BACKGROUND

1. Technical Field

[0001] The present invention relates generally to damping, particularly to ships and their hulls.

2. Description of Related Art

[0002] A moving apparatus (e.g., a propulsion device, such as a rotating propeller) may generate loads on and/or other non-motive forces in the surrounding water (e.g., forces not in the propulsion direction, and/or pressure waves created by the apparatus). These loads may be transmitted into the hull. A rotating propeller may create non-motive loads that act on the hull. Some loads may be periodic (e.g., as the propeller tips pass closest to the hull, and/or harmonics thereof). Some loads may be sporadic and/or stochastic. These loads may be disturbing to passengers and/or damage cargo. In some cases, these loads may damage the ship.

[0003] A mechanical part (e.g., a hull, a beam, and the like) is typically designed to be as stiff as possible. However, while a part might be stiff, it is not absolutely rigid. Loads imparted to the hull (stress) typically induce deformation within the hull (strain). For periodic loading, the resulting strain is typically periodic, which may result in fatigue. Fatigue may be difficult to detect, and often is not apparent until it results in catastrophic failure. Forces transmitted from the propeller to hull via the water may generate concomitant loads on the rest of the ship (e.g., within the hull). Components within the hull may be subject to such loads for years (e.g., whenever the ship is moving), which may induce fatigue. Japanese patent document JPH 1071993 A describes a "Vibration Control Device for a Marine Vessel." (Title, machine translation) German patent document DE 10 2012 108 967 Al describes an "Elastisch gelagertes Schiffsrumpf element." (Title)

SUMMARY OF THE INVENTION

[0004] A ship may comprise a propulsion device (e.g., a propeller), a hull having a decoupled portion, and a compliant surface coupled to the decoupled portion via a coupling. The coupling may include an elastic part, such as a spring, configured to position the compliant surface at a desired distance from the decoupled portion (e.g., such that an outer surface of the compliant portion is at a desired position with respect to the outer surface of the hull).

[0005] A coupling may allow a compliant surface to move with respect to the decoupled portion in a manner that minimizes the transmission of undesired forces from the exterior of the compliant surface into the decoupled portion (e.g., the rest of the ship). A compliant surface may move laterally, normally (e.g., "in and out") and/or a combination. The compliant surface may be designed move a distance that is a function of propeller diameter (e.g., at least 0.5%, 1%, 3%, or even at least 5% of propeller diameter, including at least 10% of propeller diameter). In an exemplary ship, a compliant surface may be configured to move, with respect to the decoupled portion, a distance that is at least 0.5cm, including at least 1cm, at least 2 cm, including at least 5 cm, including at least 10cm, including at least 30 cm.

[0006] In an embodiment, a ship comprises a hull having a decoupled portion, a propeller, and a ducktail. The ducktail may include a compliant surface, particularly a compliant surface that includes a point having a nearest distance to the propeller. The compliant surface may be coupled to the decoupled portion via a coupling comprising an elastic part (e.g., a spring) configured to position the compliant surface at a desired distance from the decoupled portion. The coupling may allow the compliant surface to move over a desired distance with respect to the decoupled portion. The desired distance maybe at least 0.5%, particularly at least 1%, particularly at least 3% of a diameter of the propeller. In some cases, the propeller may have a diameter that is greater than 70% of a draft of the ship.

[0007] The decoupled portion may include the ducktail, such that the compliant surface is coupled to the (substantially noncompliant) ducktail. In some embodiments, substantially the entire ducktail includes the compliant surface, and the coupling couples the ducktail to (the decoupled portion of) the rest of the hull.

[0008] The ship may comprise a pocket shaped to create an open volume behind the compliant surface. The elastic part may comprise a pressure vessel (e.g., a bag) disposed in and/or formed as part of the pocket. A compressor may pressurize the pressure vessel (e.g., with a gas). In some cases, the compliant surface includes gaps through which a fluid may flow. Liquid (e.g., seawater) may flow through the gaps, dissipating energy. In some cases, a compressor pressurizes a pocket behind the compliant surface with a gas that exits the pocket via gaps in the compliant surface.

[0009] A coupling may comprise a lossy part (e.g., a shock absorber) configured to dissipate energy associated with movement of the compliant surface. The lossy part may generally transform directed energy (e.g., linear momentum) into randomized energy (e.g., heat). The lossy part may comprise gaps through which a fluid (e.g., oil, water, gas, air) flows. The lossy part may comprise a liquid, a foam, a gel, particulate material, and the like. The lossy part may be disposed in a gap behind the compliant surface.

[0010] A ship may comprise a ducktail, which may comprise a compliant surface. The ducktail may be integrated to the hull and/or extend from a transom (e.g., a virtual transom). The ducktail may be integrated into the decoupled portion of the hull (e.g., a portion of the ducktail includes the compliant surface, but the rest of the ducktail is relatively stiff). A ducktail and compliant surface may be integrated (e.g., such that the entire ducktail complies). A ship may comprise a large area propeller, which may be located aft of a transom of the ship. A ship may comprise a ducktail coupled to the ship via a coupling, such that substantially the entire ducktail forms the compliant surface. A propeller (e.g., large area propeller) may be located below the compliant surface (e.g., below the ducktail). In some cases, the ducktail is disposed above the propeller (which may be located aft of the transom).

[0011] A compliant surface may be located at (e.g., replacing) the portion of the hull that is nearest to the propeller. A nearest distance between the propeller tip and the hull may be below 30%, including below 25%, including below 20% of the propeller diameter. The compliant surface may encompass the nearest distance (e.g., out to a lateral distance comparable to the radius of the propeller)

[0012] A compliant surface may be substantially "coplanar" with the hull. A desired distance may be chosen such that at least 10%, particularly at least 20%, particularly at least 80%, particularly at least 90% of an edge portion comprising an outer edge of the compliant surface is located and shaped such that a tangent to the edge portion is coplanar with at least that part of the hull proximate to the edge portion.

[0013] A ship may comprise a hull having a length greater than 30 meters, 40 meters, or even greater than 50 meters. The ship may have a transom that substantially demarcates an end of an internal volume of the ship. The ship may have a propeller (e.g., a large area propeller), which may be disposed aft of the transom, and a ducktail disposed above the propeller. The ducktail may be attached to the transom and/or integrated with the transom and/or otherwise integrated with the hull, and have a length that is between 2% and 5% of the length of the ship. A large area propeller may have a diameter that is greater than 70% of a draft (102) of the ship, particularly greater than 80%, particularly greater than 85%, particularly greater than 100% of the draft. The ducktail may include a compliant surface. The ducktail need not include a compliant surface in certain embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG. 1 is a schematic illustration of a ship, according to some embodiments.

[0015] FIG. 2 is a schematic illustration of a compliant surface, according to some embodiments.

[0016] FIG. 3 schematically illustrates a coupling, according to some embodiments.

[0017] FIG. 4 illustrates an exemplary embodiment.

[0018] FIG. 5 illustrates an exemplary embodiment.

[0019] FIG. 6 illustrates an embodiment comprising a ducktail.

[0020] FIG. 7 illustrates an embodiment comprising a ducktail.

[0021] FIGS. 8A and 8B are schematic illustrations of models of viscoelastic subcomponents, according to some embodiments.

[0022] FIG. 9 illustrates an exemplary embodiment.

[0023] FIG. 10 illustrates an exemplary embodiment.

DETAILED DESCRIPTION OF THE INVENTION

[0024] A structure may be subject to loads, such as pressure waves and/or other forces (e.g., from the environment). Various embodiments may reduce the transmission of loads into a ship and/or protect the hull and components therein from various external forces.

[0025] For some ships, the propulsion system may generate non- motive loads that act on the hull (e.g., pressure waves associated with propeller rotation). A rotating propeller (and/or other propulsion device, such as a water jet) may generate non-motive forces in the surrounding water, which may act on the hull. Portions of the hull close to the propeller (e.g., near the point that is closest to the propeller tip when the tip is closest to the hull) may be particularly susceptible to pressure waves generated by the propeller (e.g., as the tip "sweeps past" the nearest point on the hull). These loads may be transmitted to (and even through) the hull. Stress caused by these loads may induce strain in the hull and/or internal components, which may cause damage. In some cases, a loud, disturbing "banging" or "knocking" may result. Some loads are periodic; some loads may induce oscillation within the hull. In some cases, a surface of the hull may be damaged. In some cases, interior portions of the hull (e.g., a frame) and/or other components of the ship may be damaged. [0026] For some vessels, propulsion may be improved by locating the propeller as close as possible to the hull. A propeller may be located such that at least a portion of the propeller's tip is located in the boundary layer (of flowing water) proximate to the hull as the ship is moving. A "nearest distance" between the propeller tip and the closest point on the hull may be minimized (e.g., to increase efficiency). The nearest distance may be no greater than 25%, including below 20%, including below 15% of a diameter of the propeller. At the design stage, the boundary layer may be determined using suitable computational simulation methods (e.g., computational fluid dynamics, or CFD) to represent expected vectors and gradients during steaming. The edge of the boundary layer may be identified using commonly accepted fluid-flow guidelines.

[0027] FIG. 1 is a schematic illustration of a ship, according to some embodiments. A ship 1 may have hull 100 and a propeller 110. A water line 5 and draft 102 may be determined (e.g., based on an unloaded state, a fully loaded state, and the like). A draft may be a design draft, a lightship draft, an operating draft, and/or a fully loaded draft. A region 105 of the ship (e.g., of the hull) proximate to the propeller may be particularly susceptible to non-motive loads (e.g., pressure pulses in the surrounding water transmitted from the propeller to the hull). The ship may be protected from these loads with a suitably sized and located compliant surface. [0028] FIG. 2 is a schematic illustration of a compliant surface, according to some embodiments. In this example, a compliant surface is substituted for a portion of the (noncompliant) hull that is nearest the propeller. A compliant surface may be disposed in other locations.

[0029] A nearest distance 120 may be defined by a point on the hull (or hydrodynamic extension thereof) that is closest to the tip of the propeller and the corresponding point on the propeller tip (nearest to the hull/extension). For some ships, a portion of the hull surrounding the "nearest point" may face particularly high loads from the propeller (as compared to remote portions).

[0030] The ship may include a compliant surface 130 and a decoupled portion 101. Compliant surface 130 may be coupled to the decoupled portion via a coupling 140. The coupling may comprise an elastic part 150 (FIG. 3) which may include a spring or other device that provides rebound. Coupling 140 may be configured to position the compliant surface at a desired distance 125 from the decoupled portion. In an embodiment, desired distance 125 is chosen such that, when the propeller is not rotating, compliant surface 130 is substantially

"coplanar" with the surrounding (decoupled) hull (notwithstanding that the compliant surface and hull are typically curved). The compliant surface and surrounding hull may form a smooth hydrodynamic surface over which water may flow. Compliant surface 130 may be slightly "proud" with respect to the rest of the hull. Compliant surface 130 may be slightly "recessed" with respect to the rest of the hull.

[0031] A compliant surface may be designed to be hydrodynamically neutral (or even beneficial) with respect to flow past the hull, yet compliant with respect to pressure pulses and/or normal forces acting on the hull. In some cases, a compliant surface may improve hydrodynamic flow over the hull.

[0032] In some embodiments, the compliant surface includes the point defining nearest distance 120 (as in FIG. 2). A compliant surface may be located in a portion of the hull that does not include the nearest distance.

[0033] The coupling typically enables the compliant surface to flex or move with respect to the decoupled portion (e.g., when the ship is being propelled). In some cases, the coupling lets the compliant surface "comply" with various forces (e.g., the non-motive loads created by the propeller), minimizing the transfer of these loads to the rest of the ship. In some cases, the compliant surface is intrinsically sufficiently compliant. Compliant surface 130 may move a relatively large distance when the propeller tip sweeps past the hull, then return to an equilibrium position after the tip has moved past.

[0034] Compliant surface 130 may move over a distance 170, which may be in one or more directions. Distance 170 is typically chosen according to ship size, speed, propeller diameter, rotation rate, the length of nearest distance 120, typically in combination with expected loads (e.g., based on finite element models and computational fluid dynamic models of pressure pulses from the propeller acting on the hull). Distance 170 is typically designed to be large enough that the resulting motion of compliant surface 130 minimizes the transmission of loads (causing that motion) to decoupled portion 101. Distance 170 is typically chosen to be small enough that adverse affects of such motion (e.g., disturbance of the hydrodynamic flow) are minimized. Distance 170 may be lateral (with respect to compliant surface 130), "in and out" with respect to the surrounding hull, and/or a combination thereof. Distance 170 may be greater than 2cm, including greater than 5cm, or even greater than 10 cm. Distance 170 may be between 3 and 200 cm, including between 4 and 100 cm, including about 5 to 30 cm. In some cases (e.g., lateral displacement), distance 170 may be between 0.5 and 15 cm, including between 1 and 8 cm.

[0035] A hull typically comprises a shell or skin supported by a plurality of beams 100"'. For a typical ship, a set of larger beams (longitudinal or lateral) are spaced 1.5 to 3.5 meters apart to form a primary skeleton of the hull, and smaller beams are disposed between (e.g., orthogonally to) the larger beams, typically at a spacing of 0.5-lm. A distance between beams is typically chosen according in concert with a thickness of the shell to achieve a desired stiffness of the shell/beam/hull combination. [0036] For a ship having a compliant surface, a relatively large "opening" in the skeleton of the ship (as compared to typical inter-beam distances) may be created to accommodate the compliant surface. For a ship, an embodiment may comprise an opening having at least one dimension that is over 0.5m, including over lm, including over 2m, including over 4m, including over 6m. An opening may include at least two dimensions (e.g., a length and a width) that are larger than 50% of the propeller diameter, including greater than 75%, including greater than 100%, including greater than 110% of the propeller diameter. An opening may be at least 2 square meters, at least 5 square meters, or even at least 10 square meters. A compliant surface (e.g., one or more dimensions 132) may be sized to match an opening (e.g., fit within, subject to a desired tolerance and/or gap).

[0037] A compliant surface may have a dimension 132 (e.g., a length, width, diameter, and the like) chosen according to an expected load size, ship size, propeller size, and/or combination thereof. A compliant surface may have an area that is between 20% and 300% of the propeller area, including between 50% and 200%. For an exemplary (e.g., Ropax) ship (at least 50 meters long, propeller diameter 2-6 meters), a compliant surface may have at least one, particularly at least two, dimensions 132 (e.g., orthogonal to each other) that are correspondingly 2-6 meters. Dimension 132 may be greater than 50cm, including greater than lm, including greater than 3m. For some ships, a compliant surface may have an area greater than 3 m ^A 2, including greater than 10 m ^A 2, including greater than 20 m ^A 2, including greater than 40 m ^A 2. Dimension 132 may be different in lateral and longitudinal directions. Dimension 132 may be between 80% and 160%, including between 90% and 140% of the propeller diameter. In some embodiments, an area of compliant surface 130 is between 50% and 500% of the propeller area, including between 80% and 300%, including between 100% and 200%.

[0038] An embodiment may comprise a double hull, which may comprise an outer hull 100' and an inner hull 100". Inner and outer hulls may be separated by an internal volume (e.g., to contain leakage in from the outer hull or out from the inner hull). The hulls 100', 100" and beams 100"' may be designed to form a stiff structure (e.g., with the inner and outer hulls connected by the beams to form a stiff sandwich). A compliant surface may be decoupled from an inner hull, from an outer hull, and/or from both hulls.

[0039] In some cases, a hull may comprise an acoustically rigid structure (e.g., proximate to the nearest tip distance and/or between the proximate surface and the rest of the hull). An acoustically rigid structure may substantially reduce the transmission of loads (e.g., acoustic waves) to the rest of the hull. An acoustically rigid structure may include unevenly spaced stringers, with spacing and dimension chosen according to an expected loading frequency (e.g., associated with propeller rpm).

[0040] A compliant surface may include a combination of materials designed to reflect pressure waves. In some cases, a plurality of materials (e.g., layers) may be chosen according to an expected frequency with which the tip passes the nearest distance (e.g., the frequency of the propeller rotation and/or a harmonic thereof). The acoustic properties of the surface may be designed to absorb and/or reflect the incoming waves, reducing their transmission to the rest of the ship.

[0041] FIG. 3 schematically illustrates a coupling, according to some embodiments. Elastic part 150 may be configured to position compliant surface 130 such that the edge(s) of compliant surface 130 are coplanar with their adjacent counterparts on the proximate surface of the (decoupled) hull, such that water flows smoothly over compliant surface.

[0042] Elastic part 150 may be designed according to the expected loads acting on compliant surface 130. Elastic part 150 may have a stiffness chosen according to an expected range of loads (e.g., normal, shear, hydrostatic) imparted to compliant surface 130 and/or the surrounding decoupled hull. A stiffness of elastic part 150 may be small enough that elastic part 150 allows compliant surface 130 to move a distance 170 that is long enough to effectively isolate decoupled portion 101 from the non-motive loads acting on compliant surface 130. The stiffness may be large enough that hydrodynamic and/or other operational constraints (e.g., fuel economy) are not adversely affected.

[0043] A compliant surface may be designed to be "more flexible" than the natural compliance of prior hulls (e.g., the intrinsic elastic deformation associated with the shell and beams, which are often designed to be stiff).

Distance 170 typically scales with ship size, propeller size, and in some cases, propulsion thrust. Distance 170 may be increased as the nearest-distance to the propeller tip decreases.

[0044] A compliant surface may (under the expected loading) move a distance 170 that is at least 0.5 cm, including at least 1cm, including at least 3cm, including at least 6cm, including at least 10 cm. In some cases, a compliant surface may move a distance between 2 and 50 cm, including between 4 and 30 cm. A compliant surface may move at least 20 cm, including at least 40cm. In an exemplary implementation, compliant surface 130 may move (e.g., in and out) a distance 170 that is between 3 and 20 cm, including between 4 and 15 cm.

[0045] Coupling 140 may be designed to minimize unwanted harmonics. Coupling 140 may comprise a plurality of couplings, which may be located at various places on the compliant surface. The couplings may couple the compliant surface to various places on the decoupled portion 101. [0046] Coupling 140 may comprise a lossy part 160 configured to dissipate the loads acting on the compliant surface (e.g., by pressure waves generated by the propeller tip). Lossy part 160 may be coupled to compliant surface. In some cases, lossy part 160 is coupled to the decoupled portion 101. Lossy part 160 may convert directional motion (e.g., in direction 170) into dissipative (e.g., turbulent, or nondirectional) motion.

[0047] In some embodiments, a "pocket" 200 behind the compliant surface may be shaped to create an open volume 201 behind the compliant surface. This volume may be pressurized and/or filled (e.g., with a liquid, a foam, a gel, a particulate material, and the like). A pressurized open volume may create an elastic coupling comprising an in-situ generated hydrostatic pressure vessel (e.g., the pocket and compliant surface combine form a

hydrostatic "spring"). In some cases, open volume 201 may be at least partially filled with seawater. In some cases, open volume 201 may be substantially entirely filled with liquid. Open volume 201 may be at least partially gas-filled, including substantially entirely gas-filled. Pocket 200 may be substantially entirely between an inner and outer hull (not shown). Pocket 200 may be integrated with (e.g., built into) both and inner and outer hull.

[0048] Lossy part 160 may comprise a viscous coupling and/or "shock absorber" configured to dissipate energy associated with movement of compliant surface 130, minimizing the transfer of energy from the compliant surface 130 to the decoupled portion 101 of the ship. Lossy part 160 may comprise one or more gaps (322) through which fluid flows as compliant surface 130 moves.

[0049] During operation, external forces (e.g., associated with the propeller tip passing by the hull) may load compliant surface 130. Coupling 140 allows compliant surface 130 to move in response to these forces, minimizing the transfer of these forces to decoupled portion 101. In some embodiments, a lossy part 160 dissipates the energy associated with these forces.

[0050] In an embodiment, coupling 140 comprises an elastic part 150 formed by open volume 201 (e.g., at least partially filled with a gas) and a lossy part 160 comprising gaps through which fluid (e.g., gas or liquid) flow. The fluid may be seawater, which may be pushed through the gaps by movement of the compliant surface.

[0051] FIG. 4 illustrates an exemplary embodiment. Compliant surface 130 may be coupled to decoupled portion 101 via one or more springs 310. In some embodiments, a coupling includes one or more gaps 320 in or around compliant surface 130. In some cases, compliant surface 130 may include a pivot 330, which may couple a portion of compliant surface 130 to the decoupled portion. A pivot may be located "upstream" with respect to an expected hydrodynamic flow direction. The hinge may be located "downsteam" or to the side. A coupling may comprise one or more pivots, hinges, linkages, sliding surfaces, bearings, and the like.

[0052] Gaps may be designed to achieve a desired set of flow criteria (e.g., flow volume, flow rate, frictional forces created by the flow). These criteria may include the expected viscosity of the fluid flowing through the gap(s) (e.g., air, fresh water, seawater). Gaps may be configured to achieve a desired hydrodynamic effect on the water flowing past the compliant surface. Gaps may be configured to enable the in-situ formation of a coupling (based on the geometry of the compliant surface and its interaction with volume 201).

[0053] FIG. 5 illustrates an exemplary embodiment. In some cases, gaps 320 are configured to at least partially "seal" an open volume 201 behind the compliant surface. The seal may be designed to "leak" in a controlled fashion, which may be used to induce fluid flow in desired locations. In some cases, a compressor 400 may be fluidically coupled to compliant surface 130 (e.g., via open volume 201). The compressor may generate a flow of fluid (e.g., a gas or liquid into volume 201) that acts on or around compliant surface 130. In an embodiment, compressor 400 provides a gas that pressurizes volume 201 to form a coupling. [0054] In an embodiment, gaps 320 are sized, shaped, and located to allow gas to "leak out" through the gaps. Compressor 400 may be sized to generate sufficient gas flow and pressure to replenish this gas.

[0055] An apparatus may comprise a damping material (e.g., gel, foam, sand, water, and the like). In some cases, an interior container (e.g., a bag, balloon, box, and the like) may contain a damping material (e.g., loosely packed gravel, beads, and the like, and/or a liquid).

[0056] FIG. 6 illustrates an embodiment comprising a ducktail. A ship may comprise a transom 180 (e.g., that may substantially define an internal volume of the ship). The internal volume may be governed by internal mass (e.g., center of gravity) constraints, regulatory constraints, and the like. In some cases, the hydrodynamic length of the ship may be extended (beyond the transom) with a so-called "ducktail." A ducktail may extend past the transom a distance of about 2-4% of the length of the ship, thereby increasing the

hydrodynamic efficiency without increasing internal volume and/or dimensions of the ship. A ducktail may be attached to the transom. A ducktail may be integrated with the transom and/or hull.

[0057] In the embodiment shown in FIG. 6, a ship 2 comprises a ducktail 190. For illustrative convenience, ducktail 190 is demarcated from transom 180. Ducktail 190 may also be integrated with the hull and/or other portions of the ship. In this example, the propeller is disposed aft of the transom; in certain embodiments it need not be.

[0058] Ducktail 190 may include compliant surface 130 coupled to the ship via a coupling. In an embodiment, coupling 140 couples ducktail 190 to the hull (e.g., to decoupled portion 101). Coupling 140 may allow ducktail 190 to move "up and down" and/or "fore and aft" with respect to decoupled portion 101. Ducktail 190 may include gaps (not shown) through which fluid may flow. Substantially the entire ducktail may act as a compliant surface (e.g., as in FIG. 6). A ducktail may comprise a decoupled portion. Only a portion of the ducktail may include the compliant surface. For example, a hull may comprise a substantially noncompliant ducktail. A portion of the ducktail (e.g.,

incorporating the nearest distance to the propeller) may include a compliant surface.

[0059] Various embodiments may comprise a large area propeller (LAP). An LAP may increase propulsion efficiency. An LAP may have a diameter that is greater than 70%, including 80%, including 85%, including 90%, including 100%, including 105% of the draft of the ship. In an embodiment, a propeller 110 (e.g., a large area propeller) is located aft of the transom (e.g., below a ducktail, which may comprise a compliant surface 130). [0060] FIG. 7 illustrates an embodiment comprising a ducktail. A ship 3 may comprise a ducktail 190 and a propeller 110 (e.g., disposed below the ducktail 190 (e.g., aft of a "transom" 180 of the ship,)). The ducktail may be stiffly coupled to the ship and/or integrated with the hull 100 (e.g., forming part of the decoupled portion of the hull). The ducktail may include an optional compliant surface 130 (e.g., the decoupled portion includes at least a part of the ducktail, which itself includes the compliant surface coupled to the ducktail via a coupling 140). The ducktail does not incorporate a compliant surface in certain

embodiments. A propeller may include a LAP. Such a combination of aft- located propeller (particularly an LAP) and ducktail may provide for increased propulsion efficiency. A ship may include a transom, which may be a

structurally distinct component of the hull or a "virtual" boundary demarcating an aftward end of the ship. In an embodiment, a LAP is disposed aft of a "virtual transom" (e.g., a plane demarcating an interior volume of the ship) and the ducktail extends aftward of the virtual transom (e.g., such that the LAP is substantially below the ducktail). In such an implementation, the hydrodynamic length of the ship may be increased subject to a particular interior volume (associated with the location of the virtual transom). By locating the LAP below the ducktail, water may be guided by the ducktail to keep the LAP immersed (notwithstanding a diameter that extends close to, or even above, the surface of the water when the ship is not moving).

[0061] FIGS. 8A and 8B are schematic illustrations of models of viscoelastic subcomponents, according to some embodiments. Using computer simulations, a viscoelastic model of the hull (e.g., with compliant surface, coupling, and decoupled portion) may be used to design an apparatus. The design may be iteratively simulated and modified to achieve a desired behavior. Computer simulations (e.g., FEM, CFD) may be used to design a hull, decoupled portion, compliant surface, coupling, gaps, and the like. A desired set of input constraints (e.g., ship size, propeller size, propeller location, rotation speed, ship speed, and the like) may be used to design and simulate the behavior of compliant surface 130. Such simulations may be used to design a compliant surface having a desired shape, gap(s) and the like, and a coupling having desired elastic (and optionally viscous) performance. A coupling may be simulated with one or more combinations of elastic and (optionally) lossy components.

[0062] A variety of established simulation models exist to describe the behavior of viscoelastic subcomponents (e.g., spring and dashpot models).

Changes in elastic and viscous behavior may be readily implemented in these models, and viscoelastic subcomponents may be "mixed and matched" as desired to create various designs for a compliant surface coupling (e.g., a combination of multiple series and/or parallel subcomponents). These designs may be simulated (e.g., using FEM modeling), and the expected behavior of the compliant surface may be assessed. In an embodiment, a coupling comprises a plurality of couplings, at least one of which (and preferably several of which) may be represented as a "spring and dashpot" viscoelastic subcomponent.

[0063] FIG. 8A illustrates an exemplary "spring and dashpot" subcomponent of a coupling, in which a "spring" (e.g., representing elastic part 150) and a "dashpot" (e.g., representing lossy part 160) couple compliant surface 130 to decoupled portion 101 in parallel. FIG 8B illustrates a subcomponent in which the "spring" and "dashpot" are in series. Series and parallel

subcomponents may be combined.

[0064] FIG. 9 illustrates an exemplary embodiment. A ship 900 may comprise a compliant surface 130 coupled to the decoupled portion 101 via substantially rigid edge couplings 910. Edge couplings 910 may comprise welds, bolts, rivets, and the like. Compliant surface 130 may be designed to flex in a "drum-head" fashion by choosing a suitably thin interior portion (demarcated by dimension 132). Such a configuration may provide for substantially water-tight sealing of the compliant surface, yet still provide requisite compliance. Edge couplings 910 may be relatively thicker than an inner portion of the compliant surface, such that the boundary portion of the compliant surface is not damaged during use.

[0065] FIG. 10 illustrates an exemplary embodiment. A ship 1000 may comprise a compliant surface 130 coupled to a bag 1010. Bag 1010 may be substantially sealable, and may be filled with a material 1020 designed to dissipate energy imparted to the compliant surface. Material 1020 may comprise a liquid (e.g., water, oil), a gel, a foam, bearing balls, gravel, sand, beads, and the like. A lossy part 160 may include bag 1010 (e.g., filled with sand). An elastic coupling may include a bag 1010 (e.g., pressurized with gas).

[0066] Various features described herein may be implemented independently and/or in combination with each other. An explicit combination of features does not preclude the omission of any of these features from other embodiments. The above description is illustrative and not restrictive. Many variations of the invention will become apparent to those of skill in the art upon review of this disclosure. The scope of the invention should, therefore, be determined not by the above description, but instead should be determined with reference to the appended claims along with their full scope of equivalents.