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Hydrofoil Seakeeping / Motion Sickness Design Issues

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(Last Update: 20 Apr 02)

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Seakeeping / Motion Sickness Graphs

[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.

RHS 160F  - Graph of Rough Sea Behaviour

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 (


[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:

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 ( website: 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

Follow up...

[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:

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 (


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