RECENT AD VANCES IN THE SEAKEEPING
ASSESSMENT OF SHIPS
T H E A U T H O R S
Kathryn K . McCreight is a member of Ihe Ship Dynamics Division at the David W. Taylor Naval Ship Research and Development Center. She has worked on a range of projects, including some related to modeling the dynamic characteristics of SWATH ships, assessing the seaworthiness of ships, and analyzing the relationship between hullform characteristics and seaworthiness of SWATH designs. She received a B.A. in mathematics from Wells College in 1968 and an M.S. in hydromechanics from George Washington University in 1979.
Ralph G . Stahl received his B.S. degree in physics from Drexel University in Philadelphia. Together with the curriculum associated student training program he has been associated with the David W. Taylor Naval Ship R&D Center (DTNSRDC) and its predecessor organizations throughout his professional career. For the past five years he has participated in the development of SWATH ship seakeeping performance assessment technology which encompasses the development of initial design concepts and characterizing corresponding dynamic qualities.
A B S T R A C T
Three factors affect the operability of a ship in a seaway: the motion characteristics of (he ship, the environment, and the mission requirements. A method is presented which predicts the operability of a ship at specific geographical loca-tions. Analysis of operability is carried out using transfer functions which represent Ihe motion characteristics of a ship, wave data for the North Atlantic and for the North Pacific, and limiting motion criteria for a specific mission. From these three factors, operability indices are developed. Operability indices include the percent of time of operation (PTO) and the limiting significant wave height ( L S W H ) . Contours which describe bands of constant values of the percent of time of operation for a mission are detennined. In developing the in-dices and resultant contours, operability in the presence of each of a large number of wave spectra is weighted according to probability of occurrence of that wave spectrum. The prob-ability of occurrence of wave spectra for the winter and for the entire year for 57 points in the North Atlantic and 21 points in the North Pacific is used for various combinations of signifi-cant wave height and spectral modal period. Composite wave data for the general North Atlantic or general North Pacific also are utilized.
The operability for mobility criteria of six hullforms rang-ing hi displacement from approximately 3,000 to 9,000 tons is compared. Both monohull and S W A T H configurations are considered. Comparison of operability as a function of signifi-cant wave height, as a function of displacement, and as a func-tion of speed is made using winter and annual wave statistics for the general North Atlantic. Some results also are presented for the general North Pacific. Operability contours for the North Atlantic are presented for the hullforms. Tabulated limiting significant wave heights for various operating
condi-tions are presented. The effect of systematic variacondi-tions in per-formance criteria on perper-formance is presented as a function of speed.
INTRODUCTION
T
n the ship design process, it is advantageous to be able to evaluate the seaworthiness of candidate hullforms early in the design process so that hullforms which meet design requirements and which have superior seakeep-ing performance can be selected. In order to evaluate the operability of a ship in an ocean environment, it is necessary to predict the responses of a hullform to a seaway, to represent the enviromnent in a meaningful way, and to quantify those variables which would affect performance of potential missions. The result of this evaluation can be represented as the percent of the time a particular ship could carry out a particular mission without degradation in performance. This is referred to as an operating index and is the result of a complex analysis. This method requires representing these three components — ship motions, environment, perfor-mance criteria — reasonably accurately and in forms which facilitate evaluation.In the analysis described in this paper, the following assumptions are made:
1) Work by Salvesen, Tuck, and Faltinsen [1] and Lee [2] is the basis of the Mathematical modeling of the responses of the monohull and SWATH ships to waves. Subsequent work led to the development of the com-puter programs SMP (ship motions program) for con-ventional monohull ships {3], [4], [5] and SSEP (SWATH seakeeping evaluation program) for SWATH ships [6].
2) The spectral ocean wave model (SOWM) developed by Pierson [7] has been utilized by others to hindcast the wind and wave environment at many world locations. Bales [8] has recently published a comprehensive discus-sion of SOWM and related topics. Development of computer programs to sort this data [9] has resulted in tables such as those in reference [10] which include distributions of significant wave height as a function of spectral modal period. This data is used for each loca-tion of interest.
3) The seaway is assumed to be described as the sum of regular waves according to the development by St. Denis and Pierson [11]. The Bretschneider wave spectral formulation is used. Since this formulation is a function of significant wave height and spectral modal period, it can be used in conjunction with the SOWM data.
4) Short crested seas are modeled using the cosine-squared spreading function. A l l predominant wave headings are assumed to be equally probable.
5) A set of simple performance criteria is utilized. Using these sources and assumptions, ship transfer functions are developed, pertinent wave spectra are utilized, and seakeeping performance limits relevant to a particular mission are selected. For each spectrum it is determined if any of the seakeeping performance limits are exceeded. By carrying out such an evaluation for an appropriate range of ship speeds and relative wave headings, the average percent of time a ship could operate in the selected wave spectrum is estimated. By applying a weight to each of the spectra to reflect the probability of occurrence of that spectrum, an overall operating index is determined.
EVOLUTION OF METHODS
Those who have used this approach include Com-stock. Bales, and Gentile [12] and Olson [13]. In calculating operating indices, Comstock et al used three wave spectra, representing sea states 4, 5, and 6. The Bretschneider spectral formulation was utilized. The SOWM data was used to select the spectral modal periods. For each of three significant wave heights, the spectral modal period which was most likely to occur in the general North Atlantic was chosen. These three spectra were then appropriately weighted so that the sum of their probability was 1.0. Operating indices for the general North Atlantic were calculated for several ships and several sets of performance criteria. In addi-tion, speed-polar plots detailing the criteria which limit operability for each wave spectrum as a function of ship speed and relative wave heading were presented.
Olson calculated the performance at four spectral modal periods (7, 9. 11, and 13 seconds). He used responses to spectra with a unit significant wave height. Assuming linearity, he then calculated the responses to
spectra with these modal periods and any significant wave height. By applying appropriate probabUities of occurrence to spectra for seven significant wave height bands for each of the four modal periods, probabilities of occurrence of spectra were developed for the winter and the summer m the general North Atlantic. Operating indices were then calculated. In addition, for each modal period and for each operating condition, the limiting significant wave height (LSWH), or the highest significant wave height at which none of the criteria was exceeded, is calculated. His analysis included three dimensional speed-polar plots with the vertical axis representing the LSWH.
The method presented in this paper is a refinement and extension of the approach utilized by Olson. Prin-cipally, this method differs in that SOWM significant wave height-modal period data for many geographical locations and for winter and annual seasonal groupings for the North Atlantic or the North Pacific are utilized in the calculations. This significantly increases the reliability and the range of applicability of the analysis. This also facilitates detailed analysis and comparison of the operability of ships. A broad range and a relafively fine grid of spectral modal periods and significant wave heights and corresponding probabilities of occurrence is considered. The fifteen spectral modal periods con-sidered range from 3.2 to 25.7 seconds. The percent of time of operation for each ship operating condition in the presence of each spectrum is weighted according to the probability of encountering that spectrum, in order to determine a composite percent of time of operation for each location. Rather than calculating a LSWH for each modal period (as done by Olson), one LSWH is calculated which is based on a range of appropriate probable spectra. The form of the wave data base lends itself to the development of contours corresponding to constant percents of operabihty.
S I G N I F I C A N T WAVE HEIGHT (m)
Figure 2. Percent of Occurrence of Significant Wave Heiglit for tlie General North Atlantic Basm
SOWM WAVE DATA
A major element in the seakeeping performance analysis presented in this paper is the spectral ocean wave model (SOWM) data. In Figure 1 the geographical locations for which SOWM wave data are utihzed are indicated with numbers. There are 57 points ih the North Atlantic and 21 points in the North Pacific. For each geographical location, SOWM data was generated to represent the ocean environment at 6 hour intervals for a period of 10 years. In this paper, analysis of that data for December, January, and February (winter) and for all months (annual) is utilized. In addition to data for the individual points, composites for the North Pacific and the North Atlantic for the two seasonal groupings have been developed. The data has been sorted into significant wave height-spectral modal period bins. The significant wave height band increment is 0.5 meters. The fifteen spectral modal periods range from 3.2 to 25.7 seconds with each modal period representing the center period for each bin. For each of the resultant significant wave height-modal period com-binations, a probability of occurrence has been deter-mined from the SOWM data.
In Figure 2 the probability of occurrence of wave spectra is given as a function of significant wave height for winter and annual groupings. Since the values for the North Pacific and North Atlantic are virtually iden-tical, only one set of curves is presented. In Figure 3 the significant wave height distribution is given for three points in the North Atlantic. Winter data is utilized. The geographical points considered have approximately the same longitude, with latitude varying approximately 10 degrees. As latitude increases, there is a notable shift toward a higher probability of occurrence of higher significant wave heights. The probabilities of
occur-rence of spectra are for a discrete number of spectra. However, for ease of presentation this data is presented using curves rather than bar graphs in Figures 2 and 3. In Figure 4 the probabilities of occurrence of spectral modal periods for all significant wave heights up to 2.5, 5.0, 10.0 and 15.0 meters for the North Pacific-Wmter, North Pacific-Annual, North Atlantic-Winter, and North Atlantic-Annual are presented. The 15.0 meter curve is presented for only one case since the probability of occurrence of wave heights higher than 10.0 meters is significant only in that case. The North Atlantic-Winter graph and the North Pacific-Winter graph are similar as are the corresponding annual graphs. However, for each geographical region, the winter and aimual modal period distributions are distinct. By determining the dif-ferences between the curves on each graph, it is possible to determine the probability of occurrence of each significant wave height band as a function of modal period. For each location-season grouping, the range of modal periods narrows as significant wave height in-creases, but the range of modal periods for which there is a significant probability of occurrence remains broad.
OPERABILITY ASSESSMENT METHOD In this paper, two major operability indices are calculated for a given mission. One is the predicted per-cent of time of operation (PTO) of the ship. The other is the hmiting significant wave height (LSWH), or the highest significant wave height at which none of the limiting motion criteria is exceeded. Variables in the analysis include the region or geographical location and season (and corresponding probabihty distribution for the wave spectra); short or long crested seas; the limiting motion criteria; ship speeds and equally spaced relative wave headings. Weightings which reflect the probabihty
S I G N I F I C A N T W A V E HEIGHT (ml
Figure 3. Percent of Occurrence of Significant Wave Height for Three Points hi the North Atlantic Basin
20 tu o z tu CC t: : J u o O 10 u. () ;2 tu O cc u 20 o I U K CC D O Ü O 10
^ I 1
\ r -G E N E R A L N O R T H P A C I F I C - W I N T E R < 10.0 m" < 5.0 tn < Z5 1 \ \ 1 — r ~ G E N E R A L N O R T H P A C I F I C - A N N U A L o ti: G E N E R A L N O R T H / I A T L A N T I C - W I N T E R G E N E R A L N O R T H A T L A N T I C - A N N U A L 10 20 S P E C T R A L M O D A L P E R I O D (sec) 30 0 10 20 S P E C T R A L M O D A L P E R I O D (sec) 30Figure 4. Percent of Occurrence of Spectral Modal Period for Significant Wave Height Bands
of operating at the various speed-heading combinations also are variable.
In calculating the PTOs, all spectra which have any probabihty of occurrence are considered. The PTOs for each speed-wave heading operating condition reflect a weight for the PTO for each wave spectrum according to the probabihty of encountering that spectrum. PTOs are tabulated for each speed-wave heading combina-tion. The following average PTOs are then tabulated: the average of the PTOs for all relative wave headings for each speed; the average of the PTOs for all speeds for each relative wave heading. Weightings which reflect the likehhood of operating at each speed-wave heading are then applied to the individual PTOs, resulting in a composite PTO. In addition, composite PTOs which in-clude the effect of the speed-wave heading weightings are presented as a function of significant wave height. In calculating the LSWHs, responses to spectra which fall within a 95% or a 50% probabihty of occurrence band at each significant wave height are considered. I f the 50% band is chosen, then for each tabulated significant wave height the modal period band includes the most probable modal period and adjacent modal periods which constitute 50% of the spectra which occur at that significant wave height. The same procedure ap-phes for the 95% case.
The LSWH is a boundary in that the ship is predicted to be fully operable for all significant wave heights up to the LSWH. Consequently, these tabulated LSWHs are
conservative since h is possible that criteria would be ex-ceeded at a particular significant wave height for one wave spectrum which has some probability of occur-rence but that operabihty would not be hmited for other probable spectra with the same or higher significant wave heights. For each speed-relative wave heading combination, for the chosen band, the LSWH is calculated and the response which hmited operability (corresponding to the LSWH) is tabulated. In addifion, a larger table of LSWHs is developed. I n this larger table, the LSWH is presented for each speed-relafive wave heading combination for each of the 15 spectral modal periods. This table is more informadve than the compressed LSWH table in that it facihtates analysis of operabihty for all spectra that might be encountered, but it needs to be used in conjunction with data related to the hkehhood of various spectra occurring.
Once the PTOs are calculated for the geographical points in either the North Atlanfic or the North Pacific, a separate computer program is used to present the PTOs at the appropriate geographical location and to generate the contours. The contouring capabihties which are a part of a commercially available plotting package are used to interpolate among the PTOs to pro-duce hues which represent constant PTOs. These con-tour plots allow for analysis of ship operabihty at dif-ferent locations in the world. Although the calculations for operabihty in the general North Afiantic and the general North Pacific are useful, the increased detail
T A B L E 1. Mobility Performance Criteria RoQ»
Pitch*
Vertical acceleration at bridge* Slanu Deck Wetnesses 8.0 degrees 3.0 degrees 0.4 g's 20.0 per hour 30.0 per hour *Significant amplitude
which the contour plots provide allows for more de-tailed analysis of seakeeping performance.
The software used to carry out the above analysis is incorporated in the computer program SWATH seakeepmg evaluation program (SSEP). SSEP was developed to evaluate the motions and performance of S W A T H designs. However, the seaworthiness operabihty analysis component of SSEP can be utihzed for any hullform for which transfer functions have been generated in the required form. The analysis package has been developed so that evaluation of many ships and many sets of performance criteria is feasible in a relatively short period of time and at a relatively low cost.
APPLICATION OF METHOD
The method described above is demonstrated with the analysis of the operabihty of six hullforms. These huhforms include a monohuU frigate, a monohull destroyer, and a SWATH frigate design. These will be referred to as Frigate, Destroyer, and SWATH Frigate in results m this paper. In addition, two monohull designs and another SWATH design which resulted from a project recently commissioned by the Naval Studies Board are included. (The wave data base ac-cessed by the computer program SSEP has been expand-ed since the Naval Studies Board study was executexpand-ed. In addition, all calculations in that study were for longcrested seas. Consequently, although the trends are the same, the results in this paper differ somewhat from those presented to the board.) The designs for the Naval Studies Board were defined to be a payload driven monohuU, a payload driven SWATH, and a seakeeping driven monohull which would have the same operabihty as the payload driven SWATH. These wUl be referred to as Payload monohuU, Payload SWATH, and Seakeep-ing monohuU m results m this paper. The latter is a
geoshn of the HuU 23 which is described by Lin et al in reference [14]. The methodology developed by N . Bales [151 to opthnize seaworthiness was utUized in develop-ing HuU 23. In designdevelop-ing HuU 23, consideration also was given to calm water resistance characteristics. With the exception of the destroyer, aU huUforms have ac-tivated control systems. These active control systems are designed to aUeviate roU motion for the monohuUs and heave and pitch motions for the SWATHs.
AU calculaüons presented in this paper are for short crested seas, which are represented using the cosme squared spreading function. The probability distribu-tions for the wave spectra for each region or geographical location are based on tabulated values such as those used in developing Figure 3. For the analysis reported here, 120 operating conditions, resulting from combmafions of five ship speeds (5, 10,
15, 20, and 25 knots) and 24 reladve wave headings (0 to 345 degrees in 15 degree increments) have been included.
In this paper only one set of criteria is used. It represents the composite of personnel and huU hmits and is referred to as the mobihty criteria [12] as given in Table 1. (The locations at which the responses are evaluated, as weU as huUform displacements, are given in Table 2.) The criteria represent the ship morions which would resuU in degradation of personnel perfor-mance or would potentiaUy resuU in damage to the huU. These criteria have evolved within the seakeeping evaluation community and have resuhed from a range of efforts as noted above.
In Figure 5 the PTOs for the general North Atlantic-Winter are presented for each design as a function of significant wave height. There are notable differences among the predicted operabUity of the huUforms, par-ticularly at higher significant wave heights. Most notable is the consistently high operabihty of the SWATH Frigate, particularly given hs smaU displace-ment. Note that its displacement is equal to that of the Payload monohuU. (See Table 2.) The operabUity of the Payload SWATH and the Seakeeping monohuU are vh-tuaUy identical at aU significant wave heights. The SWATH Frigate, the Payload SWATH, and the Seakeeping monohuU retain high operability up to a mid sea state 7.
In Figure 6 the average percent of fime of operation (PTO) in the general North Atlantic for the winter and annual cases is presented as bar graphs. The percentages
T A B L E 2. Locations Used for Assessment
Frigate Payload
SWATH Frigate
SWATH
Payload Destroyer Seakeeping Bridge Accelerations* Slams* Deck Wetnesses* 4.9 3.0 0.0 7.6 3.0 0.0 2.0 3.0 1.8 6.4 3.0 1.3 5.5 3.0 0.0 6.9 3.0 0.0 Displacement, LTSW 3,600 5,400 5,400 7,000 7,800 9,100 •Station • [ Naval Engineers Journal, May 1985
100 80 f) 60 1 40 l ü O (E Ml SWATH R I G A T E D E S T R O Y E R F R I G A T E P A Y L O A D 20 5 10 S I G N I F I C A N T W A V E H E I G H T (m) _ L _ J
\
L 4 6 7 SEA S T A T E 8Figure 5. Percent of Time of Operation in the General North Atlantic-Winter as a Function of Significant Wave Height for Six Hullforms
are presented as functions of the ships' displacements. This data differs from that in Figure 5 in that the prob-ability of occurrence of the various sea spectra across aU sea states is included. In this presentation, as weh, the
F R I G A T E • ANNUAL I ^ W I N T E R P 40 D E S T R O Y E R S E A K E E P I N G 4000 6000 8000 DISPLACEMENT (LTSWI
Figure 6. Percent of Tune of Operation as a Function of Displacement for Six Hullforms
two SWATHs and the Seakeeping monohull have cc parable PTOs. PTO calculations for these huUforms ing the three spectra and corresponding weights used reference [12] result in PTOs which are equivalent those in Figure 6 for all designs except the Frigate. F this huUform the PTOs which result from using t three spectra is about five percentage points lower th those for the general North Atlantic given in Figure UtUization of the weighting of spectra used m referee [13] results in PTOs which are approximately the sar as those in Figure 6.
In Figure 7 the PTOs for the general North Atlan* and the general North Pacific for both winter and a nual cases are presented for each of the hulls. Tl averages over all relative wave headings for each of tl five speeds considered are presented. These results she that for each of the two seasonal groupings, the PTC are essenfially identical. This is a reflection of the spe. tral modal period-significant wave height distributior given in Figure 4 which were simUar for each season grouping. Note that for aU speeds for the Frigat Payload monohuU, and Destroyer, the operabUity m th winter is 8 to 10 points lower than it is for the total yea whereas, for the other three configurations, there minimal reduction in operabUity in the winter.
In Figure 8 contour curves of the PTOs for the s: huUforms for the North Adanfic-Winter are presentee As expected, there are notable differences amor huUforms and at different geographical locations. Th, figure shows that all designs are predicted to be operab;
O G E N E R A L N O R T H A T L A N T I C - A N N U A L • G E N E R A L N O R T H A T L A N T I C - W I N T E R • G E N E R A L N O R T H P A C I F I C J k N N U A L • G E N E R A L N O R T H P A C I F I C - W I N T E R P A Y L O A D S W A T H J L T I r -• -• -• D E S T B O V E R J 1 I I L 10 16 20 S P E E D I k n o n l 1 0 16 S i r e E D I k n o o l
Figure 7. Percent of Thne of Operation as a Function of Ship Speed for Six Huilfomu
a large percent of the time at the southern geographical points. The operabihty of the Frigate and the Destroyer and, to a lesser degree, the Payload monohull degrades significantly as latitude increases. Operability of the two SWATH designs and the Seakeeping monohull design remains high at all geographical locations. Operabihty of the Payload SWATH and the Seakeeping monohuU are virtuaUy identical at aU points. Operabihty of the
SWATH Frigate also is exceUent. This is noteworthy, given its relatively smaU displacement of 5,400 LTSW. In Table 3 additional information concerning operabihty is presented. For each hullform and for each speed and several relative wave headings, the highest significant wave height at which none of the criteria is exceeded and the corresponding hmiting criterion is dicated. Since the locations for which motions are of
in-P A Y L O A D VATH ; \ \ SWATH ^ ^ " ^ ^ ^ 95 A S E A K E E P I N G
Fignre 8. Contours of Percent of Time of Operation in tlie North Atlantic Basin for the Winter
T A B L E 3. Limitiiig Signlficaot Wave Heights (Meters) and I Lhnithig Criteria for the General North Atbmtic T A B L E 3a. Frigate
Predominant Relative Wave Heading
Speed, Quar- Fol- Average
knots Head Bow Beam tering lowing PTO»' 5 4.2 (R) 3.1 (R) 2.4 (R) 2.5 (R) 3.1 (R) 38 10 4.4 (P) 4.8 (R) 3.3 (R) 3.4 (R) 4.5 (R) 7/ 15 3.9 (S) 4.4 (S) 5.6 (R) 4.9 (R) 6.4 (P) 85 20 3.6 (S) 4.0 (S) 5.7 (S) 6.1 (R) 6.7 (P) r/ 25 3.4 (S) 3.8 (S) 5.5 (S) 7.4 (P) 6.9 (P) 87 Average PTO 73 76 79 83 87 — Whiter T A B L E 3d. Payload S W A T H
Predominant Relative Wave Heading
Speed, Quar- Fol- Average
knots Head Bow Beam tering lowing PTO** 5 6.7 (S) 7.5 (S) 11.6 (P) 7.4 (?) 6.6 (P) 97 10 6.6 (S) 7.4 (S) 10.7 (P) 5.4 (P) 4.6 (P) 94 13 6.7 (S) 7.5 (S) 11.3 (R) 5.9 (R) 5.0 (R) 93 20 6.6 (S) 7.4 (S) 10.1 (R) 6.1 (R) 5.7 (R) 95 25 6.5 (S) 7.3 (S) 9.3 (R) 8.0 (R) 9.4 (R) 95 Average PTO 1Ö 99 95 9?, T A B L E 3e. Destroyer Predominant Relative Wave Heading T A B L E 3b. Payload Monohull
Predominant Relative Wave Heading
Speed, Quar- Fol- Average
knots Head Bow Beam tering lowing P T O " 5 4.8 (P) 5.3 (P) 5.0 (R) 6.0 (R) 5.9 (P) 85 10 4.5 (P) 5.0 (P) 6.0 (P) 6.7 (P) 6.2 (P) 89 15 4.3 (P) 4.8 (P) 6.1 (P) 7.0 (P) 6.6 (P) 88 20 4.2 (P) 4.7 (P) 6.1 (P) 7.2 (P) 6.6 (P) 88 25 4.2 (P) 4.7 (P) 6.1 (P) 7.2 (P) 6.7 (P) 88 Average PTO 76 82 92 94 91
Speed, Quar- Fol- Average
knots Head Bow Beam tering lowing PTO** 5 5.6 (R) 4.4 (R) 3.5 (R) 4.0 (R) 5.2 (R) 75 10 5.2 (S) 5.4 (R) 4.0 (R) 4.2 (R) 5.2 (R) 80 15 4.7 (S) 5.1 (S) 4.3 (R) 4.3 (R) 5.6 (R) 82 20 4.4 (S) 4.9 (S) 4.1 (R) 3.9 (R) 5.4 (R) 81 25 4.2 (S) 4.7 (S) 4.4 (R) 4.4 (R) 6.4 (R) 83 Average PTO 81 84 73 76 91 T A B L E 3f. Seakeepmg MonohuU Predominant Relative Wave Heading
Speed, knots 5 10 15 20 25 Average PTO
Speed, Quar- Fol- Average
knots Head Bow Beam tering lowing P T O ' *
T A B L E 3c. S W A T H Frigate
5 7.2 (P) 7.3 (R) 5.7 (R) 7.2 (R) 8.2 (P) 94 T A B L E 3c. S W A T H Frigate 10 6.5 (S) 7.6 (P) 9.5 (P) 9.3 (P) 8.5 (P) 97 15 5.9 (S) 6.4 (S) 9.5 (P) 9.6 (P) 8.8 (P) 97 Predominant Relative Wave Heading 20 5.4 (S) 6.0 (S) 9.5 (P) 10.0 (P) 9.1 (P) 96 Quar- Fol- Average 25 5.1 (S) 5.6 (S) 9.5 (P) 10.2 (P) 9.2 (P) 95 Head Bow Beam tering lowing P T O " Average
PTO 90 95 97 98 97
7.9 (P) 8.6 (P) 9.4 (P) 6.1 (P) 5.5 (P) 96 Legend for Exceeded Criterion
8.1 (S) 9.4 (S) 9.4 (P) 5.0 (P) 3.2 (P) 95 (Q = rate for control surface deflection 8.1 (S) 9.2 (S) 13.5 (R) 2.5 (Q 5.3 (R) 96 (P) = pitch
7.8 (S) 8.7 (S) 11.4 (R) 9.1 (R) 9.3 (R) 98 (R) = roU 7.7 (S) 8.5 )S) lO.O (R) 8.4 (R) 9.6 (R) 98 (S) = slams
**Average for all operating conditions, including those not presented 96 98 99 95 94 in this table
terest fall on the ships' centerhnes, these responses are equal for waves coming from port or starboard at the same angle. This reduces the number of tabulated cases. Also included are the average PTOs, with averages across both speed and heading. These averages are bas-ed on all the operating condhions considerbas-ed in this study. As can be seen, pitch, roll, and slams are the most frequently limiting criteria. Since short crested seas have been assumed, roh can be a hmiting criterion at all headings; whereas, for a symmetric ship in longcrested seas, roU is theoretically zero in head and fohowing seas.
CRITERION SENSITIVITY STUDY
In Table 3 the criteria which hmit performance for various operating conditions are given. However, the
table does not reflect how dominant a given criterion is. That is, if the hmiting value of one criterion is changed, the overaU operabihty may or may not change. As one approach to evaluating this dominance, a systematic in-vestigation was made of the effect of varying criteria on operabihty. The mobihty criteria given in Table 1 were used as the base criteria. Each of the criteria was then varied, m steps of about 50 percent with ah other criteria retaining the values hsted in Table 1. PTOs for the North Atlantic-Winter for each huUform are presented in Figure 9 for the variations indicated in the legend. This figure shows that altering roU by the amounts chosen has a substantial effect on the predicted performance of aU huUforms. With the exception of the roU effect, there is httle change in the PTOs for the SWATH Frigate, the Payload SWATH, or the Seakeep-ing monohuU design. Those variations which do occur
o a o & l O O i -4 R O L L 1 2 * R O L L 5 ' P I T C H 7' P I T C H CO 6 0 -JO ZO 0 < ï 8 0 -O O 6 0 -i >- 4 0 — u. O ( 20 -S T A N D A R D ( -S E E T A B L E 11 V E R T I C A L A C C E L E R A T I O H a . t i l V E R T I C A L A C C E L E R A T I O N O l O r t » S L A M S <5 M / h t S L A M S
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• -_ • • • • o 1 D E S T R O Y E H I 1 1 1 TOO ao » • » » » D a • S W A T H F R I G A T E J I L 10 15 20 S P E E D I k r w l i l S P E E D ( k n o t i )Figure 9. Percent of Time of Operation as a Function of Ship Speed for Systematic Variations in Operating Criteria for Six Hullforms.
are not significant, relative to the accuracy of the evaluation technique. The Destroyer shows insensifivity to the criteria at 5 and 10 knots. There is substantia variation for the Frigate and the Payload monohuU design across all speeds.
Figure 9 shows that the hullforms can be divided into two groups: the Frigate, the Payload monohuU, and the Destroyer which are sensitive to variations in criteria and the Payload SWATH, the SWATH Frigate, and the Seakeeping monohull which are insensidve to aU criteria except roU.
The Frigate has the largest sensitivity to changes in the criteria. As speed increases the sensitivity to the roU criterion decreases due to the effects of the automafic anfiroU system. At 5 and 10 knots the Frigate is insen-sidve to the other criteria, but at the higher speeds, criteria changes result in variations in performance up to about 10 points. The Payload monohuU is sensitive to changes in roll, most notably at 5 knots. Decreasing the other criteria does not decrease predicted operabihty; increasing the criteria results in increased operabihty up to 10 points. The Destroyer which has no antiroU fins is notably sensidve to variations in the roU criterion. A decrease in the roU criterion from 8 to 4 degrees results in a reduction of predicted PTO of about 30 points. This reduction does not improve with speed, due to the absence of antiroU fins. The Destroyer also is sensitive to the vertical acceleration criterion with the sensitivity
increasing with speed up to a reduction in the PTO of 10 points at 25 knots.
The Payload SWATH, SWATH Frigate, and Seakeeping monohull are essentially insensitive to changes in aU criteria except reduction in the roU criterion. For the Seakeeping monohull,the reducdon in PTO is alleviated as speed increases. This is not true for the two SWATH hullforms where a reduction in the PTO of ,15 points is indicated at 25 knots. This dif-ference between the Seakeeping monohuU and the SWATHs results from there being active antiroU fins on the Seakeeping monohuU and none on the SWATHs. For the SWATHs existing fins with an appropriate con-trol algorithm could be utUized to reduce roU motions.
As noted above, the criteria are considered to be in-dependent. That is, it is assumed that performance would be degraded if ship responses exceed the hmit for any one of the criteria. For each speed and heading, the PTO for a mission with criteria limits which were in-cluded in the sensitivity study could be determined. The PTO would be the minimum of the set of PTOs resulting from each of the appropriate criterion varia-tions. However, since the resuhs presented in the figures are averages for all the headings, operability for a mis-sion with criteria within the ranges considered here can oiUy be estimated. If, for example, criteria for a mission were identical to the standard set, except with a slam criterion of 10 slams per hour, the PTOs could be ap-proximated by the minima of the PTOs for the standard set and the 10 slams per hour set and would approx-imately equal the standard set PTOs. In contrast, if a 4 degree sigruficant roll limit were appropriate, the PTOs would correspond to the 4 degree roU variation PTOs. I f a 6 degree roU limit were approriate for a mission, the PTOs would be between those for 4 and 8 degrees.
This implies that for a variety of missions with a broad range of hmiting values for the performance criteria, the Payload SWATH, the SWATH Frigate, the Seakeeping monohuU, and, to a lesser extent, the Destroyer, operabihty would not be degraded from the mobihty PTOs. Missions wUh more restrictive roU criteria would have significantly degraded performance for all huUforms except the Seakeeping monohuU where the PTO remains close to 90 percent even with the reduction in the roll limit to 4 degrees.
CONCLUSIONS
The SOWM wave data demonstrates that there are significant variafions in significant wave height distribu-don with season and with longitude. A broad range of spectral modal periods occur for all significant wave heights.
The results in this paper show a range of predicted operabihty for mobility criteria for the four monohuUs and two SWATHs. Operabihty of the Frigate, the Payload monohuU, and the Destroyer vary with speed and geographical location; whereas, operability of the SWATH Frigate, the Payload SWATH, and the Seakeeping monohuU is consistendy high.
These latter three hullforms were relatively insensitive to systematic variations in all performance criteria ex-cept roll. For these two SWATHs and the Seakeeping monohuU for any mission with a roU hmit of 8 degrees or more and with other limits within the ranges con-sidered, operabihty would be insensitive to geographical location and ship speed. Even with a roU hmit of 4 degrees, the operability of the Seakeeping monohuU would remain close to 90 percent.
It should be noted that the consistently superior operabihty of these three huUforms is not accidental. The Seakeeping monohull was designed so that seawor-thiness was optimized. Although SWATHs are in-herently seaworthy, high operabihty is not inevitable. These SWATH hullforms were designed with an awareness of what hullform characteristics resuU in good seakeeping, although other constraints resuhed in less flexibihty in the design of the Payload SWATH than the SWATH Frigate.
Active control systems also contribute to high operabihty. The Frigate, the Payload monohull, and the Seakeeping monohull all of which have active antiroU systems show less sensitivity to variations in the roU criterion than the other hullforms. The SWATH designs include active control systems which aUeviate only ver-tical plane motions. The results in this paper confirm the need to utUize existing fins on SWATHs to also alleviate roll. For ships with equipment with sensitivity to roll, adequate roU stabihzation capability is essential to sustained operability.
ACKNOWLEDGEMENTS
The development of the evaluation tool described in this paper has been funded over a period of years by the Exploratory Development Program on Ships and Sub-marines Technology. This development benefited from many U.S. Navy projects, including the Exploratory Development Program on Surface Waves which sup-ported development of the wave data base.
Ms. Dana GentUe of ORI, Inc. developed the ex-tended wave data base utilized by the computer pro-gram. Ms. Beverly Shnon of David W. Taylor Naval Ship Research and Development Center (DTNSRDC) developed the computer program that generates the con-tour plots.
Technical discussions with Mr. Edward Comstock of Naval Sea Systems Command during the course of the Naval Studies Board effort were of great value and pro-vided insights mto the seakeeping interests of the naval design conununity. The discussions with him during that effort influenced this effort. Mr. David Walden of DTNSRDC sized the Seakeeping monohuU from the Hull 23 and developed the transfer functions for the monohuUs with the support of Ms. Dana GentUe, m conjunction with his participation in the Naval Studies
Board effort. Mr. Geoffrey Cox and Dr. Ernest Zamick of DTNSRDC modeled the automatic control systems for the monohuU and SWATH designs, respectively.
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