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Principles of Naval Architecture Second Revision Volume 1 + Stability and Strength Edward V. Lewis, Editor 1988 Published by Architects and Marine Engineers 601 Pavonia Avenue Jersey City, NJ The Society of Naval Copyright €& 1988 by The Society of Naval Architects and Marine Engineers, It is understood and agreed that nothing expressed herein is intended or shall be construed to give any person, firm, or corporation any right, remedy, or claim against SNAME or any of its officers or members 3 Library of Congress Catalog Card No. 8860829 ISBN No. 0939773007 Printed in the United States of America First Printing, April, 1988 ! 1 r t Foreword This revision of Principles of Naval Architecture began in 1978. It had been only eleven years since the prior revision but that time span was an explosive one in maritime technology. It was during this period that containerships became a commercial reality as did barge-carrying ships. Tankers of unprecedented size, some exceeding a half-million deadweight tons, became the norm. Rolkon, rolloff ships were built, as were liquefied natural gas carriers. Heavy lift ships appeared, Tug-barges, the size of ships, joined with ingenious mechanical linkages went into ocean service. The Manhattan was ice-strengthened and traveled north of Canada to Alaska. Off-shore drilling rigs of unique shapes and forms went to work in the most severe sea conditions imagrinable. Concern for the sea as an important element of the environment became real after the Torrey Canyon broke up, spilling 100,000 tons of oil. In the United States, the passage of the 1970 Merchant Marine Act provided a tremendous stimulus to merchant shipbuilding, ship operations, and maritime research. A worldwide upsurge in these same activities resulted from a very healthy global maritime economy. The sum total of these stimulating activities provided the impetus for expanded design technology, enhanced shipbuilding productivity measures, and extremely creative maritime research activity. The capture of these technological advances in this revision of Principles of Naval Architecture was the goal of the Control Committee. K is our hope that we have done that. Our authors and Controi Committee members were chosen for their extensive backgrounds as well as their involvement in these rapidly growing fields. In fact, one of the greatest continuing difficulties as the book progressed was in deciding where to divide “peseareh” and “principles” in determining which material would be included in many of the chapters. T hope we have done that well. 1 do most sincerely thank the members of the Control Committee, the authors, the headquarters staff, and particularly our editor, Ned Lewis for their efforts. I hope you, the reader, will benefit from their most commendable, professional contributions. The surge in maritime economic well-being ended later in the time period between revisions with the Arab oil embargo, the resulting crash in the world economy, and the precipitous drop in trade between nations... too many ships chasing too little cargo. With that decline came a corresponding decrease in technological growth. Survival, not growth, became the watchword. The most telling example of the depth of the decline since then is the fact that, as this Foreword is being written, not one merchant ship is on order or under construction in the United States. Maritime research funds, throughout the world, have become an endangered specie. When maritime activity will again emerge, when technological growth again becomes a competitive necessity, no one can say. Until then we can at least take heart in knowing that this revision of Principles of Naval Architecture is a reflection of the latest technology, having taken advantage of probably the single most produetive brief period of growth, from a maritime technology viewpoint, in the history of our profession. Let's hope the current valley of worldwide maritime inactivity won't last for tao long. Let's hope for better times, further technological growth, and the need once more, not too far away, for the next revision of Principles of Naval Architecture. JOHN J. NACHTSHEIM Chairman, Contro! Committee Preface The aim of this second revision (third edition) of the Society's successful Principles of Naval Architecture was to bring the subject matter up-to-date through revising or rewriting areas of greatest recent technical advances, which meant that some chapters would require many more changes than others. The basic objective of the book, however, remained unchanged: to provide a timely survey of the basie principles in the field of Naval Architecture for the use of both students and active professionals, making clear that research and engineering are continuing in almost all branches of the subject. References are to be ineluded to available sources of additional details and to ongoing work to be followed in the future. The preparation of this third edition was simplified by an earlier decision to incorporate a number of sections into the companion SNAME publication, Ship Design and Construction, which was revised in 1980. The topics of Load Lines, Tonnage Admeasurement and Launching seemed to be more appropriate for the latter book, and so Chapters V, VI, and XI became IV, V and XVII respectively, in Ship Design and Construction. This left eight chapters, instead of 11, for the revised Principles of Naval Architecture. At the outset of work on the revision, the Control Committee decided that the increasing importance of high-speed computers demanded that their use be discussed in the individual chapters instead of in a separate Appendix as before. It was also decided that throughout the book more attention should be given to the rapidly developing advanced marine vehicles. In regard to units of measure, it was decided that the basic policy would be to use the International System of Units (5.1). Since this is a transition period, conventional U.S. (or “English” units would te given in parentheses throughout the book. This follows the practice adopted for the Society's companion volume, Ship Design and Construction. The U.S. Metric Conversion Act of 1975 (P.L. 94-168) declared a national policy of increasing the use of metric systems of measurement and established the U.S. Metric Board to coordinate voluntary conversion to 8 L The Maritime Admin- istration, assisted by a SNAME Ad Hoc Task Group, developed a Metric Practice Guide to “help obtain uniform metric practice in the marine industry,” and this guide was used here as a basic reference. Following this guide, ship displacement in metric tons (1000 kg) represents mass rather than weight. (In this book the familiar symbol, A, is reserved for the displacement mass). When forces are considered, the corresponding unit is the kilo-Newton (kN), which applies, for example, to resistance and to displacement weight (symbol W, where W = Ag) or to buoyaney forces. (See Chapter 1.) When conventional or English units are used, displacement weight is in the familiar long ton unit (2240 Ib), which numerically is 1.015 x metric ton. A conversion table also is included with the symbols and abbreviations or Nomencelature at the end of this volume. This first volume of the third edition of Principles of Naval Architecture, comprising Chapters I through IV, covers almost the same subject matter as the first four chapters of the preceding edition. Thus, it deals with the essentially static principles of naval architecture, leaving most dynamic aspects to the remaining volumes. Chapter E deals with the graphical and numerical description of hull forms and the calculations needed to deal with problems of flotation and stability that follow. Chapter II considers stability in normal intact conditions, while Chapter III discusses flotation and stability in damaged conditions. Finally, Chapter EV deals with principles of hull structural design, first under static calm water conditions, and then introducing the effect of waves which also is covered more fully in Volume II, Chapter VII on Seakeeping. These first four chapters were found to require Jess revision than those dealing, for example, with maneuverability and motions in waves. The latter required more time than anticipated. Some of the principal changes may be noted: In Chapter I there is some rearrangement and change of emphasis. A few additions were made, such as developable lines and a containership, as well as a conventional cargo ship, as examples. (Continued) Table of Contents Volume 1 Page Introduction .. . Editor's Preface.. Foreword. iv Acknowledgments Chapter 1 SHIP GEOMETRY NorMAN À. HAMLIN, Professor, Webb Institute of Naval Architecture 1. Ships Lines.........c.cceccssesereess 1 5. Hydrostatic Curves and Caleulations 2. Displacement and Weight 6. Bonjean Curves.. .. Relationships ... . 16 7. Wetted Surface 3. Coefficients of Form 18 8. Capacity 4. Integrating Rules and Methods. . 2 Chapter 2 INTACT STABILITY LAWRENCE L. GOLDBERG, University of Maryland 1. Elementary Principles... 88 8. Drafts Trim and Displacement 2. The Weight Estimate. 89 9. The Inclining, Experiment . 3. Metacentric Height. Kal 10. Submerged Equilibrium . 4. Curves of Stability. . 8 11. The Trim Dive 5. Effect of Free Liquids and Special 12. Methods of Improving Stability, Cargoes.......cersseecerescarirenenem 93 Drafts and List 6. Effect of Ch: ght on 13. Stability when Grounded Stability...... 102 14. Intact Stabi of Unusual Ship 7. Evaluation of 8 . 106 Forms... Chapter 3 SUBDIVISION AND DAMAGE STABILITY GrorgE CG. NICKUM, President, Nickum & Spaulding Associates 1. Introduetion.. nã 5. Subdivision and Damage Stability 2. Fundamental of Damage 146 Calculation as Computer... 3. Subdivision and Damage 6. Definitions for Regulations. Damage Stabihty Calculations 149 7. Subdivision and Damage Stability 4. Manual Subdivision and Damag: Criteria ..cseeceseesesceceeertenees Stability Caleulations....... 152 8. Alternate Equivalent Passenger Vessel Regulations............cc.o Chapter 4 STRENGTH OF SHIPS J. RANDOLPH PAULLING, Professor, University of California, Berkeley 1. Introduction.. 205 5. Reliability of Struetures..........ceo. 2. Ship Structur: 208 3. Analysis of Hull Gird Nomenclature . Girder Stress and Deflection. 288 Index 4. Load Carrying Capability and Structural Performance Criteria .... 275 Page viii 176 178 180 194 290 301 305 mi Acknowledgments All of the authors and the Editor first wish to acknowledge their indebtedness to the authors of the corresponding chapters of the preceding edition. The former have made extensive use of the original text and figures, The preceding authors were the late W. Selkirk Owen and the late John C, Niedermair (Chapter 1), Charles S. Moore (Chapter IN), James B, Robertson, Jr. (Chapter III) and Donald F. MacNaught (Chapter IV). The Control Committee, under the chairmanship of John J. Nachtsheim provided essential guidance, as well as valuable assistance in reviewing early drafts of the manuscript. Many members of the Committee provided extra help in areas of their particular expertise. Individual authors acknowledgments follow. Norman A. Hamlin—as well as the Editor—wishes to thank Webb Institute of Naval Architecture for allowing him to devote some of his time to work on Chapter I and for furnishing needed secretarial assistance. Prot. Hamlin also appreciates the help of a number of individuals and former Webb Institute students at MARAD, Coast Guard, NAVSEA, American Bureau of Shipping and shipyards and design agencies—in particular, Kevin H. Calhoun, George H. Levine, Ronald K. Kiss (member of Control Committee), James L. Mills, Jr., and Francis J. Slyker. Lawrence L. Goldberg (Chapter II) acknowledges helpful information received from William A. Cleary, U.S. Coast Guard (member of Control Committee) and text material for Section 14, Intact Stability of Unusual Ship Forms, from George Wachnik, DTNSRDC, Daniel Savitsky, Director of the Davidson Laboratory, E.G.U. Band and David Lavis (of Band, Lavis and Associates) and Robert G. Tucker, current head of the Stability Branch, NAVSEA. George Nickum (Chapter III) acknowledges helpful information and comments received from William A. Cleary, U.S. Coast Guard (member of Control Committee). J. Randelph Paulling (Chapter IV) acknowledges the assistance of John F. Dalzel, DTNSRDEC, in providing text material and helpful comments, particularly on Sections 2,7-2.10 dealing with long- term probabilities. He also wishes to acknowledge the general guidance and appreciation for ship structural analysis received through many years of close association with H. A. Schade of the University of California. A number of other individuals provided invaluable assistance through personal discussion and commentary on all or part of the chapter. In this regard, the assistance of Alaa Mansour of the University of California, Douglas Faulkner of the University of Glasgow, €. S. Smith of AMTE, Dunfermline, Scotland, Stanley Stiansen, Donald Liu and H. Y. Jan of the American Bureau of Shipping are gratefully acknowledged. Especial thanks are in order for the assistance of his student, Jan Otto DeKat, who performed the computations and prepared the plots of structural loading contained in Fig. 8. Finally, the Editor wishes to thank the authors for their fine work and for their full cooperation in making suggested revisions, He acknowledges the indispensable efforts of Trevor Lewis-Jones in doing detailed editing and preparing text and figures in proper format for publication. viii 2 PRINCIPLES OF NAVAL ARCHITECTURE necessary to deal with the molded form, and therefore it is not unusual to find the molded form of wooden vessels delineated on a separate lines drawing. In the sheer plan of Fig. 1, the base line, repre- senting the bottom of the vessel, is parallel to the DWL, showing that the vessel is designed for an “even- keel” condition. Some vessels—especially tugs and fishing vessels—are often designed with the molded keel line raked downward aft, giving more draft at the stern than the bow when floating at the DWL; such vessels are said to have a designed drag to the keel. 1.2 Perpendiculars; Length Between Perpendicu- tars. A vertical line in the sheer plan of Fig. 1 is drawn at the intersection of the DWL, which is often the estimated summer load line (defined subsequently), and the forward side of the stem. This is known as the forward perpendicular, abbreviated as FP. A slight inconsistency is introduced by this definition of FP in that the forward side of the stem is generally in a surface exterior to the molded form by the thick- ness of contiguous shell plating—or by the stem thick- ness itself if the stem is of rolled plate. A corresponding vertical line is drawn at the stern, designated the after perpendicular or AP. When there is a rudder post the AP is located where the after side of the rudder post intersects the DWL. In Fig. 1 the AP is drawn at the centerline of the rudder stock, which is the customary location for merchant ships without a well defined sternpost or rudder post. In the case of naval ships, it is customary to define the AP at the after end of the vessel on the DWL. Such a location is also sometimes chosen for merchant ves- sels—especially vessels with a submerged stern profile extending well abaft the rudder. Fig. 2 shows the var- ious locations of the AP here described. An important characteristic of a ship is its length between perpendiculars, sometimes abbreviated LBP or Lpp. This represents the fore-and-aft distance be- tween the FP and AP, and is generally the same as the length L defined in the American Bureau of Ship- ping Rules for Building and Classing Steel Vesseis (Annual)!. However, in the Rules there is included the proviso that L, for use in the Rules, is not to be less than 96 percent and need not be greater than 97 per- cent of the length on the summer load line. The sum- mer load line is the deepest waterline to which a merchant vessel may legally be loaded during the sum- mer months in certain specified geographical zones. Methods for determining the summer load line are covered in the discussion of freeboard in Ship Design and Construction (Taggart, 1980). When comparing different designs, a consistent method of measuring ship lengths should be used. Overall length is invariably available from the vessel's plans and LBP is usually also recorded. However, for * Complete references are listed at end of chapter. hydrodynamic purposes, length on the prevailing waterline may be significant; alternatively, an “effec- tive length” of the underwater body for resistance considerations is sometimes required. One useful method of determining the after end of effective length is to make use of a sectional area curve, whose ordinates represent the underwater cross sectional area of the vessel up to the DWL at a series of stations along its length. (See Section 1.7.) The ef- fective length is usually considered as the overall length of the sectional area curve. However, if the curve has a concave ending, a straight line from the midship-cross-sectional area can be drawn tangent to the curve, as shown in Fig. 3. The intersection of this straight line tangent with the baseline of the graph may then be considered to represent the after end of the effective length. On many single-screw designs it has been found that the point so determined is close to the location of the AP. Such an effective length ending might then be used in caleulating hull form coefficients, as discussed in Section 3. A similar defi- nition for the forward end of effective length might be adopted for ships with protruding bulbous bows extending forward of the FP. It is important that in all calculations and measure- ments relating to length, the method of determining the length used, and the location of its extremities be clearly defined. 1.3 Midship Section; Parallel Middle Body. An im- portant matter for any ship is the location and shape of the midship cross section, generally designated by the symbol (%, which was originally used to indicate the fullest cross section of the vessel. In some of the early sailing ships this fullest section was forward of the midlength, and in some high-speed ships and sailing yachts, the fullest section under water is somewhat abaft the midlength. In any case, the usual practice in modern commercial vessels of most types is to locate Q) halfway between the perpendiculars, while in naval ships it is usually midway between the ends of the DWL. In many modern vessels, particularly cargo vessels, the form of cross section below the DWL amidships extends without change for some distance forward and aft, usually including the midship location. Such ves- sels are said to have parallel middle body. The ship in Fig. 1 has no parallel middle body, but the form of section under water changes but slightly for small distances forward or abaft the fullest section, which is located amidships. 1.4 Body Plon Stations; Frame Lines; Deck Lines. In order to simplify the calculation of underwater form characteristics, it is customary to divide the LBP into 10-—or 20, or 40—intervals by the body plan planes. The locations of these planes are known as body plan stations, or simply stations, and are indicated by straight lines drawn in the profile and half-breadth plans at right angles to the vessel's baseline and cen- terline, respectively. The intersections of these planes SHIP GEOMETRY MEC NOVAS NÓNLVIS OSONVAXA TYNOSVIO 2518 | Nie SENTINELIVA HO HEOVtTB AV Nyid HIIHS HO SUSOUA a E 4 E A EN E z mg 6 48 É Jem E a ! mi Ei = S À 45 ug E Ê : f / + y BLUES p N ul | - PE Lj) — ui A as e ug i TE upsi6 I E l começa | | | SN | e SOR IV OSO NA 4 T SENA! f a Fig. 1 lines drawing SHIP GEOMETRY 5 CAMBER to " o TUMBLE HOME AT MAIN DECK E MAIN, DECK AT SIDE TOP OF MAIN DECK BEAM + - — jar — 2 —— | TUMBLE HOME AT SECOND ed | 7 r Deéx t j á : TOP OF SECOND DECK BEAM | | E | SECOND DECK AT SIDE ! N MOLBED DEPTH To MAIN DK. ATE To, i CENTERLINE, SECOND ok or SHIP] MOLDED AT ' DRAFT 1 | AT : vEHALE-SIDE OIMENSION OF =Afio FLAT PORTION AT KEEL ca bia TT TT] DEAORGE CAR BF MODE ONE-HALF OF BREADTH, MOLDED Fig. 4 Midship section, motded form respective deck; i e., the surface at the top of the deck beams, and are consequently referred to as molded deck lines at side or at center as the case may be. In the lines drawing, Fig. 1, the curve of the main deck at the side is projected into the sheer plan as the curveC FP and into the body plan as J'D* F” for the fore body and as F“E"C” for the after body, and also into the half-breadth plan as the curve CF, which is known as the half-breadth line of the main deck. Through the point where the molded sheer line of the main deck at side intersects the midship station in the sheer plan, there may be drawn a level line called the molded depth line of main deck at side. At any particular station, the vertical distance between this line and the sheer line of deck at side is known as the sheer of the deck at that station. The sheer of a deck would, therefore, be zero at the midship station, and it may be zero for an appreciable distance either for- ward of or abaft amidships. Of particular interest are the values of sheer at FP and ÁP. The sheer line of deck at side in some vessels, par- ticularly yachts, may dip below the level of the molded depth line at side. This usually occurs, if at al], in the region immediately abaft amidships, and the sheer of the deck in such a region is measured below the level of the molded depth line at side and is considered to have a negative value. The molded lines of the principal transverse bulk- heads are sometimes also shown on final drawings. 1.5 Molded Base Line; Molded Dimensions, The molded base line, drawn in the sheer plan and body plan as a straight horizontal line, represents an im- portant reference datum, both for design and construc- tion purposes. The line, in fact, represents a plane in space to which many vertical heights are referred. It also represents the bottom of the vessel's molded sur- face, and so is coincident with the top surface of the flat plate keel on most straight-keel ships with a single thickness of shell plating. In the event the keel line of a ship is straight, but the vessel has a designed drag to the keel, it usually slopes downward aft. In this case the molded base line may mark the bottom of the molded surface amidships, orat the AP, When drawing the lines for such a vessel, the bottom of the molded surface is shown as a raked line. In the event the vessel is designed with an external hanging bar keel, extending below the shell plating surface, the bottom of keel is drawn in the sheer plan to complete the lower contour of the vessel. However, on most other ships, only the bottom of the molded surface is drawn. In the case of ships with “in and out” riveted plating, the keel plate is usually an “out” strake and the bottom of keel is then below the molded base line by not only its own thickness but that of the first outboard, or garboard strake, as well. The molded depth of a vessel is the vertical distance ó PRINCIPLES OF NAVAL ARCHITECTURE between the molded base line and the molded depth line of the uppermost deck at side as shown in Pig. 4. The distance from X to Bin Fig. 4 is one-half of the important dimension known as the molded beam or molded breadth of the vessel, which is normally a max- imum at the midship station. 1.6 Characteristics of the Sections. In Fig. 4 from the point A the molded line of the bottom of the midship section extends towards the side in a straight line AC. This line often is inclined upwards slightly and inter- sects, atthe point €, the vertical line EB drawn tangent to the widest part of the underwater body. The line AC is known as the floor line, and the dis- tance BC is referred to variously as the deadrise, rise of floor, or rise of bottom. For the ship shown in Fig. 1, the deadrise is 0.305 m. The point Kin Fig. 4 at the vessel's centerline is at the lowest part of the molded surface and the distance KA is the halfside dimension of the fiat portion of the molded surface in the vicinity of the keel ie., to the beginning of the deadrise. This half-side dimension is small in vessels having a hanging bar keel, being sim- ply the half-thickness of the bar forming the keel, but in vessels having a dished-plate keel it will be consid- erably more, depending upon the size of the ship. It does not apply at all to ships with no deadrise. The curved portion of the section, as at D, which joins the floor line with the side, is known as the tura of bilge and may be further described as a “hard” or as an “easy” turn of bilge, where hard refers to a small radius of curvature. The turn of bilge throughout the parallel middle body is usually, but not necessarily, a circular are, and the radius of this curve is known as the bilge radius. The molded line of the side above the waterline some- times extends inhoard somewhat to meet the line of the top of the main deck beam. In Fig. 4 this inter- section is at the point F. The horizontal distance EF is known as tumble home at the deck. The opposite of tumble home is known as fare, and it is measured in a similar way. A horizontal line through Fin Fig. 4 meets the cen- terline of the section at P; the distance PH is called camber or round of beam. The camber curve may be an arc of a circle, a parabola, or several straight lines. Standard past practice has been to provide about 2 percent of the total breadth of the ship as camber amidships, and then to use the camber curve so de- termined as applicable to all other fore and aft loca- tions. The use of camber accomplishes the important function of assuring that rain water and water shipped aboard will drain off readily. 1,7 Sectional Area Curve. À fundamental drawing in the design of a ship—particularly relative to re- sistance—is the sectional area curve, shown in Fig. 3 for a ship with some paralle! middle body. The sectiona] area curve represents the longitudinal distribution of cross sectional area below the DWL. The ordinates of a sectional area curve are plotted in distance-squared units. Inasmuch as the horizontal scale, or abscissa, of Fig. 3 represents longitudinal distances along the ship, it is clear that the area under the curve represents the volume of water displaced by the vessel up to the DWL, or volume of displacement. Alternatively, the ordinate and absci of the curve may be made non-dimensional by dividing by the mid- ship area and length of ship, respectively. In either case, the shape of the sectional area eurve determines the relative “fullness” of the ship (See Section 3). The presence of parallel middle body is manifested by that portion of the sectional area curve parallel to the baseline of the curve. The shoulder is defined as the region of generally greater curvature (smaller ra- dius of curvature) where the middle body portion of the curve joins the inyard sloping portions at bow or stern. The centroid of the vessel's sectional area curve is at the same longitudinal location as the center of buoy- aney, LCB, and the ratio of the area under the sectional area curve to the area of a circumscribing rectangle is equal to the prismatic coeficient, €, (See Section 3 Fig. 3 also shows the custumary division of the un- derwater body into forebody and afterbody, forward of and abaft amidships, respectively. Entrance and run, which represent the ends of the vessel forward of and abaft the parallel middle body, are also shown. 1.8 Molded Drafis; Keel Drafts; Navigational Drafts; Draft Marks. In general, the amount of water a vessel draws, or draft, is the distance measured vertically from the waterline at which the vessel is floating to its bottom. Drafts may be measured at different lo- cations along the length. They are known as molded drafts if measured to the molded baseline; keel drafts if measured to the bottom of the keel. Mean draft is defined as the average of drafts forward and aft. Ships are customarily provided with draft marks at the ends and amidships, arranged in a plane parallel to station planes and placed as close to the perpendic- ulars as practical. These draft marks are for the guid- ance of operating personnel, and therefore the drafts indicated should be keel drafts. The marks are painted in a readily visible color to contrast with the color of the hull. Arabic numerals are usually used on mer- chant vessels, although Roman numerals also appear on some naval ships, particularly in way of appendages that extend below the baseline. The bottom of the numeral is located at the indicated waterline. For many years it has been the practice to use numerals 6 inches high and to mark the drafts in feet at every foot above the keel. Thus, if one were to see the numeral half immersed, the prevailing draft would be three inches deeper than the half-immersed number in ft. With the ultimate conversion to the metric system in the United States a reasonable practice would seem to be that adopted by Australian maritime authoriíties (Australian Dept. of Transport, 1974). This provides that drafts be shown in meters at every meter in Arabic nnasa ns ssa NAS 8 PRINCIPLES OF NAVAL ARCHITECTURE body is a bilge of constant radius, r, connecting to flat bottom and/or side, with a change in curvature of the transverse section from 1/7 to O at the point of tan- gency. Although such a section is not fair, its shape is not necessarily disadvantageous. It can be made fair if desired by easing the transition in curvature. On the other hand, continuity in both first and second deriv- atives does not guarantee fairness, inasmuch as the achievement of fairness has always been and probably will continue to be a matter of opinion or judgment. An additional condition implied by the term fairness is that of consisteney, that is, each projection of any point on the surface onto the corresponding reference plane must agree with the locations of its other pro- jections. For example, consider a point P to be on the surface of the ship in Fig. 1 at station 7 and 4 ft (1.22 sm) above the molded base line, This point would be shown in the sheer plan at P”. Its location in the body plan would be on transverse section 7, and on the 4- ft WL. The horizontal distance of the point P from the ship's centerplane would be determined by the distance in the body plan of the point P” from the ship's cen- terline, as PE”. The point P, in the half-breadth plan would be at the ordinate for station 7 and on the 4ft WL and its distance from the ship's centerline would be P,R, as shown in that plan. À test of consistency of the point P would be that the distance P,R, in the half-breadth plan must equal P"R” in the body plan. In case the point P had been originally selected on the surface at à location where no transverse section, waterline, or buttock already existed, a check of fair- ness would require one to introduce any two of these three types of intersecting planes through the point, find the corresponding projections of the lines of intersection and proceed as before. The process of fairing a set of lines is invariably an iterative, or cut and try one, requiring patience and perseverance. It consists essentialiy of investigating the fairness or suitability of each line of the vessel in succession. It often happens that, after testing and accepting a number of lines, the next line to be com- sidered will require changes to be made to it that will be so far-reaching as to affect some of the lines pre- viously accepted. It then becomes necessary to make whatever changes seems best, all things considered, and to proceed anew through the same fairing steps as before, Usually several such difficulties have to be overcome successively before the whole fairing proe- ess is completed. Thus, the process may be laborious. Fairing lines for a new ship design is normally ac- complished at least twice—first in the design phase, and second in the construction phase, at which time the lines are faired either full-scale, on the mold loft floor, or in the optical detailing room to a scale of 1/ 10 or 1/20 of full size, or by computer as discussed in Section 1.16. In the design phase, there is greater free- dom to make changes and to achieve hull form features which the designer favors. Curves are usually drawn using a combination of free hand sketching, ship curves and flexible battens (or splines) held by batten weights (“ducks”). Waterlines are usually drawn by the last of these methods. A uniform batten will be fair between a pair of ducks, but it can be forced into an unfair overall curve by the ducks. Hence, a customary method of fairing or smoothing is to adjust the ducks —and hence the batten defining the waterline— until any one of the ducks can be removed without the batten moving. This is intended to assure that changes in curvature are made gradually. In the final design or construction phase, the lines are reasonably well defined at the start. The process of fairing is more localized and directed at achieving consistency among the various views. However, the larger scaie used in this case is intended to assure that local deviations, which may not have been evident in the earlier small-scale design phase, will be eliminated. 1.12 Developing e Set of Lines. The development of a set of lines presupposes a tentative (or final) se- lection of suitable hull dimensions, coefficients (section 3)» LCB, sectional area curve (Fig. 3) and design water- line. This selection is based on considerations of dis- placement, capacity, trim, stability, resistance and propulsion, all of which are discussed in other chapters, as well as in the chapter on Mission Analysis and Basic Design, Ship Design and Construction (Taggart, 1980). Fig. 5 is a generalized plot whereby the ofísets of a sectional area curve may be drawn to fit prescribed hull features (prismatie coefficients and LCB.) In order to use Fig. 5, one enters Fig. 5a with LCB and total Coto get Cr, and Cp; these are then used in Fig. 5b to find the sectional area curve ofísets. Given the desired hull characteristics, the process of drawing and fairing a preliminary small-scale set of lines generally begins with fixing the profile of the vessel im the centerplane, the design waterline and deck line in the half-breadth plan, and the midship body plan section. Intermediate sections may next be sketched in to satisfy the pre-determined sectional area curve, often by reference to previous designs and typ- ical hull forms (SNAME Hydrodynamies Committee, 1966). A few additional waterlines, between the deck and the DWL, and between the DWL and the baseline, are then drawn in the half-breadth view using half- breadths at the stations and making as small and as few changes as possible in these. The sections in the body plan are then changed to achieve consistency with the waterline half-breadths, and section areas checked, A few buttocks are then drawn in and checked and the process repeated. Alternatively, diagonals, rather than waterlines, are preferred by some designers as a fairing medium, and are used to check the consis- teney of section shape variation from station to station before buttocks and intermediate waterlines are drawn. Liberal use of the eraser is required, the draw- ing frequently being made on the back-of transparent cross-section paper, chosen so that the grid of the paper matches the grid of waterlines, buttocks and SHIP GEOMETRY 9 | Ha ice = % LA LGB = % L FORO = ou é ' 5 E y 2 E 4 E N os? 4 os | a vi e H 0.80 E) 4º 080 t ] ou é, PQ Pet] 03 o o 7 “TESS See E MEN o SOS | ES Dr, ca A a S > DS 072 dl e E r asas rs SISAS E be St] >< S>< emu e ves no 068 CorrF ni q ES SS] Eo=0= o EaS ><, Eo=0= | a E pa RR es p< Ses * o O E! ep RS aa Ss “a e Gs] a Brel 4d Pl que o 058 Say 98] asse os ma Cego | 8 dm | o |: 056 2 so 056 |. || ea; : E E 7 : é 5 À 3 est a | AFTEREOOY PRISMATIC COEFF, Cos 5 o80 ass 0% 075 oo FE no pc : T 5 12 pe po E os ta 15 09 [o] VMA 07 az es os 4 SIATIONAREA >< 12 cad ns 1 MIDSHIP AREA - 04 17 ô E o L— 2 ! uz 8 02 DP a 18% [DD a = o ES | o 19 E STA. 194 | 9 nu o 085 0.80 015 o% 065 060 085 6) FOREBOON PAISMATIC COEFF,, Cpe Fig. 5 Generalized plot of sectional areas, including forebody and afterbody prismatic coefficient as functions of longitudinal center of buoyancy (a & b) | | TOCOCOCOSTCCOC ELOI CECOLHUCCCHCTCCO SHIP GEOMETRY n Toble 1—Typical Table of Offsets Halfbreadths, m Half Bottom A WL BiLWL 164 WL 248 WL 2mtWIL sf WL Station Siding tangent 12]19m 2488m 4877 m 7.815 m 8.230 m 9.754 m Station 0, FP 9 — 0.759 0.581 0.108 — 0.133 0, FP u 0.994 — 1.308 1.432 1.270 1172 1.245 1.613 % 1 0,488 — 1.968 2.488 2.730 2.962 3.140 3.610 1 1x 0.571 — 2.978 3.848 4.626 5.102 5.859 5.886 1% 2 0.660 — 4.824 5.594 6.575 7315 7.597 8.093 2 8 “ 0.860 7.509 8.909 10.173 10.792 10.956 11.195 3 4 ” 3.882 10.293 11.208 11.830 11.986 12.007 12.033 4 5 ” 9.144 11,417 11.916 12.089 12.089 12.089 12.039 5 6 ” 6.268 10.344 11.338 11.983 12.039 12.039 12.039 6 7 ” 2.824 6.833 8.490 10,627 11,703 11.899 12.039 7 8 " 0.679 3.314 4.428 6.788 9,458 10.271 11.246 8 A ” 0.660 2.207 2.896 4.518 7.806 8.417 9.976 Bh 9 0.660 — 1.445 1.778 2.508 4.677 5.962 7.978 9 EA 0,432 — 0,549 0.568 0.600 1553 8.057 5.410 9% 10, AP — — — — — — — 2.130 10, AP 10-ft aft, — — — — — — — — 10-ft aft (3.048m) (3.048m) Table 1 (continued) Halfbreadths, m Buttock Heights, m I H HI IV V 40-ft WL Main Foc'sle att eft 16-ft 2 32-ft Station 12.192 m Deck Deck 1.219 m 2488m ASMm T3lbm 97%4m Station 0, FP 0.879 2.387 4477 12,872 14.967 — — — o, PP % 2.75 4.483 6.674 0.911 11.586 15.335 — — EA 1 4.823 6.518 847 0.878 2.438 12,284 15.888 — 1 1% 6.988 8.404 9.934 0178 0787 6.401 12.808 17.066 1% 2 8.979 66 11.011 0.083 0.868 1.654 7815 14.167 2 3 11.484 11.944 0,019 0,089 0.859 Lil 8.810 E) 4 12.039 — 0.016 0,048 0,117 0.251 0.891 4 5 ” — r r O111 0.178 0.279 5 6 " “ — ” ” 0.311 0.213 0.835 6 7 12.089 ” — 0.016 0.048 0.994 1524 3.708 7 8 11.932 12.089 — 0.044 0.517 2.953 5.347 7.630 8 ESA 11.389 11.890 — 0.175 1.600 5.264 7.325 9.508 8% 9 10.252 11.370 — 0.676 4712 7.461 9.223 11.510 9 ZA 8.236 10.001 — 7.074 7,852 9.389 11.271 14.478 9% 10, AP 4.861 6.826 — 9.098 9.989 12.211 — — 10, AP 10-£t aft, 2.658 4.558 — 10.598 11.919 — — — 10-ft aft (3.048m) (8.048m) much as one millimeter = 0.0397 in. = 1/25 in., very nearly. A complete set of ofísets for the various lines of the vessel, arranged in tabular form, is known as a table of offsets. The typical example given in Table ! applies to the ship shown in Fig. 1. Sometimes such tables are included on the lines plan. The ofísets originally sup- plied to the loftsmen are usualiy marked “prelimi- nary.” After the lines have been faired on the loft floor, another set of offsets, known as the “returned” or “finished” table of ofísets is usually lifted from the floor and returned to the drafting office. This finished set should include ofisets lifted for every frame station throughout the ship, in addition to those for the lines stations. Fairing ship lines on a mold loft floor is time con- suming and requires substantial amounts of floor space. To overcome these disadvantages, some ship- yards in the 1950s began to have the preliminary lines redrawn and refaired to a scale of one-tenth of full size, the work being done on large drawing tables with precise drafting instruments. Originally 1/10-scale drawings of structural parts were made and photo- graphically reduced to 1/100 or less of full seale. The photographic negatives were then projected optically full-size onto the plates for marking and cutting. Later DOC COCSCVETLCOCOCCCCVECODOVCCIVOCOVTCTO OC STUTVICVETTITETTT f t NS To find ruling between deck edge and chine: 1. 2 a 4. Find points M and s im profile as projections em PRINCIPLES OF NAVAL ARCHITECTURE ara Fig. 7 Lines of small developable surface vessel ur EDGE = Fig. 8 Construction drowing for developable surface lines Curve GHL) is the intersection of plane DGJF with à eylindical Draw DF, tangent to chine at E. surface with vertical elements through deck edge. Draw DG, EH and F5 in half-breadth plan parallel to each other To find ruling between stem profile and chine: at arbitrary angle. 1. Draw PA and PB tangent to chine at P. Project to deck edge in profile. 2. Project point A in half breadth at CL, to point 8 in profile. from half-breadth 3. Draw BC tangent to stem profile at €, giving end C of ruling PE. where DG, ER and FJ are parallel Draw curve Gt in profile cutting deck edge at L. . M is midpoint of GL and is end of ruling EM Plane DGJF is tangent to chine at E. 
