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
constrai ned 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:
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 01league , 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-
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.
Figure 1-Pitching motion. keel slamm ing, and , sea spray while
refueling in moderate to heaving seas. April 1962.
42
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
Zambresky 5 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.
B
~
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a.
o
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o
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DIRECTIONAL SPECTRA REQUIREMENTS
6
But more still needs to be accomplished. N. Bales
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)
>
co
~
1
"D
(l)
.~
co
(l)
~
Wave frequency,
W
Figure 2-Prediction of ship response, e.g., rms pitch
RAO{w} S {w} dw] V2 .
[J
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 spaceborne 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 Wa ve Specfra
8~---------.----------.----------,
Primary heading
Sign ificant wave height
Ship speed = 20 knots
6
3.6 meters
Long -crested
waves
en
Q)
~
Ol
Q)
~
~
Ol
4
Short-crested
c
co
ern
E
a:
2
~------
Symmetric cosine 2
(a ppl ied to two-parameter
spectra of Fig. 2)
Following
seas
o
120
60
Ship heading angle to predominant
wave direction (degrees)
Head
seas
Figure 4-Comparison of pred icted ro lli ng (side-to-side) motion
using Bretschne ider long-crested and short·crested sea models.
12 ~----'-----'-----.-----.-r---'---71
- - Hogben and
Lumb (visual )
- - Hindcast
climatology
Q)
>
6
co
rn
~
Q.
E
+-'
C
co
u
rn
3
Q)
Eco
~
c
180
.~
Swell-corrupted , wind-driven sea (SOWM )
Figure 3-G eneric comparison of cosine·squared directional
model against a more representative hindcast directional spectrum , showing a swell-corrupted wind-generated sea.
Resonant pitch •
and roll
(j)
0
5
m
7
9
11
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 .
Table 1-Required directional wave-parameter resolutions
for ship·response prediction.
Parameter
Resolulion
Significant wave height
±O.3 meter for Sea States
4- 7 (1.25-9 meter)
Modal
± I second for wa es
from 3-24 econds
'V
a e period
Directional preading
± 7.5 degrees for primary
and econdary system
(or IS-degree increment
about the compass)
44
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. GeoJohns H opkin APL Techni'al Dige I. \ ·olume
. ,\ ·umber I (/9 - )
Practical Seakeeping Using Directional Wa ve Spectra
Bales -
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 SOWM I
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-
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
3.5r----.---.r---.----.r---.----.----~~
(a)
~CIl
.-
~
3.0
1986)
- - Buoy: significam wave height
= 4.1 meters
-g 2.5
~ 8
(52.5°N,137.5°W
1200 GMT, April 9, 1986)
- - GSOWM : significant wave
height = 4.08 meters
~ ~ 2.0
+-,
'
UN
Q) CIl
Q.(j)1.5
CIl +-'
Q) Q)
i6 E 1.0
S
0.5
o
Probable (95 percent) damage
D
Possible (5 percent) damage
o No damage but occasional wet (stern) IVDS doors
®
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.
Operating condition incurred damage to the top
mast structure
,315
Waves
(SOWM: 8.2 meters,
14 seconds
270 r--r--r-~--~~
oL-~---i---L~~===c===-
__~
1.6r----1r---~1r---~1r---~1----~1r---~1----~1~
~
.~
(b)
- - Buoy: significant single amplitude_
pitch = 1.0 degree
1.4-
Q)~
~ ~ 1.2co c
;; a
-
- - GSOWM: significant single
amplitude pitch = 0.8 degrees
(significant single amplitude
= 2 x RMS amplitude
~ ~ 1.0Q.CIl
~'iO.8-
Q)
-
Q)
Q)
+-'
§ 0>0.6 fa
-
Q)
U"O
~ ~0.4f-
-
100 (e)
~
'en
c
Q) -
"0 CIl
_ "0
- - Buoy: significant single amplitude
= 4.9 degrees
- - GSOWM : significant single
amplitude = 4 .0 degrees
80
co C
~ ~
60
c:::J
40
Q.CIl
CIlN
~
CIl
Q) Q)
a
~
OJ
Q)
u"O
c~
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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 , Vo lum e 8, N um ber I (1 987)
20
"0
ex::
0.4
0.8
1.2
1.6
2.0
2.4
Wave encounter frequency (RPS)
2.8
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
Practical Seakeeping Using Directional Wa ve Spectra
Bales -
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 GSOW M 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
4 .0 (a)
"?: _
-2
-
'iii
~ c 3 .0
1:)
53 .9 °N , 153 .7 ° W
0200 GMT, Ap ril 12, 1986
Buoy: significant wave height
= 3.4 meters
3.5
0
U
~ ~ 2 .5
+-'
'
UN
~ ~
en ~
2.0
-
E1.5
~
55.0 0 N, 152 .5°W
0000 GMT, April 12, 1986
GSOWM : significant wave height
= 4.7 meters
Cll-
~
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 peronnel 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 comparion of forecast and Geo at data ha e re entl been
reported b Pickett. 9
1.0
0.5
Distance between
Geosat measurement
and GSOWM grid po int
o~LJ--~~~~~==~--~--~
2 . 0r---'-~-.----.----.----.---.----._.
(b)
"?:
.iii
c
~ -1.6
en
-
1:)
~
C
0
+-'
-
Buoy: significant single amplitude
pitch = 0 .8 °
-
GSOWM: significant single
amplitude pitch = 1.3 °
(significant single amplitude
= 2 x RMS amplitude
~ ~ 1.2
en
en '
... Nen
Q.
0)
0)
::::l
0>
c
a < 50 nm i
b50- 100nm i
c 100-200 nm i
I
Geosat spatial and
temporal error
range = _ 0.35 m
-.:; 12
0)
0)
O)
4 -5 hr
5-6 hr
6-7 hr
3
14 r----.-----.----~----._--~,_--_.--__,
~
U1:)
c-
1
2
Examp le: (a, 2 ) ind icates a distance of <50 nmi
w ith a 5-6 hour t ime difference
~ 0.8
o
T ime difference
Geosat - GSOWM
0.4
=
b, 3
1216
0619
£
B
b. 3 ) (a , 1
1216 1216
0623 1601
0::
0)
200r---.-.--.----.----.----r---~--~_.
(e)
"?:
.iii
~
1:)-
160
~-g
Buoy : significant single amplitude
= 4 .3 °
0
Cll
~
GSOWM : significant single
amplitude = 6 .6°
6U
f
0>
+-'
Cll
4
en
0
0)
~ 80
<.9
OJ
2
0)
40
0
o
a::
o~~~~~
o
________ ________ ____
~
~
0.4
0.8
1.2
1. 6
2.0
2.4
Wave encounter frequency (RPS )
0
~
2
4
6
10
12
8
GSOWM sign if icant wave he ight (feet )
14
2 .8
Figure a-Compari so n of GSOWM , buoy measurements and
motion predictions. The disagreement between spectra provides
a poor forecast of ship motion .
46
6
.iii
,
en
c~
0)
1)
C
Q.en
0)
c
1218
1634
C
... N
C
8
~
+-'
~ ~120
en
>
Cll
U
-
en
+-'
-
f
Figure 9-Comparison of Geosat and GSOWM signi ficant wave
heights in the northw estern Pac ific for December 16-18, 1986.
The comparison gene rally show s that the GSOW M fo recas ts
are somewhat high . 1217 1707 = date and time of Geosat;
Decem ber 16-18, 1986.
John H opkins APL Technical Dige
I,
Volume
,
umber I (/9
)
Bales -
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)
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 Hydrody namics, 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 Sig-
nijicam 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