Examples of wave piercing hulls, please?

Well given that this assumption is roughly correct, (which it is if you actually calculate them values, which I have many times) how does this affect the natural period of pitch?

As for the rest of it, you’re getting ahead of yourself again.

So if we can now say the denominator is barely change, what about the numerator??

Well, if you calculated the IL and IL.avm, the values here too, are barely changed by the addition of the WP bow. (I’ve done the calc’s in the past..if you don’t believe, please try the calculations yourself).

This is assuming the WP bow is no more than 10% of the LWL and has minimal buoyancy; which is pretty much true for them all.

Thus, with very little change in the values of the numerator and dominator, what has changed….er…nothing! Therefore the natural period of pitch is pretty much unchanged from without a WP to one with a WP, with everything else remaining the same.

Follow so far??

 

Is it correct that the formula above is based on an assumption of small amplitude ocillations for which the instantaneous waterplane shape is sufficiently close to the static waterplane shape?

 

No.

But true for small angles of inclination. Since the resorting force is based upon an assumption of little or no change at small angles of inclination.

 

Well there is an assumption thats not adequate to draw conclusions from. A small vessel lets say under 40m, with a wp bow vs conventional bow, there would be large differences in the restoring force in moderate seas. Especially at supercritical periods at high speeds, i don't see how your reasoning applies adhoc?

 

"Small amplitude ocillations" when pitching is concerned and "small angles of inclination" appear to me to be equivalent.

I assume that "assumption of little or no change at small angles of inclination" means an assumption that the ratio of restoring force to angle of inclination has little or no change at small angles of inclination, not the restoring force itself.

 

Yes you can. This was the whole purpose of “playing” as you put it, but now the act has closed the stage is empty you’re crying foul??

Either you understand the mechanisms that influence and directly effect the natural periods of roll/pitch/heave or you don’t. If you do, then how does what you “feel” or “think” changes the facts? Just because it may not align with your personal feelings and thoughts does not change the laws of physics!

Please explain how so?

 

Correct.

 

What are the limits in wave height and wave length/period relative to size and other characteristics of a vessel to using linear assumptions in estimating a vessel's response to waves?

 

Aahh..that's the million dollar question!

We can make general assumptions and indications, and easily calculate the natural periods of roll/pitch/heave and verify them with model tests. However, when encountering waves and when these waves are approaching resonance (i.e. the ratio approaches unity) the angles of inclination fall outside the limits of applicability, which is why model testing is required to obtain the RAOs.

 

What if the periods of encounter with the waves is away from the natural periods?

For periods of encounter considerably longer then the natural periods I would expect the vessel to behave in a "quasi-static" mode which might be described as "riding over the waves".

For periods of encounter considerably shorter than the natural periods I would expect the amplitudes of roll/pitch/heave to decrease with decreasing periods of encounter.

 

When presenting RAOs, the usual format is the have the ROA response on the Y-axis and the wave frequency on the x-axis. Some sometime use the wave length/ship length as the x-axis, but this doesn’t show the whole picture, hence common to use the wave encounter frequency for the x-axis.

The RAO only describes the relative non dimensional response. This response needs to be converted into an acceleration. Thus, whether one “considers” the response to look like “riding over the waves” or not, the actual vertical acceleration is the appropriate measure, not the visual imagery.

This is not true across all vessels. Take a SWATH for example. Its heave response is pretty much unity at low frequencies of encounter, when tuned correctly. Thus a wave of 1.0m shall result in a 1.0m heave. BUT, the vertical accelerations, i.e. once the response is converted into motions of acceleration, the value is low. So a heave response of a SWATH will be different to that of a catamaran, to the point of looking very bad, yet the vertical accelerations shall be very different indeed, the swath being superior. This is the difference between “contouring” and “platforming” behaviour. Thus it is all type specific and requires investigation.

 

My understanding is using the RAOs and the frequency domain usually implies there is a linearity assumption, either implicit or explicit.

I agree that acceleration is usually the appropriate matter when occupant comfort is concerned. For frequencies considerably lower than the natural frequency the acceleration would usually be proportional to the frequency.

The "riding over the waves" visual imagery is similar to the description Faltinsen uses of "a cork floating on the water" (Hydrodynamics of High-Speed Marine Vehicles, p259).

Wouldn't the SWATH have a considerably lower natural frequency in heave than a conventional catamaran? Also lower in pitch and roll?

 

He simply uses this analogy to describe the heave response only; to understand the meaning of the graphic representation shown in fig.7.34. Thus, how do you define “riding over the waves”?

It all depends how it is tuned and the size of comparison of vessels, but generally yes this is true.

 

Adhoc, what a load of clap trap... physics? You are adulterating the physics with your assumptions and simplifications using static equations... and you dont even realize it?

I played the game your way, and i reject that your simplified formula is adequate at predicting the motions as it ignores the above waterline differences of a WP bow vs Conventional Bow. The damping and exciting forces are also different, and in reality the hull inertia and moments would also be different due to the larger geometry of a conventional bow.

I submit the following RAO analysis for 2 identical 90m catamaran hulls in terms of below waterline shape, mass distribution etc... everything is identical except the topsides were flared out into a slightly overhanging bow with more conventional shape - so to put it in your terms, the box had more volume up front... or the buoyancy distribution ABOVE the waterline was different.

The WP hull has a typical WP shape with reduced bouyancy bows typical of what weve seen by many of the large high speed ferry builders like incat crowther etc. The models were given identical sea states, namely a head sea of the JONSWAP standard, with 4m swell and 10s period, and a model speed of 40kts. The natural period can be identified with the peak RAO response for those that do not know...

So first the WP hull;


And the conventional hull;


Seems like a considerable difference to me despite being hydrostatically identical...?

 

Oh dear, I see I’ve hit a nerve!

Please show me where the natural period of pitch, which I posted above is incorrect.

See that’s where you’re showing your ignorance on the subject. Which is why you’ve resorted to the diatribe. It does not. It assumes for small angles of inclination.

For contribution of ABOVE water, that is referring to the restoring force. The damping force is not even mentioned (we didn't get that far )…which also needs to be taken into account. The exciting function is the wave, nothing else!!!...so you’re now saying you change the wave from one vessel to another…aahh..i see now..you’re cooking the books to make one hull look better. In your zeal, you’re rushed head first like bull into a china shop! So I see no need to try and explain further as you reject the known and accepted equations of motion, and must have come up with your own. Which I am very eager to see presented. So, please do

If you’re going to just plug numbers into a program and assume they are correct how on earth will you ever learn? So, ok lets play ..this is fun.

With a 10 sec period this gives the wave length of 156m. At a head sea condition the period of encounter is 2.24rads-1, or a frequency of 0.36hz.

Firstly.
Looking at your first picture, this is about the same thus that is correct.

However when looking at the second, the encounter frequency has changed! Hmm..so the vessel is either going faster or the wave period has changed. Therefore there is a difference in basic input parameters between the first and second model, thus not credible.

Secondly.
The graphs shows the pitch and heave to be coincident, this is also incorrect. This is impossible with a catamaran of this size, WP or otherwise. Again your input data is incorrect.

Thirdly.
The first graph, shows a response of 6.5 times in heave!!! So you’re getting a heave of 26m…wow!!!....and in the second graph a heave of 40m…wooaahh!!..again, not credible.

Forthly.
The natural period of heave for a cat of circa 90m is around 5.0-5.5 seconds. Your first graph indicates it is around 2.8seconds. Again, this is the value one would expect for a 20m cat, thus not credible input data. The data is also very different from the second, which indicates a heave of 4.0seconds. So adding those small bit which you initially agreed makes little difference, SUDDENLY makes a HUGE difference. Again, not credible.

You can pontificate all you like, but it won’t improve your understanding of motions and seakeeping