pitching control

Try to learn the basics before posting. Copying what I have wrote and presenting that as your own statement makes you look like a troll.

 

So, no understanding of coupled pitch and heave, no understanding of rigid body vibrations, no understanding of periods of motion and encounter etc etc etc...

And your eruladite retort is:

Gosh, such an intelligent reply. Full of knowledge understanding and experience....yawn

What a waste of bandwidth.

 

Nostalgic. That was the first thing I learned. Chapter II of PNA page 101 of the early edition. The new PNA has 3 volumes.

 

You've got to hand it to those Chinese junks with their bow and stern that temporarily take on sea to stabilize pitching, I suppose a sugar scoop does that to some degree.

 

The traditional ones had a porous bow. The bow was performed to increase the damping.

 

Yes, what ingenuity, I think the stern had the same in some , I wonder if sliding hatches were part of the design that covered the holes in fair weather, Graingers next big thing perhaps...

 

It is important to note here that a boat that is highly 'stiff' in pitching will have a fast and large response to pitching in waves. This is the same as a boat with high initial stability (in roll) having a fast, uncomfortable roll speed.

The reverse bow that you see in fast catamarans aims to reduce pitch stiffness, likely because it is high as a result of high prismatic coefficient*. Thus pitch response to waves is reduced which gives a smoother, faster ride in waves at the cost of increased risk of pitchpoling. Note that response to waves/external forces depends on the entire submerged shape, so both bow and stern (and everything in between) are relevant. The reverse bow still results in more submerged volume forward as the bow pitches down, just less than a flared bow.

LCB can be used to find equilibrium pitch angle for a given pitching moment (forward force at some height) and LCG. LCF (for inclined waterplanes) can then be used to find change of angle for a given change of pitching moment.

*I appreciate that this is a simplification

 

I thought the increase in popularity of the very narrow reverse bow was linked to the use of rudder foils to control pitch. Rudder foils pulling down the stern replace the less efficient forward volume lifting the bow, the resulting much slimmer bow offers less resistance and less likelihood of pitch poling. The use of forward foils helps even more.

Of course if the rudder ventilates or cavitates at the wrong time it can all go to hell very quickly.

 

I appreciate you are stating a simplification. However, it is overly simplified.

You correctly state:

So, where does a vessel get its high stiffness from??...its waterplane area.

In a reverse bow, or dreadnought type bow, the waterline length of the floating DWL remains the same. Which mnas the waterplane inertia remains the same, which means the pitch stiffness remains the same; everything else remaining the same



The only benefit, is the slight increase in waterline length.

In addition, the dreadnought type bow is much finer at the extreme of the bow, which means it is relatively unaffected by a passing wave much more so than a conventional bow - assuming a minor wave amplitude and wave length less than vessel length. Only once the passing wave is in a region of higher reserve bouncy will the vessel start to respond. So it has the "appearance" of slicing or cutting through a wave, this is merely a result of minimal to zero buoyancy at the bow, that's all. It does not change the pitch stiffness, as the waterplane area remains unchanged - with all other factors remaining the same.

The amount of added damping, when you calculate it and actually test it, is again, minimal to negligible.

 

I disagree that the pitch stiffness remains the same. Waterplane inertia is a simplification that assumes the shape of the waterplane stays constant for small changes in (pitch) angle. Given that the effect of a reverse or raked bow is to change the shape of the waterplane as angle changes we need a more nuanced approach. Consider the shape of the newly immersed wedge as the bow tilts down (or a wave impinges on the bow):

Thus for a given change in angle the raked bow will shift the LCB & LCF forwards more than the reverse bow, resulting in a greater restoring moment which we call stiffness.

This is a very good point that I had not considered.

 

Not saying (theoretically) there is none. However, have you actually gone through the exercise of calculating the pitch-stiffness of the before and after hull forms in the conditions you cite?

When you do, you'll realise, there is next to zero difference. This is also supported by endless tank testing.
What we "feel" and "think", from what we understand about the theory side, is reduced to just that a nice elegant theory of the mechanics, but in reality, plays no part.
Since the amount of actual buoyancy change in the fwd part of the bow is very small because the angle of entry is fine, hence how much actual real change in the WPA and ipso facto change in pitch stiffness is there, in terms of factual metrics.

So when you do go through this exercise (as I have many teams in the past) you'll see the movement of the LCB/LCF in, situations like that which you post is .....yup very small indeed....so minor its contribution/change to the pitch stiffness is negligible. But please, for your own education, prove this to yourself.

So, theoretically, yes one can argue there must be a change in the LCB/LCF owing to the change in shape, as there is, but this is not supported by the actual numbers of actual hull forms that adopt a change from normal to dreadnaught bow, noted above, under the same conditions, in percentage terms of a real cause and effect.

 

Why are you dealing in Hz and not omega? Making a longer period (i.e. omega2< omega1) means that omega 2 has a longer natural period. Reducing the radius of gyration while leaving the WP area the same is effectively increasing the damping which decreases omega and increases natural period.

 

Maybe a little late to comment on this thread, but when I look back to Pitbull’s original post (OP) and the comments that followed, I could not help but feel that the original question was still needing answers.

I personally agree with comments that pitching can be partly lowered through less symmetry …. first by making the ends quite different in section, as well as making the keel profile less of a symmetric banana shape, all as well explained by Tony (Grainger) in his article. Lowering upper mast weight helps too, due to a reduction in the mass moment of inertia.

But the OP raised some apparent contradictions for the writer, when he felt that increased upper buoyancy (or flare) should reduce pitching, while most modern designs show sides that are more vertical. So perhaps this comment will help to explain this.

The problem with vee’d bow sections is that when diving into a wave, their increase in buoyancy is too much! The resulting up-thrust throws the bows high into the air and then of course, the bows have to fall …now with so much added momentum that they plunge deeper than ideal, only to gain even more buoyancy to repeat the cycle over and over ... aggravating the pitching effect. If the bow sections are more vertical-sided, the bow is raised less and stays more horizontal, so reducing the pitching action overall. From practical experience, I have found this does indeed help. I have written about this before in a 2014 article for SAIL entitled by them as ‘Take a Bow’.

https://smalltridesign.com/pdfs/SAIL-take_a_bow article.pdf

Also, being as this thread also raised the debate on Vee’d, circular or deep bow sections, perhaps readers would be interested in the following article that clarifies my point of view re the advantages for the deep box section with more vertical sides, even though written for a trimaran. PBB had invited me to explain the unusually good performance of my hard-chine design after their sister publication WB ran tests and gave a very positive review on it. I think it will add some clarity to the attributes and choice of alternativc sections.

https://smalltridesign.com/pdfs/W17ProBoatOctNov2017.pdf

And to those not previously familiar with my website, please feel invited to explore the nearly 200 articles posted to date that are presented to answer many other quasi-technical questions about multihulls.

Mike at: www.smalltridesign.com

 

Wow, I thoroughly enjoyed this , although it was just slightly too technical for me to comprehend at my current understanding of naval architecture, it answered some questions and confirmed some hunches, thank you.

 

Thanks and glad it was helpful. The SAIL article was tweaked from an earlier one I wrote in 2013 and personally, I always found the original more useful and accurate.
(Despite better graphics and photos, sometimes editors just mess things up ;-). If interested in bow shapes, try this 2013 version
Reverse Bows — Pros & Cons https://smalltridesign.com/Trimaran-Articles/design/reverse-bow.html