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AD-A245 643

A TRIDENT SCHOLAR PROJECT REPORT
NO. 184

OPEN-WATER RESISTANCE AND SEAKEEPING CHARACTERISTICS OF SHIPS WITH ICEBREAKING BOWS

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UNITED STATES NAVAL ACADEMY ANNAPOLIS, MARYLAND

92-02845
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U.S.N.A. - Trident Scholar project report; no. 184 (1991)

OPEN-WPTER RESISTANCE AND SEAKEEPING CHARACTERISTICS OF SHIPS WITH ICEBREAKING BOWS

A Trident Scholar Project Report by

Midshipman Casey J. Moton, Class of 199 U.S. Naval Academy

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Annapolis, Maryland

Advisors:

Professor Roger H. Comp n Professor Bruce C. Nehing Naval Systems Engineering D pjt

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Accepted for Trident Scholar Committee

Chair "Date

USNA-153 1-2

REPORT DOCUMENTATION PAGE

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Form Approved AM8 No 070-470188

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113May 199 1ia
4. TITLE AND SUBTITLE

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5. FUNDING NUMBERS

OPEN-WATER~ RESISTANCE AND SEAKEEPING CHAATRISTICS OF SHIPS WITH ICEBREAKING BOWS
6. AUTHOR(S)

Casey J. Moton
7. PERFORMING ORGANIZATION NAME(S) AND AORESS(ES) 18. PERFORMING ORGANIZATION REPORT NUMBER

U.S.

Naval Academy, Annapolis, MD

U.S.N.A. - TSPR; 184 (1991)

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Accepted by the U.S.

Trident Scholar Committee.
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13. ABSTRACT (Maximum 200 won~s)

Most research conducted on icebreaking ships has concentrated on their performance ir. ice fields. One area that has been neglected is the performance of such ships durinrtheir transit from their homeport to the ice field. The experimental research under-taken is intended to show how variation of icebreaking hull shape parameters will aff'ec Open-water powering and seakeeping performance. Based on a current U.S. Navy icecapable ship hull form, a parent huil and four systematically varied hull forms were designed, fabricated, and tested in calm water and regular waves in the U.S. Naval Academy's Hydromechanics Laboratory 38 0-foot towing tank. Bow shape parameters considered to be of major importance-for icebreaking--specifically, the waterline angle and the section flare angle at a point 10 %~ of the waterline length aft of the fozward perpendicular--were varied over ranges dictated by current "good icebreaker practice." Calm water resistance as well as pitch, heave, relative vertical motion, and added resistance due to waves in long crested head seas were determined on the basis of model tests using eight foot long models.

UIIUECTTRMS15. IAL Ice-breaking vessels Hulls (Naval architecture) Ships--Seakeep~ing
17. SECURITY CLASSIFICATION OF REPORT

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The experimental research undertaken as the core of this Trident Scholar project is intended to show how variation of icebreaking hull shape parameters will affecopen-water powering and seakeeping performance.specifically. with both a light icebreaking mission requirement and either a cargo-carrying or a research mission requirement. Bow shape parameters considered to be of major importance for icebreaking performance . seakeeping is of little importance in ice covered waters. a parent hull systematically varied hull forms were designed. The recent interest in "ice-capable" ships. the waterline angle and the section flare angle at a point 10% of the waterline .S. and tested in calm water and regular waves in the U. and. dictates that ships designed to meet such requirements have greater emphasis placed on their open-water transit characteristics. and four form. Powering requirements are dominated by resistance in ice. of course. One area of their operations which has been neglected is the performance of such ships during their transit from their homeport to the ice field. fabricated.S.ABSTRACT Most research conducted on icebreaking ships has concentrated on their performance in ice fields. Naval Academy's Hydromechanics Laboratory 380 foot towing tank. Navy ice-capable ship hull Based on a current U.

.were varied over ranges dictated by current "good icebreaker practice.2 length aft of the forward perpendicular . and added resistance due to waves in long crested head seas were determined on the basis of model tests using eight foot long models. heave. relative vertical motion." Calm water resistance as well as pitch.

43 5.......51 6...... INTRODUCTION...90 APPENDICES..... STILL WATER POWERING RESULTS....................... ......................... ........ SUGGESTIONS FOR FUTURE RESEARCH..79 8.........59 7..................11 3......... BASIC ICEBREAKING THEORY........92 .......3 TABLE OF' CONTENTS SUBJECT ABSTI CT..88 REFERENCES..... 17 .... SEAKEEPING RESPONSES... PARENT HULL SELECTION AND BOW FORM VARIATION 4.. EXPERIMENTAL TEST PROGRAM......9 2...... FLOW VISUALIZATION ANALYSIS........ ...... PAGE NO...................85 9.........1 1............... CONCLUSIONS.........

.... 4-3. 6-8... ... .... 6-4.......... .. Example of a Knuckled Forefoot on a Typical .. 5-2... ... Definition of Bow Form Angles .. Forebody 5 . Normalized Model Relative Bow Motion @STA2...... ..... Forebody 2 . .. 2-2.. . 6-2..... ........ 6-5.. 4.. CR versus Fn . . ....... ..... 70 ... Afterbody ... ..... 2. . I *.... ...*...... PAGE 13 13 19 23 26 28 30 31 32 33 34 36 40 44 45 48 4-4........ .... Shimansky Icebreaking Coefficient Parametric .....67 ..... .67 ......... Forebody 3 . ... Lines Plan... .. Curve of Icebreaking Pressure Coefficient... ... 4..... ... 6-3...... . Lines Plan.. Normalized Normalized Normalized Normalized Model Model Model Model Pitch Pitch Heave Heave Response....... 5-1..67 4. 71 Normalized Model Added Resistance in Waves.... Lines Plan..... Thickness ...... Bow 5 After Cutting by the NC Mill Machine ITTC Description of the NAHL 380' Tow Tank Dynamometry and Carriage Towing Attachment ITTC Description of the NAHL 120' Tow Tank .01 fps fps fps fps . .. .4 LIST OF FIGURES FIGURE 2-1. 3-11.. Flow Visualization Test Run in the 120' Tank .. ..." fps .. .*... Comparison. ..... fps . 50 53 54 57 63 64 67 68 .... . 7-1..._.5 knots .. ..'Fb=l . 75 .. 3-6. ... Comparison Plot.67 4..... 3-7.. Normalized Model Added Resistance in Waves...... Lines Plan...P..01 fps . 3-8. ........... *... 3-9. 6-1.... 2..*. Lines Plan.... .. .... . Forebody 4 .....*.. Icebreaker .I.... Normalized Model Relative Bow Motion'@STA2. Lines Plan.. With Comparison Against Other Icebreakers . 3-1.. Response. * 3-2. 3-5. 4-2... ... .... 6-7... . 4-1. ... .01 76 fps .... Ship Velocity in Ice as a Function of Ice ..... . T-AGS OCEAN (ICE) ... ... . Response.......... 5 knots ...... 3-10...... 5-3.01 2.... .. .... . 3-3. . Response... Forebody 1 (Parent)..... 2.... 82 Flow Streamline Comparison. 6-6.. 12.. 7-2.. .. Comparison Plot. Still Water EHP versus Ship Speed. Total Ship Resistance versus Froude Number...... .... . 81 Flow Streamline Comparison. . .. 3-4..... Lines Plan...*.*.. e Bw .

3-2..................... 69 Expanded RBH @STA2 Response... 10 kts .... 15 kts .. 72 Expanded RBM @STA2 Response... Vs=15 kts ... 15 kts .. 15 cts ... 6-2a........ 72 .. .... 10 kts .... 39 EHP Comparison. 65 Expanded Pitch Response.. 5-1. 6-4a. 6-3a. PAGE Model Parameters ... 6-1.... 38 Ship Parameters.. 55 Pitch and Heave Natural Frequencies .. 6-4b...... 65 Expanded Heave Response........... 10 kts ........................... 6-2b.......5 LIST OF TABLES TABLE 3-1... 69 Expanded Heave Response..... 62 Expanded Pitch Response. 6-3b...........

SAX/(BWL X T) DESIGN WATERLINE EFFECTIVE HORSEPOWER ICEBREAKING HULL PRESSURE COEFFICIENT . INC. ITTC 1957 V/(L x BWL x T) FRICTIONAL RESISTANCE FORMULATION COEFFICIENT CFm CFs CP CR CTm CTs C Cx DWL EHP Fb MODEL FRICTIONAL RESISTANCE COEFFICIENT SHIP FRICTIONAL RESISTANCE COEFFICIENT PRISMATIC COEFFICIENT. CT-CF MODEL TOTAL RESISTANCE COEFFICIENT SHIP TOTAL RESISTANCE COEFFICIENT VERTICAL PRISMATIC COEFFICIENT. V/(Aw x T) MAXIMUM SECTION COEFFICIENT. V/(SAx x LWL) RESIDUARY RESISTANCE COEFFICIENT. AFTER PERPENDICULAR WATERPLANE AREA AT DESIGN WATERLINE BEAM BASELINE MAXIMUM OVERALL BEAM MAXIMUM BEAM AT DESIGN WATERLINE CENTERLINE CORRELATION ALLOWANCE BLOCK COEFFICIENT.6 LIST OF SYMBOLS AME AP Awp B $ Bmx BWL t CA C1 CF ADVANCED MARINE ENTERPRISES.

KEEL TO DECK-AT-EDGE g H ITTC INTERNATIONAL TOWING TANK CONFERENCE KM L KM T kzz L LCB LONGITUDINAL METACENTRIC HEIGHT TRANSVERSE METACENTRIC HEIGHT YAW MASS GYRADIUS LENGTH LONGITUDINAL DISTANCE FROM AMIDSHIPS TO THE CENTER OF BUOYANCY LCF LONGITUDINAL DISTANCE FROM AMIDSHIPS TO THE CENTER OF FLOTATION LCG LONGITUDINAL DISTANCE FROM AMIDSHIPS TO THE CENTER OF GRAVITY LOA LPP LWL MIZ LENGTH OVERALL LENGTH BETWEEN PERPENDICULARS LENGTH ALONG THE DESIGN WATERLINE MARGINAL ICE ZONE NAHL NAVAL ACADEMY HYDROMECHANICS LABORATORY RAO RBM Rn RT RESPONSE AMPLITUDE OPERATOR RELATIVE BOW MOTION REYNOLDS NUMBER TOTAL RESISTANCE SAX MAXIMUM SECTIONAL AREA .7 FP FPS Fn FORWARD PERPENDICULAR FEET PER SECOND FROUDE NUMBER ACCELERATION DUE TO GRAVITY HULL DEPTH.

8 S1/3 $I/IO SWH T TF TLR TSD AVERAGE OF 1/3 HIGHEST NUMERICAL VALUES AVERAGE OF 1/10 HIGHEST NUMERICAL VALUES SIGNIFICANT WAVE HEIGHT DRAFT TRANSFER FUNCTION TOP LEVEL REQUIREMENT TECHNICAL SUPPORT DEPARTMENT USNA UNITED STATES NAVAL ACADEMY Vm Vs MODEL VELOCITY SHIP VELOCITY aWATERLINE ANGLE FLARE ANGLE "1 ICEBREAKING COEFFICIENT ICECUTTING COEFFICIENT SCALE FACTOR ICEBREAKING HULL EFFICIENCY STEM ANGLE WATER DENSITY AMIDSHIPS 172 I go 0 p A V DISPLACEMENT VOLUMETRIC DISPLACEMENT .

More break recently. The mission requirements of such ships often include operating in areas of lesser ice . mission of these ships is to After all. icebreakers have enabled the accomplishment of both commercial and military Arctic/Antarctic missions. and the maintenance of economic routes in the Northwest Passage. INTRODUCTION Icebreakers have long played a vital. overlooked role in maritime operations. however. as many of their ports and coastal areas are ice-covered much of the year. U. designers of icebreakers have concentrated on the ship performance in an ice field. The United States has recognized the importance of icebreakers. and many northern harbors. the primary through ice. driven by the goal of improving Hull forms are ice-breaking capability. Countries such as Canada and the Soviet Union have always recognized the importance of icebreakers.S. minimizing total resistance in ice. research in ice-covered waters. and lessening structural loads and damage due to ice impacts. essential to the economic and military Icebreakers are survival of such countries. Traditionally.including platform supply and oceanographic research. the Great Lakes.9 1. search and rescue. there have been needs identified requiring ships whose primary missions require the ability to perform unescorted missions in ice-covered waters . yet to much of the world.

and relative bow motion at Station 2 (of 20) were measured in regular. analyzed and then compared. specifically open water powering and seakeeping performance. little research has been done to quantify how varying the hull form parameters which affect icebreaking will affect seakeeping and powering. These ships are normally homeported in distant U. flow visualization in calm water. To date. move the designer to investigate ways to vary hull form so as to satisfy these operational concerns. ports and thus must make long open ocean transits to and from their ice-covered operating operate areas.10 thickness such as the Marginal Ice Zone (MIZ). long crested waves. The goal of this project is to take a parent hull which is representative of ships that must both operate in ice and make long open water transits. The results for each model were . Pitch. Tests were performed on the selected parent and four variations. These tests included effective horsepower (EHP) in calm open water.S. designed although to the effectively icebreaking requirements are less than those of the larger polar icebreakers. safely These and ships still must be in ice. heave. added resistance due to waves. and seakeeping in head seas. New concerns. and to perform model tests on a series of systematic shape variations of that parent.

ice. angles. is a complex matter. the ship progresses at a relatively slow but steady forward speed. In the continuous mode.ii 2. it which may not be A brief introduction familiar to into the some naval icebreaking process. as are trim The most characteristic feature of this mode is that icebreaking is performed by flexural bending of the ice along the entire forebody waterline from the stem to the section of maximum beam. the ship begins to lose the capability to maintain a steady forward speed. Then the raked stem of the icebreaker rides up onto the ice. a small specialty within naval architecture. As ice thickness increases. BASIC ICEBREAKING THEORY Icebreaker design. The process of icebreaking can be divided into two basic modes: the continuous mode and the ramming mode. and enters a transition into the ramming mode of icebreaking. and there are aspects and terms within architects. . Vertical accelerations are small. initial failure of the ice occurs by simple crushing. the icebreaker can no longer sustain constant speed. and a look at a current method of quantifying some of the geometric characteristics of icebreaking hull forms is in order. and As the stem strikes the then charge ahead towards the ice. In the ramming mode. dependent largely on ice strength and thickness. It first must back away from the ice.

Ramming mode analyses tend to be much more empirical and difficult to verify. applied to the ice at the stem of the icebreaker causes structural failure of the ice sheet. backs away from the ice and repeats the The ship then process [1]. while continuous mode analyses tend to be more theoretical and easier to substantiate.12 resulting in increasingly large bow up trim angles. The ship's weight. the important idea on which to focus is that the best hull form must maximize "the conversion of [forward] thrust into a combination of downward (to break. Fortunately. This failure usually results in both radial and circumferential breaks which result in floating ice fragments. Ramming mode performance is much more difficult to analyze due to its transient nature."[2] Stem and . and increased resistance to forward motion until progress stops. certain key hull form parameters have been shown to improve performance in both continuous and ramming modes. When considering these hull parameters. Intuitively. and submerge the ice) and transverse (to move the ice out of the [ship's] path) forces. the shape of an icebreaker's hull must have a large effect on its icebreaking capability. Continuous mode performance is easier to analyze and describe due to its steady nature. Figure 2-1 shows how ship velocity varies with ice thickness and indicates the approximate operational limits of the continuous and ramming modes. tip.

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14 forebody form determine this capability more than any other parts of the hull. forward of amidships and entrance angles are This full forebody characteristic improves maneuvering. where they may cause serious damage and (2) shaping the stern such that astern operation into broken ice will not result in damage or lack of ship control/mobility when backing down. when a ramming attempt is unsuccessful. but may cause open water resistance to increase sharply and may affect seakeeping performance. This is accomplished by As especially when in the ramming mode. the station of maximum beam is usually well quite large. primarily in the ramming mode. the ship will have to use its engines to extract itself from the ice. The major goal of this study is to provide guidance to the designer relative to the tradeoffs between continuous mode icebreaking and open ocean performance as they are affected by . In particular. a result. The stern and afterbody have little effect on the normal icebreaking capability of the ship. the center of buoyancy is rather far forward (relative to non-icebreakers). The primary design concerns are (1) preventing ice chunks from flowing into the rudders. screws and after appendages. The stem angle of the ship plays an important role in icebreaking. designing the forebody of an icebreaker to be quite full. More displacement forward is an objective. plays a major role in determining the Stem angle force extraction magnitude.

the flare angle. total transverse force to the total longitudinal These coefficients are defined as follows [3]: f tanatan3 (l+tan2 a) 1/2 dx 0 m f l+tan2 a+tan2 2 /2 tan 2a (l+tan a) dx 2 a+tan 2 P 0-ftan (1) o= (l+1/vh) (2) Here. 0. fi 1. and the stem angle. These coefficients are dependent on two hull form angles. have developed and published a widely accepted method of predicting icebreaker performance in the continuous mode icebreaking. then used the coefficients in a method to Kashteljan the predict resistance of a ship while actually breaking ice. and the waterline angle. Shimansky and Kashteljan. is the icebreakinQ coefficient. the icecutting coefficient. P. are defined in Figure 2-2. Shimansky began the work by defining coefficients dependent on forebody form and relating them to total downward force and the ability to break ice. dependent only on the icebreaking coefficient. Both of these. which relates force. go is hull efficiency. The first coefficient. a. which relates the total vertical force to the total longitudinal force. The second coefficient is '2. The coefficients may be calculated .15 bow shape. Two Soviet naval architects.

Kashteljan's algorithm is especially useful because it accounts for ship size. and 3. and. m. are the two coefficients commonly calculated to facilitate comparisons of different icebreaker hull forms. and Kashteljan's method. The correlation between the predicted resistance using Kashteljan's method and full scale results from tests involving the icebreakers MOBILE BAY and KATMAI BAY are very close. By determining the value of these coefficients for each hull. velocity. more importantly for this project. are the generally accepted standard for predicting force relationships and resistance in continuous mode icebreaking. Shimansky's coefficients. bow form. one can postulate that the series hull forms represent acceptable shapes for icebreaking ships. ice strength and ice thickness. to Recommended values for these coefficients are 1.0 and 72 to the station of maximum beam. Any hull having coefficients to have good continuous respectively these is close considered icebreaking characteristics.4 [4].0. the significance of the coefficients I0 and n2 [5].16 mf tana (1+tan 2 a) 1/2 -dx 2 a+tan P 2a tan+tan (l+tan2a) 1/2 dx 2 f f1 f l+tan 2 a+tan 2P by integrating expressions involving the flare and waterline angles from the forward perpendicular . verifying the validity of his arguments. .

The parent was to be representative of such ships. The desired hull form was to have a mission which required light ice operation.S. related Peter literature of and through Marine consultation Zahn. Selection of the parent hull form was done both through analysis of icebreaking with Mr. The systematic variation systematic series was limited by the practical constraints of time and money to four variants and the parent. but which also included long open ocean transits from its homeport to the MIZ operational area. and Mr. Thus.17 3. the nature of the of the parent was determined. of Band Lavis and Associates. Navy icebreakers and MIZ ships. a parent hull selected and defined by a standard lines drawing. there were to be no special appendages which might mask the effects of basic hull shape on open water performance. form could be Knowing these characteristics. both of whom have extensive experience in designing U. Daniel Bagnell. Advanced Enterprises (AME). the first major task was to identify the important hull form characteristics of icebreakers. . skegs. propeller shaft bossings. PARENT HULL SELECTION AND BOW FORM VARTATION After formulation of the problem. with no unusual features which would lessen the general usefulness of the performance data acquired from the model tests.S. Coast Guard and U. rudders. Once a parent form was selected. In addition.

The flare angle.C. Kashteljan suggested the consistent with classical angle. Melberg. often have a prominent forefoot (as in Figure 3-1) which is especially useful in the ramming mode of icebreaking. To ensure that the parent and its variants satisfied the light icebreaking requirement.69 0. is near 45 ° for medium and heavy icebreakers. The waterline angle.0 3. 0. L.70 As far as bow form angles. typical to icebreakers. a. defined earlier in Figure 2-2 are concerned. but often less for auxiliary icebreakers.1 0.57 < < < < L/B B/T CB Cp < < < < 5.5 2. practice to the [7].42 0. P. al suggest "good practice" limits on the following design variables for polar icebreakers: 3. defined with following values. research was done to determine ranges of hull parameters [6]. Such a knuckle in the stem prevents the bow from riding so far onto the ice that extraction becomes extremely difficult barring .7 0. which are The stem Soviet respect design waterline. is generally near 30*. Most icebreakers have a longitudinal center of buoyancy (LCB) forward of amidships. This places the center of gravity forward Icebreakers and thus facilitates the icebreaking process. and a station of maximum beam as far forward as possible while still maintaining reasonable waterline angles. generally should fall between 24 ° to 300 for icebreakers.18 and special stem forefoot shapes were not included in the shapes tested. et.

19 4-3 ) -J 4-) 0 0 S- C) .

the loss of stability when effectively grounded becomes a concern. transom stern.#.20 failure of the ice. Mr. twin screws and rudders for good low speed maneuverability and station keeping. with large after deck area L/B of around 5. was oceanographic research in the MIZ. Bagnell. 3.O) in the general icebreaker range No forefoot knuckle Several different hull forms were considered. in turn. or.6 Forebody angles (a. This requirement. 4. results in Most ships of this type have providing a flat. twin rudder Transom stern. the BAL #77 icebreaker. 6. 5. the DDI icebreaker. in the higher limits of the icebreaking range. and a planned ice-capable research ship for the National Science Foundation (NSF). Among the hull forms considered were the POLAR Class. Because none of the foregoing icebreakers had an oceanographic mission requirement . form requirements dictated by the oceanographic The hull research mission included a large after deck area to facilitate overthe-stern research. A list of general hull characteristics for the parent form was drafted. Twin screw. the Japanese SHIRASE. Zahn and Mr. again with the practicing icebreaker naval architects. representative of those requiring light icebreaking and efficient open-water transits. The MIZ oceanographic research ship with light icebreaking capabilities should have: 1. 2. but the middle of the research ship range. It was decided that a suitable mission. with LWL about 300 feet C8 of about 0.

the hull lines drawing. the automated hull geometry package in use at the U. Most fell within the overall hull parameter value ranges.e. a transom stern and large deck area aft for oceanographic research.S. i. hull Ideally. twin rudders. and all represent "currently accepted practice. the search for a current icebreaker design to use as a parent led to the FY92 T-AGS OCEAN (ICE).. the use of an automated (computeraided) means of lines development was necessary. With the requirements to design five systematically related hulls and to fabricate them within a severely constrained time period so that tank testing in all five could be performed. and thus had insufficient after deck area and excessive freeboard aft.21 besides the NSF ship." The NSF design was considered unacceptable from a powering standpoint because of the excessive slope of the afterbody buttocks. would greatly facilitate both the model fabrication and the systematic variation of the forebody shape for other members of the series. a form already defined in FASTSHIP. an ice-capable oceanographic survey ship designed to satisfy mission requirements developed by the Oceanographer of the Navy. Naval Academy. A practical consideration in adopting a parent hull form was the availability of good hull geometry definition. The resulting ship design featured twin screws. Perhaps purely serendipitously. their sterns were of conventional cruiser form. The ship's mission required it to .

Also.5 Station 2 (10% °. In addition. Naval Academy is shown in Figure 3-2. This ship will be a light icebreaker. and a station of maximum beam forward of amidships. a tight bilge radius joining sides of approximately constant slope with a constant 15 ° deadrise bottom. al. a waterline angle of 20. an MIZ characteristic.50 at forward perpendicular). the preliminary lines were available from Advanced Marine Enterprises FASTSHIP surface file. and a flare angle of 24. or ice-capable ships. (AME) as a A reduced scale lines plan of the T- AGS OCEAN (ICE) parent after final fairing at the U. besides being a ship incorporating the kind of compromises necessary between icebreakers and research-oriented ships. intended to break a maximum of three feet of first-year ice. low freeboard aft (advantageous for research). covers many of the operational characteristics and requirements of the parent hull [8]. hull parameters fell within the accepted range of light icebreaking. . The ship had a large amount of parallel midbody (30% LPP). a report detailing the "Feasibility Studies for an Ice Capable Oceanographic Research Survey Ship FY92 T-AGS OCEAN (ICE)" by Strasel. a LWL of about 318 feet. et.22 make long open-water transits ending in operations in the MIZ.S. with a L/B of 5. design has no knuckled forefoot. a stem angle of 36 ° . The T-AGS OCEAN (ICE) Finally. LPP back from the Parameters slightly outside of the acceptable range for most icebreakers were rationalized since the classical values were given for medium and heavy icebreakers.48.

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24 Once the parent was chosen, the next major task was to decide upon the hull parameters to be varied, the ranges of the variations, and those parameters to be held constant. Again, the only practical restriction was that four variations could be designed, built, and tested plus the parent within the limited time available. Logically, the number of

parameters to be varied systematically needed to be low, so that it would be possible to In addition, it isolate the effects of the was desirable the to select

variations. parameters

considered to be

important to

icebreaking

performance of the ship. After studying much of the current literature on

icebreaking hull forms,

it was decided that the two most

important and reasonable val.es to vary were the flare angle, P, and the waterline angle, a. as defined in Figure 2-2 at a point 10% of LPP aft of th2 for.'ard perpendicular (Station 2) at the design that waterline. these quantify All of were the the references best mode cited to

indicated

values the

ones

mathematically

continuous

icebreaking

effectiveness of a ship, both in relation to its resistance in ice and its icebreaking capability. Specifically,

Kashteljan's widely accepted icebreaker design methods use these angles in icebreaking resistance equations, in the form of the coefficients, AO and 17" One side effect of the a

importance placed on these two angles is also noteworthy: large data base exists for various icebreakers.

A primary

25 consideration in their variation was that they should not go so far as to cause doubts as to the icebreaking performance of the systematically varied hull forms. This was particularly

important as ice testing of models is beyond the technical scope of this project. of the Such testing is not within the

capabilities Laborato-y.

U.S.

Naval

Academy

Hydromechanics

Once the decision to vary these angles was made, it was necessary to define a range over which they would be varied. Again the objectives were to modify them in a systematic

manner, with changes large enough to be noticeable, but not so large that they placed the hull form out of normal icebreaking ranges. Advanced Marine Enterprises (AME) provided

information [9] which correlates good hull angles with ice loading, under the assumption that the loading is a function of a pressure coefficient, Fb, which is a function of a and P. Assuming that reduced hull loads are a desirable

characteristic of an ice capable hull, reduce Fb as much as possible.

it is desirable to

A value of Fb = 1.00 is taken

to represent the nominal value of the pressure coefficient and any combination of a and P yielding Fb = 1.00 wo~id also be nominal. a and P. Figure 3-3 presents a plot of Fb = 1.00 versus both Values of a and P at 10% LPP aft of the FP for some

"heavy" icebreakers are plotted to define the full end of the reasonable range of these angles. The box on this curve

defines the traditional ranges of Soviet design practice.

M (10 E0 4-L -f 13 L S- 00 0 t)L() 00 r4 ) 0 0 0 . O 4-5 0~ 4-) 0a)I 4-4 0 fi' 44C-. 11 ' C 1~0 '0 (A> Ut 0 E.4-3 > C >0 ) Q) 4-~4 4-- I 4-00 u 4-) 4.26 0 LnC .

effects of the afterbody on the open-water performance could be disregarded in a comparative analysis. any as to have zero static trim. . and the afterbody (aft of Station 9). while light icebreakers (or even non-icebreakers) have lower values. While the angles could be changed to the predetermined values. all models were ballasted so By using a common afterbody. As a rule. These "constant" characteristics were the draft. AME provided the initial surface file for the parent Final fairing was done hull form during the summer of 1990. while one (Bow 3) had lower values. other characteristics of the hull should. Figure 3-3 also shows the parent hull form and the four different combinations of a and P which were chosen as the tested modifications. intended to provide a reasonable curve along which values of a and P could be chosen. Figure 3-4 shows the lines of the common afterbody which was present for all models. remain constant. It is not the purpose of this graph to provide the It is only feasible combinations of these bow form angles. waterline length. ships intended for heavy icebreaking have larger values of a and P. Three of the bow variants had angles larger than the parent. as much as possible. In addition. while maintaining them in a range where the icebreaking effectiveness can not be strongly doubted. The previously mentioned FASTSHIP hull definition program was used in the bow variation process. maximum sectional area (and shape).27 Placing one of the four variants within this box was desirable.

28 z ~ ~- C ~ 0 c*: w C --- z -~ C z -~ C C. ci -~ WCJ ci: I -~ 0 - ci o C.t: ci ~i C E - U . r.

although FASTSHIP facilitated the hull fairing process overall. taking an already designed and faired surface file and attempting to force the flare and waterline angles to set values while refairing the hull was a difficult process. Extreme afterbody necessary. Bow 3 was the only forebody with smaller values of a and 0 .S. care at in fairing all forebodies at and the common 9 was was their Not common the interface same cross Station only section shape required. Figures 3-5 through 3-9 show the lines for each of the series forebodies. Bow 2 had the next larger values of a and p. It should be noted that. By so doing. which resulted in a small increase in LWL of about 0. to be Onecommon afterbody five models constructed. continuity of longitudinal hull slopes and curvature must exist across the joint at Station 9. and the added geometric restriction application as imposed by the intersection at Station 9 made the task even more difficult. The change in the angles did not The only cause great difficulty in fairing for this bow. Bow 1 was the parent. only the geometric changes in the forebodies would be affecting the performance of the hulls.an afterbody section (from Station 9 to the stern) and and a forebody bow or bow were section. also. change was a slightly different stem angle.05 inches for the model. Naval Academy. The hull form was split into two different surfaces . FASTSHIP was not designed for such a specialized this.29 on the file at the U. but.

Co.30 C W Lr) cI f- . .

/ .31 c'J Co.

32 C: (1) - 0 z w w L .

33 - - - -CN rcr zc .

> .34 __IN. N N 1-4- -~I cm- c.

35 than the parent. the resulting for a hull P shape fell within for Bow With the recommended icebreakers. It is noted that these non- systematic hull changes were introduced only if absolutely necessary to fair in the angles for that bow. and a slight decrease in LWL (0. Figure 3-10 presents the values of the two Shimansky coefficients for each bow modification. any local unfairities in the lines are practically unavoidable when using FASTSHIP in such an unconventional manner. As with Bow 2. Also plotted are the values of the coefficients . ranges and established Soviet The station of maximum beam was even farther forward to fair the hull with the new required a. 5 was the final bow. For both Bow 4 and Bow 5. with the largest values of a and P. Bow 4 had values of a and 1 which were large enough to cause new problems in fairing. the LWL was kept constant. slight areas of unfairness were resolved in the Such as-built models by close interaction with the model maker during the final hand fairing process. while the beam almost to the FP had to be increased at the waterline to enable the large P value.04 inches for the model). calculated using the sets of values of a and P at equal length intervals from the FP to the station of maximum beam as measured from the model lines plans. In addition. fairing using FASTSHIP resulted in a similar change in stem angle. Bow 5 faired. but the location of the station of maximum waterline beam was extended forward somewhat to enable the increases in a.

36 / CN 4C ) z3 / / 04 / / E Q CILJ 0 00 * 004- Q Ln~ -x re L .

icebreakers. 5 falls near other heavier icebreakers. some of which Bow 4 falls among medium on the Great Lakes. as expected their angle variations from the parent are the least. Bow l's coefficients place it in the light since icebreaking category. a and 0. FASTSHIP was used to create numerical data files for each surface. waterline cuts were made by the NC mill machine.S. All hulls were milled from blocks of high density. Bow 4 and Bow 5. The desired molded hull shape was physically defined by waterline cuts spaced no more than a quarter inch apart over the entire length of the models. with the bow angles. and the MACKINAW. due to their larger bow angles and their increased beam in the forebody. Naval Academy's Technical Support Department (TSD). a scale factor. Bow 2 and Bow 3. fall fairly close to Bow 1. 1. After final lines preparation. of 39. including the PIERRE RADISSON hull form.37 for many other icebreakers. are much nearer the normal icebreaker range.75 are presented in Table 3-2. Bow operate including the WIND Class. Figure 3-11 shows Bow 5 after the final Each hull closed cell foam. the GLACIER. . These files (NC) were used to interface with the numerically controlled milling machine in the model shop of the U. A summary of model shape parameters is provided for all bows in Table 3-1. This figure confirms that in no case did any of the series hull forms exceed normal icebreaker ranges. including the Shimansky coefficients and The expanded ship parameters.

04 13.003 -4.712 0.989 -4.858 0.604 9.774 8.205 1.38 TABLE 3-1.25 23.282 0.764 9.111 0.581 0.433 1.5 36.858 0.5 22.065 190.688 0.686 0.459 3.674 0.0 29.056 0.577 0.846 0.751 3. Model Parameters (1=39.298 13.584 1.595 0.584 1.199 1.635 1.416 1.854 2.459 3.644 1.311 14.682 7.5 18.25 23. LCF: + forward amidships .678 0.331 31.5 20.694 0.590 8.75 16.5 36 1.433 1.003 -3.858 8.673 CVP 0.459 3.577 0.584 1.877 3.678 0.433 1.433 1.5 36.665 LOA (ft) B.293 KM' (ft) KM I (ft) 0.293 13. Bmy (ft) (ft) (ft 3 ) (lb) (ft 2 ) V A WSA LCB* (in) Kzz (ft) LCF* (in) Awp C_ Cp C__ _Cy (ft2 ) 0. 673 0.013 -4.5 (°) (0) 1.011 8.429 0.957 8.517 10.286 13.052 8.5 26.503 2.018 188.842 0.433 1.001 189.223 ?_2 + A: in Fresh Water.377 1.99 13.566 2.998 186.0 31.329 14.858 0.492 1.202 2.658 3.687 10.876 0.75) Bow 1 Bow 2 Bow 3 Bow 4 Bow 5 LPP (ft) 8.709 0.096 192.125 2.700 at 0 __ (°) _ 24.234 0.459 3.858 0.513 2.016 8.584 1. Tank test temp.470 2.854 9..5 42.004 -2.244 1.305 1.99 13.857 0. 66 13.459 2.011 8.91 13. * LCB.895 0.

61 3.857 -15.75 16.503 2.751 1.595 0. V A (ft) (ft) (ft) (ft) 318.331 3.5 18. 59 ° F * LCB.39 0.673 0.97 58.25 23.9 20926 320.05 341.25 56.895 0.8 21198 318.42 341.97 58.5 42.66 LCF (ft)* Awp (ft2 ) CR CP CP C_ CVP KMT (ft) -16.858 0. LCF: + forward amidships .674 0.32 341.25 15444 0.858 0.07 4.81 0.61 7.87 80.658 1.673 12.199 3.876 0.223 L22_= 3.34 KM' (ft) t RO (°) (0) 24.0 29.00 188505 5384.590 -8.842 0.14 79.688 0.97 58.665 13.877 1.08 15341 0.04 -15.78 15345 0.678 11.644 + 4: in Salt Water.09 0.21 56.97 58. Ship Parameters Bow 1 Bow 2 Bow 3 Bow 4 Bow 5 LPP LOA Buj B.98 79.5 36.63 343.97 58.21 56.00 188294 5378.5 36.858 0.09 584.5 26.39 TABLE 3-2.35 528.00 189526 5414.5 36 31.694 0.00 194454 5554.8 21023 316.90 16247 0.5 20.858 0.04 79.66 526.8 21352 (ft3 ) (LTSW)+ WSA (ft 2 ) LCB (ft)* Kzz (ft) 3.846 0.38 560.581 0.42 341.0 21136 318.01 6.00 192494 5498.25 23.492 2.21 56.5 t () _n 1.682 11.577 -11.577 0.678 0.65 15890 0.566 1.86 533.0 31.686 11.99 79.858 0.5 22.21 56.

Bow 5 After Numerically Control led Mil Iino.40 Figure -')-I. .

After the milling of each surface. Turbulent flow is necessary in A testing since all flow around actual ships is turbulent. the process to produce a hard. Then each section was smoothed. smooth. wetting Six different surfaces.41 section was lightened by removing ruch of the interior foam to permit the installation of dynamometry needed for testing. Wet sanding primed and sprayed with high visibility enamel. was gridded The completed model facilitate flow from the FP to Station 6 to visualization tests and relative bow motion observations. After fairing. concluded surface. all local unfairities which resulted from the unorthodox application of FASTSHIP (see above) were removed. using the appropriate lines plan as the reference. the common stern and each of the five bows. At this point. Each model was then ballasted in still . each surface was coated with a thin layer of epoxy and light fiberglass cloth to provide surface toughness. single layer of between the two plastic tape was halves of each placed around the joint model to prevent flow disruption or leakage. the hull sections were faired by hand. Cylindrical studs were placed on the hull at points 5% of the LPP back from the stem to induce turbulent flow conditions at all tested Reynolds numbers. were completed in this manner. Hull rigidity was provided by a wooden box structure installed within each section. For each test the bow was aligned carefully and attached to the stern with four bolts to insure longitudinal rigidity.

25*LWL.42 water to a draft corresponding to 18 feet at ship scale at an even trim. Finally. The model was . dynamic ballasting procedures were followed to set the pitch gyradius at a nominal value of 0. then ready for testing. This was done by setting the yaw gyradius with the bifilar suspension method. yaw gyradius is assumed to equal pitch gyradius. During the bifilar method.

the .5% considered acceptable). EXPERIMENTAL TEST PROGRAM The basic goals estimate the still of the experimental water effective program were to (EHP) by horse power measuring model resistance and speed.43 4. and the still water flow patterns around the bow for each model.S. The International Towing Tank Conference (ITTC) description of this facility is shown in Figure 4-1.8 feet per second (ship speeds 3 to 18 kts). Naval Academy Hydromechanics Laboratory (NAHL). roll. Before testing for each model. It also shows the box The depth Blockage structure used to increase longitudinal rigidity. For all tests. the dynamometer restrained the model in surge. The towing point was held constant for all models at a point 2. effects were not a problem in the tests. The still water EHP tests covered a range of model speeds from 0.134% (with less than 0. since the blockage area ratio was less than 0. The EHP and seakeeping tests were performed in the 380 foot towing tank of the U.8 to 4. Figure 4-2 shows Bow 5 attached to the dynamometer and the towing carriage.2 inches aft of amidships and 1 inch below the DWL. sway.2 fps. heave. the seakeeping responses of pitch. at intervals of 0. and yaw. of the fresh water for all tests was sixteen feet. and relative vertical motion at Station 2.

t - t( ..44 L1 I La y L uj LO H ~L" L w .

Notice the dynamiometry and the w()(d(ri box for longitudinal rigidity. .45 Figure 4-?. Model attachment to the 3IXO' 'an P'owered Carriaqe.

For each run. water runs.46 variable reluctance force block was calibrated. regular head seas. 2.67 and 4. heave. These speeds corresponded to those called out in the seakeeping requirements section of the Top Level . slope for the tests was 1/60. and resistance in waves were measured for each model in long crested. Regular sea tests enabled the data at a tested speed to be summarized in the form of response amplitude operators (RAO's) so that ship response statistics in any desired sea state conditions. Speed model speed and resistance were recorded and analyzed. The nominal wave Repeat speed runs were done to confirm Video tapes were made of all still The wave frequencies ranged from those low enough to produce asymptotic limits of response to those high enough to produce near zero responses in pitch and heave. induced sinkage converted and trim in still water were measured and at the forward and after to vertical movements perpendiculars. specified by modal frequency and significant wave height (SWH). Between each test run. relative bow motion at Station 2. and the transducers rezeroed as necessary. could be computed assuming the applicability of the principle of linear superposition. Extra runs were done near the frequencies of maximum response to establish the correct shape of the peak. Seakeeping tests were run at two discrete model speeds. validity of the data. a sufficient time was allowed for generated waves to dissipate.01 fps (10 and 15 kts ship speed). Seakeeping responses of pitch.

and resistance were calibrated. Before each regular wave model test. model run was delayed until the generated waves reached the carriage start point. tests were done to estimate the natural pitch and heave frequencies by artificially inducing a response at zero speed in still water. the transducers for heave (sinkage). The consistent tuft size was chosen so that they provide the most accurate picture of the . (sinkage at the bow point) were recorded for each run. yarn tufts were cut and affixed to the model at all waterline and station grid intersections below the DWL and back to Station 6 (of 20). (trim) angle.47 Requirements (TLR) for T-AGS OCEAN (ICE). encountered wave height total resistance. description of this tank is shown in Figure 4-3. pitch (trim). Model speed. and recorded data were only used during the interval of steady state speed and encountered wave height. Flow visualization tests were conducted in the 120' towing tank of the NAHL using the powered carriage. In addition. Video tapes were made of each run to observe deck wetness problems and relative bow motion at Station 2. a sufficient amount of time was All allowed for the generated wave systems to dissipate. pitch (measured by a sonic and heave Each probe). The ITTC Before each model was tested. The TLR requirements specify that the ship be able to maintain 15 knots at all headings in an 8' SWH. After each run. transducers were rezeroed as necessary. and 10 knots in a 12' SWH [10].

48 I0 m zz I -~r: 4- 1 C) 0 0~I- .

accessible windows along a portion of its length allowed easy video taping of the tufts. Tests were run at model speeds corresponding to 5. All raw experimental data from the still water. The forebody from the Figure stem back to Station 6 was video taped for each run. 10.49 flow pattern in which they were placed. regular wave. The flow directions were then traced onto a similar profile view of the model on paper for qualitative analysis and comparison. . since Blockage flow near effects the hull were was not the considered relevant measurement of interest at very low speeds. For the same reason. 7.5.5. and flow visualization tests are summarized in a separate report for general use [11]. 4-4 shows an actual flow visualization test run in the 120' tank. no transducers for drag or motions were necessary. three-strand tufts were attached to the hull by a dollop of rubber cement.25 inch long. The 1. clear plastic overlays with a profile view of scaled using forebody showing stations and waterlines FASTSHIP to match the model gridding as it appeared on the television monitor were used to record the tuft flow directions for each model at each test speed from the video tapes. and 15 knots ship speeds. the Later. 12. These tufts were NOT present during the EHP and The 120' tank was chosen because the easily seakeeping tests. The model with tufts attached was allowed to soak for several hours before the flow visualization tests were run.

Notice the video camera setup and the tank observation windows.50 Figure 4-4. . Model during Flow Visualization tests in the 120' Tank.

and model velocity were respectively. resistance coefficient A value for CTm. STILL WATER POWERING RESULTS Values of total model resistance (lbs) and corresponding model velocity (fps) were obtained for each test run. Values of CTm based on measured data plotted against Vm for each model.51 5. The ITTC 1957 expansion resistance formulation for CF and a correlation allowance. CA. of 0. plot of CR A comparison versus the for all five series members . the Froude resistance [12] at was used to calculate values of total ship corresponding ship speeds.0004 were used throughout this project for both model and ship. was derived from the model the total total model resistance as follows: C-1. CR was calculated by subtracting CFm from CTm at each model speed. Using the faired model CTm data. The residuary resistance coefficient. model wetted surface area. tank water density. RT(4) where RTm. The author then created faired CTm curves based on his interpretation of the plotted data. Po' Sim' and Vm are total model resistance. The temperature of the fresh water in the 380' tow tank was also measured and recorded.

the curve rises sharply. It does not provide for losses associated with the propulsive system of the ship. and then the sharp rise. function of this set of curves is to show the similarity in curve shapes. in this case. as predicted. and it is apparent that the shape of the curves. are very similar. The primary effects become significant and the Above a Fn of 0.2). bilge keels. At these speeds.25. does not include the resistance associated with appendages such as rudders. have similar Systematic variations of a parent hull should resistance curves. series bows. Above a Froude number of about 0. (i.. no hulls for geometrically similar shapes.e. followed by a hump (Fn=0. wavemaking curve begins to rise. EHP begins at zero and gradually increases with . and. EHP represents the power that would be required to tow the ship at a certain speed through calm water. it can be observed that no laminar flow problems (see Chapter 3) were present in the tests.125. or bossings. CR becomes constant since only form drag exists wavemaking occurs). These curves are much more smooth than the CR curves. and these do. Total ship resistance was converted to effective horsepower. This plot applies to both model and ship scale At very low speeds.125).52 1 nondimensional Froude number (Fn = V/(gLWL) /2 ) is shown as Figure 5-1. five Figure 5-2 compares the EHP curve for each of the plotted against ship speed (Vs (kts)). as a function of ship speed for final comparison. with a consistent hollow (Fn=0.

53 .3 0 Lflj -L IC-CD LO -7 J 0 .cl 00 a)E Q) ) E 4.

:- S.54 cL O IE ILLJ Q) -H' ~0 - S- cf :.L 4-. SI 0.M C L ) f o 0 0 ci dH] .:mDLJ tucclc L ~ 4 -I-- (L-) -. C.

has the lowest EHP.7 2. This was expected since Bow 5.1 -9. Table 5-1. about 10% less than the parent. the finest. should produce the largest bow wave system. have somewhat less of a difference while still . The slope of the curve also increases until EHP At the is rising extremely quickly at speeds above 15 knots. presents a quantitative comparison of the five bows at a nominal design speed of 15 kts. should produce the smallest. At higher speeds. no readily apparent trend in the relative values of EHP is discernible. Bow 2 and Bow 4. Bow 5 had the highest EHP. although fuller than the baseline.2 % Difference from Baseline At 15 kts. The percentages were calculated as follows: EHPx-EHP~xO EHP1 X100 5 [%Difference] x (5) Table 5-1 Full Scale Still Water Powering Comparison at Vs = 15 knots EHP Bow 1 Bow 2 Bow 3 Bow 4 Bow 5 2428 2280 2196 2289 2480 -6. Bow 3. the finest. the fullest.5 -5. below. while Bow 3 had the lowest.55 ship speed. and Bow 3. lower speeds.

do fall more within the normal icebreaking range.56 showing a power advantage. but must be considered simultaneously with the knowledge that it falls on the boundary representing the lightest icebreaking capability in terms of the Shimansky parametric comparison shown earlier as Figure 3-10./A values [13]. Finally. Bow 5. resistance In it. and the POLAR Class in particular fall near the curves for the tested bows. and the POLAR Class. The maximum drop of ten percent in Bow 3 is significant. a ratio of total ship (LTSW) is plotted against This presentation serves to values for all hulls. Bows 2 and 4. the "R" Class. The other ships have values which form curves similar in shape to those of the tested bows. is the only bow at this speed with an EHP higher than Bow 1. the most ice- capable of the icebreakers. These other icebreakers for other the include WYTM 140. as characterized by the Shimansky comparison. Most remarkably. although their percent differences are less significant. . and those of the "R" Class. the WIND Class. Figure 5-3 presents a uifferent form of the open water ship resistance data. has a relatively low penalty in still water powering. normalize the total resistance Superimposed icebreakers. and its percent increase of just over 2% is fairly modest. the fullest. the B-AL. Bow 5. the B-AL. (lbs) to displacement Froude Number for all five bows. on the curves are the R.

/ V) ~ - 4->ci L 7: LflCO -C> S- ] 10 -1 -4 -4 0 ( ..57 ow Uo C) a~() w/ ~ * -n Ln () 'r.kyUr/q MSkLL /.zl .

58 This comparison serves as a basic check oi. . Any unusual features in the test results as compared to operating icebreakers could have cast both into doubt. both the testing procedures and the validity of the choice of parent hull.

functions developed from the measured data and were used for fairing purposes. transfer functions were obtained for pitch. and when squared Transfer become response were amplitude operators (RAO's). The relative motion transfer function was developed The added after division by the encountered wave height.59 6. SEAKEEPING RESPONSES For each regular. Pitch transfer functions were in the form of double pitch amplitude (20 in degrees) per unit wave height (Hw in inches). Relative bow motions and added resistance in waves were not analyzed for Bow 4 due to inconsistency of the acquired data. heave.* Model speeds corresponding to full scale ship speeds of 10 and 15 knots were chosen for the series models. relative bow motion at Station 2. . Heave transfer functions were in the dimensionless form of double heave amplitude (2Z) per unit wave height. bow motion (RBM) at Station 2 was obtained Relative by visual observation of the relative vertical motion between the water surface and the model gridding from each video taped test run*. Transfer functions (TF's) present the double amplitude of the response per unit wave height. head seas test run. and added resistance in waves at two discrete speeds. resistance in waves RAO was obtained by subtracting the faired Relative bow motions at Station 2 were not acquired for Bow 1 due to gridding problems above the design waterline.

Relative Bow Motion Station 2. the model transfer functions were used to predict the significant double amplitude responses of pitch. In the final step of the response in head seas data analysis. head seas. RAO yields the transfer function in units of ((lbs) 1/ These model transfer functions were plotted versus model encounter frequency. and faired curves drawn.60 still water resistance in pounds at the same model speed from the average total resistance in pounds of the model at each wave frequency in regular seas. calculated Hand drawn curves were chosen over computer because they do allow intuitive curves are curves The interpretation. and Figures 6-7 and 6-8. Figures 6-3 and 6-4. for faired transfer between function in the comparison bows following Figures 6-1 and 6-2. For each response. . the first of the two figures applies to the lower model speed. These values were then divided by the square of the wave height in feet. These curves represent the author's best interpretation of the data and were created with the knowledge that models in a systematic series should have curves with somewhat similar response characteristics. Added Resistance in Waves. Taking the square root of this 2/(ft). heave. and relative motion at Station 2 in irregular. (RBM) at Figures 6-5 and 6-6. Pitch. while the second applies to the higher speed. as added resistance in waves is considered proportional to the square of the wave height [14]. presented figures: Heave.

head seas at each corresponding ship speed (10 and 15 kts). A computer program written in BASIC was used to combine and expand the transfer functions with sea spectra to response spectra in irregular. included as Appendix A sample run output of this program is 6-1. the natural response frequencies for pitch and heave were obtained experimentally of predicting the encounter frequencies for the purpose at which maximum (resonant) responses should occur. Significant response double as did the other three amplitudes" were calculated using the principle of linear superposition at the same seastates specified in the T-AGS OCEAN (ICE) TLR (SWH 12' at 10 kts. in this context. 8' at 15 kts). Added resistance values. did not appear to drop to any logical asymptotic limit within the tested range of wave frequencies. defined using the ITTC The one- irregular wave parameter systems were wave spectrum equation. peak-to-peak periods as possible As many distinct from each were measured natural response test. once calculated after the testing. . responses. and the remaining periods "Significant". The significant double amplitude responses are presented within tables later in this chapter. The highest and lowest values for each bow in pitch and heave were dropped. As stated in Chapter 4.61 Added EHP in irregular waves was not predicted. means the average of the one-third highest responses.

982 0. and Bow 5 has the lowest peak response. Bow 1 and Bow 2 have the highest peak responses. at near zero encounter frequencies. but are close and support the validity of the tests.004 0. These frequencies are not in exact agreement with the experimentally obtained resonant frequencies. Note that the purpose of these natural frequency tests was to confirm the validity of the regular wave test results. These natural average frequencies are presented below in Table 6-1. respectively.082 1. At both speeds.848 0.62 were averaged.070 1.67 and 4. Table 6-2a and 6-2b compare the expanded significant double amplitude pitch responses for each bow at 10 and 15 kts in the corresponding seastates. . Pitch and Heave Pitch Bow 1 Bow 2 Bow 3 Bow 4 Bow 5 Figure 6-1 and 1. rise to a maximum at resonance.966 6-2 show the Heave 1. from this The natural frequency of motion was calculated peak-to-peak period. Table 6-1 Natural Frequencies of Motion (Hz).092 1.012 1. Bow 3 and Bow 4 have similar but lower peak responses.01 fps. and then decline again to zero at high frequencies.064 model pitch transfer functions at 2.071 1. the pitch responses follow the wave slope In both cases.

63 Lo) S CN oL uC- /jE-4 CD CD C) CDL co m oc CL C. .a) (~ *27 -O C CGcz -J. q~l.

64 LO 4-1 L 0 CU 44) LO 'n ~ g2E (L S o) - -~ a) Z)ALU W Il .

65 respectively. S1/3 is the average of the one-third highest

responses the ship would experience, while Si/i0 is the average of the one-tenth highest responses. In the last column are

the percent differences between the significant responses for each bow from the baseline (Bow 1).

[%Difference] = (S11 3 ) .- (S11 3 ) I xlO0
(S11 3 )1

(6)

Table 6-2a Significant Pitch Responses (10 kts) NATO Seastate 5 (12'SWH, 25.5 kt Wind) Si1 SS_3 I ( ) I)
Bow 1 7.21 ()

% Diff
---_

9.19

-

Bow 2 Bow 3 Bow 4 Bow 5

7.22 6.08 6.26 4.66

9.21 7.75 7.98 5.95

0.2 -15.7 -13.2 -35.3

Table 6-2b Significant Pitch Responses (15 kts) NATO Seastate 4 (8' SWH, 20.8 kt Wind)

1 Sl3 Bow 1

(U)

S110

(0)

% Diff ----

3.36

4.29

Bow 2 Bow 3 Bow 4 Bow 5

3.29 2.78 2.88 1.97

4.19 3.55 3.67 2.51

-2.1 -17.3 -14.3 -41.4

66 At each speed and seastate, Bow 5 has the lowest pitch

response by far.

One should note that although the transfer

functions at 4.01 fps are higher than those at 2.67 fps, the lower significant wave height specified for the higher ship speed results in noticeable decreases in pitch response. Figures functions for 6-3 and 6-4 present the model and 4.01 fps, heave transfer At both

2.67

respectively.

speeds, the normalized response in very low frequency waves begins at one. The normalized responses gradually begin to

decline towards zero at high frequencies, with a resonant peak at the natural frequency. The heave response follows the

pattern of the pitch response, with Bow 1 and Bow 2 being the highest, Bows 3 and 4 at midrange, and Bow 5 being the lowest. At both speeds, Bow 5 experiences almost no resonant peak in ics heave response - quite a desirable characteristic. pitch, Tables 6-3a and 6-3b present the expanded As for double

amplitude heave responses for each bow at 10 and 15 kts in the corresponding seastates, respectively.

67

4--10

P-47-

-

/1

or

N co
(LH/,Z
4L

0
.AP001

) No L F-- ( r C C~0 cu) - m5wuti MGJH .68 Inq EE 7 C)4 a)0 4 a.

36 $im (ft) 10.3 As with pitch. Bows 1 and 2 experienced the highest responses.78 4. respectively.70 3. Figures 6-5 and 6-6 present the relative bow motion at Station 2 transfer functions at 2.66 Bow 2 Bow 3 Bow 4 Bow 5 8.60 7.3 -33.67 8.60 10.47 -2.15 % Diff 4.67 and 4.8 -22. 25. hamper analysis. Since . 20.69 Table 6-3a Significant Heave Responses (10 kts) NATO Seastate 5 (12'SWH.9 -48.88 2.37 6.01 fps.1 -21.92 4.5 kt wind) % Diff ---- I____(ft) Bow 1 8.41 9.6 -18.94 3.10 5. as RBM response should be strongly correlated to pitch and heave responses and their relative phases.72 4.42 5.65 3.1 -11.46 7. There are no data for either Bow 1 or Bow 4 as This does not seriously explained in the earlier footnote.8 kt wind) I SitBow 1 Bow 2 Bow 3 Bow 4 Bow 5 (ft) ISl1 (ft) 6. while Bow 5 experienced the lowest responses with a maximum percent difference of almost 50%.0 Table 6-3b Significant Heave Responses (15 kts) NATO Seastate 4 (8' SWH.14 0.

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7 N/O -43.4 N/O 12.5 kt wind) -I Bow 1 Bow 2 Bow 3 Bow 4 Bow 5 S1 1 3 (ft) J S.8 20. 20. 25.8 N/O 19.3 -27. Visual observation of video taped regular waves tests of all the models supports the validity of this assumption.2 N/O 37.6 N/O 28. Table 6-4a Significant RBM @Sta2 Responses (10 kts) NATO Seastate 5 (12'SWH.4 .0 Table 6-4b Significant RBM @Sta2 Responses (15 kts) NATO Seastate 4 (8' SWH.. The percent difference in this table is with respect to Bow 2. (ft) J % Diff N/O 29. Tables 6-4a and 6-4b compare the significant relative bow motion responses at Station 2 at 10 and 15 kts respectively.8 kt wind) ISl Bow I Bow 2 (ft) So (ft) % Diff N/O 22.2 28.6 N/O 15. the same is assumed true for RBM. The RBM curves begin at zero at low encounter frequencies.9 N/O 16.4 N/O -22.9 N/O ---- Bow 3 Bow 4 Bow 5 16.2 22. reach a resonant peak.6 N/O -48. and approach a value of one asymptotically as the high frequency. and Bow 4 to be near Bow 3. short wavelength waves encounter the hull.72 the previous trends have shown Bow 1 to be near Bow 2.

had a lower frequency of occurrence than did Bows 4 or 5. the chances of RBM being larger than H are greater than for any other combination tested. With a S1/10 response amplitude of 37.2 on Bow 2. as .01 fps. deck wetness was much more common. then it is possible that the forecastle may either plunge forefoot may emerge.73 When analyzing relative bow motion data. reaches a value greater than H. The video taped test runs were also used to observe deck wetness trends during regular wave testing. possibly causing great damage to the sonar. 4. and 3. however. Bows 1. H. into the water or that the Forefoot emergence would especially be dangerous on a ship with a bow sonar dome. 2.67 fps. general observation revealed that the finer bows. 2. the importance of the response magnitudes depends primarily upon the depth (vertical distance from keel to deck at edge) of the ship at the station of interest. On T-AGS OCEAN (ICE) and all four If the RBM variants. At first this observation seems to make little sense. at Station 2 is 38 feet. None of the models experienced any significant At deck wetness problems at the low test speed. the only significant probability of either deck plunging or forefoot emergence would be on Bow 2 (and presumably Bow 1) at 10 kts in seastate 5 (12' SWH). Deck wetness can be a serious hindrance to the efficient performance of a ship in open water. the depth. At the two design conditions set in the TLR. Although no formal analysis was done concerning deck wetness.

By observing the tapes. they tend to drive through the waves Responses are still low. Figures 6-7 and 6-8 present a comparison of the model added resistance in waves transfer functions for 2. displacements of Bows 4 and 5 are centered further forward (more capable in ice). Because the hulls.74 Bows 4 and 5 have had lower seakeeping responses than the parent. as long as overall maximum beam is not increased. more than do the others. At higher RBM's. Perhaps a better method of improving deck dryness involves modifying the hard chine shown in the lines drawings above the design waterline. the water reaches this chine and suddenly is free to move up the near vertical side of the model until it reaches the deck-at-edge and causes deck wetness. The original purpose of this chine was to allow some flare at the DWL amidships without increasing the maximum beam to an unreasonable level. the author noticed that when the bow began to pitch downwards.01 . the high flare served to push the rising water away from the model. when one considers the trend in LCB among the answer becomes clear. however. but wetness This problem may be solved without losing For instance. the However. deck wetness may be reduced significantly. freeboard forward could be increased by adding a bulwark. This is not as much a concern near the forward perpendicular. stem to By maintaining as much flare as possible near the the deck-at-edge (reducing the chine sharpness forward).67 and 4. the advantages gained in seakeeping. becomes a problem.

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respectively. This is logical. RBM @Sta 2. previously. The transfer function curves follow the same trend seen in the earlier responses. i. During the testing. there is evidence Although not precisely measured. as added resistance in waves is almost completely a function of the pitch and heave responses [15]. (from observing the test runs in regular seas) that the stern would experience some slamming problems when moving in a seaway. The only . and then slowly decrease with increasing encounter frequency. The exact magnitude of this undesirable side effect is unknown. The bottom of the transom sits just above the free surface when the ship is floating at the design draft without trim. In summary. Bow 1 has the highest added resistance due to waves. This arrangement is chosen to prevent structural difficulties when backing in ice (the stern would also greatly increase the in-ice resistance while backing). an interesting and possibly important side effect of the hull form was observed. and added become better. this slow decrease prevented the use of the model data for ship scale added resistance predictions. The There are no data for Bow 4 as discussed response curves begin at zero for low encounter frequencies.. and Bow 5 has the lowest response.77 fps. the results reveal that as flare angle (P) and waterline angle responses analyzed resistance in waves - (a) are increased. decrease.e. approach resonant response sharply. Again. heave. all four seakeeping pitch.

78 detrimental effect observed involved the disadvantage of increasing deck wetness. . and a possible solution has been proposed by the author.

flow visualization tests were As described in conducted to determine the effect of the systematic flare and waterline angle variations on the hydrodynamic flow in the area from the stem to the sonar. After review of the ship's . hydrographic sonars for the bottom mapping and survey function ship requires minimal flow [16]. FLOW VISUALIZATION ANALYSIS The mission requirements of the T-AGS OCEAN (ICE) necessitate installation and use of both wide beam and multibeam. ice flow near the sonar. The primary concern of interference lies with noise around the sonar windows. especially bubble sweepdown. The TLR for the with the sonar interference throughout the speed range of its operation. The questions concerning bubble interference are particularly valid for ice-capable ships. Chapter 4. deep and shallow water. at low speeds. since many may feature ice lubrication systems having the purpose of reducing the total ship resistance by producing bubbles near the bow which will move over the hull while traveling in ice-congested areas. Flow streamlines were traced over profile views of each tested bow at each of five speeds by analyzing the patterns of the tuft flow directions. and. The proposed location of the sonar will be on the flat of bottom between Stations 5 and 6 (25 to 30% LPP aft FP).79 7.

5 kts. the streamlines tend to cross the buttock planes.80 operational characteristics. be a severe The effect does not appear to concern.5 knots ship speed are presented in Appendices 7-1 (a-e) and 7-2 (a-e). presenting both ends series makes good sense. only the operating range as stated in the TLR. pattern orderly of change and from Bow 3 to so that Bow 5 for each speed ot The is the logical. In Bow 3. flow follows the shape of the buttocks near Stations 5 . see Figure 2-1). it was decided to compare the streamlines at two of the tested speeds. Figure 7-1 compares the flow streamlines for Bow 3 and Bow 5 at 5 kts ship speed. 12. although the reason is not clear at this speed. while Figure 7-2 makes the same comparison at 12. The streamlines for all five bows at 5 and 12. 5 and 12. the chance of ice sweepdown would be of much greater relevance.5 knots corresponded with the high end of the sonar Additionally. for each bow. so that there is some indication that the flow might possibly sweep underneath the hull near Stations 5 and 6. as they define the full range of bow angles. rather than following them. 5 knots was chosen since the sonar would presumably be operating while moving at the lower end of the speed scale to minimize normal hull and propulsion noise (and certainly if the operational area were ice covered. At 5 kts no noticeable surface wave was observed for any of the bows. since at the low one.5 kts ship speed. but may be of speed. results for Bow 3 and Bow 5 are presented in the main body of this report. In Bow 5.

0 KNOTS .0 NOTES: (1I) Pr-oposed bottom mapping sonar. 2. Flow Stream-line Comparison BOW 3 at 5.Figure 7-1.system loca~tion: between Stations 5&t (2) No noticeabie 5urface wave at this low speed BOW 5 at 5.0 KNOTS 5.-1rlovl NO G4 7TT.

82 FIGURE 7. Flow Streamline Comparison BOW 3 at 12.-2.5 KNOTS .5 KNOTS (I) Proposed ttom mapping sonar system locat~on: between Stations 59b BOW 5 at 12.

and begins to move into the next crest at Stations 5 and 6. which is of minimum amplitude in Bow 3. This trough and subsequent crest are so much more pronounced in Bow 5. the two fullest. almost definitely an effect of the increasing waterline angles. increased wave resistance). this would effectively keep much of the bubbles or ice away from the sonar system. A substantial bow surface wave profile has developed. The usual penalty of fuller bows was discussed in Chapter 5 (i. a trough near Stations 3-5. that the surface wave tends to "pull" the streamlines up with it and across the buttocks towards the free surface in the vicinity of Stations 5 and 6.e. had the most pronounced bow waves. As Figure 7-1 shows. both the observed effects and the reason for them become much clearer. and progresses to a maximum amplitude in Bow 5. In Bow 5.83 and 6. but as quantitative analysis at 15 kts showed. The generated surface wave has its first crest at Stations 0-2.5 kts. it becomes evident why the streamlines tend to follow the buttocks or even cross them flowing up the ship's side at this speed.. 12. Bow 3 again has streamlines which tend to cross the buttocks and could cause some problems with the operation of the sonar. Bow 4 and Bow 5. the EHP increase the in Bow 5 at this in speed is bearable areas of considering advantages gained other . At the high end of the speed range for sonar operation. This would almost certainly serve to significantly decrease interference with the sonar as compared to the finer bows at 12.5 kts.

There is one other observation made during the flow Bow waves had an unexpected visualization tests which was unrelated to the flow and which occurred for all bows at all speeds. The distinction between them at 12. if any. the comparison of still water EHP for each bow). causing bubbles to form which flowed along the bottom of the aft part of the ship. especially when the surface of the water was still unsteady. benefit. This allowed a chance to observe the flow while backing at a low speed. the author feels it worthwhile to note it for future review. is not known.84 performance. suggests two potential problems . The behavior of the stern. the stern tended to slap against the free surface.the first dealing with the possibility of slamming in heavy seas. During backing. until finally being swept out near the beginning of the parallel midbody. with the transom above the free surface at design draft. After each run. Their relevance on the design of the ship must be considered. and the second being these flow-related problems. . the carriage was returned at a low speed to the start position. The significance of this flow condition. where waves were allowed to dissipate before the next test.5 kts is even less clear than at 15 kts (See Figure 5-2.

a. Bow 5. of a ship with a traditional icebreaking bow have been shown to cause changes in the open-water powering. heave. P. both speeds corresponding Bow 5 had reductions from 40 to 50% with respect to the parent hull form at 15 knots in a significant wave height of 8 feet. addition of a bulwark.85 8. (3) Deck wetness becomes an increasing problem as the Possible solutions include center of buoyancy moves forward. ship. . and hydrodynamic flow characteristics of that of the experimental data In particular. seakeeping. CONCLUSIONS Variations in the flare angle.2% with respect to the parent hull form at 15 knots. or a softening of the hard chine to allow the flare to extend up to the deck-at-edge. relative bow motion at all Station decrease 2 and at added resistance and in waves responses seastates. had a modest EHP increase of 2. analysis indicates that: (1) Bow angle variations may result in a reduction of still water effective horsepower by as much as 10% (Bow 3) at 15 knots. the pitch. The fullest bow. (2) As 0 and a are increased. and the waterline angle.

or ice under the stern of the ship when backing down. especially in Bows 4 and 5. 15 knots. the light end of the design range for Changing angles in the direction of Bow 5 yields the best of many worlds. (6) A possibility exists for flow to sweep bubbles. Based on these results. Such an effect could prevent ice and/or bubbles from a bubbler hull lubrication system from interfering with the sonar. with only slight disadvantages. Bow 3. . and waterline angles may be providing the benefits of: greater icebreaking capability. much better seakeeping overall. icebreaker's flare it has become clear that an increased. (5) A tendency exists for the generated surface wave to sweep flow streamlines away from the planned bottom mapping sonar location between Stations 5 and 6. had improved seakeeping responses. less acoustic interference with a bottom mapping sonar at the range of operating speeds.86 (4) The possibility of slamming exists on both the flat transom stern and the relatively flat run leading to the transom when the ship is experiencing heavy pitch motions. it already represents icebreakers. and all with only a modest increase in still water powering requirements at a typical operating speed. Although the finest bow. debris.

flare The on The positive effects of increased are becoming more widely is an seakeeping destroyer.87 As long as these modifications are applied to ships with traditional icebreaking bows. example of this principle being put into practice. . waterline accepted. ARLEIGH BURKE (DDG 51). they should be applicable for most ice-capable ships.

Using the same models. there is a need to continue this research into other aspects of icebreaker performance.88 9. and the seaway responses of pitch. could be a series to of more variations using same parent used effectively quantify methods to decrease deck wetness as the center of buoyancy moves forward and displacement increases. would be better varied in another series. relative bow motion. Experimentation to evaluate methods to improve roll response while still remaining within the normal icebreaker design ranges would be very useful. Another major problem affecting the performance of The icebreakers in open-water is their roll characteristics. the Additionally. and added resistance in waves. . as factors which most influence roll. including the maximum beam and the midships section shape. on calm water powering. a and P. present series would not be suitable for investigating roll. heave. SUGGESTIONS FOR FUTURE RESEARCH Although the present systematic variation of a traditionally designed icebreaker has addressed the effect of varying the bow form angles. analysis of other seakeeping responses such as slamming pressures and vertical accelerations at the center of gravity and at the bow would be useful in order to more fully describe the effects of the systematic variations on open-water seakeeping.

also of the Naval Academy Ms.89 Although extensive steps were taken to insure that all bow variations kept the hull within standard icebreaking design ranges. Peter Zahn and Mr. Mr.S. John Hill. . Mr. Bruce Nehrling who served as my Trident Scholar. Advisors for this project. and the later provision of the lines for T-AGS OCEAN (ICE). Mcqt importantly. especially with the use of FASTSHIP. Mr. for assisting me with all the computer applications necessary to complete this project. such testing should confirm that Bows 2. and the rest of the staff of the Naval Academy Hydromechanics Laboratory for their assistance in completing the experimentation and analysis. Hydromechanics Laboratory. Stephen Enzinger.4. Nancy Anderson. Mr. Daniel Bagnell for their advice on the selection of a parent hull. and 5 are in fact better icebreakers than their parent. In particular. ACKNOWLEDGEMENTS The author of this Trident Scholar Report wishes to gratefully acknowledge the assistance of the following people: Mr. Don Bunker. Dr. in-ice testing of the models to confirm that they remain effective icebreakers would be of great benefit. Tom Price of the U. Roger Compton and Dr. Naval Academy's Technical Support Department for the construction of the five forebodies and one stern involved in this project.

John Wiley and Sons. [8] Strasel. p. Aug 1987. PredictinQ Icebreaking Capabilities of Icebreakers. SNAME Chesapeake Section Meeting.90 REFERENCES [1] Lewis. [6] Melberg. Casey J. May 1969.C... 1-3 Apr 1970. USCG. MA-RD-840-89006 Report. L. 2-6. 1-3 Apr 1970 . by USACRREL. [2] Melberg . SNAME Spring Meeting. Coast Guard Icebreaker Series". Dynamics of Marine Vehicles..FY92 T-AGS OCEAN (ICE)". et al. MA-RD-840-89006 Report. [9] Advanced Marine Enterprises. "Systematic Series of Icebreaking Bow Shapes: Open Water Resistance and Head Seas Response Measured Data Base". [10] Strasel. Jack W. p. 3-7. [7] Kashteljan. al. 2 (CG-316-2). "The Design of Polar Icebreakers". [12] Lewis. 11 Dec 1990. Rameswar. June 1985. [13] Enzinger. Icebreakers. 1-3 Apr 1970. Washington: Maritime Administration. ed. 9. p. et al.. 2-5. NY. "The Estimation of Icebreaker Powering and Propulsion".C.. [3] Zahn. "Resistance Tests on U. U. et. Naval Academy Hydromechanics Laboratory.. 227. "The Design of Polar Icebreakers". Inc. 2. 7. p. Washington: Office of Engineering. 18 Jan 1990. 1972.. [5] Zahn. 1988. Erik S. Principles of Naval Architecture.. April 1991. L. Stephen. Edward V..C... et al.. et al. Stephen. SNAME. Leningrad: Sudostroyeniye.. et al. [14] Bhattacharyya. 1973.. "Feasibility Studies for an Ice Capable Oceanographic Survey Ship . V. 1978.. p.S. p. USNA EW Report No. Aug 1987. p. Peter. p. SNAME Chesapeake Section Meeting. SNAME Spring Meeting. p.S. Vol 2. Enzinger. Peter. New York.I. "The Design of Polar Icebreakers". "The Estimation of Icebreaker Powering and Propulsion". Inc. Bunker Donald. Report EW-10-85. 9. [11] Moton.FY92 T-AGS OCEAN (ICE)". L. p. SNAME Spring Meeting. 2-5. Hull Form Angles T-AGS OCEAN (ICE).. 11 Dec 1990. "Feasibility Studies for an Ice Capable Oceanographic Survey Ship . 1. et al. . EW-6-91. Trans. Naval Engineering Division Report No. [4] Melberg. Job 7210-22-5.

11 Dec 90. 224.. Inc.91 [15] Bhattacharyya. et al. Rameswar. NY. Dynamics of Marine Vehicles.1978." SNAME Chesapeake Section Meeting. . p. [16] Strasel. Erik S. John Wiley and Sons.. New York.. "Feasibility Studies for an Ice Capable Oceanographic Survey Ship FY92 T-AGS OCEAN (ICE).

8969 0.96~ 2 .OOOE±00 0.111E-01 0.1* 3E-01 0.OOOE+00 0.2956 1.+00 HEAVE 0. (WAVES) SPECTRUM 0?C99'7 0.4983 0.000E+00 O.OOOE+00 0.00 APPENDIX 6-1.OOOL+OO 0.160E-07 0.227E+01 0.000E+00 0.000E+00 0.3986 0.OOOE+00 0.OOOE+00 0.5979 0.5C 0.285E+00 0.343E-03 0.71 C 2.374E+00 0.9966 1.5945 1.145E+01 0.OOOE+00 0.374E-03 0.166E+01 0.102E+00 0.000E-+00 0.915E+00 0.414E+00 0.OOOE+00 0.308E401 0.301E+01 0.151E-18 0. RBM SPECTRUM HEAVE SPECTRUM PITCH SPECTRUM RES.274E+01 0. heave.OOOE+00 0.637E+00 0.781E-01 0. Sample Output of Ship Motiors Program used to expand model TF's for pitch.OOOE+00 0.129E-08 0.302E-01 0.191E+01 0. and RBM .218E+01 C.OOOE+00 O.OOOE+00 0.0962 1.851E+01 0.000E+0l0 0.98 KNOTS 4 IN SEA STATE ITTC (ONE PARAMETER) SIG.310E+01 0.OOOE+00 0.674E+00 0.6976 0.4949 1. (WAVES) CF/ A'vO.000 ft WIND SPEED =20.111E-02 0.0OF :ii( H1GHEST HLHEST 12.000E+00 0.476 3.000E+00 0.OOOE+00 PITCH 0.474E+01 0.223E-02 O.OOOE+00 0.000E+00 0.OOOE+00 0.000E+00 0.246E+.764E-02 0.250E+00 0.780 Kts ENCOUNTER FREQ.7973 0.500E-04 0.155E-18 0. WAVE HEIGHT = 8.OOOE+00 RES.326E-04 0.OOOE.OOOE±0O 0.OOOE+0O 0.8935 1.00 0.223E+01 0.000E+00 0.39S72 1.243E-09 0.276E+01 C.1959 1.185E+02 0.644E-20 0.000E+00 0.02 0.000E400 0.OOOE+00 0.440E-01 0.000E+00 0.9932 0.177E+02 0.2990 0.322 15.203E+01 0.664E+00 0.653E+00 0.316E-+01 0.6942 I.247E+01 0.827E+01 0.1993 0.147E+00 0.OOOE+00 0.000E+00 0.OOOE+00 0.000E+00 0.110E+01 0.106E-01 0.341E+00 0.356E-01 0.000E+00 0.388E-23 0.OOOE+00 0.793E 1.945E+00 0.169E-07 0.145E+01 RBM 0.191E+01 0.166E+01 0. ENCOUNTER SEA SPECT.279E+00 0.92 APPENDICES LONG CRESTED HEAD SEAS MOTION RESPONSE SPECTRA FOR BOW 5 AT A SPEED OF 14.150 1.

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