Glossary for the Statics and Dynamics of Marine Vessels Adapted from Introduction to Naval Architecture (1983), The ITTC Dictionary of Ship Hydrodynamics (1975), The ITTC Symbols and Terminology List (2005) Ship Design and Construction (1980), U. S. Navy Damage Control Manual (DCM, 1945), various textbooks, current IMO documents and Wikipedia

Added mass—The total hydrodynamic force, per unit acceleration, exerted on a ship or other body in phase with and proportional to the acceleration. Advance—The distance by which the center of gravity (CG) of a ship advances in the first quadrant of a turn. It is measured parallel to the approach path, from the CG position at rudder execute to the CG position where the ship has changed heading by 90°. Maximum advance is the distance, measured parallel to the approach path from the CG position at rudder execute to the tangent to the path of the CG normal to the approach path. The first of these terms is the most commonly used. Advance coefficient (J)—A parameter relating the speed of advance of the propeller VA to the rate of rotation n, given by J = VA/nD, where D is the propeller diameter. The advance coefficient may also be defined in terms of ship speed V, in which case it is given by .JV, = V/nD. Afterbody—That portion of a ship's hull abaft amidships. After peak—The compartment in the stern, abaft the aftermost watertight bulkhead. After perpendicular—See length between perpendiculars. Amidships—In the vicinity of the midlength as distinguished from the ends. Technically it is exactly halfway between the forward and the after perpendiculars. Amplitude—The magnitude of the extreme of a sinusoidal quantity with respect to the mean value. The double amplitude is the magnitude of the difference of the extreme. Angle of attack (α)—The angle, measured in the plane containing the lift vector and the inflow velocity vector, between the velocity vector representing the relative motion between a body and a fluid and a characteristic line or plane of the body, such as the chord line of an airfoil or hydrofoil. Synonymous with angle of incidence. Appendages—The portions of a vessel extending beyond the main hull outline, including such items as rudder, shafting, struts, bossings, and bilge keels. Archimedes' Principle—The principle that states that buoyant force acting on a body partially or completely immersed in a fluid is equal to the weight of fluid displaced. Aspect ratio (AR)—The ratio between the span of a hydrofoil or airfoil, measured at right angles to the liquid flow, to the chord c of the hydrofoil, in the direction of flow. When the chord varies in length across the span, the aspect ratio is the span b divided by the mean chord c obtained generally by dividing the hydrofoil projected area A, into the square of the span b, 2 i.e. b /AP. Athwartship—Across the ship, at right angles to the fore-and-aft centerline. Back (of blade)—The side of a propeller which faces generally in the direction of ahead motion. This side of the blade is also known as the suction side of the blade because the average pressure there is lower than the pressure on the face of the blade during normal ahead operation. This side of the blade corresponds to the upper surface of an airfoil or wing. Ballast—Any solid or liquid weight placed in a ship to increase the draft, to change the trim, or to regulate the stability. Baseline—A fore-and-aft reference line at the upper surface of the flat plate keel at the centerline for flush shell-plated vessels, or the thickness of the gar board strake above that level for ships having lapseam shell plating. Vertical dimensions are measured from a horizontal plane through the baseline, often called the molded baseline. Beam (B)—A dimension expressing breadth or width of a body or ship in a transverse horizontal direction. When not otherwise defined the beam is the molded breadth of a ship, measured amidships at the designed waterline. According to the position where the breadth is measured, it is named beam, extreme: maximum beam wherever it occurs on the hull above or below water. beam, immersed, maximum: maximum beam of the underwater body. beam, maximum section (BX): beam measured on the designed waterline at the maximum section area. beam, midlength (BM): beam at the midsection of the designed waterline. Beam, molded—The maximum breadth of the hull measured between the inboard surfaces of the side shell plating of flush-plated ships, or between the inboard surfaces of the inside strakes of lap seam- plated vessels. Beam, deck—An athwartship horizontal structural member, usually a rolled shape, supporting a deck or flat. Bilge—Intersection of bottom and side. May be rounded or angular as in a chine form hull. The lower parts of holds, tanks, and machinery spaces where bilge water may accumulate. Bilge keel—A long longitudinal fin fitted at the turn of the bilge to reduce rolling. Commonly it consists of plating attached to the shell plating. Bilge strake—Course of shell plates at the bilge. Blockage—The effect of the boundaries of a channel or tunnel on the flow around a body. Blockage correction—A correction made to the results of hydrodynamic experiments made in a channel or tunnel of one cross-section in order to estimate the equivalent results for another cross-section. Specifically a correction made to the results of a resistance experiment in a towing tank in order to estimate the equivalent results in unrestricted water. Block coefficient (CB)—The ratio of the underwater volume of a ship to the volume of a rectangular block, the dimensions of which are the effective length, draft, and beam. The relationship is expressed as a decimal. Body plan—A drawing consisting of two half transverse elevations or end views of a ship, both having a common vertical centerline, so that the right-hand side represents the ship as seen from ahead, and the left- hand side as seen from astern. On the body plan appear the forms of the various cross sections, the curvature of the deck lines at the side, and the projections, as straight lines of the waterlines, the buttock lines, and the diagonal lines. Bollard pull—The pull force exerted by a ship at zero ship speed. It is the sum of the propeller thrust and the interaction force on the hull. Bonjean curves—A set of curves, each of which represents a plot of the cumulative area of a station on the lines plan, from the base line to any point above it. Bossing or boss—The curved swelling outboard portion of the ship's shell plating that surrounds and supports the propeller shaft. Boundary layer—The region of fluid close to a solid body where, due to viscosity, transverse gradients of velocity are large as compared with longitudinal variations, and shear stress is significant. The boundary layer may be laminar, turbulent, or transitional. Boundary layer thickness (δ)—The distance normal to the surface of a body at which the speed attains that in an equivalent inviscid flow. For practical purposes this is sometimes taken as 99 percent of the inviscid flow speed or 98 percent of the total head. Bow line—The intersection of the molded hull surface forward of amidships with any vertical longitudinal plane not on the centerline. See buttock. Bracket—A plate used to connect rigidly two or more structural parts, such as deck beam to frame, or bulkhead stiffener to the deck or tank top (usually triangular in shape). Breadth, molded— See beam, molded. Breakwater—Inclined bulwark-like structure on a weather deck to deflect overboard water coming over the bow or over the gunwale and moving aft. Breasthook—A triangular plate bracket joining port and starboard side stringers at the stem. Broaching—An involuntary and dangerous change in heading produced by a severe following or quartering sea. Bulkhead—A term applied to the vertical partition walls that subdivide the interior of a ship into compartments or rooms. The various types of bulkheads are distinguished by their location, use, kind of material, or method of fabrication, such as forepeak, longitudinal, transverse, watertight, wire mesh, and pilaster. Bulkheads that contribute to the strength of a vessel are called strength bulkheads, and those that are essential to the watertight subdivision are watertight or oil tight bulkheads. Gastight bulkheads serve to prevent the passage of gas or fumes. Bulkhead, after peak—A term applied to the first main transverse bulkhead forward of the sternpost. This bulkhead forms the forward boundary of the after peak tank. Bulkhead, collision or forepeak—The foremost main transverse watertight bulkhead. It extends from the bottom of the hold to the freeboard deck and is designed to keep water out of the forward hold in case of bow collision damage. Bulkhead deck—The bulkhead deck is the uppermost deck up to which the transverse watertight bulkheads and shell are carried. Bulkhead, screen—A term applied to a light nonwatertight transverse bulkhead fitted in some Great Lakes ore carriers. Its greater flexibility allows it to survive the effects of the unloading machinery. Buoyant Volume— Buttock—The intersection of the molded surface abaft amidships with any vertical longitudinal plane not on the centerline. See bow line. Camber—The rise or crown of a deck, athwartship; also called round of beam. Camber (of a hydrofoil)—The maximum separation of the mean line and the nose-tail line. Capacity plan—A plan outlining the spaces available for cargo, fuel, fresh water, water ballast, etc., and containing cubic or weight-capacity lists for such spaces and a scale showing deadweight capacities at varying drafts and displacements. Casing, engine and boiler—Bulkheads enclosing a large opening between the weather deck and the engine and boiler rooms. This provides space for the boiler uptakes and access to these rooms, and permits installing or removing large propulsion units such as boilers or turbines. Cathodic protection—Protection of a ship's hull against corrosion by superimposing on the hull an impressed current, provided by a remote power source through a small number of inert anodes. Also accomplished by fitting aluminum, magnesium, or zinc anodes in the underwater portion of a ship or in tanks, which waste away by galvanic action. Cavitation—In most engineering contexts, the process of formation of the vapor phase of a liquid when it is subjected to reduced pressure at constant ambient temperature. In general, a liquid is said to cavitate when vapor bubbles form and grow as a consequence of pressure reduction. Cavitation damage—Deformation and/or erosion of materials in cavitated regions, associated primarily with the high pressures developed during cavity collapse. Celerity—See wave speed. Center girder—A vertical plate on the ship's centerline between the flat keel and inner bottom or rider plate, extending the length of the ship. Also called center vertical keel (CVK) or center keelson. Centerline (C)—The middle line of the ship, extending from stem to stern at any level. Center of buoyancy (B)—The geometric centroid of the submerged volume of a body or ship through which the total buoyancy may be assumed to act. Its position, measured as the distance from midships or from the fore ( FB ) or after perpendicular ( AB ) is called the longitudinal center of buoyancy and from the base line or keel ( KB ) the vertical center of buoyancy. Center of flotation (F)—The geometric centroid of the area of the waterplane of any waterline. Its position measured as the distance from midships or from the fore or after perpendicular is called longitudinal center of flotation (LCF) and is generally expressed as a ratio of the waterline length. Center of gravity (G)—The center through which all the weights constituting the ship and its contents may be assumed to act: The distance measured from midships, the foreward perpendicular ( FG ) or the after perpendicular ( AG ), and from the baseline or keel ( KG ) are called longitudinal (LCG) and vertical center of gravity (VCG), respectively. Chine—A more or less sharp corner or knuckle in the hull form, continuous over a significant length of the ship, as in the junction of side and the bottom in planing craft. The chine is known as soft when the corner is rounded, and hard otherwise. Chord (of a hydrofoil, airfoil, or propeller blade) (c)— The length of the straight line connecting the extremities of the mean line of a hydrofoil section. It passes through, or nearly through, the fore and aft extremities of the section. Synonymous with nosetail line. Chord length, mean (ĉ)—The quotient obtained by dividing the expanded or developed area of a propeller blade by the span from the hub to the tip. Coefficient, drag (CD)—A relationship between the drag D of a ship or body and the dynamic pressure times a specified area. It is customary to express it as CD = D/qA. Coefficient of lift (CL)—A relationship between the lift force L developed by a ship or body and the dynamic pressure times a specified area. It is customary to express it as CL, = L/qA. 3 Coefficient of inertia of waterplane, longitudinal (CIL) — CIL = 12 IL / BL 3 Coefficient of inertia of waterplane, transverse (CIT) — CIT = 12 IT / B L Cofferdam—Narrow void space between two bulkheads or floors that prevents leakage between the adjoining compartments. Collision bulkhead—See bulkhead, collision. Compartmentation—The subdividing of the hull by transverse watertight bulkheads so that the ship may remain afloat under certain assumed conditions of flooding. Complex system—A system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts. A system’s complexity may be of one of two forms: disorganized complexity and organized complexity. In essence, disorganized complexity is a matter of a very large number of parts, and organized complexity is a matter of the subject system (quite possibly with only a limited number of parts) exhibiting emergent properties.. Complex adaptive systems (CAS) — are special cases of complex systems. They are complex in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience. Control surfaces—Control surfaces are the rudders, planes, and other hinged or movable devices used for controlling the motion of a body or ship. Correlation allowance coefficient--For the ship-model correlation allowance, the resistance coefficient of the form CA corresponding to the resistance form RA, the suffix A is to denote the additional resistance to be added to the smooth-ship prediction to complete the ship-model balance. This allowance covers not only such items as roughness allowance but also the method of extrapolation used and the scale effects on resistance, wake, thrust deduction, and other propulsive factors. A coefficient of this kind lends itself to subdivision into different components, such as those due to structural roughness (CAS), paint roughness (CAP), and so on. Correlation allowance, model-ship (RA)—This is the addition that has to be made to the resistance of the "smooth" ship, as predicted from the model results, to bring it into agreement with the actual ship performance determined from full-scale trial or service results. The correlation allowance depends upon the method used to extrapolate the model results to the smooth ship, the ship length and type, the basic shell roughness of the newly painted ship, fouling, weather conditions at the time the ship measurements were taken, and scale effects on the factors making up the model and ship propulsive coefficients. Counter—The overhanging portion of the stern of a ship, which lies between the designed waterline and the deck and which projects abaft the waterline termination. Coupling—The influence of one mode of motion on another, for instance, coupling between heave and pitch. Damping—A characteristic property of a dynamic system, which dissipates energy and the consequent reduction or decay of the motion. Damping, viscous—A reduction in vessel motion caused by viscosity and/or flow separation resulting in energy dissipation. Damping, wave— Damping coefficient—The ratio of damping force or moment amplitude to velocity amplitude as a function of frequency. Dead flat—The portion of a ship's structure that has the same transverse shape as the midship frame. See parallel middle-body. Deadrise—Athwartship rise of the bottom from the keel to the bilge. Deadweight—The carrying capacity of a ship at any draft and water density. Deadweight includes weight of cargo, fuel, lubricating oil, fresh water in tanks, stores, passengers and baggage, and crew and its effects. Deadwood—The portion of the hull of a vessel that displaces a volume small in proportion to its weight, but which is provided for the support of a propeller shaft, structural strength, docking support, protection when grounding, or for other reasons. It is placed generally at the after end, but not necessarily on the center line. Specifically, the thin portion of the hull at the stern of a vessel immediately forward of or in the vicinity of the rudder. Deck—A platform in a ship corresponding to a floor in a building. It is the plating, planking, or covering of any tier of beams either in the hull or superstructure of a ship. Deck, bulkhead—See bulkhead deck. Deck, freeboard—Deck to which freeboard is measured; the uppermost continuous deck having permanent means of closing all weather openings. Deck, platform—A lower deck, usually in the cargo space, that does not contribute to the longitudinal strength of the ship. Deck, shelter—See shelter deck. Deck, tonnage—The tonnage deck constitutes the upper boundary of the internal volume of the measurable portions of the ship as defined by the tonnage regulations. Deck, weather—Uppermost continuous deck with no overhead protection. Deck beam—See beam. Deck height—The vertical distance between the molded lines of two adjacent decks. Deck stringer—The strake of deck plating that runs along the outboard edge of a deck. Deckhouse—An enclosed erection on or above the weather deck that does not extend from side to side of the ship. Deep tanks—Tanks extending from the bottom or inner bottom up to or higher than the lowest deck. They are often fitted with hatches so that they also may be used for dry cargo in lieu of fuel oil, ballast water, or liquid cargo. Density, mass (ρ)—The mass per unit volume of a substance. Depth, molded—The vertical distance from the molded baseline to the tip of the freeboard deck beam at side, measured at mid-length of the ship. Deterministic system is a system in which no randomness is involved in the development of future states of the system. Deterministic models thus produce the same output for a given starting condition. See also stochastic system Diagonal—The trace on the outside of a body marking the intersection of a plane passing through it at an angle other than 90° to the baseplane. Dimensionless characteristic length (U) — R. E. Froude’s dimensionless characteristic length U =∇1/3 = cube root of the volumetric displacement Diameter, steady-turning—The diameter of the circular arc described by the center of gravity of a ship when it has achieved a steady-turning state. Diameter, tactical—The distance travelled by the center of gravity of the ship normal to its original approach path in turning through 180°. Tactical diameter is equal to the transfer at 180° change of heading. Displacement, light—The weight of the ship including hull, machinery, outfit, equipment, and liquids in machinery. Displacement, loaded (Δ)—The displacement of a ship when floating at her greatest allowable draft. It is equal to the weight of water displaced and is the sum of the light displacement and the deadweight. Displacement mass (ΔM)— Displacement volume ( ∇ ) Double bottom—Compartments at the bottom of a ship between inner bottom and the shell plating, used for ballast water, fresh water, fuel oil, etc. Doubling (doubler) plate—A plate fitted outside or inside of and faying (touching) against another to give extra local strength or stiffness. Downflooding angle— Draft (T)—The depth of the ship below the waterline measured vertically to the lowest part of the hull, propellers, or other reference point. When measured to the lowest projecting portion of the vessel, it is called the extreme draft, when measured at the bow, it is called forward draft, and when measured at the stern, the after draft. The average of the forward draft and the after draft is the mean draft, and the mean draft when in full-load condition is the load draft. Draft marks—The numbers on each side of a ship at the bow and stern, and sometimes amidships, to indicate the distance from the lower edge of the number to the bottom of the keel or other fixed reference point. The numbers are 6 inches high and spaced 12 inches bottom to bottom vertically in English units. Drag—The designed excess of draft aft over that forward when fore and aft drafts are measured from the designed waterline. Drag (D)—The fluid force acting on a moving body in such a way as to oppose its motion; the component of the fluid forces parallel to the axis of motion of a body. Drag is the preferred term in aerodynamics and for submerged hydrodynamic bodies, while resistance is generally used in ship hydrodynamics. The various forms of drag are defined in relation to resistance. See also resistance. Drag coefficient (CD)—The non-dimensional ratio of the drag per unit of a representative area of a body to the dynamic pressure far ahead of the body. Dynamic positioning—A means of holding a ship in a relatively fixed position with respect to the ocean floor without using anchors, accomplished by two or more propulsive devices controlled by inputs from sonic instruments on the sea bottom and on the ship, by gyrocompass, by satellite navigation, or by other means. Dynamic pressure—See pressure, dynamic. Dynamic stability—The characteristic of a body, such as an aircraft, rocket, or ship that causes it, when disturbed from an original state of steady motion in an upright position, to damp the oscillations set up by restoring moments and gradually return to its original state. (McGraw Hill Dictionary of Scientific and Technical Terms) See Equilibrium and Stability Effective length (L)—The length used for speed-power calculations and the coefficients for it. Effective length is determined from the sectional area curve by excluding any abrupt tailing off at the after end of the curve such as often occurs with single- screw, cruiser stern ships. In multi screw normal vessels, it is usually the load waterline length, but in single-screw ships with either cruiser or fantail sterns, it is usually the length from the forward perpendicular to about the middle of the propeller aperture. Efficiency, hull (ηH.)—The ratio between the useful work done on the ship and the work done by the propeller or other propulsion devices in a given time that is effective power PE and thrust power PT respectively. Efficiency, propeller, behind hull (ηB)—The ratio between the power PT developed by the thrust of the propeller and the power PD absorbed by the propeller when operating behind a model or ship. Efficiency, propulsive or quasi-propulsive (ηD)—The ratio between the useful or effective power PE and the power delivered to the propeller or the propulsion device PD. Efficiency, relative rotative (ηR)--The relative rotative efficiency is the ratio of the propeller efficiencies behind the hull and in open water, as already defined. Efficiency, shafting (ηS)—The shafting efficiency is a measure of the power lost in shaft bearings and stern tube. Efficiency, propeller, open water (η0)—The ratio between the power developed by the thrust of the propeller PT and the power absorbed by the propeller PD when operating in open water with uniform inflow velocity VA. Entrance—That portion of a ship's body forward of the parallel middlebody or the point at which the slope of the sectional area curve is zero. Equilibrium, Static— situations with no unbalanced forces and no accelerations. Quasi-static equilibrium conditions: situations with only slightly unbalanced forces and low accelerations. Near-equilibrium dynamic conditions: situations where using average or periodic unbalanced forces and assuming average or periodic accelerations is the only way to analytically solve otherwise complicated problems. This includes dynamic situations which can be assumed to be periodic or a stationary random process so that Fourier Transform methods are valid in the frequency domain. Far-from-equilibrium dynamic conditions: significant unbalanced forces and complex accelerations make time domain analysis of the pressure and velocity field equations of fluid mechanics “non-algorithmic in a useful way”. This includes all situations in which a non-stationary random process is present. (Note that Newton’s Second Law for rigid bodies does not have these restrictions.) Even keel—This term is used to define the condition in which the ship has her keel parallel to the water surface. For vessels in which the keel is not straight or normally parallel to the water surface, "zero trim" or "level trim" is preferred to even keel. Expansion trunk or tank—A trunk extending above a space which is used for the stowage of liquid cargo. The surface of the cargo liquid is kept sufficiently high in the trunk to permit expansion without risk of excessive strain on the hull or of overflowing, and to allow contraction of the liquid without increase of free surface. Face (of blade)—The side of the propeller blade which faces downstream during ahead motion. This side of the blade is also known as the pressure side because the average pressure on the face of the blade is higher than the average pressure on the back of the blade during normal operation. The face corresponds to the lower surface of an airfoil or wing. Face plate—Generally a narrow stiffening plate fitted along the inner edge of web frames, stringers, etc., to form the flange of the member. Factor, magnification—The ratio of output amplitude at a certain frequency to input amplitude. Factor, tuning (Λ)—The ratio of excitation frequency to natural frequency (or the ratio of natural period of a motion to period of encounter). Fair—To smooth or fair up a ship's lines; eliminating irregularities; to assemble the parts of a ship so that they will be fair, i.e., without kinks, bumps, or waves. Fairwater—A term applied to plating fitted around the ends of shaft tubes and strut barrels, and shaped to streamline the parts, thus eliminating abrupt changes in the water flow. Also applied to any casting or plating fitted to the hull for the purpose of preserving a smooth flow of water. Fantail—The overhanging stern section of ships that have round or elliptical after endings to uppermost decks and that extend well abaft the after perpendicular. Also called counter. Faying surface—The surface between two adjoining parts. Fin—A fixed or movable hydrofoil, attached to a ship generally in a longitudinal direction, to improve the dynamic stability or maneuverability, or to provide a lift force to windward, as in the fin keel of a sailing yacht. Flange—The part of a plate or shape bent at right angles to the main part; to bend over to form an angle. See also face plate. Flap—A hinged movable auxiliary hydrofoil forming the aftermost portion of a main hydrofoil. Flare—The spreading out of the hull form from the central vertical plane, with increasing rapidity as it rises from the waterline to the rail; usually in the forebody. Also a night distress signal. Flat—A partial deck, usually without camber or sheer. Floodable length—The length of ship that may be flooded without sinking below her safety or margin line. The floodable length of a vessel varies from point to point throughout her length and is usually greatest amidships and least near the quarter length. Floor—Vertical transverse plate immediately above the bottom shell plating, often located at every frame, extending from bilge to bilge. Flow, laminar—The flow of a viscous liquid in which layers of laminae of fluid appear to slide smoothly past each other. Momentum transfer and shear between neighboring layers of fluid are due to molecular interactions only. Flow, regime--A term referring to the state of the flow in any region; the principal recognized regimes are laminar, transitional, turbulent, and separated flows. Flow, reversed—Flow occurring in an eddy or in a separated zone in which the local flow has a component opposite in direction to that of the main flow. Flow, secondary—A transverse flow induced by the boundary layer geometry and by pressure conditions existing in the main flow. Flow, separated—The detachment of the main fluid flow from a solid surface due to an adverse longitudinal pressure gradient sometimes caused by a sudden change of the direction or the curvature of the surface. The fluid in the separated flow contains eddies and may be nearly static or may contain a region of reversed flow. Flow, steady—Flow in which the velocity pattern is independent of time Flow, transitional—An unstable state of viscous flow between the laminar and turbulent regimes. Flow, turbulent—A flow in which there are rapid and apparently random fluctuations both in the magnitude and in the direction of velocity. The velocity fluctuations may also be described by a random spectrum of vortices of varying size and strength. Turbulent resistance is higher than that in laminar flow at the same Reynolds number, because of the high momentum exchange by transverse fluctuations. Flow, uniform—Flow in which all velocity vectors are parallel and equal. Flow, viscous—The flow of a fluid where the flow characteristics include the effects of the shear forces acting on the fluid and within it. Fluid, perfect or ideal—A hypothetical fluid which is homogeneous, inviscid, and incompressible. Flush deck ship—A ship constructed with an upper deck extending throughout her entire length without a break or a superstructure such as forecastle, bridge, or poop. Force, damping—A force that tends to reduce motion and, if assumed to be linear, is proportional to the velocity. Force, exciting—A fluctuating external force that causes motion of a body, as when a ship encounters a train of waves. Force, restoring—A force tending to return a body to its equilibrium position when it has been displaced by an external force. Fore—A term used to indicate the portion or portions of a ship at or adjacent to the bow. Also applied to the parts of the ship lying between amidships and the stem, as forebody, forehold, and foremast. Forebody—That portion of the ship's body forward of amidships. Forecastle—A superstructure fitted at the extreme forward end of the upper deck. Forefoot—The lower end of a ship's stem, which curves to meet the keel. Forepeak—The watertight compartment at the extreme forward end. The forward trimming tank. Form effect—The difference between the viscous resistance of a model or a ship and the two-dimensional frictional resistance of a flat plate of the same length and wetted area and at the same speed in a given fluid. The difference arises because of the augmented speed of flow around the ship form as compared with that along a flat plate and the pressure resistance of viscous origin. See also form factor. Form factor (r or k)—The ratio between the total viscous resistance coefficient of a model or a ship C. and the two-dimensional frictional resistance coefficient of a flat plate C„ at the same free stream Reynolds number. Forward or fore perpendicular (FP)—See length between perpendiculars. Foundation—The structural supports for the boilers, main engines or turbines, and reduction gears are called main foundations. Supports for machinery space auxiliary machinery are called auxiliary foundations. Deck machinery supports are called steering engine foundation, winch foundation, etc. Frame—A term used to designate one of the transverse members that make up the rib-like part of the skeleton of a ship. The frames act as stiffeners, holding the outside plating in shape and maintaining the transverse form of the ship. See also longitudinal. Frame spacing—The fore-and-aft distance, heel to heel, of adjacent transverse frames. Freeboard—The distance from the waterline to the upper surface of the freeboard deck at side. Freeboard deck—See deck, freeboard. Freeing port—An opening in the lower portion of a bulwark, which allows deck water to drain overboard. Some freeing ports have hinged gates that allow water to drain overboard but that swing shut to prevent seawater flowing inboard. Free surface—Liquid in a partially filled tank or compartment that tends to remain horizontal as the vessel heels or rolls. Frequency (f)—The number of cycles occurring per unit of time: f = 1/T, where T is the period. Frequency, circular (ω)—In any cyclic motion, or in any periodic motion that may be represented by a cyclic motion, the circular frequency is the angular velocity. If ω is in radians per second, ω = 2π/T, where T is the period. Froude number (Fr or FN)—A dimensionless parameter expressing the condition of dynamical similarity for flow systems influenced by gravity and inertia alone. In particular it defines the speed at which geometrically similar models and ship will develop wave systems that are geometrically similar. It is given by: Frv= / gL. The length term L is usually the length of the ship. Other forms of the Froude number use some other characteristic dimension, such as the cube root of the volume of displacement, the submergence depth, or the depth of water in restricted waterways. Froude depth number, Frvghh = / 1/3 Froude displacement number: Fr∇ =∇ v/ g Full scantling ship—A ship designed with scantlings and weather-deck closing arrangements qualifying the ship for minimum freeboard, measured from the uppermost continuous deck, according to the International Load Line Convention. Fully developed sea Gangway—A passageway, side shell opening, or ladderway used for boarding a ship. Garboard strake—The strake of bottom shell plating adjacent to the keel plate. Geosim—One of a series of models that differ in absolute size but are geometrically similar. It is a contraction of the expression "geometrically similar model." Girder—A continuous member running fore and aft under a deck for the purpose of supporting the deck beams and deck. The girder is generally supported by widely spaced pillars. Also, the vertical fore-and- aft plate members on the bottom of single or double- bottom ships. Girth—The distance around the perimeter of any transverse station, section, or frame, between two selected points. For wetted-surface calculations, these two points are generally the waterplane intersections. Graving dock—A structure for taking a ship out of water, consisting of an excavation in the shoreline to a depth at least equal to the draft of ships to be handled, closed at the water side end by a movable gate, and provided with large capacity pumps for removing water; blocks support the ship when the dock is pumped out. Gravitational acceleration (g)—The acceleration, due to the earth's gravitational field, of a freely falling body in a vacuum. This is not strictly constant and over the earth's surface it varies by as much as 1/2 percent. For most terrestrial engineering purposes it is usual to disregard this variation, and for convenience the following international standard value has been agreed on: 9.80665 m/s2 (32.1737 ft/s2). Green water—Water shipped on the deck of a ship in heavy seas, as distinct from spray. Ground tackle—A general term for anchors, cables, wire ropes, etc., used in anchoring a ship to the bottom. Group velocity—see wave, group velocity Gudgeon—Bosses or lugs on sternpost drilled for the pins (pintles) on which the rudder hinges. Gyradius (radius of gyration) (k xx, kyy, kzz)—The square root of the ratio of mass moment of inertia (referred to body axes) to the mass of a body. Harmonic—Sinusoidal, in referring to a function or motion. Hatch (hatchway)—An opening in a deck through which cargo and stores are loaded or unloaded. Hatch coaming—The vertical plating bounding a hatch for the purpose of stiffening the edges of the opening and resisting entry of water below. Head (h)—The height of a given fluid that the pressure in question would support. Heading—The instantaneous direction of the projection of the forward longitudinal axis of a ship in a horizontal plane, defined by points of the compass or degrees of azimuth. Heaving—The vertical oscillatory motion of a specified point in a vessel, usually the center of gravity. Although the heaving of a ship is a motion confined to operation in waves, it is possible with a high-speed planing craft for such motions to occur in calm water under some conditions. See porpoising. Heave-to—To maintain control of a ship, especially in extremely heavy weather, with the minimum possible speed through the water. Heel or list—A steady inclination of a ship about a longitudinal axis; to be distinguished from rolling, which is an oscillatory motion. Hogging—Straining of the ship that tends to make the bow and stern lower than the middle portion. See sagging. Holds—The large spaces below deck for the stowage of cargo; the lowermost cargo compartments. Horn, rudder—A heavy casting or weldment projecting down from the hull immediately abaft the propeller to support the gudgeon fitted to take the single pintle of a semi-balanced rudder. Hub—The central portion of a screw propeller to which the blades are attached and through which the driving shaft is fitted. Also known as the boss. Hull—The structural body of a ship, including shell plating, framing, decks, bulkheads, etc. Hull girder—That part of the hull structural material effective in the longitudinal strength of the ship as a whole, which may be treated as analogous to a girder. Hydroelasticity—The study of the interaction between the inertial, hydrodynamic, and elastic forces in a structure subjected to hydrodynamic loading. Divided into dynamic hydroelasticity, where these three forces are co-existent, or static hydroelasticity where inertial forces are absent. Analogous to aeroelasticity. Hydrofoil—A structure externally similar to an airplane wing designed to produce lift and operate in water. Hydrofoil, span (b)—The length of a hydrofoil from tip to tip, from root to tip if cantilevered, or from end support to end support, measured normal to the direction of relative liquid motion. Inboard—Inside the ship; toward the centerline. Inertial instability—generally, instability in which the only form of energy transferred between the steady state and the disturbance in the fluid is kinetic energy. (McGraw Hill Dictionary of Scientific and Technical Terms) Inner bottom—Plating forming the top of the double bottom; also called tank top. Intercostal—Made in separate parts: between floors, frames or beams, etc.; the opposite of continuous. Keel—The principal fore-and-aft component of a ship's framing, located along the centerline of the bottom and connected to the stem and stern frames. Floors or bottom transverses are attached to the keel. Keel, center vertical—The vertical centerline web of the keel. Keel, flat plate—The horizontal, centerline, bottom shell strake constituting the lower flange of the keel. Keel blocks—Heavy wood, steel, or concrete blocks on which the ship rests during construction. Keelson, side—Fore-and-aft vertical plate member located above the bottom shell on each side of the center vertical keel and some distance therefrom. Kinematic viscosity—See viscosity, coefficient of kinematic. Knee, beam—Bracket connecting a deck beam and frame. Knot (Kt)—A unit of speed, equaling one nautical mile per hour; the international nautical mile is 1,852m (6,076.1 ft). Knuckle—An abrupt change in direction of the plating, frames, keel, deck, or other structure of a ship. Lap—A joint in which one part overlaps the other. Laying off—The development of the lines of ship's form on the mold-loft floor and the making of templates from those lines. Also called laying down. Left-handed propeller—A propeller that rotates in the counterclockwise direction when viewed from astern. Length, effective—See effective length. Length, mean wetted, of a planing craft—The mean length of the portion of the bottom of a planing craft actually wetted when under way. Length, overall (LOA)—The extreme length of a ship measured from the foremost point of the stem to the aftermost part of the stern. Length between perpendiculars (LPP)—The length of a ship between the forward and after perpendiculars. The forward perpendicular is a vertical line at the intersection of the fore side of the stem and the summer load waterline. The after perpendicular is a vertical line at the intersection of the summer load line and the after side of the rudder post or sternpost, or the centerline of the rudder stock if there is no rudder post or sternpost. Lift (L)—The fluid force acting on a body in a direction perpendicular to the motion of the body relative to the fluid. Lightening hole—A hole cut in a structural member to reduce its weight. Lightship weight—See displacement, light. Liner—A flat or tapered strip placed under a plate or shape to bring it in line with another part that it overlaps; a filler. A high-speed passenger or cargo vessel. Lines—A drawing depicting the form of a ship to the molded shape and dimensions showing the stations (transverse sections or frames), waterlines, bowlines, buttocks, and profile. From the lines drawn full size on the mold-loft floor, templates are made for the various parts of the hull. See also molded lines. Line shafting—Sections of main-propulsion shafting between the machinery and the tail shaft. List—If the centerline plane of a ship is not vertical, as when there is more weight on one side than on the other, she is said to list or to heel. Load waterline (LWL)—The line on the lines plan of a ship, representing the intersection of the ship's form with the plane of the water surface when the ship is floating at the summer freeboard draft or at the designed draft. Lofting—The process of developing the size and shape of components of the ship from the designed lines; traditionally, making templates using full scale lines laid down on the floor of the mold loft; today, largely performed at small scale using photographic or computer methods. Long-crested seas—A wave system in which all components advance in the same direction. Two-dimensional waves. Longitudinals—Fore-and-aft structural shape or plate members attached to the underside of decks, flats, or to the inner bottom, or on the inboard side of the shell plating, in association with widely spaced transverses, in the longitudinal framing system. Maneuverability—The quality that determines the ease with which the speed, attitude, and direction of motion of a body can be changed or maintained by its control devices. Margin line—A line, not less than 3 inches below the top of the bulkhead deck at side, defining the highest permissible location on the side of the ship of any damage waterplane in the final condition of sinkage, trim, and heel. Margin plate—The outboard strake of the inner bottom. When the margin plate is turned down at the bilge it forms the outboard boundary of the double bottom, connecting the inner bottom to the shell plating at the bilge. Maximum section coefficient (CX)—The ratio of the area of the maximum vertical transverse cross section of the underwater body of a ship to the product of the waterline beam and the draft at that section. Mean line—The mean line is the locus of the midpoint between the upper and lower surface of an airfoil or hydrofoil section. The thickness is generally measured in the direction normal to the chord rather than to the mean line. The maximum distance between the mean line and the chord line, measured normal to the chord line, is called the camber. The term camber line is often used synonymously with mean line. Metacenter, transverse (M) and longitudinal (ML)—The intersection of the vertical through the center of buoyancy of an inclined body or ship with the upright vertical when the angle of inclination approaches zero as a limit, for transverse or longitudinal inclinations respectively.

Metacenter, transverse and longitudinal; height above the baseplane ( KM and KM L)—The height, measured vertically, of the transverse or longitudinal metacenter above the baseplane of a ship in the upright position. KM = KB + BM

Metacentric height, transverse (GM ) and longitudinal (GM L)—The distance between the center of gravity and the transverse or longitudinal metacenter, measured vertically in the equilibrium position. It is positive when M is above G when the ship is said to have positive metacentric stability; i.e., on inclination to a small angle a restoring moment arises that acts to return the ship to the vertical. Metacentric height, transverse coefficient (CGM) The dimensionless distance between the center of gravity and the transverse or 1/3 longitudinal metacenter, measured vertically in the equilibrium position. CGM = GM/U where U =∇ = cube root of the volumetric displacement

Metacentric radius, transverse ( BM ) and longitudinal ( BM L)—The height, measured vertically, of the transverse or longitudinal metacenter above the center of buoyancy of a ship in the upright position. Geometrically, BM is the radius of

curvature of the locus of the center of buoyancy related to transverse inclinations, and BM L, the radius of curvature of the locus of the center of buoyancy related to longitudinal inclinations. Midship—See amidships. Midship section—A drawing showing a typical cross section of the hull and superstructure (when appropriate) at or near amidships, and giving the scantlings of the principal structural members. Molded—An adjective used to indicate the generally fair form and dimensions of the hull as determined by the lines to the inside of the shell plating. Molded lines—Lines defining the geometry of a hull as a surface without thickness; structural members are related to molded lines according to standard practice (unless otherwise shown on drawings), e.g., the inside surface of flush shell plating is on the molded line, also the underside of deck plating. Mold loft—A floor space for laying down (laying off) the full-size lines of a ship and for making templates to lay out the hull's structural components. Moment, exciting—A fluctuating external moment that causes motion of a body or ship when encountering a train of waves. Moment, pitching—Exciting moment in pitch. Moment of area, second (or moment of inertia)—The summation of the products of the elements of an area or surface and the squares of their distances from a given axis, generally in the surface. Specifically for a ship: second moment of the waterplane area (or moment of inertia), longitudinal (IL) about the transverse axis through the center of flotation. second moment of the waterplane area (or moment of inertia), transverse (IT) about the longitudinal axis through the center of flotation, generally the intersection of the waterplane and the centerplane. second moment of free-water surface (or moment of inertia) generally within a ship, calculated about an axis passing through the center of area of that surface, parallel to the expected heeling or rolling axis. Moments of inertia (Ixx ,Iyy.,Izz) (mass)—The summation of products of elementary masses and the squares of their distances from the respective body axes through the center of gravity—equal to the mass times the square of the gyradius or radius of gyration. Mooring—Securing a ship at a pier or elsewhere by several lines or cables so as to limit her movement. Natural period of motions: heave, pitch, roll (Tz, Tθ, Tφ,)—The time for one complete cycle of the motion resulting when a body is displaced in calm water from its equilibrium position by an external force and then is released. Nautical mile—A distance of 1,852 m (6,076.1 ft). See knot. OBO—Abbreviation for a vessel designed to carry oil, bulk cargos, or ore cargos. Offset—One of a series of distances, measured from reference planes (normally from the centerplane), used for defining the size and shape of a body or ship. One-compartment subdivision—A standard of subdivision of a ship by bulkheads, which will result in the ship remaining afloat with any one compartment flooded, under specified conditions as to permeability of the compartment and the draft of the ship before flooding of the compartment. Outboard—Abreast or away from the centerline towards the side; outside the hull. Overhang—Any portion of the above-water hull of a ship that, when projected downward on to the designed waterplane, lies outside that designed waterline; it may be at the bow or stern, or anywhere along the sides. Panel line—A production line where individual plates, framing members, webs, etc., are successively welded together to form an assembly unit that may include some items of outfit. Panting—The pulsation in and out of the bow and stern plating as the ship alternately rises and plunges deep into the water. May also occur abreast the propellers of a multiscrew ship. Parallel middlebody—The amidship portion of a ship within which the contour of the underwater hull form is unchanged. Parametric stability criteria —are expressed in simple mathematical form and are intended to reproduce the prescribed safety level associated with a dynamic mode of stability failure. Period (T)—The length of time for one complete cycle of a periodic quantity or phenomenon, such as the rolling of a ship from port to starboard and back to port. Period of encounter of a ship in waves (Te)—The time of a periodic quantity or phenomenon, such as the rolling of a ship from port to starboard and back to port. Perpendiculars—Straight lines perpendicular to the designed load waterline of a ship through a fixed point as stated by classification rules. Specifically: aft or after perpendicular (AP): through a fixed point at the stern; generally the aft side of the stern post, or centerline of the rudder stock in ships without a stern post. forward perpendicular (FP): through a fixed point at the bow; generally the intersection of the fore side of the stem with the load waterline. Pillar—Vertical member or column giving support to a deck girder, flat, or similar structure. Also called stanchion. Pintles—The pins or bolts that hinge the rudder to the gudgeons on the sternpost or rudder post. Pitch (P)—The pitch of a propeller blade section at radius r is given by P = 2πr tan φ where φ is the angle between the intersection of the chord line of the section and a plane normal to the propeller axis. This angle is called the pitch angle. Also called geometric pitch. Pitch, variable—A propeller blade for which the pitch is not the same at all radii is said to have variable pitch or varied pitch. A propeller which has the same pitch at all radii is said to be a constant pitch propeller. Pitching—The angular component of the oscillatory motion of a hull about a transverse axis. Although pitching of a ship is a motion confined to operation in waves, it is possible with a high-speed planing craft for such motions to occur in calm water under some conditions. See porpoising. Pitch ratio—The ratio of the pitch to the diameter of the propeller. Generally, the face pitch or geometric pitch at the 70- percent radius is used to compute the pitch ratio. Any measure of pitch can be used with the diameter to form a pitch ratio. Poop—A superstructure fitted at the after end of the upper deck. Porpoising—The oscillation of a high-speed craft, primarily in calm water, in which heaving motion is combined with pitching motion. The motion is sustained by energy drawn from the thrust. Pounding—The impact of a water surface against the side or bottom of a ship hull, whether caused by ship velocity, water velocity, or both. Pounding is differentiated from slamming in that the impact, although heavy, is not in the nature of a shock. Power, brake (PB)—The power measured at the engine coupling by means of mechanical, hydraulic, or electrical brake. Power, effective (PE)—The power required to tow a ship, usually without her propulsive device, at constant speed v in unlimited undisturbed water: PE = RTv. The power may be for the ship either with or without appendages. If the latter, it is usually known as the naked or bare hull, effective power. Power, shaft (PS)—The power delivered to the shafting system by the propelling machinery. Power, thrust (PT)—The power developed by the propeller thrust T at the speed of advance VA: PT = TVA. Power delivered (PD)—The power delivered to the propeller: PE, = 2πQn. Power in waves, mean increase in (PAW)—The mean increase in power in wind and waves as compared with the power in still water at the same mean speed. Pressure, dynamic (q)—The pressure change corresponding to the reduction of the momentum of a fluid element to zero, q =(½)ρv2. Pressure, stagnation—The total pressure measured at a stagnation point. Pressure, static—The static pressure p at a point in a stream flow is that which would be recorded by a pressure gauge advancing with the speed of the local fluid and thus static with respect to it. Pressure, total—This is the sum of the static and dynamic pressures. Prismatic coefficient (CP)—The ratio of the volume of displacement to the volume of the cylinder having the length L and cross section of the maximum section of the ship. This is sometimes called the longitudinal prismatic coefficient and is given

by: CP = ∇ / LAx. The prismatic coefficient can also be referred to the different parts of the ship, such as afterbody, forebody, entrance, and run. In any case the assumed length, as well as the cross section area if different from the above, is to be clearly indicated. Prismatic coefficient, vertical (CVP)—The ratio of the volume of displacement to the volume of a vertical cylinder having as

horizontal section the waterline and as height the draught at midships. It is given by: CVP= ∇ /AWT. When different, the draft of the transverse section having maximum area is used (TX). Probability— Conditional probability Joint probability Marginal probability Mean Values and Moments Probability Density functions Probability Distribution functions

Profile—The outline of a ship when projected on the fore-and-aft vertical plane; also, the outline of parts of the ship, such as the stem, stern, and rudder, when similarly projected. Note: This definition also covers the contour of any flat or curved surface that acts as a hydrofoil or as a control surface; examples are the profiles of diving planes on submarines, fitted generally in a horizontal plane, and the profiles of the blades on a screw propeller. Propeller— Most generally, any device that will produce thrust to propel a vehicle. The most common form is the screw propeller, which basically consists of a central hub and a number of fixed blades extending out radially from the hub. Lift is generated by the blades when the propeller is rotated. Om component of the lift force produces the desired thrust and the other component creates torque, which must be overcome by the engine to sustain rotation. basic screw propeller: a propeller that may be described as fixed pitch, subcavitating, open (unducted), and fully submerged. Variations on this basic type are listed below. adjustable-pitch propeller: a propeller whose blades can be adjusted to different pitch settings when the propeller is stopped. contrarotating propeller.- two propellers rotating in opposite directions on coaxial shafts. controllable-pitch propeller: a propeller having blades that can be rotated about a radial axis so as to change the effective pitch of the blades while the propeller] is operating. This allows full power to be absorbed for all loading conditions. If the pitch can be adjusted to the extent that reverse thrust can be achieved without reversing the direction of rotation of the shaft then the propeller is sometimes called a controllable reversible-pitch propeller. cycloidal propeller: a propeller consisting of a flat disc set flush with the under surface of the vessel with a number of vertical, rudder-like blades projecting from it. The disc revolves about a central axis and each of the blades rotates about its own vertical axis. The axis of each blade traces a cycloidal path. The blade motion can be varied so as to produce a net thrust in any desired direction in a plane normal to the axis of rotation. It is used where excellent maneuverability is required. ducted propeller: a propeller with a short duct mounted concentrically with the shaft. The duct, or nozzle, is shaped so as to control the expansion or contraction of the slipstream in the immediate vicinity of the propeller. In one form (the Fort nozzle) the flow is accelerated, whereas in the other form (pump jet) the flow is decelerated. A pump jet is sometimes also defined as a ducted propeller with stator vanes regardless of whether the flow is accelerated or decelerated. fully cavitating propeller: a propeller designed to operate efficiently at very low cavitation numbers where a fully developed cavity extends at least to the trailing edge of the blade. The blade sections of such propellers have relatively sharp leading edges for more efficient supercavitating operation and thick trailing edges for strength. Also known as supercavitating propeller. interface propeller: a propeller of the fully cavitating ventilated type designed to operate with only a portion of the full disc area immersed. These propellers are considered for high speed applications to vehicles such as surface effect ships where the appendage drag associated with the shafts and struts of a fully submerged propeller would result in a considerable increase in resistance. Also known as partially submerged or surface propellers. ring propeller: a propeller with a very short duct attached to the tips of the blades and rotating with the propeller. Also called a banded propeller. steerable ducted propeller: a ducted propeller in which the duct can be pivoted about a vertical axis so as to obtain a steering effect. sup,ercavitating propeller: see fully cavitating propeller. tandem propeller: two propellers fitted to the same shaft, one behind the other, and rotating as one. ventilated propeller: a propeller of the fully cavitating type, but with pro vision to introduce air into the cavities in order to achieve fully developed, stable cavities at lower speeds than would otherwise be possible. vertical axis propeller: synonymous with cycloidal propeller. Quenching—In steelmaking, an operation consisting of heating the material to a certain temperature and holding it at that temperature to obtain desired crystalline structure, and then rapidly cooling it in a suitable medium such as water or oil. Quenching is often followed by tempering. Rabbet—A groove, depression, or offset in a member into which the end or edge of another member is fitted, generally so that the two surfaces are flush. A rabbet in the stem or stern frame would take the ends or edges of the shell plating, resulting in a flush surface. Randomness is a lack of order, purpose, cause, or predictability in non-scientific parlance. A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution. Random process or Stochastic process —is the counterpart to a deterministic process (or deterministic system) in probability theory. Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. Ergodic Random Process—represents a stationary random process that possesses the property that almost every member of the ensemble exhibits the same statistical behavior that the whole ensemble has. Thus it is possible to determine this statistical behavior by examining only one typical sample function.. Such processes are said to be ergodic and the mean values and moments can be determined by time averages as well as by ensemble averages. Gaussian Random Process—.a Gaussian random process with a normal density function is one of the few for which it is possible to write a joint probability density function for any number of random variables. It is also the only one for which a complete statistical analysis can be carried through in either the linear or nonlinear situations. (expand) Non-Stationary Random Process: — includes all random processes which so not meet the requirements for stationarity as defined below. Unless further restrictions are imposed, the properties of a non-stationary random process are generally time-varying functions which can be determined only by performing instantaneous averages over the ensemble of sample functions forming the process. In practice, it is often not feasible to obtain a sufficient number of sample records to permit the accurate measurement of properties by ensemble averaging. (Bendat and Piersol, 1971, p13) Pseudo random process— a process that appears random but is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process. Such a process is easier to produce than a genuine random one, and has the benefit that it can be used again and again to produce exactly the same numbers, useful for testing and fixing software. Stationary Random Process—A process for which the mean variances, covariance functions and probability densities are independent of time translations, i.e Fourier transforms and inverse transform pairs are well defined. System dynamics— is an approach to understanding the behavior of complex systems over time. It deals with internal feedback loops and time delays that affect the behavior of the entire system.[1] What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. These elements help describe how even seemingly simple systems display baffling nonlinearity. Rail—The rounded member at the upper edge of the bulwark, or the horizontal pipes or chains forming a fencelike railing fitted instead of a bulwark. Rake—A term applied to the fore-and-aft inclination from the vertical, of the mast, smokestack, stem, etc. In river and some ocean barges, it is the end portion of the hull, in which the bottom rises from the midship portion to meet the deck at the headlog. Resistance (R)—The fluid force acting on a moving body in such a way as to oppose its motion; the component of the fluid forces acting parallel to the axis of motion of a body. Resistance is the preferred term in ship hydrodynamics, while drag is generally used in aerodynamics and for submerged bodies. Total resistance is denoted by RT. See also drag.

Resistance, coefficient (CF, CR, CS, CT, CV, CW, etc.)—The nondimensional ratio of any specific component of resistance per unit area to the dynamic pressure far ahead of the body. Resistance, frictional (RF)—The component of resistance obtained by integrating the tangential stresses over the surface of a body in the direction of motion. Resistance, frictional specific (CF)—An alternative name for the coefficient of frictional resistance, in which the reference area is taken to be the wetted area under consideration. Resistance, pressure (RP)—The component of resistance obtained by integrating the normal stresses over the surface of a body in the direction of motion. Resistance, residuary (RR)—A quantity obtained by subtracting from the total resistance of a hull a calculated friction resistance obtained by any specific formulation. Resistance, spray (RS)—The component of resistance associated with the expenditure of energy in generating spray. Resistance, viscous (RV—The component of resistance associated with the expenditure of energy in viscous effects. Resistance, viscous pressure (RPV)—The component of resistance obtained by integrating the components of the normal stresses due to viscosity and turbulence. This quantity cannot be directly measured except for a fully submerged body when it is equal to the pressure resistance RP. Resistance, wavebreaking (RWB)—A resistance component associated with the breakdown of the ship bow wave. Resistance, wavemaking (RW)—The component of resistance associated with the expenditure of energy in generating gravity waves. Resistance, wave pattern (RWP)—A resistance component deduced from measurements of wave elevations remote from the ship or model where it is assumed that the subsurface velocity field, and hence the momentum of the fluid, can be related to the wave pattern by means of linearized theory. The resistance so deduced does not include wavebreaking resistance. Resistance in waves, mean increase in (RAW)—The mean increase in resistance in wind and waves as compared with the still- water resistance at the same speed. Resonance—The dynamical condition of a simple, uncoupled system where the excitation frequency is equal to the natural frequency. Note: In a coupled system, the dynamic condition where the excitation frequency corresponds to the frequency of maximum response to unit exciting force over a range of frequencies. Response amplitude operator—The square of the ratio of response amplitude to excitation amplitude of a forced harmonic motion applied to a linear system as a function of frequency. Revolutions per minute, mean increase in waves—The mean absolute increase in revolutions per minute, as compared with those in calm water, necessary to maintain speed in wind and waves. Reynolds number (Re or RN )—A dimensionless parameter expressing the condition of dynamical similarity for flow systems influenced by viscosity and inertia alone. For equal values of Reynolds number and the same orientation to the flow, the specific resistance coefficients of all geometrically similar smooth surfaces are identical as long as the uninfluenced speed fields are similar and the flow is influenced by viscosity and inertia alone. It is given by: RevL= ρ //μν= vL . The length term L is usually the length of the surface, but the distance from the leading edge of the surface to a specific point, the diameter of a body, or the thickness of the boundary layer is sometimes used as a length term. Rider plate—A continuous flat plate attached to the top or bottom of a girder. Rigging—Chains, wire ropes, fiber lines, and associated fittings and accessories used to support masts and booms used for handling cargo and stores and for other purposes. Rise of floor—See deadrise. Right-handed propeller—A propeller that rotates in the clockwise direction when viewed from astern. Righting arm—The horizontal distance between the center of gravity and the vertical line of action through the center of buoyancy at any angle of heel. Righting arm coefficient (CGZ)—The dimensionless horizontal distance between the center of gravity and the vertical line of 1/3 action through the center of buoyancy at any angle of heel. CGZ = GZ/U where U = ∇ = cube root of the volumetric displacement Righting moment—The product of the righting arm and the displacement of a ship at any angle of heel. Rolling—The angular component of the oscillatory motion of a ship measured about a longitudinal axis. Roll rate—Angular velocity in degrees/secons Root—The part of the propeller blade adjacent to the propeller hub. Ro-Ro or Ro/Ro—Abbreviation for a vessel designed to carry vehicles, so arranged that the vehicles may be loaded and unloaded by being rolled on or off on their own and/or auxiliary wheels, via ramps fitted in the sides, bow, or stern of the vessel. Rudder—A control surface which by its action or movement controls the steering or the turning of a ship in a horizontal plane. Specifically, a hinged or movable control-surface appendage in the form of a hydrofoil, placed either at the bow or at the stern of a ship, or at both ends, to apply a turning moment to the ship. Rudder types are listed below. balanced or semi-balanced: a control surface in the form of a swinging rudder in which a fraction of the area is placed forward of the vertical turning axis to reduce the operating torque in the ahead direction. compound: a control device in the form of a fixed vertical appendage, to the after edge of which is hinged a movable or swinging rudder. See also flap. contra: a rudder with a curved blade, designed to be mounted abaft a propeller to take advantage of the rotation in the slipstream and to produce a forward thrust on the rudder. flap: a control device in the form of a moving rudder that is hinged for practically its entire vertical height to the hull, to a skeg, or to a fin which has an are large in proportion to that of the rudder. This type of rudder takes its name from the flaps on airplane wings; both function by building up large pressure differentials on the fixed parts of the ship or airplane to which they are attached. offset: a rudder offset from the centerplane of a shit either to port or starboard. spade: a control device in the form of a moving appendage that projects below the stern of the shit without any fixed supports in front of it or below it Rudder post—A vertical or nearly vertical member of the ship's structure upon which the steering rudder is hung or supported. Rudder stock—The portion of the rudder, concentric with the axis of rotation, which provides bearing support and also transmits the operating torque. Rudder stop—Lug on stern frame or a stout bracket on deck at each side of the quadrant, to limit the swing of the rudder to approximately 37 degrees port or starboard. A rudder angle of 35 degrees is the maximum usually used at sea (45 degrees on inland waterway vessels). Run—That part of a ship's body aft of the parallel middle body or the point at which the slope of the sectional area curve is zero. Safety level is a quantity related to a likelihood of failure, including, but not limited to, a probability of failure during finite period of time. The term “safety level” is further understood to be a level of safety from stability failure. See stability Sagging—Straining of the ship that tends to make the middle portion lower than the bow and stern. See hogging. Scale effect—The change in any force, moment, or pressure coefficients, flow pattern, or the like, due to a change in absolute size between geometrically similar models, bodies, or ships. These variations in performance due to differences in absolute size arise from the inability to satisfy simultaneously all the relevant laws of dynamical similarity (e.g., gravitational, viscous, and surface tension). Scantlings—The dimensions of a ship's frames, girders, plating, etc. Scantling draft—The maximum draft at which a vessel complies with the governing strength requirements. Usually used when the scantling draft is less than the geometrical draft corresponding to the freeboard calculated according to the load line convention. Scarf—A connection made between two pieces by tapering their ends so that they fit together in a joint of the same breadth and depth as the pieces connected. It is used on bar keels, stem and stern frames, and other parts. Scoop—An opening in the surface of the underwater body of a ship, which may or may not be fitted with a projection extending beyond that surface, designed for catching and taking water into a ship. Scuppers—Drains from decks to carry off accumulations of rainwater, condensation, or seawater. Scuppers are located in the gutters or waterways, on open decks, and connect to pipes usually leading overboard and in corners of enclosed decks to the bilge. Sea chest—An enclosure, attached to the inside of the underwater shell and open to the sea, fitted with a portable strainer plate. A sea valve and piping connected to the sea chest passes seawater into the ship for cooling, fire, or sanitary purposes. Compressed air or steam connections may be provided to remove ice or other obstructions. Seakeeping—In general, a term covering the study of the behavior and performance of ships in a seaway. As an adjective, a term signifying a ship's ability to maintain normal functions at sea. Seakindliness—The quality of behaving comfortably in a seaway; that property of a ship producing easy motions in a seaway. Seam—Fore-and-aft joint of shell plating, deck and tank top plating, or a lengthwise edge joint of any plating. Section—The intersection of a plane with a body or ship that it passes through in any position or direction; specifically for a ship, any transverse section perpendicular to the designed waterplane, such as the 1) area, maximum section (As) or 2) area, midship section, midlength section, midsection, or midstation section (A,). Sectional area coefficients (CX), CM)—The maximum transverse section coefficient CX is given by CX = AX /BXTX where AX is the area of the maximum transverse section; BX and TX, are the beam and draft at this section respectively. The midship section coefficient CM is given by CM = AM /BMTM where. AM is the midship section area; BM, and TM are the beam and draft at midships respectively. Sectional area curve--A diagram of transverse section areas up to the designed waterline plotted on a base of length L, representing the distribution of underwater volume along the length of a ship; this diagram may be made dimensionless by plotting each ordinate as the ratio of the area A of any section to the area AX of the maximum section and by plotting the position of that section as a fraction of the ship length L along the base from selected reference points (generally forward and after perpendiculars or midships). Sections—A general term referring to structural bars, rolled or extruded in any cross section, such as angles, channels, bulbs, Tees, H- and I-bars (or beams). Sometimes called profiles. Shaft tunnel, shaft alley—A watertight enclosure for the propeller shafting large enough to walk in, extending aft from the engine room to provide access and protection to the shafting in way of holds. Shape—A rolled bar of constant cross section such as an angle, bulb angle, channel, etc; also to impart curvature to a plate or other member. Shear stress (T)—The tangential resisting force per unit area acting on a boundary. In a viscous fluid, the shear stress is the tangential resisting force per unit area acting on any boundary within the fluid. The specific value of the shear stress at a wall is denoted by Tw. Sheer—The longitudinal curve of a vessel's decks in a vertical plane, the usual reference being to the ship's side; in the case of a deck having a camber, its centerline sheer may also be given in offsets. Due to sheer, a vessel's deck height above the baseline is higher at the ends than amidships. Sheer strake—The course of shell plating at strength deck level. Shell plating—The plates forming the outer side and bottom skin of the hull. Ship—A vessel intended for marine transportation, without regard to form, rig, or means of propulsion. Short-crested seas—An irregular wave system in which the components advance in various directions. Three- dimensional waves. Shoulder—The portion of a ship at the junction of the middlebody with the entrance or the run, where the waterlines approach or reach their maximum width. Singing—Intense discrete frequency sound radiated from the propeller when the blades vibrate. Generally thought to be due to the shedding of Karman vortices from the trailing edges of the blades at a resonant frequency of the blade vibration. Sinkage—The steady-state lowering of a ship's position of flotation in the water; to be distinguished from heaving, which is an oscillatory motion. SI units—The system of units now being used internationally is the Systeme International d'Unites (SI). The conversion table in appendix C provides conversion factors for U.S. Customary units, and MKS units that differ from SI units, which are used in this volume. Proper use of significant figures and rounding-off techniques should be given due consideration when using the conversion factors. Skeg—A projection from a fixed appendage applied to the underwater hull of a ship, generally to increase the lateral area and give increased swing damping and dynamic stability to the hull. A skeg is usually of large lateral area compared to its transverse thickness, is usually fitted in a vertical plane, and is in the after part of the vessel. Skew-back—The displacement of any blade section along the pitch helix measured from the generator line to the reference point of the section. Positive skew-back is opposite to the direction of ahead motion of the blade section. Also called skew. Slamming—Heavy impact resulting from a vessel's bottom forward making sudden contact with the sea surface after having risen on a wave. Similar action results from rapid immersion of the bow in vessels with large flare. Span (b)—The distance from tip to tip of a hydrofoil or airfoil. The distance from root to tip in the semi- span. Specific gravity—The dimensionless ratio of the weight of unit volume of the designated substance to the weight of unit volume of fresh water. Spectral density, one dimensional (S(ω))—A function of frequency whose integral over any interval represents the energy contribution of all the component waves of a random function in that interval. Speed, corresponding—The speed of a ship vS related to that of a model vM, or vice-versa, according to Froude's law of

comparison: vvSM= λ , where λ is the scale factor. Speed, ground—The speed of a ship relative to the ground, that is the speed including the effects of tide and currents. When the ship is moving through still water the ground speed is the same as the true water speed. Speed, hump (in high-speed craft)—The speed at which the resistance reaches a maximum before a planing craft enters the planing phase, or a hydrofoil craft enters the foilborne phase. Speed of advance of a propeller (vA)—When a propeller behind a ship or model is producing the same thrust at the same rate of rotation as in open water the corresponding speed v, determined from the open- water propeller characteristics is termed the speed of advance of the propeller. This is usually less than the ship speed vS. Springing—A vibration of the complete vessel induced by wave forces in conjunction with the ship's elastic properties. More pronounced in ships having a high length-to-depth ratio. Squatting—The increase in trim by the stern assumed by a ship when under way over that existing when at rest. Stability (ITTC)—The tendency of a ship to remain upright or the ability to return to her normal upright position when heeled by the action of waves, wind, etc. Capsize (MCA): When a vessel is heeled to any angle from which it cannot recover without assistance. Damaged Condition analysis including dynamic stability considerations, subdivision, and free communication with the sea Dynamic Stability (IMO) is the resistance to stability failures in a seaway. Impaired Static Stability:(DCM) including 1. Addition of topside weight, 2. Removal of low weight 3. Shifting of cargo 4. Other off center weight shifts and additions including free surface effects 5. Deterioration of reserve buoyancy (including water trapped on deck) 6. Flooding Intact stability failure (IMO) is a state of inability of a ship to remain within design limits of roll (heel, list) angle and combination of lateral and vertical accelerations. Partial stability failure (IMO) is an event that includes the occurrence of very large roll angles and/or excessive accelerations, which will not result in loss of the ship, but which would impair normal operation of the ship and could be dangerous to crew, passengers, cargo or ship equipment. Two subtypes of partial stability failure are intended to be included in the development: 1. roll angles exceeding a prescribed limit, and 2. combination of lateral and vertical accelerations exceeding prescribed limits Total stability failure, or capsizing (IMO), results in total loss of a ship’s operability with likely loss of lives. Capsizing could be formally defined as a transition from a nearly stable upright equilibrium that is considered safe, or from periodic motions near such equilibrium, passing through a far from equilibrium state that is intrinsically unsafe (or could be considered unacceptable from a practical point of view) Static equilibrium stability: The condition where the static heeling moment equals the static righting moment. Stanchion—Vertical column supporting decks, flats, girders, etc; also called a pillar. Rail stanchions are vertical metal columns on which fence-like rails are mounted. See rail. Steering gear—A term applied to the steering wheels, leads, steering engine, and fittings by which the rudder is turned. Usually applied to the steering engine. Stem—The bow frame forming the apex of the intersection of the forward sides of a ship. It is rigidly connected at its lower end to the keel and may be a heavy flat bar or of rounded plate construction. Stern, cruiser—A spoon-shaped stern used on most merchant ships, designed to give maximum immersed length. Stern, transom—A square-ended stern used to provide additional hull volume and deck space aft and(or) to decrease resistance in some high-speed ships. Stern frame—Large casting, forging, or weldment attached to the after end of the keel. Incorporates the rudder gudgeons and in single-screw ships includes the rudder post. Sternpost—Sometimes, the vertical part of the stern frame to which the rudder is attached. Stern tube—The watertight tube enclosing and supporting the tail-shaft. It consists of a cast-iron or cast- steel cylinder fitted with bearing surface within which the tailshaft, enclosed in a sleeve, rotates. Stiff—A vessel is said to be stiff if she has an abnormally large metacentric height. Such a ship may have a short period of roll and therfore will roll uncomfortably. The opposite of tender. Stiffener—An angle, T-bar, channel, built-up section, etc., used to stiffen plating of a bulkhead, etc. Stiffness—A relative term indicating resistance to deformation or bending. Strain—The deformation resulting from a stress, measured by the ratio of the change to the total value of the dimension in which the change occurred. Strake—A course, or row, of shell, deck, bulkhead, or other plating. Streamline—A line in a fluid such that its tangent at any point is parallel to the instantaneous velocity of the fluid at that point. Strength deck—The deck that is designed as the uppermost part of the main-hull longitudinal strength girder. The bottom shell plating forms the lowermost part of this girder. Stress—The force per unit section area producing deformation in a body. Stringer—A term applied to a fore-and-aft girder running along the side of a ship at the shell and also to the outboard strake of plating on any deck. Stringer bar—The angle connecting the deck plating to the shell plating or to the inside of the frames. The strength deck stringer bar is usually called the gunwale bar. Strut—Outboard column-like support or V-arranged supports for the propeller shaft, used on some ships with more than one propeller instead of bossings. Suction side—The low-pressure side of a propeller blade. Synonymous with the back of the propeller blade. Analogous to the upper surface of a wing. Supercavitating flows—Flows in which attached, fully developed cavities extend beyond the trailing edge of the body about which the cavity is formed. Superstructure—A decked-over structure above the upper deck, the outboard sides of which are formed by the shell plating as distinguished from a deckhouse that does not extend outboard to the ship's sides. Surface, wetted (S)—The surface area of the underwater body of a ship. This generally includes the area of the appendages that give an appreciable contribution to the frictional drag, such as bilge keels, propeller bossings, and rudder. Surging—The longitudinal oscillatory motion of a specified point in a ship, usually the center of gravity (or origin of body axes). Swash bulkhead, swash plate—Longitudinal or transverse nontight bulkhead fitted in a tank to decrease the swashing action of the liquid contents as a ship rolls and pitches at sea. Their function is greatest when the tanks are partially filled. Without them the unrestricted action of the liquid against the sides of the tank might be severe. A plate serving this purpose but not extending to the bottom of the tank is called a swash plate. Swaying—The transverse oscillatory motion of a specified point in the ship, usually the center of gravity. Tailshaft—The aftermost section of the propulsion shafting in the stern tube in single-screw ships and in the struts of multiple-screw ships, to which the propeller is fitted. Tank, trimming—A tank located near the ends of a ship. Seawater (or fuel oil) is carried in such tanks as necessary to change trim. Tank, wing—Tanks located well outboard adjacent to the side shell plating, often consisting of a continuation of the double bottom up the sides to a deck or flat. Telegraph—An apparatus, either electrical or mechanical, for transmitting orders, as from a ship's bridge to the engine room, steering gear room, or elsewhere about the ship. Tempering—After quenching, the material is reheated to a predetermined temperature below the critical range and then cooled. In steelmaking this is done to relieve stresses set up by quenching and to restore ductility. Template—Wood or paper full-size patterns to be placed on materials to indicate the size and location of holes, plate edges, etc; also to indicate the curvature to which frames, for example, are to be bent. Tender—A vessel is said to be tender if she has an abnormally small metacentric height. Such a ship may have a long period of roll but may list excessively in a strong wind and may be dangerous if a hold is flooded following a collision. The opposite of stiff. Also a small general utility boat carried aboard ship. Thrust (T)—The force developed by a screw propeller in the direction of the shaft. Tiller—An arm, attached to rudder stock, which turns the rudder. Tonnage, gross—Under vessel-measurement rules of various nations, a measure of the internal volume of spaces within a vessel in which one ton is equivalent to 2.83 m3 or 100 cu ft. Under the International Convention on Tonnage Measurement of Ships (ICTM), 1969, a standardized numerical value that is a logarithmic function of spaces within a vessel. There is no definition of a ton under ICTM because the value per unit of volume is greater on a vessel of large volume than on a vessel of small volume. Gross tonnage according to the national and canal rules generally includes spaces bounded by the under surface of the uppermost complete deck, the side frames, and the floor frames or the inner bottom if it rests on the floors or if the double bottom is for water ballast, plus closed-in space in deck structures available for cargo or stores or for the berthing or accommodation of passengers or crew. Rules vary greatly as to exclusion or inclusion of various spaces. Gross tonnage 3 according to ICTM is GT = K1 V in which V is the total molded volume of all enclosed spaces of the ship in m and K1 is 0.2 + 0.02 log10V. (Still true?) Tonnage, net—Net tonnage, according to national and canal rules, is derived from gross tonnage by deducting an allowance for the propelling machinery space and certain other spaces. Net tonnage according to ICTM is a logarithmic function of the volume of cargo space, the draft to-depth ratio, the number of passengers to be accommodated, and the gross tonnage. Torque (Q)—The torque delivered to the propeller aft of all bearings. Tramp ship—A general breakbulk cargo ship that has no set trade route or schedule. Transformation temperature—The temperature above which the ferrite form of iron in shipbuilding and other steel is transformed to the austenite form, and below which the ferrite form recurs. The microstructure of the steel is changed upon passing through this temperature. Transverse—A deep member supporting longitudinal frames of bottom or side shell or longitudinal deck beams. At right angles to the fore-and-aft centerline. Trim—The difference between the draft forward and the draft aft. If the draft forward is the greater, the vessel is said to "trim by the head." If the draft aft is the greater, she is "trimming by the stern." To trim a ship is to adjust the location of cargo, fuel, etc., so as to result in the desired drafts forward and aft. Tumblehome—The slant inward from the vertical of a transverse section of a hull above the designed waterline. It is the opposite of flare. Vapor pressure—The pressure of vapor in equilibrium with its liquid state. It is then also called the saturated vapour pressure or vapour tension, which for a given substance depends only upon the temperature. Viscosity, coefficient of dynamic (μ)—The ratio of the shearing stress in a Newtonian (linear Stokesian) fluid to its rate of shear deformation. Viscosity, coefficient of kinematic (ν)—The ratio of the coefficient of dynamic viscosity to the mass density of fluid. Wake—The wake is a term used to describe the motion imparted to the water by the passage of the ship's hull. It is considered to be positive if its direction is the same as that of the ship. Water, restricted—A term describing a body of water in which the boundaries are close enough to the ship to affect her resistance, speed, attitude, maneuvering, and other performance characteristics, as compared with her corresponding characteristics in an open, unlimited, body of water. Principally, "restricted" applies to the proximity of the water boundaries in a horizontal direction. Water, shallow—A term describing a body of water in which the boundaries are close enough to the ship in a vertical direction to affect her resistance, speed, attitude, maneuvering, or other performance characteristics as compared with her corresponding characteristics in water of unlimited depth. Water, standard fresh—Water having zero salinity and a temperature of 15° C (59° F), with density p = 999.00 kg/m3 (1.9384 lbs2/ft4), kinematic viscosity ν = 1.13902 x 10-6 m2/s(1.22603 x 10-5 ft2/s). Water, standard salt—Water having 3.5 percent salinity and a temperature of 15° C (59° F), with density p = 1,025.87 kg/m3 (1.9905 lbs2/ft4), kinematic viscosity ν = 1.18831 x 10-6 m2/s (1.27908 x 10 -5 ft2/s) . Waterline—The intersection line of the free-water surface with the molded surface of a ship, either in still water or when she is surrounded by waves of her own making. The intersection line of any selected plane, parallel to the baseplane, with the molded surface of a ship. The angle of the waterline at the bow in the horizontal plane neglecting local shape at stem is the angle of entrance. The angle of the waterline at the stern in the horizontal plane neglecting local shape of stern frame is the angle of run. Waterplane—Any selected plane through a ship form and parallel to the baseplane, specifically designed waterplane: corresponding to the designed waterline. maximum waterplane: corresponding to the waterline of a ship at the draft at which the waterplane area is maximum. Waterplane area (Aw)—The area enclosed by a waterline. Wave—A disturbance of the surface of a fluid that usually progresses across the surface as the result of circular or other local motions of the fluid components. A standing wave is a special case of a wave that does not advance. amplitude (ζA): the radius of orbital motion of a surface wave particle, equal to one half of the wave height. celerity (cW) :wave phase velocity cLTWWW= / celerity, deep water: the linear wave phase velocity in deep wateris cgLWW= /2π components: the waves of different frequencies and directions found by spectral analysis to compose an irregular sea, or the large number of finite waves used to approximate such an irregular sea. Crest elevation direction, angle of (μ): the angle between the direction of a component wave and the x0 axis. encounter, angle of (μE): the angle between the longitudinal axis of the ship and the direction of the wave encounter. frequency (fw): the reciprocal of wave period fw = 1/T; or circular frequency ω =2πfw.= 2π/T. group: A series of waves in which the wave direction, length (period), and height vary only slightly. group velocity (cG): The average :rate of advance of the energy of a finite train of gravity waves. For deep water, the group velocity is half the phase velocity. height ( Hw): the vertical distance from wave crest to wave trough, or twice the wave amplitude of a harmonic wave. height,downcrossing ( Hd): the vertical distance between a successive crest and trough. height, upcrossing (Hu) the vertical distance between a successive trough and crest height, significant:((H1/3d and H1/3u )the average apparent height of the third highest waves in an irregular pattern. instantaneous elevation (c): the instantaneous elevation of a point in a wave system above the level of the undisturbed surface. length (Lw, λW): the horizontal distance between adjacent wave crests in the direction of advance. length, apparent (Lw,the horizontal distance between adjacent wave crests of an irregular sea in the direction of advance. 2 number (k or κ) : κπ==2/LgW ω / period (TW): time between the passage of two successive wave crests past a fixed point. period, apparent (Td or Tu): the time elapsing between the occurrence of two successive crests of an irregular sea, or between two successive downward or upward crossings of zero in a record. period, significant (T1/3d or T1/3u): The average period of the highest one-third of the waves in a given wave record profile: the elevation of the surface particles of a wave plotted as a function of space in fixed time. slope of surface: the surface slope of a wave profile perpendicular to the crest in space coordinates. Maximum wave slope of a regular harmonic or trochoidal wave is πH/LW. shallow water waves: Waves in water sufficiently shallow that the water depth is less than one-twentieth of the wave length standing wave: A wave produced by the propagation in opposite directions of two identical wave trains. The resulting water surface oscillates only in the vertical direction with alternating nodal and antinodal points. steepness ratio: the ratio of wave height to length. swell: freely propagating wind-generated waves that have propagated out from the area of generation train: a continuous sequence of wave crests and hollows travelling in the same direction. trochoidal: a profile closely approximating that of a regular surface gravity wave in a fluid; it can be geometrically constructed by tracing the path of a point on the radius of a circle as the circle rolls along the underside of a horizontal line. Web frame—A built-up frame to provide extra strength, usually consisting of a web plate flanged or otherwise stiffened on its edge, spaced several frame spaces apart, with the smaller, regular frames in between. Wetness—The quality of a part of the ship, usually the weather deck forward, with respect to its liability of being wet as a result of motions of ship and waves. Whipping—The transient ship-hull vibration induced by impulsive excitation forces. For example, fore-bottom slamming, bow-flare slamming, shipping of water and stern slamming. See also springing. Yawing—The angular component of the oscillatory motion of a hull about a vertical axis.