SUSAN L. BALES

PRACTICAL SEAKEEPING USING DIRECTIONAL WAVE SPECTRA

During the past decade, ship dri ers, owners, and de igner ha e realized that knowledge of the prevailing wave environment can be put to good use in improving hip-seakeeping performance. The wave height is important, but ignorance of the wave length and wave direction( ) can ha e equally adverse effects on ship performance. This article identifies some sensiti ities of hips to the wa e pectrum and pro ides resolution requirements for engineering applications .

INTRODUCTION

For decades, ocean-going Navy ship hulls had been designed merely to optimize calm-water performance. That is, ship hull forms had been developed to en ure maximum speed in calm water. Nearly 20 year ago, an attempt was made to consider hip performance in waves, i.e., seakeeping. Such early attempts resulted in less than optimum ships. Using the best ad ice a ailable at the time, the Navy designed several clas es of hip to maintain speed in a seaway defined by a P ierson­Moskowitz Sea State 5 pectrum. Thus, the ships were constrained to perform well in about a 3-meter unidirec­tional seaway with a fixed modal period. The result was that the ships were well tuned for a wave pectrum that may never occur in nature . Actually, lower sea states could (and did) cause much more excessive motions of the ships from other combinations of wave height, peri­od , and direction.

About 10 year ago, the Navy decided to try again. By then, naval architect worldwide had adopted the Bretschneider two-parameter spectrum combined with a cosine-squared angular dependence to reflect direction­al spreading of the seas about a gi en, fixed primary direction. These spectra were initialized with wa e heights and periods deri ed from visual ob ervation from ship of opportunity. Thus, probabilitie of occurrence were developed for the spectra by the joint occurrence statis­tics of the wave height and period . While this meth­odology was a va t impro ement, it had the follo ing fau lts:

42

1. Reliable global height and period stati tics were un­available.

Susan L. Bales i head of the Ocean En­ironment Group of the Ship Surface D -

namic Branch , the Da id Taylor aval Ship R&D Center, Bethe da, MD 20084.

2. i ual e timate of v a e conditions were/ are bi­a ed b the capabilit of the ob erver, hip ize hipping lane , etc.

3. Sv ell-corrupted \ ind-generated ea \ ere ignored .

In 19T , the a eized an opportunit to addre the e deficiencie. The p tral 0 ean Wa Model (SOWM), ba ed on the theorie of Pier on and hi 01-league , I had been made op rational at the Fleet u­merical Weather Center b Lazanoff and Ste en on.­The SOWM pro ided t\ ice-dail foreca t of directional \ a e pectra throughout the orthem Herni phere. Con­currentl , Fleet commander v ere calling for improved eakeeping performance. Too often, U.S. ships were just

not able to keep up \ ith A TO allie and So iet coun­terpart . Figure 1 illu trate a hip pitching-and-slamming problem that clear! limit fon ard peed . The turning point came from the man re earch program initiated a a re ult of a ork hop held at the a al Academy in 1975. 3 Some of the program are identified in Ref. 3. Of prime intere there i the program propo ed b the En ironment Group, chaired b Cumrnin of the Da id W. Ta lor a al Ship R&D Center. The group \! hi h con i ted of na al architect oceanographer meteorol-

Figure 1-Pitching mot ion. keel slamming, and, sea spray while refueling in moderate to heaving seas. April 1962.

Johns H opkin APL Technical Dige l. \' olume . umber I (/9 )

ogists, and modelers, postulated the concepts that have become, in many cases, the state of the art. For instance, a massive wave-hindcasting effort resulted that has been reported in numerous papers, articles, and atlases (e.g., Ref. 4).

At present, the Navy has addressed, to some extent, all of the deficiencies. In ship design, the Bretschneider cosine-squared spectra are still routinely used, but they are initialized by hindcasted significant heights and mo­dal periods. For specific investigations where multidirec­tional seas are critical, either Cummins' stratified sample of hindcast directional or other SOWM spectra are used. The SOWM has been replaced by a global version (GSOWM) implemented by Clancy, Kaitala, and Zambresky5 in 1985. However, the Navy is still deriv­ing great benefit from the SOWM hindcasts, and the GSOWM forecasts are now being used operationally with other sensors and models to analyze ship seakeep­ing behavior during ship deployments.

DIRECTIONAL SPECTRA REQUIREMENTS

But more still needs to be accomplished. N. Bales 6

and Walden and Grundman 7 have clearly demonstrat­'ed that ship hull forms can be optimized to the seaway. In fact, acceptable operability in northern latitudes can probably be extended upward by several sea states by desensitizing the natural resonances of the ship hull to the estimated prevailing wave conditions. The engineer­ing community has developed a highly sophisticated ship­motion program that requires a directional wave spec­trum as the forcing function. Given the wave spectrum, most motions in moderate to heavy sea states are predict­ed to within ± 10 percent accuracy when compared to towing-tank simulations.

The response amplitude operators (defined as the square of the ship-transfer function) are different for ev­ery ship and depend on its size, shape, appendages, hull form, and ballast condition. They also vary for every combination of speed and course relative to the prevail­ing seaway. In Fig. 2, it is obvious that the frigate (about 122 meters long) has substantially more response in pitch (the vertical angular motion about the center of gravi­ty, as seen in Fig. 1) and at higher frequencies than does the aircraft carrier (about 274 meters long). Clearly, the wave spectrum (plotted on the lower portion of Fig. 2) that most closely aligns with the response function peak causes the greatest pitch motion. The wave spectra in the figure are Bretschneider unidirectional spectra for a fixed height but for varying modal periods.

A deficiency in ship motion prediction remains in the modeling of wave directionality. The cosine-squared law is still applied to spectra such as those in Fig. 2, occa­sionally using SOWM/ GSOWM spectra, as mentioned previously. Figure 3 illustrates what is presently used ver­sus what is really needed in order to achieve adequate information about swell-corrupted wind-generated seas. The importance of directionality is clearly illustrated in Fig. 4, where there is about a factor of two between predicted ship-rolling (side-to-side) angles for unidirec­tional (long-crested) and cosine-squared (short-crested)

Johns H opkins APL Technical Digest, Vol ume 8, N umber 1 (1987)

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Figure 2-Prediction of ship response, e.g., rms pitch [J RAO{w} S {w} dw] V2 .

beam seas (seas traveling 90 degrees to the major ship axis).

Another side of the problem lies in the operational application of directional wave spectra. Future tactical­decision aids require a good in-situ directional wave spec­trum. The Navy's Tactical Environmental Support Sys­tem (TESS) will require a reliable spectrum in order to predict ship responses. Required spectral resolutions are given in Table 1. These resolutions are based on the known variability of the ship's transfer functions, as il­lustrated for pitch in Fig. 2. Figure 5 shows some generic sensitivities to modal wave period as ship length and hull form are changed.

Several approaches could help achieve the data re­quirements of Table 1. It is not clear that ships at sea can depend on a single land-based forecasting system nor does a single space borne system seem to be emerging that could accomplish the requirements. The optimum is to have available data from a variety of sensors and models so that the tactician can select data to appropriate levels of complexity and resolution. Such a strategy might in­clude the following elements:

1. Deploy a disposable wave buoy that, by teleme­try, provides acceleration data to be rapidly pro­cessed (on board) into wave-height spectra. The current cost is about $4,000 per buoy, including an­tenna and receiver. Processing requirements are minimal. Total cost could probably be decreased to about $500.

43

Bales - Pracfical Seakeeping Using Direcfional Wave Specfra

Primary heading

~------

Symmetric cosine 2 (a ppl ied to two-parameter

spectra of Fig. 2)

180

Swell-corrupted , wind-driven sea (SOWM )

Figure 3-Generic comparison of cosine·squared directional model against a more representative hindcast directional spec­trum , showing a swell-corrupted wind-generated sea.

Table 1-Required directional wave-parameter resolutions for ship·response prediction.

Parameter

Significant wave height

Modal 'V a e period

Directional preading

44

Resolulion

±O.3 meter for Sea States 4- 7 (1.25-9 meter)

± I second for wa es from 3-24 econds

± 7.5 degrees for primary and econdary system (or IS-degree increment about the compass)

en Q)

~ Ol Q)

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6

4

2

Sign ificant wave height Ship speed = 20 knots

120

3.6 meters

Long-crested waves

Short-crested

60 o Following Ship heading angle to predominant Head

seas wave direction (degrees) seas

Figure 4-Comparison of pred icted ro lli ng (side-to-side) motion using Bretschneider long-crested and short·crested sea models.

12 ~----'-----'-----.-----.-r---'---71

Q) 6 > co ~ +-' C co 3 u ~ c

.~ (j)

0 5

-- Hogben and Lumb (visual )

-- Hindcast climatology

Resonant pitch • and roll

7 9 11

rn Q.

E rn Q)

E co m

Most probable modal wave period (seconds) 17

Figure 5-Significant wave height versus the most probable mo­dal wave period showi ng sh ip pitch and ro ll resonant period ranges.

2. U e the di po able wa e buo together \ ith the shipboard na igation radar (e.g . the SP -64) to get direction information a \' ell. Trizna and hi colleague at the a al Re earch Laborator are currently exploring thi technique.

3. Deploy an Endeco/ Data ell or other portable directional wa e buo . Co t range from 1 ~ 000 to $80,000 and are related to buo ize and th re­quired pectral re olution.

4. Use pace or aircraft remotel en ed data. Geo-

Johns H opkin APL Techni'al Dige I. \ ·olume . ,\ ·umber I (/9 - )

sat altimeter wave-height data appear to be the only hopeful sign for the United States in the near term, with the delays in the Shuttle Imaging Radar Pro­gram and the recent (December 1986) apparent de­mise of the Navy Remote Ocean Sensing System. It is clear that the United States now lags both Ja­pan and Europe in a national space-oceanography program, particularly one to support military environmental-monitoring requirements. Routine deployment of aircraft sensors has not yet been es­tablished as a requirement. But from the Navy bat­tle group viewpoint, aircraft sensors may offer a viable alternate to some spaceborne systems, par­ticularly for timely local weather forecasting.

5. Use properly validated GSOWM and other land­based forecasts of directional wave spectra. In a statistical sense, we have found the SOWMI GSOWM data to be quite reliable, and, on some occasions, individual forecasts could be used to provide meaningful guidance to the ship driver. Figure 6 is a speed polar-graph for a ship that en­countered high waves in the Northeast Pacific. Here, the concentric circles represent ship speed in increments of 5 knots. The radial lines represent ship-to-wave relative headings. The @ represents the operating condition of 17 knots in port bow seas, a condition in which severe damage was in-

o Probable (95 percent) damage

D Possible (5 percent) damage

o No damage but occasional wet (stern) IVDS doors

® Operating condition incurred damage to the top mast structure

Waves (SOWM: 8.2 meters, 14 seconds ,315 270 r--r--r-~--~~

180 Ship speed/heading plane

Figure 6-Speed polar-graph of a ship operating in the north­eastern Pacific on March 8, 1974, where a heading change of about 30 degrees would have reduced the probability of dam­age by 90 percent ; speed changes would have far less impact, if any.

Johns H opkiIlS A PL Technical Digest , Volume 8, N um ber I (1 987)

Bales - Practical Seakeeping Using Directional Wa ve Spectra

curred by the 8.2-meter waves. The wave forecasts agreed well with the ship observations. The red area represents conditions posing a 95 percent probabil­ity of damage, while the yellow area represents con­ditions posing more than a 5 percent probability of damage. If this wave forecast and speed polar­graph had been available to the captain, he would have quickly seen that a slight (30-degree) change of course to port would have drastically reduced the potential of damage to the ship. It is planned to incorporate these types of tactical decision aids into the Tactical Environmental Support System.

The usefulness of Fig. 6 is obvious, but the forcing function or directional seaway must be well defined to predict ship motion. Figure 7 illustrates a North Pacific case where buoy and GSOWM data are compared and

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-- Buoy: significant single amplitude = 4.9 degrees

- - GSOWM : significant single amplitude = 4 .0 degrees

0.4 0.8 1.2 1.6 2.0 2.4 2.8 Wave encounter frequency (RPS)

Figure 7 -Comparison of GSOWM and buoy measurements and motion predictions for an aircraft carrier. The agreement be­tween spectra permits a good forecast of ship motion.

45

Bales - Practical Seakeeping Using Directional Wa ve Spectra

the resulting pitch and roll motion is computed for an aircraft carrier. The Delft Disposable Wave Buoy, a stan­dard for developing wave-height spectra, was deployed along a ship's route. The GSOWM forecasts were tak­en for the clo est temporal and patial GSOWM grid­point. The point spectra (Fig. 7a) agree well with the forecasts, and the resulting predicted pitch and roll responses (Figs. 7b and 7c) a re al 0 comparable to the predictions.

Figure 8 provides a com pari on during the arne ship transit when the measured and foreca t spectra differ. The GSOWM spectrum contain substantially more energy than that derived from the buoy vertical-acceler­ation measurement, resulting in a ubstantial difference between the two predicted ship re ponses. The e differ­ences could be even larger for a frigate, which ha more

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55.0 0 N, 152.5°W 0000 GMT, April 12, 1986

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o~~~~~ ________ ~ ________ ~ ____ ~ o 0.4 0.8 1.2 1. 6 2.0 2.4 2 .8

Wave encounter frequency (RPS )

Figure a-Compari son of GSOWM , buoy measurements and motion predictions. The disagreement between spectra provides a poor forecast of ship motion .

46

re pon e in the modal a e-frequency region of the wave pectrum . Analyticall deri ed hip-re ponse transfer

function were u ed to de elop both Fig. 7 and 8. Wave forecasts can al 0 be u eful e en when they are

at ariance with mea urement of the local area. For ex­ample, GSOWM wa e height can be scaled by Geosat altimeter a e height. During recent ship trials in the Northwe t Pacific, the foreca t wa e period and direc­tions agreed well with tho e ob erved by experienced per-onnel and with tho e deri ed from ship-motion

measurement . Ho e er, the forecast wave energy of the GSOWM directional pectra appeared to be too high. Figure 9 pro ide a compari on of these data during De­cember 16-18, 1986. The darkened circle represent the Geosat er us GSOWM ignificant wa e heights. The colored line approximate the error associated with the altimeter height a deri ed by Monaldo. 8 In general, the GSOWM data for the period indicate a 30 percent higher ignificant wa e height than what was measured. If the two point with a di tance greater than 100 nauti­cal mile bet een the grid point and the 0 erflight point are excluded, the GSOWM data indicate a 22 percent greater height. The conclu ion here i that in orne case the GSOWM pectra can be caled b imple height data to de elop a directional wa e pectra. Other compari-on of forecast and Geo at data ha e re entl been

reported b Pickett. 9

Distance between Geosat measurement

and GSOWM grid po int

a < 50 nmi b50-100nmi c 100-200 nmi

T ime difference Geosat - GSOWM

1 4-5 hr 2 5-6 hr 3 6-7 hr

Example: (a, 2 ) ind icates a distance of < 50 nmi w ith a 5-6 hour t ime difference

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b, 3 f 0)

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0) > 8 Cll

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~ C 0> . iii +-' 4 Cll en 0 0)

<.9 2

0 0 2 4 6 8

1216 0619

b. 3 ) (a , 1 1216 1216

f

0623 1601 c 1)

1218 1634

10 12 14 GSOWM sign if icant wave height (feet )

Figure 9-Comparison of Geosat and GSOWM signi ficant wave heights in the northwestern Pacif ic for December 16-18, 1986. The comparison generally shows that the GSOWM forecasts are somewhat high . 1217 1707 = date and t ime of Geosat; Decem ber 16-18, 1986.

John H opkins APL Technical Dige I, Volume , umber I (/9 )

CONCLUSIONS

This article has established some of the practical ap­plications for which accurate directional wave spectra are required. The spectral resolutions required for prac­tical ship applications have been identified, though it is expected that they will be achieved only in incremental steps. From the engineering viewpoint, climatological data are generally sufficient. They can be developed by hindcasting techniques or by global wave measurements, although the latter can probably be achieved only by means of spaceborne sensors. Spaceborne altimeters such as those on Seas at and Geosat appear to provide ade­quate estimates of wave heights. These height estimates can be used to "tune" land-based global models or sea­based regional models and measurements. It is not yet clear that space sensors such as the synthetic aperture radar will provide the full directional wave-energy spec­tra. The article by Beal in this issue describes some of the limitations of synthetic aperture radar at the shorter wavelengths of interest. Further measurements and in­tercomparisons in realistic sea states should help resolve this question.

Naval engineers must take advantage of every techno­logical edge in order to gain even the slightest improve­ment in seakeeping. A better knowledge of the prevailing wave environment will improve operability. Additional­ly, real-time measurement of global wave conditions could vastly improve forecasting products available to the Fleet. But to counterbalance the vulnerability of satellites, it is essential that both in-situ and shipborne sensor develop­ment be accelerated. With the recent cancellation of the Navy Remote Ocean Sensing System program, these al­ternative approaches take on added importance.

With regard to national responsibilities, joint agency programs are required in the areas of sensor develop­ment, data assimilation into models, and model valida-

Johns Hopkins APL Technical Digesf , Volume 8, N umber I (/987)

Bales - Practical Seakeeping Using DirecTional Wave Spectra

tion. A critical problem here is in identifying areas of responsibility. Such national programs should be reflec­tive of NASA's fundamental science interests, the Na­vy's interest in improving Fleet readiness and operability, and NOAA's interest in supporting commercial fishing, offshore industry, and the civilian population in gener­al. Such programs can be established only through care­ful interagency negotiation and cooperation.

REFERENCES

1 W. J. Pierson, L. J. Tick, and L. Baer, "Computer Based Procedures fOJ Preparing Global Wave Forecasts and Wind Field Analyses Capable of Using Wave Data Obtained from Spacecraft ," in Proc., 6fh Naval Hydrodynamics Symposium, pp. 499-532, Washington , D.C. (1966) .

2 S. M. Lazanoff and N. M. Stevenson, An Evaluation of a Hemispheric Oper­ational Wave Specfral Model , Fleet umerical Weather Center Technical Note 75-3 (1975).

3 Seakeeping in the Ship Design Process, Research and Technology DirecfOrafe Reporf of fhe Seakeeping Workshop, Naval Sea Systems Command , Wash­ington, D.C. (1975).

4 S. L. Bales, " Development and Application of a Deep Water Hindcast Wind and Wave Climatology," in Proc., imernafional Symposium on Wave and Wind Clima fe Worldwide, Royal Institution of aval Architects, London (1984).

5 R. M. Clancy, J. E. Kaitala, and L. V. Zambresky, " The Fleet Numerical Oceanography Center Global Spectral Ocean Wave Model," Bull. Am. Mefeorol. Soc. 67, 498-512 (1986).

6 N. K. Bales, "Optimizing the Seakeeping Performance of Destroyer-Type Hulls," in Proc., 131h Symposium on Naval Hydrodynamics, pp. 479-504 (1980). .

7 D. A. Walden and P. Grundman, "Methods for Designing Hull Forms with Reduced Motions and Dry Decks," Nav. Eng. 1. 97, 214-223 (1985).

8 F. Monaldo, Expecled Differences in lhe Comparison of Wind Speed and Sig­nijicam Wave Heighl Made by Spaceborne Radar Allimelers and Buoys, JH UlA PL Technical Report SIR86U-017 (1986).

9 R. L. Pickett, "Ocean Wind and Wave Model Comparison for Geosat," in Proc. , imernalional Workshop on Wave Hindcasfing and Forecasling (1987).

ACKNOWLEDGMENTS-I wish to acknowledge the support received from the Ocean Environment Group, Surface Ship Dynamics Branch , of the David W. Taylor aval Ship R&D Center (DT SRDC) under a variet y of efforts. The results reported are primarily derived from the Surface Wave Spectra for Ship Design Program, P .E. 62759 , administered by the aval Ocean R&D Activity for the Office of Navy Technology, for which DTNSRDC has been the lead lab­oratory .

I am grateful for the special efforts of A. L. Silver , W . L. Thomas III, and R. J. Bachman of DTNSRDC for their preparation of Figs. 7, 8, and 9 .

47