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[30 Mar 01] The seakeeping performance of fast ferries is often illustrated by way of graphs of RMS vertical acceleration levels (typically expressed in g's) versus motion frequency for particular sea conditions. To illustrate this I am including such a plot as obtained from a Rodriquez brochure for the RHS 160F series of surface piercing hydrofoils. As can be seen from the graph, the acceleration levels of the hydrofoil (presumably at its CG location) are indicated for a range of relative headings to the waves for a frequency range from 0.1 Hz to 8 Hz. On top of this are indicated the limits for 10% motion sickness (ie the MSI level, although exposure period is not indicated on the graph) and also ISO limits for human exposure to vibration at higher frequencies. I would like to ask how these graphs are generated as it is not clear to me exactly what they are illustrating.
Real ships operate in irregular waves where there is not a constant encounter frequency or wave height with every successive wave which is encountered by the ship. Only in model tests can regular waves with a single height and period be generated to establish the performance of model boats or ships in under idealized regular conditions. The Rodriquez graph suggests the data is for Low Sea State 6 seas (Significant Wave Height of 4m or more but well less than 6m). As this is an irregular seaway, I am not clear of the meaning of the unbroken plots of RMS vertical acceleration over the large range of frequencies from 0.1 Hz to 4 Hz (corresponding to encounter periods from 10 seconds down to 0.25 seconds) that are given for the craft at various different relative headings to the wave direction. It seems to me that it may be some sort of de-composition of the irregular motion data from sea trials back into a response for a series of theoretical regular wave conditions? If that is the case, then what is the meaning of comparing these ship response curves with the various Motion Sickness Index (MSI) or ISO vibration limits?
What I would have expected is that each run from sea trials in a particular seaway would generate a single data point only on the graph of RMS acceleration versus modal encounter frequency. Runs into head seas in a given seaway would have a higher modal encounter frequency than beam seas which in turn would be higher than the encounter frequency for runs in following seas where the ship and waves are traveling in the same direction.
I have only used the Rodriquez graph as an example to illustrate my uncertainty. Various designers and builders of fast catamaran and monohull ferries have used a plot format almost identical to that of Rodriquez for their hydrofoils, hence there must be a logical explanation of the interpretation of such graphs. I would welcome a reply which helps to explain it. My understanding is that the original tests on volunteers in a test rig to establish trends in the occurrence of motion sickness were performed at various regular frequencies of vertical motions. I have never properly understood how the jump has been made from this data to the case of irregular vertical motion exposure although I am familiar with the formula that should be used to calculate MSI levels for irregular vertical motions such as in a real seaway. Can anyone give suggested references which will also help to clarify this for me? -- Martin Grimm (email@example.com)
[1 Apr 01]Here's my take, based on reading Vol. III of "Principles of Naval Architecture" - maybe some of the NAs out there can fill in or correct this:
- The graphs you're looking at are wave response spectra, not the response to the boat to a particular set of waves. These are really averages over all random seas. Note that the units are RMS g's - the average of the acceleration squared - which is much like a standard deviation.
- There are idealized wave height spectra which are based on oceanographic research. Typically these show the wave height-squared vs. frequency for different sea states or wind conditions (assuming the wind has been blowing for a long time over a wide area). There are even specialized wave height spectra for different parts of the world, such as the North Sea. These spectra are for regular waves, in which all the waves are marching in the same direction.
- In addition to the wave height spectra, there are also wave direction spectra which account for the fact that the waves in a random seaway can be coming from a variety of directions, but there will still be a direction from which most of the waves are coming. So when you multiply the wave height spectrum by the wave direction spectrum, you end up with a composite spectrum for a random seaway as a function of both wave length (or frequency) and direction.
- I would guess the plot you've shown is probably based on a wave height spectrum for an open ocean seaway with a significant wave height of 4 m (the average of the highest 1/3 of the waves) - the plot is labeled "Sea S. Low 6", and a sea state 6 would have a range of 4 - 6 m with an average of 5 m. It could also be from a random seaway with the wave directions distributed in, say, a cosine-squared fashion about the dominant direction. This defines the operating environment.
- For a given boat, one can calculate the dynamic response to a given wave of a given size from a given direction. If the boat is subjected to the same wave for a long time, the boat response will settle down to being a sine wave of the same frequency but possibly a different amplitude and shifted in phase (the peaks of the boat response won't occur at the same time as the peaks in the wave). Above a certain frequency, the boat will be increasingly unresponsive to the wave because it is too massive to follow it. At very low frequencies, the boat will follow the wave almost perfectly and the boat response will be the same as the wave. In between, there may be a resonant frequency at which the boat's response will actually amplify the wave. This response of the boat to waves of a given frequency is given in terms of response amplitude operators, or RAO's, which are the ratio of the size of vertical response of the boat to the size of the wave. There's a different RAO for every point on the boat - for example, the bow RAO is greater than the one at the center of gravity because the bow moves up and down as the boat pitches. The total response of the boat comes from summing the individual responses of the boat to the individual waves.
- So when you multiply the wave spectrum times the RAO as a function of frequency, what you get is another spectrum which represents the statistics of the boat's motion to a random seaway. This is what you're looking at in the plot. One could also generate the same results by running a simulation of the boat in a seaway and repeating the simulation many times (hundreds or thousands) with random variations in the sea and averaging the results (a Monte Carlo analysis).
I have a question of my own regarding the graph: I have seen the same boundaries for acceleration used in other reports, and I believe they are described in an ISO standard. However I've not been able to find it. Can anyone provide me with the standard? -- Tom Speer (firstname.lastname@example.org) website: www.tspeer.com fax: +1 206 878 5269
[3 Apr 01] I was able to put my hands on relevant documents fairly quickly. In the Rodriquez graph, the motion sickness limit curve on the left and vibration limit curves on the right come from ISO 2631-1978 (E) "Guide for the evaluation of human exposure to whole-body vibration," Second edition 1978-01-15, and a later amendment and a later addendum. As close as I can determine quickly, the motion sickness curve is for 10% of the crew sick in a 4-Hour exposure. The curves were derived from human performance experiments in ship motion simulators to be compared with a 1/3-octave analysis of ship motion spectra - in this case, the vertical acceleration at some specified location on the ship. In the case of fast ferries, ride comfort is a primary concern. And this type of a plot shows the frequencies at which the human body is most susceptible to motion sickness and most sensitive to structure-borne vibration (from machinery and hull pounding in heavy seas, for instance). To derive a single-value criterion for design studies, we analyzed the ship motion spectra of frigates and destroyers in heavy seas. In cases where the peak in the motion spectra reached the sickness limit curve, we integrated the motion spectra and found limit values clustered around a root-mean square (RMS) average of 0.2 G vertical acceleration. The analysis of high-speed craft would likely yield a different single value. Now to the documents, the base ISO 2631-1978 (E) and Amendment 1 of 1982-04-01explain the "Fatigue decreased proficiency" end of the spectrum - 1.0 Hz and above. Addendum 2 "Evaluation of exposure to whole-body z-axis vertical vibration in the frequency range 0.1 to 0.63 Hz," of 1982-05-01, explains the motion sickness range - though the limit curves are shown as linear "buckets." The smooth curves, from which Rodriquez picked one, were shown in the human performance analysis reported by O'Hanlon, J.F. and McCauley, M.E., "Motion sickness incidence as a function of the frequency and acceleration of vertical sinusoidal motion," Aerospace Medicine, April 1974. -- John H. Pattison
[3 Apr 01] To Tom Speer: I believe I have a copy of the standard you are seeking details for, but can't trace it at the moment. Here are a pair of references to that standard from another document I have. I don't know if it has been updated since:
ISO 2631/1-1985(E), "Evaluation of Human Exposure to Whole-Body Vibration - Part 1: General Requirements", 1985, International Organization for Standardisation.
ISO 2631/3-1985(E), "Evaluation of Human Exposure to Whole-Body Vibration - Part 3: Evaluation of Human Exposure to Whole-Body Z-Axis Vertical Vibration in the Frequency range 0.1 to 0.63 Hz", 1985, International Organization for Standardisation.
It seems part 1 deals in part with the range of frequencies above 0.63 Hz but I can't be sure. My feeling is that this is more associated with vibration due to propulsion machinery on larger merchant ships than with wave induced whole ship motions. The standard was drafted in around 1972 and first released, already as ISO 2631, in 1974 with the title "Guide for the Evaluation of Human Exposure to Whole-Body Vibration". Although I have never come to terms with the various models of the effect of ship motions on humans, I found that the approach proposed by the late Peter R. Payne seemed to have an elegant unified approach across the whole frequency range. He also came from a background of planing craft and hydrofoil design so would have had high speed craft motions in mind. For details, see:
Payne, Peter R., On Quantizing Ride Comfort and Allowable Accelerations, paper 76-873, AIAA / SNAME Advanced Marine Vehicles Conference, Arlington, Virginia, 20-22 September 1976.
Back to my seakeeping / motion sickness question: If you indeed believe the Rodriquez data I used as an example is a motion response spectrum where the actual measured irregular time trace of acceleration has been de-composed into its frequency components, then that is also the way I viewed it except that I didn't say so as clearly in my original question. Going on from this common interpretation we have made, I feel that doing this spreads the total 'energy' associated with the acceleration time trace across a large frequency range and thus makes the resulting plot appear as having a far lower magnitude of acceleration than if a single equivalent RMS acceleration based on the complete irregular acceleration time series had been plotted at a single frequency corresponding to, say, the average frequency of the acceleration peaks in that irregular signal. The current approach for assessing Motion Sickness Index for an irregular vertical motion on a ship is to treat the irregular oscillation as if it was the same as a sinusoidal motion having the same RMS acceleration and a frequency corresponding to the average period of the acceleration peaks of the irregular motion, or more commonly the average period of the displacement peaks is used. This is fairly well described in the following text book:
- Lloyd, A.R.J.M., "Seakeeping - Ship Behaviour in Rough Weather", Ellis Horwood Series in Marine Technology, Ellis Horwood Ltd, 1989.
That book appears to have an error in the equation for calculating MSI but that may have been corrected in the more recent and revised issue of this excellent reference book on the subject. -- Martin Grimm (email@example.com)
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