested)
It's very easy to design 2 different hull shapes, with the same position of center of buoyancy and same lwl and same displacement, where the one with a higher value of prismatic coefficient has less volume at the ends.

Pitching is caused by many factors, including in the order of importance:
- waves, their height and the frequency at which they are met by the hull(s)
- variation of aerodynamic forces, and the frequency of that variation.
It is also effected by the natural frequency of the boat, which in turn is effected by mass moment of inertia and shape and size of the boat near the waterplane.

The most effective way of mitigating pitching is the use of hydrodynamically lifting foil at the aft end of the boat moving at high speed. But that is not so effective in a sailing cruising catamaran which is not fast enough for it to work effectively without excessive area and the associated viscous drag. Lifting foil is also the only practical way for usual size sailing catamarans I know of, which reduces pitching in the inertial frame of reference. There are impractical methods including using a gyroscope.

Waterplane shape, and the changes of buoyancy due to that, can only mitigate pitching relative to moving surface of water. Ideal pitch damping relative to that would mean that the boat pitches at the very same frequency and magnitude as the surface does relative to the moving center of gravity of the boat, not that there is no pitching at all. Such remaining pitching could be very uncomfortable in some conditions, and in that case less such pitch damping would be much better.

That depends in which conditions you like to mitigate pitching. Effectively what you propose changes the frequency of pitching motion. If the natural frequency is moved away from the wave encounter frequency, then it is effective, otherwise it increases pitching.

The scientific approach requires first defining the conditions in which you intend to sail, and the performance of the boat in those conditions. If for example you will never sail fast upwind in a high choppy sea state, there is no point in mitigating pitching in such conditions and compromising pitching in other conditions.
The optimum shapes (if such even exists) are very unlikely to be the same for a 8 m lwl and 32 m lwl catamarans in the same conditions.

 

Thank you all for your comments.

To FastSailing's final point: looks like this site: NWW3 Product Viewer https://polar.ncep.noaa.gov/waves/viewer.shtml?-multi_1-latest-pacific-tp- may have the info I need on significant wave height and period. If I learn that the maximum wave period is around 15s, how do I turn that into a boat design, is there some simple relationship between center of water plane and center of gravity that I can treat as a pendulum length ?

 

No, but google up: "longitudinal metacentric height" or "longitudinal metacenter" or "longitudinal GM" to learn about natural frequency about transverse axis of a boat.
Then take into account that wave period means time required for a wave to travel 1 wavelength relative to stationary object, not relative to a moving boat, which is what you need. Going against the waves the effective period shortens, and going the opposite way it becomes longer.

For the design issue this might eventually help:
https://ia800202.us.archive.org/26/items/theoryofseakeepi00korv/theoryofseakeepi00korv.pdf
after some time spent on it I presume.

 

We need to be fairly careful here as all of what has been said is not exactly correct. Any periodic motion of a vessel in a seaway, like pitching, has three components that have to be managed. First is the natural period controlled by the mass moment of gyration, principally controlled by the mass distribution of the vessel and gravity. Second is the damping, mostly controlled by the hull shape, volume distribution of the hull and the density and viscosity of the fluid. Third is the forcing function, which is a function of vessel speed, direction, hull shape, fluid density and viscosity, and gravity. Because the third (the sea way encounter) tends to be the broadest, lowest, and totally unmovable response peak; and the first (radius of gyration) tends to be the highest, narrowest, and least moveable; that leaves only the shape and volume distribution of the hull for damping as a viable means to "tune " the hull. This is why you generally see weights concentrated amidships (force the natural frequencies down), narrow bows and flat floors aft (to force the damping up) so they don't overlap the relative high frequency of wave encounter.

FWIW, I would no longer use Theory of Seakeeping by Korvin—Kroukovsky for something like this. Dynamics of Marine Vehicles by Rameswar Bhattacharyya is a better text for this as ToS was written in the late 1950's as a stimulus for studies whereas DoMV written in 1978 references ToS and is a "how-to" cookbook that you can use to write your own code. (FORTRAN-77 anyone?).

 

The key is in the LCF and LCB location.

Pitching occurs about the LCF.
Heave occurs about the LCB.

The closer you make this distance the less and less pitching and coupling of the 2 motions you get.
If you consider a multihull extreme, like a Swath vessel, it's ideal hydrostatics has the LCB and LCF coincident with each other, thus, as a wave approaches, it just heaves, no pitching.

Thus if you design your hull that has a minimal coupling between the LCB and LCF in most conditions of loading, is a great start! But to do this in reality....aaahh..not so easy!

 

What?
1 kHz is higher frequency than 1 Hz. If you could change natural frequency of some boat regarding pitching from 1kHz into 1 Hz, would you force the natural frequency down or up?
Concentrated weights result a higher natural frequency, not lower for the same hull shape and displacement in the same fluid. In theory, perfectly concentrated weight reduces moment of inertia towards zero, resulting infinite natural frequency.

Wave encounter frequency for a small boat might be 0.01...0.1 Hz while the natural frequency might be > 1 Hz.
For a big ship going faster towards incoming waves, wave encounter frequency will be higher and natural frequency much much less than for a small boat.
Resulting wave encounter frequency > natural frequency (< 0.05 Hz).

Does Dynamics of Marine Vehicles by Rameswar Bhattacharyya take into account the different reference for damping for hull, and for foil or gyroscope?
Or does it incorrectly assume perfect damping by hull surfaces would result no pitching?

 

Heave is translational motion, and as such it's not about any point. All the points of a perfectly rigid object would have exactly the same velocity if no rotational motion would occur. Motion https://www.g9toengineering.com/resources/translational.htm

Pitching is rotational motion, and can be considered to happen about a reference point. But a perfectly rigid object has exactly the same rotational motion no matter what point is used as a reference. Changing a reference point will only change the amount of translational motion.

You can not separate motion of an object for translation and rotation components by using more than one reference point, LCF and LCB.

A big ship might not practically be a perfectly rigid object, but a small boat is certainly close enough to ignore any sagging or hogging due to seaway, when considering pitching or heaving motions. In structural analyses this is of course not the case.

 

Well, when I was racing, when sailing upwind we concentrated weight near the fore and aft center of the boat as recommended by many, many racing guru's to reduce pitching.
It worked.......

 

Indeed it is. But, you are only showing your ignorance on the subject by then stating this:

Heave is a pure vertical displacement of the vessel. As such if you were to place a weight at the bow, would a vessel displace in the vertical axis only….no…it would trim. Ergo, this is not pure heave alone. If you place the weight at the LCG, what occurs, it heaves - nothing else, just pure displacement about its vertical axis. Since the LCG and LCB are coincident - otherwise the vessel is not in equilibrium. Thus, Heave occurs about the LCG, a "single" point of reference.

Correct, and where is that reference point?
It is the LCF:



You seem to be unaware of both these simple characteristics of hydrostatics/dynamics of a vessel.
Are you a 1st year naval architecture student?

Again you’re showing your ignorance on the subject. Each motion has a different axis of motion and thus a different response, but is easily analysed by referencing its own axis of motion.

Sorry this is utter nonsense and a non sequitur.

 

Wrong.
If you add weight to the LCF, there is only heave motion. If LCB and LCF are not at the same place, adding weight at LCB (same as LCG as originally at equilibrium) will result the vessel being no more in equilibrium in pitch, resulting both heave and pitch motion.
Heave is translational motion, and thus does not occur about any point or axis.
Again you’re showing your ignorance on the subject of translational motion and rotational motion.

 

Of course, since for small boats, natural frequency is usually higher than wave encounter frequency, thus centralizing weight results even higher natural frequency moving it further away from wave encounter frequency, therefore less or no resonance.

 

You fail to understand an analogy in order to assist your understanding, but it appears to have gone over your head. Since in your zeal to post you’re throwing the baby out with the bath water as you’re failing to understand the purpose of the question what “design” is about and how to achieve the desired effects.

As noted:

The LCG and LCB must be continent, otherwise, the vessel experiences a couple and rotates, or trims, to align the LCG with the LCB, since the LCG and LCB must be coincident for a floating body to be in equilibrium. Therefore any lever between the LCG and LCB will cause a trimming moment. And since the moment to change trim, the MCT 1cm is determined from the GML – it is dependent on the LCB, ergo reducing this distance between the LCB and the LCF so that they are coincident results in just heave. But to design a hull form like this is not easy at all. Why do you think floating buoys are circular in shape….because the LCB and LCF are coincident, it just heaves! The Japanese even designed a RFS Swath, the RFS (resonance free swath) based on this simple principle. Since unlike the design of a buoy, a vessel with its LCB and LCF coincident is terribly difficult, but not impossible.

This is still nonsense and a non-sequitur.

And now you’re getting confused with natural frequency of the rigid body in air and the natural periods of motion of a floating body. The two are not the same.

Are you a 1st year student?