Abstract
The invention concerns a vessel for floating in a body of water, comprising a hull having an aft hull section and an aft body arranged at a distance from the aft hull section, thereby forming a passage into which water can flow. The aft body and the aft hull section are designed to minimize the vessel's stern wave during forward movements.
Claims
1-21. (canceled)
22. A vessel for floating in a body of water comprising: a longitudinal hull with an aft hull section comprising a separation line defined as a line extending in a transverse direction of the hull at which a water flow originally flowing along the hull is separated from the aft hull section above a minimum forward propulsion of the vessel and wherein the separation line further is defined by the aft hull section having an abrupt change of direction in a longitudinal vertical plane of the hull, an aft body arranged at a distance from the aft hull section at a location between the water surface and 110% of a draft of the hull when the vessel is floating motionless in a body of water at a lightweight waterline, forming a passage between the aft body and the separation line, wherein the aft body comprises: a maximum width measured in a horizontal plane in the transverse direction of the hull, a leading edge, a trailing edge and a chord line defined by a straight line in a longitudinal vertical plane of the hull extending from the leading edge to the trailing edge, a leading edge distance defined by the smaller of: a minimum distance measured in a longitudinal vertical plane of the hull between the leading edge and the aft hull section and a minimum distance measured in said longitudinal vertical plane of the hull between two parallel lines, wherein the first line is a tangent line of the aft hull section immediately in front of the separation line and the second line is intersecting the leading edge, a trailing edge distance defined by the minimum distance in said longitudinal vertical plane of the hull between the trailing edge and a water surface, and an angel defined as the angel between the first line and the water surface measured in said longitudinal vertical plane of the hull, wherein, when the vessel is floating motionless in a body of water at the lightweight waterline: the aft body and the aft hull section is configured so that the leading edge distance is at least 0.9 times the trailing edge distance, the angle is less than 20 degrees, the separation line is located at or above the water surface, the leading edge is situated less than 10% of the length of the cord line aft of the separation line, the cord line is orientated parallel with the water surface or with a positive angle relative to the water surface and the aft body and the aft hull section is configured such that, during forward propulsion of the vessel, the net force component exerted onto the vessel from the aft body in the direction of travel of the vessel is zero or negative in the full speed range the vessel is operating in.
23. The vessel according to claim 22, wherein at least a part of the aft body is located in front of the separation line.
24. The vessel according to claim 22, wherein the leading edge is situated at least half the length of the chord line in front of the separation line.
25. The vessel according to claim 24, wherein the top surface of the aft body and the aft hull section is designed such that the minimum distance in a longitudinal vertical plane between said top surface and the aft hull section in front of the separation line remains constant or near constant.
26. The vessel according to claim 22, wherein the aft body is designed to give a positive lifting force during forward propulsion of the vessel.
27. The vessel according to claim 22, wherein the aft body is designed such that, during forward propulsion of the vessel, the direction of a resulting water flow immediately downstream of the trailing edge due to a water flow passing a top surface of the aft body and a water flow passing an underside of the aft body, is orientated parallel or near parallel to the water surface.
28. The vessel according to claim 22, wherein at least a part of the trailing edge is located deeper than 35% of the draft when the vessel is floating motionless in a body of water at the lightweight waterline.
29. The vessel according to claim 22, wherein the length of the chord line is at least equal to the draft of the hull when the vessel is floating motionless in a body of water at the lightweight waterline.
30. The vessel according to claim 22, wherein the aft body constitutes an integrated part of the vessel.
31. The vessel according to claim 22, wherein the aft hull section located downstream the separation line is situated over the water surface during forward propulsion of the vessel.
32. The vessel according to claim 22, wherein the hull comprises a transom located at or above the water surface when the vessel is laying still and floating in a body of water at the lightweight waterline.
33. The vessel according to claim 22, wherein that the aft body is designed and positioned such that a part of a water flow flowing over a top surface of the aft body is lifted above the water surface during forward propulsion of the vessel.
34. The vessel according to claim 22, wherein the vessel further comprises a bow body located in front of a bow area, wherein the bow body is configured to lead the water mass passing a top surface of the bow body away from the bow area, or essentially parallel to the bow area, or a combination thereof.
35. The vessel according to claim 22, wherein the hull is a displacement hull.
36. The vessel according to claim 22, wherein the aft body and the aft hull section is configured so that the draft of the hull during forward propulsion of the vessel will be at least 80% of the draft of the hull when the vessel is floating motionless in the body of water.
37. The vessel according to claim 22, wherein the leading edge is parallel with the water surface when the vessel is floating motionless in the body of water at the lightweight waterline.
38. The vessel according to claim 22, wherein the vessel is a multi-hull vessel.
39. The vessel according to claim 22, wherein the maximum width of the aft body measured in a horizontal plane in the transverse direction of the hull is at least 50% of the maximum width of the hull measured at the water surface in the transverse direction of the hull when the vessel is floating motionless in the body of water at the lightweight waterline.
40. The vessel according to claim 22, wherein the trailing edge is located a horizontal length of at least one chord line aft of the separation line.
41. The vessel according to claim 22, wherein the length of the chord line is at least 5% of the length between perpendiculars of the vessel.
42. The vessel according to claim 22, wherein that the vessel has a planing hull.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0132] FIG. 1 is a schematic side view illustration of the aft hull section of the vessel in FIG. 5 showing the general mode of operation for the invention when the vessel is traveling at operational speed.
[0133] FIG. 2A&B show a typical prior art displacement hull, wherein FIG. 2A is a longitudinal vertical plane of the displacement hull at rest and FIG. 2B is a longitudinal vertical plane illustration of the displacement hull in motion, further illustrating the upward direction of a water flow at the aft hull section and the formation of a stern wave.
[0134] FIG. 3A-D are longitudinal vertical plane illustrations of a typical planing hull according to the prior art, at increasing Froude numbers (F.sub.N), wherein FIG. 3A shows a submerged planing hull situated motionless in a body of water, FIG. 3B shows the formation of a stern wave and turbulent reversed water flow behind the planing hull at low (displacement mode) speed (F.sub.N=0−0.5), FIG. 3C shows the formation of the stern wave at medium (transition mode) speed (F.sub.N=0.5−0.9) and FIG. 3D shows the formation of the stern wave at high (planing mode) speed (F.sub.N>0.9).
[0135] FIG. 4 show a graphic illustration of typical frictional resistance R.sub.f and total resistance R.sub.t as function of the Froude number (F.sub.N) for a prior art displacement hull and planing hull.
[0136] FIG. 5A&B show the behaviour of a displacement hull according to the invention, wherein FIG. 5A is an illustration in a longitudinal vertical plane of the displacement hull at rest and FIG. 5B is an illustration in a longitudinal vertical plane of the displacement hull in forward motion, further illustrating the direction of a water flow at the aft hull section and the formation of a reduced stern wave.
[0137] FIG. 6A&B are illustrations in longitudinal vertical planes of a planing hull with an aft body according to the invention, wherein FIG. 6A shows the planing hull floating motionless in a body of water and FIG. 6B shows the formation of a reduced stern wave behind the planing hull at speed (F.sub.N>0).
[0138] FIG. 7A-C are illustrations in a longitudinal vertical plane of an aft hull section of a vessel in accordance with the invention, submerged in a body of water, wherein FIG. 7A shows the aft hull section designed for low speed (F.sub.N<0.4) where the aft body is located closer to the water surface, FIG. 7B shows the aft hull section designed for medium speed (F.sub.N=0.4−0.6) where the aft body is located at medium depth and FIG. 7C shows the aft hull section designed for high speed (F.sub.N>0.6) where the aft body is located at same depth as the base line of the hull.
[0139] FIG. 8A-C are illustrations in longitudinal vertical planes of aft hull sections of vessels in accordance with the invention, submerged in a body of water, wherein FIG. 8A shows a separation line in the aft hull section arranged upstream/in front of the aft body, FIG. 8B shows the separation line arranged above the aft body and FIG. 8C shows the separation line arranged at the transom of the hull and above the trailing edge of the aft body.
[0140] FIG. 9A-D are perspective illustrations seen obliquely from behind of aft hull sections of vessels in accordance with the invention, wherein FIG. 9A shows an aft body arranged with its trailing edge below the transom of the hull, FIG. 9B shows an aft body arranged with its leading edge below the transom of the hull, FIG. 9C shows a vessel with the hull sides continuing in a straight line all the way back to the trailing edge of the aft body and FIG. 9D shows a vessel where the hull sides below a water surface is sloping towards the longitudinal centre line of the vessel and continuing all the way back to the trailing edge of the aft body.
[0141] FIG. 10 is a perspective illustration seen obliquely from behind of an aft hull section in accordance with the invention where the leading edge of the aft body is located straight under the transom, showing a leading edge area (A.sub.le) and a trailing edge area (A.sub.te) as herein defined.
[0142] FIG. 11 is an illustration in a longitudinal vertical plane of a hull in accordance with the invention submerged in a body of water wherein the position and alignment of an aft body and a bow body, according to the applicant's patent EP3247620B1, and their effect on a water flow during forward propulsion of the vessel.
[0143] FIG. 12 show a graphic illustration of typical total resistance R.sub.t as function of Froude number (F.sub.N) derived from numerous model tests performed on models, wherein the upper left figure (L-A) is an illustration in a longitudinal vertical plane of a typical displacement vessel according to prior art moving at low speed (F.sub.N<0.25), the middle left figure (L-B) is an illustration in a longitudinal vertical plane of a displacement vessel with an aft body according to the invention moving at low speed (F.sub.N<0.25), the lower left figure (L-C) is an illustration in a longitudinal vertical plane of a displacement vessel with an aft body according to the invention and a bow body moving at low speed (F.sub.N<0.25). The upper right figure (R-A) is an illustration of the prior art displacement vessel in the upper left figure (L-A) moving at higher speed (F.sub.N>0.25), the middle right figure (R-B) is an illustration of the displacement vessel in the middle left figure (L-B) moving at higher speed (F.sub.N>0.25), the lower right figure (R-C) is an illustration of the displacement vessel in the lower left figure (L-C) moving at higher speed (F.sub.N>0.25). The graph indicates the total resistance R.sub.t in Newton as function of the Froude number (F.sub.N) for the three vessels where the prior art displacement vessel (L-A and R-A) is marked with a solid line and with reference Rt(A), the inventive displacement vessel with the aft body (L-B and R-B) is marked with a stippled line and with reference Rt(B) and the inventive displacement vessel with an aft body and a bow body (L-C and R-C) is marked with a dotted line and with reference Rt(C).
[0144] FIG. 13 show a graphic illustration of typical total resistance R.sub.t as function of Froude number (F.sub.N) derived from numerous model tests performed on models, wherein the upper left figure (L-A) is an illustration in a longitudinal vertical plane of a typical planing vessel according to the prior art moving at a displacement mode speed (F.sub.N<0.4), the middle left figure (L-B) is an illustration in a longitudinal vertical plane of a planing vessel with an aft body according to the invention moving at a displacement mode speed (F.sub.N<0.4), the lower left figure (L-C) is an illustration in a longitudinal vertical plane of a planing vessel with an aft body according to the invention and a bow body moving at a displacement mode speed (F.sub.N<0.4). The upper centre figure (M-A) is an illustration of the prior art planing vessel in the upper left figure (L-A) moving at a transition mode speed (F.sub.N=0.4−0.9), the middle centre figure (M-B) is an illustration of the planing vessel in the middle left figure (L-B) moving at a transition mode speed (F.sub.N=0.4−0.9), the lower centre figure (M-C) is an illustration of the planing vessel in the lower left figure (L-C) moving at a transition mode speed (F.sub.N=0.4−0.9). The upper right figure (R-A) is an illustration of the prior art planing vessel in the upper left figure (L-A) moving at a planing mode speed (F.sub.N>0.9), the middle right figure (R-B) is an illustration of the planing vessel in the middle left figure (L-B) moving at a planing mode speed (F.sub.N>0.9), the lower right figure (R-C) is an illustration of the planing vessel in the lower left figure (L-C) moving at a planing mode speed (F.sub.N>0.9). The graph indicates the total resistance R.sub.t in Newton as function of the Froude number (F.sub.N) for all the three vessels where the prior art planing vessel (L-A, M-A and R-A) is marked with a solid line and with reference Rt(A), the inventive planing vessel with the aft body (L-B, M-B and R-B) is marked with a stippled line and with reference RI(B) and the inventive planing vessel with the aft body and the bow body (L-C, M-C and R-C) is marked with a dotted line and with reference Rt(C).
[0145] FIG. 14A shows a schematic illustrations of an aft hull section of the vessel in accordance with the invention, wherein drawing (a) shows a longitudinal vertical plane of the aft hull section and the position and alignment of an aft body arranged with its leading edge upstream/in front of the separation line and drawing (b) shows drawing (a) seen from behind.
[0146] FIG. 14B drawing (c) shows the aft hull section shown in FIG. 14A seen from below and drawing (d) shows the aft hull section of FIG. 14A drawing (a) illustrating a water flow during forward propulsion of the vessel.
[0147] FIG. 15A shows a schematic illustrations of an aft hull section of the vessel in accordance with the invention, wherein drawing (a) shows a longitudinal vertical plane of the aft hull section and the position and alignment of an aft body arranged with its leading edge downstream/aft of the separation line and drawing (b) shows the aft hull section shown in drawing (a) seen from behind.
[0148] FIG. 15B drawing (c) shows the aft hull section shown in FIG. 15A seen from below and drawing (d) shows the aft hull section of FIG. 15A drawing (a) illustrating a water flow during forward propulsion of the vessel.
[0149] FIG. 16 are showing upside down perspective illustrations of a model vessel with a slender displacement hull, wherein Model 16A shows a prior art model vessel and Model 16B is the same model as Model 16A but fitted with an aft body according to the invention.
[0150] FIG. 17 is a perspective illustration of a propulsion system arranged on model vessels to measure propulsion thrust in Newton [N].
[0151] FIG. 18A are two pictures from model tests showing the formation of stern waves of Model 16A and Model 16B at speed corresponding to Froude number (F.sub.N) 0.30.
[0152] FIG. 18B are two pictures from model tests showing the formation of stern waves of Model 16A and Model 16B at speed corresponding to Froude number (F.sub.N) 0.36.
[0153] FIG. 19 shows the total resistance R.sub.t as function of Froude number (F.sub.N) derived from model testing of the prior art Model 16A and the inventive Model 16B.
[0154] FIG. 20 shows upside down perspective illustrations of three different model vessels being compared in model tests, where Model 20A shows a prior art model vessel with a displacement hull, Model 20B shows a prior art model vessel with a displacement hull and a bow body, the model having the same length and displacement as the Model 20A. Model 20C shows an inventive model vessel which is the same as Model 20B except for the separation line and the aft body.
[0155] FIG. 21 shows the total resistance Rt as function of Froude number (F.sub.N) derived from model tests of the prior art Model 20A, the prior art Model 20B and the inventive Model 20C.
[0156] FIG. 22 shows upside down perspective illustrations of two model vessels, wherein Model 22A shows is a prior art model vessel with planning hull and Model 22B is an inventive model vessel with same length, width and displacement as Model 22A but having a bow body and an aft body.
[0157] FIG. 23A are two pictures from model tests showing the formation of stern waves for the prior art Model 22A and the inventive Model 22B at speed corresponding to Froude number (F.sub.N) 0.40.
[0158] FIG. 23B are two pictures from model tests showing the formation of stern waves for the prior art Model 22A and the inventive Modell 22B at speed corresponding to Froude number (F.sub.N) 0.50.
[0159] FIG. 23C are two pictures from model tests showing the formation of stern waves for the prior art Model 22A and the inventive Model 22B at speed corresponding to Froude number (F.sub.N) 0.65.
[0160] FIG. 24 shows the power consumption in watt [W] of the electrical propulsion engine as function of Froude number (F.sub.N) from model tests of the prior art Model 22A and the inventive Model 22B.
[0161] FIG. 25 is an upside down perspective illustration of a model vessel having a test set up to measure the horizontal forces in the longitudinal direction of the vessel from the aft body acting on the vessel.
[0162] FIG. 26 is a side view illustration of the aft hull section of the model vessel shown in FIG. 25 with a test set up to measure the horizontal forces in the longitudinal direction of the vessel from the aft body acting on the vessel.
[0163] FIG. 27 is a side view illustration of the aft hull section of the model vessel shown in FIG. 26 where the chord angel γ is: 0 degrees (i.e. the cord line of the aft body and the water surface is parallel) marked (A), −2 degrees marked (B) and −3 degrees marked (C). (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but is for convenience not shown in this figure).
[0164] FIG. 28 is a side view illustration of the aft hull section of the model vessel shown in FIG. 26 where the chord angel γ is 0 degrees and the draft of the hull is shown at 80 mm DV(A), at 90 mm DV(B) and at 100 mm DV(C). (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but is for convenience not shown in this figure).
[0165] FIG. 29 is a side view illustration of the aft hull section of the model vessel shown in FIG. 26 where the chord angel γ is 0 degrees, and where the geometry of the aft hull section is altered to obtain an angle β between a tangent line TH of the aft hull section and the horizontal of 4.5 degrees marked β(A) and 11 degrees marked β(B). (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but for convenience is not shown in this figure).
[0166] FIG. 30 is a side view illustration of the aft hull section of the model vessel shown in FIG. 26 where the chord angel γ is 0 degrees, and where the aft body is arranged 30 mm above the base line marked (A) and 50 mm above the base line marked (B). (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but for is convenience not shown in this figure).
[0167] FIG. 31 is a side view illustration of the aft hull section of the model vessel shown in FIG. 26 where the chord angel γ is 0 degrees, and where the cord length of the aft body is 105 mm marked (A) and 145 mm marked (B). (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but is for convenience not shown in this figure).
[0168] FIG. 32 shows a side view illustration of the aft hull section of the model vessel shown in FIG. 26: [0169] where a model vessel according to the invention (A) has a draft DV(A) of 80 mm (which entails A.sub.le=1,0*A.sub.te) and an angle β(A) for the tangent line TH of 4.5 degrees and a chord angel γ(A) of 0 degree, and [0170] a model vessel according to prior art (B) has a draft DV(B) of 100 mm (which entails A.sub.le=0.71*A.sub.te) and an angle β(B) for the tangent line TH of 11.0 degrees and a chord angel γ(B) of −2 degrees.
[0171] (The support to fix the aft body to the hull, incl. the ball bearing, load cell, propeller and rudder is the same as in FIG. 26 but is for convenience not shown in this figure).
[0172] FIG. 33 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from an aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with an aft hull section as shown in FIG. 27 having a chord angle γ of 0 degrees marked (A), a chord angle γ of −2 degrees marked (B) and a chord angle γ of −3 degrees marked (C). A positive force reading equals a backward directed force (i.e. resistance to forward motion) while a negative force reading equals a forward directed force (i.e. propulsion).
[0173] FIG. 34 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from an aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with an aft hull section as shown in FIG. 28 having a leading edge area (A.sub.le)=1.0*trailing edge area (A.sub.te) marked (A), (A.sub.le)=0.83*(A.sub.te) marked (B), and (A.sub.le)=0.71*(A.sub.te) marked (C). A positive force reading equals a backward directed force (i.e. resistance to forward motion) while a negative force reading equals a forward directed force (i.e. propulsion).
[0174] FIG. 35 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from an aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with an aft hull section as shown in FIG. 29 when the geometry of the aft hull section is altered to obtain an angle β between a tangent line TH of the aft hull section and the horizontal of 4.5 degrees marked (A), and 11.0 degrees marked (B). A positive force reading equals a backward directed force (i.e. resistance to forward motion) while a negative force reading equals a forward directed force (i.e. propulsion).
[0175] FIG. 36 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from an aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with an aft hull section as shown in FIG. 30 having an aft body located 30 mm above base line marked (A), and 50 mm above base line marked (B). A positive force reading equals a backward directed force (i.e. resistance to forward motion).
[0176] FIG. 37 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from the aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with an aft hull section as shown in FIG. 31 having a chord line length of the aft body of 105 mm marked (A), and 145 mm marked (B). A positive force reading equals a backward directed force (i.e. resistance to forward motion).
[0177] FIG. 38 shows a graphic presentation of the horizontal forces in Newton acting in the longitudinal direction of the vessel from the aft body onto the aft hull section as function of Froude number (F.sub.N). The graphs are derived from model tests performed on a model with aft hull sections as shown in FIG. 32 for a configuration according to the inventive model vessel marked (A) and for a configuration according to the prior art model vessel marked (B). A positive force reading equals a backward directed force (i.e. resistance to forward motion) while a negative force reading indicates a forward directed force (i.e. propulsion). As seen, the aft foil of the prior art model vessel marked (B) is providing a continuously forwardly directed propulsion force.
DETAILED DESCRIPTION OF THE INVENTION
[0178] In the following, embodiments of the invention will be described in more detail with reference to the drawings and definitions. However, it is specifically intended that the invention is not limited to the embodiments and illustrations contained herein but includes modified forms of the embodiments including portions of the embodiments and combinations of elements from different embodiments as come within the scope of the claims.
Definitions and Reference Numerals
[0179] Throughout this application, the following definitions, numerals and letters in drawings, shall apply: [0180] Vessel 1: [0181] All vessels that are operated from low displacement speed to above planing speed in excess of F.sub.N=1.0. [0182] Hull 2: [0183] The watertight body of a vessel 1 that makes the vessel 1 seaworthy, but excluding components such as superstructure, the aft body 4, the bow body 10, the propeller 12, the rudder, the keel, the deck, etc. [0184] Hull side 2′:
[0185] The hull sides of the vessel 1. I.e. not including the bow area 21 and the transom 7. [0186] Aft hull section 3: [0187] For a displacement vessel 1, the part of the hull 2 which is aft of the cross section of the hull 2 below a waterline 5 with the greatest cross section area, and for a planning vessel 1, the part of the hull 2 which is aft of mid ship. [0188] Aft body 4: [0189] The body that is arranged at a distance from the aft hull section 3. [0190] Water surface 5: [0191] A strait horizontal surface formed by still sea/water. [0192] Separation line 6: [0193] A defined line extending primarily in the transverse direction of the vessel 1 in the aft hull section 3 where a water flow 51 passing the hull 2 separates from the hull 2 when the vessel 1 is in forward motion above a minimum speed, for example at operational speed. Furthermore, the separation line 6 is defined by the aft hull section 3 having an abrupt change of direction in a longitudinal vertical plane of the hull 2. [0194] Transom 7: [0195] The flat or almost flat part of a hull 2 that forms the stern of a square ended vessel 1. [0196] Support 8: [0197] Support to fix the aft body 4 to the vessel 1. [0198] Stern wave 9: [0199] A wave behind or at the stern of the vessel 1 created during forward motion of the vessel 1, for example at operational speed. [0200] Bow body 10: [0201] The bow body that is arranged at the bow area 21 according to patent EP3247620B1. [0202] Propeller shaft 11 [0203] Propeller 12 [0204] Propeller sleeve (with no thrust bearing) 13 [0205] Electric motor 14 [0206] Motor housing 15 [0207] Motor suspension system 16 [0208] Load cell 17 [0209] Mounting bracket 18 [0210] Base plate 19 [0211] Ball bearing slide 20 [0212] Bow area 21: [0213] The area of the hull 2 seen from in front (over and under the water surface 5 when the vessel 1 is floating in a mass of water), but excluding the bow body 10 if any. [0214] Bow wave 22: [0215] A wave crest formed ahead of the bow area 21 due to the hull's 2 deceleration of the oncoming water flow 51. [0216] Leading edge 41: [0217] The foremost edge of the aft body 4, equivalent to “the leading edge” of an airplane wing. [0218] Trailing edge 42: [0219] The rearmost edge of the aft body 4, equivalent to “the trailing edge” of an airplane wing. [0220] Chord line 43: [0221] A straight line in a longitudinal direction of the vessel 1 extending from the leading edge 41 to the trailing edge 42. [0222] Top surface 45: [0223] The top surface area of the aft body 4 extending from the leading edge 41 to the trailing edge 42. [0224] Underside 46: [0225] The underside area of the aft body 4 extending from the leading edge 41 to the trailing edge 42. [0226] Two vertical planes 49: [0227] Two vertical planes in the longitudinal direction of the vessel 1, each intersecting the point defining the maximum width (W) of the aft body 4 in the transverse direction of the vessel 1. [0228] Passage 50: [0229] The area between the aft hull section 3 and the top surface 45 where water can flow through during forward motion of the vessel 1. [0230] Water flow 51: [0231] A flow of water relative to the vessel 1 due to vessel's 1 forward motion, for example at operational speed. Such water flow 51 is also shown as arrows in the figures. [0232] Water flow surface level 53: [0233] The top surface of a water flow 51 bordering air around a vessel 1 that can be lower or elevated relative to the water surface 5. [0234] Bow passage 56: [0235] The area between the bow area 21 and the top surface of the bow body 10. [0236] Base line 58: [0237] A horizontal line drawn in the longitudinal direction of the vessel 1 through the draft (DV) of the vessel 1. [0238] LWWL: [0239] The lightweight waterline is the waterline of the vessel 1 complete in all respect when it is floating motionless in a body of water but without consumables, stores, cargo, crew and effects, and without any liquids on board except that machinery and piping fluids, such as lubricants and hydraulics, are at operating levels. The vessel 1 thereby also have a fixed trim. [0240] DV: The draft of the vessel 1 equalling the vertical distance between the water surface 5 and the deepest part of the hull 2 when the vessel 1 is floating motionless in the body of water. [0241] TH: Tangent line of the aft hull section 3 in a longitudinal direction of the vessel 1 immediately upstream/in front of the separation line 6. [0242] TF: Line in the same longitudinal vertical plane of the vessel 1 as TH above, intersecting the leading edge 41 and parallel to line TH above. [0243] β: The angle in a longitudinal vertical plane of the vessel 1 between TH and the water surface 5 when the vessel 1 is floating motionless in a body of water. [0244] Γ: The angel between the chord line 43 and the water surface 5 in a longitudinal vertical plane of the vessel 1 when the vessel 1 is floating motionless in a body of water. A positive chord angel means that the chord line 43 is pointing upwards in the vessel's 1 direction of travel, 0 degree angel means the chord line 43 is parallel to the water surface 5 and a negative angel means that the chord line 43 is pointing downwards in the vessels 1 direction of travel. [0245] H1: Is the smaller of: [0246] i) a first minimum distance, measured in a longitudinal vertical plane of the vessel 1, between the leading edge 41 and the aft hull section 3 at or upstream/in front of the separation line 6 and [0247] ii) a second minimum distance, measured in the same longitudinal vertical plane as i) above, between the two parallel lines TH and TF. [0248] H1(w): The minimum distance H1 of i) or ii) at point w along the width of the leading edge 41. [0249] H2: The vertical distance between the trailing edge 42 and the water surface 5 measured when the vessel 1 is floating motionless in a body of water at the lightweight waterline (LWWL). [0250] A.sub.le: The leading edge area is derived from integrating H1(w) above from WL at one side of the leading edge 41 to WH at the opposite side of the leading edge 41. The leading edge area is equal to or substantially equal to the cross sectional area of a water flow 51 above the leading edge 41 at operational speed of the vessel 1. [0251] A.sub.te: The trailing edge area is the area as seen from astern constrained by the trailing edge 42, the two vertical planes 49 and the water surface 5 when the vessel 1 is floating motionless in a body of water at the lightweight waterline (LWWL).
[0252] Displacement speed: [0253] The speed range of a displacement vessel 1, usually limited by a “hull speed” of about F.sub.N=0.4.
[0254] Transition speed: [0255] The speed range of a planing hull 2 when it is in transition from displacement speed, usually at around F.sub.N, =0.4, until it reaches fully planing speed, usually at around F.sub.N=0.9.
[0256] Planing speed: [0257] The speed where dynamic lift contributes to a major part of the buoyancy for a planing hull 2, usually above F.sub.N=0.9. Since the invention, especially when operated in combination with a bow body 10 as described in patent publication EP3247620B1, does not rely on lifting the hull 2 out of the water even at speeds above F.sub.N=0.4, the reference to transition or planing speed for a hull 2 according to the invention only refers to the speed itself. Hence, it does not refer to planing of the hull 2.
[0258] Operational speed: [0259] The speed interval the vessel 1 is operating at during transit when there are no speed restrictions.
[0260] General Design Criteria
[0261] The working principle and the main objective for the invention is the same for both slow or fast vessels 1. However, certain design issues should be taken in consideration when optimizing the inventive vessel 1.
[0262] Leading Edge Area/Trailing Edge Area
[0263] The common principle for all embodiments of the invention is to allow a sufficient water flow 51 to flow over the top surface 45 of the aft body 4 through the passage 50 during forward propulsion of the vessel 1. The cross sectional area of a water flow 51 passing the leading edge 41 of the aft body 4 should be equal to, or almost equal to, the area from the trailing edge 42 of the aft body 4 and up to the water surface 5 in order to achieve equilibrium in the water mass downstream the vessel 1 and thereby prevent the formation of a stern wave 9 when the vessel 1 is in forward motion. By equilibrium is meant that the water flow surface level 53 above the trailing edge 42 is at the same level as the (surrounding) water surface 5 during forward motion of the vessel 1, for example at operational speed. In FIG. 8A-C this is achieved by having H1=H2. In FIG. 10 this is achieved by having A.sub.le=A.sub.te.
[0264] In general, the width of the aft body 4 in the transverse direction of the vessel 1 will be equal to, or almost equal to, the width of the transom 7 of the vessel 1.
[0265] Adaption to Different Speed Ranges
[0266] Advantageous embodiment for adapting the vessel for different speed ranges are shown and explained by aid of FIG. 7A-C.
[0267] When operating a vessel 1 according to the invention having a displacement hull at a low speed (F.sub.N<0.3), the aft body 4 may be positioned closer to the water surface 5. When the aft body 4 is placed closer to the water surface 5, the length of the chord line 43 can be reduced compared to a deeper positioning of the aft body 4. When operating the vessel at higher speed (F.sub.N≥0.3), there might be advantageous to position the aft body 4 deeper and to increase the length of the chord line 43.
[0268] FIG. 7A show one embodiment of the inventive vessel 1 having a typical displacement hull 2. The particular arrangement and design of the aft body 4 is optimized for operation at a speed below an F.sub.N, of about 0.3. The aft body 4 can in this particular case have a relatively short chord line 43 and be placed at a depth within the upper half of the draft DV of the hull 2, for example at 30% of the draft DV.
[0269] As the speed increases, the upward momentum in a water flow 51 passing under the aft hull section 3 upstream the aft body 4 increases. The impact from the aft body 4 onto a water flow 51 should then be enhanced. This is achieved by increasing the length of the chord line 43 and to locate the aft body 4 closer to the base line 58, as the top surface 45 of the aft body 4 will redirect the water flow 51 more effectively then the underside 46 of the aft body 4. The increased cord line 43 and deeper located aft body 4 will then effectively counteract the increasing upward momentum of the water flow 51, thereby achieving an essential horizontal direction of a water flow 51 downstream the aft body 4.
[0270] FIG. 7B shows the same hull 2 as shown in FIG. 7A but with an aft body 4 designed for a higher speed range; typically, within the speed range F.sub.N=0.4−0.6. In order to minimize the propulsion resistance, the aft body 4 is in this particular case located at a depth corresponding to about 50-60% of the draft DV of the hull 2 and the length of the cord line 43 is extended relative to the length shown in FIG. 7A.
[0271] FIG. 7C shows the same hull 2 as in FIG. 7A but with an aft body 4 designed for operational speed above F.sub.N=0.7. Here the length of the chord line 43 is extended further relative to the length shown in FIG. 7B, and the underside 46 of the aft body 4 is located at the base line 58 of the hull 2.
[0272] As a rule of thumb, the cord line 43 should be greater than the draft of the aft body 4, typical by a factor of around 2.0 or greater.
[0273] At low speed an aft body 4 with a long chord line 43, and placed relatively deep, only contributes to a minor increase in resistance compared to a smaller and higher placed aft body 4. If the vessel 1 is supposed to be operated over a wide speed range, it might be advantageous to choose an aft body 4 with long chord line 43 placed at a greater depth optimized for the highest operational speed of the vessel 1.
[0274] The optimal depth and optimal length of the chord line 43 for minimizing the total resistance R.sub.t for the vessel 1 may for example be determined by model tests and/or computational fluid dynamics (CFD) analyses.
[0275] Location of the Separation Line
[0276] The invention includes a separation line 6 at the aft hull section 3 controlling the separation of a water flow 51 from the aft hull section 3 at a defined line in the transverse direction (w) of the vessel 1 during forward motion of the vessel 1. The separation line 6 is preferably located close to the water surface 5 when the vessel 1 without payload is laying still and floating in a mass of water.
[0277] The separation line 6 can either be placed upstream/in front of, vertically above, or downstream/aft of the leading edge 41 as shown in FIG. 8A-C. For practical reason the separation line 6 will normally be within the length of one chord line 43 of the leading edge 41, and preferably within the length of half a chord line 43.
[0278] FIG. 8B-C shows the geometry of the aft hull section 3 in relation to the top surface 45 of the aft body 4 where the leading edge 41 is located upstream/in front of the separation line 6. In such design, it is preferable that the minimum distance, in a vertical longitudinal plane of the vessel 1, between the top surface 45 and the aft hull section 3 upstream/in front of the separation line 6 is held constant to avoid a change in the velocity of a water flow 51 in the passage 50 as such a change in velocity will result in increased resistance for the vessel 1, especially if the velocity of the water flow 51 is reduced in the passage 50. It should also be noted that the wetted surface, and accordingly the frictional resistance R.sub.f, will increase in the design shown in FIG. 8 B-C.
[0279] Turbulence—Design of the Aft Body and its Supports
[0280] When designing the aft body 4, including the supports 8 to fix the aft body 4 to the hull 2, it is advantageous to avoid creation of turbulence and vortexes.
[0281] If the outer ends of the aft body 4 in the transverse direction of the vessel 1 extends freely in the water during operation, it might be advantageous to reduce the thickness of the aft body 4 in a vertical plane towards the outer ends and/or to make the aft body 4 elliptical when seen from below (as shown in FIG. 14B drawing (c)) and thereby limit creation of tip vortexes.
[0282] Also winglets, as used in aviation, can be used to reduce the tip vortexes. It would then be natural to also make use of the winglets as supports 8 for the aft body 4.
[0283] The aft body 4 should preferably also be shaped according to shape of the aft hull section 3 upstream/in front of the separation line 6 and the resulting angle of attack of the water flow 51 (i.e. the angel between the water flow 51 upstream leading edge 41 and the chord line 43). Higher angel of attack requires increased length of the chord line 43. Furthermore, in order to obtain laminar water flow 51 without turbulence, and to prevent cavitation on the top surface 45, especially at higher velocity of the water flow 51, a thicker aft body 4 profile and/or more curved top surface 45, especially toward the leading edge 41, would be beneficiary. Alternatively, a high angle of attack for the front part of the aft body 4 can be avoided by keeping the angle γ of the tangent line TH low.
[0284] When attaching the aft body 4 to the hull 2 some care should be taken when designing the support 8. Besides ensuring sufficient structural integrity, the support 8 should preferably be made with a streamlined design. In addition, the support 8 should be oriented according to the direction of a water flow 51 where the supports 8 are located to avoid unnecessary propulsion resistance. It should be noted that under the aft hull section 3 of a displacement hull 2, a water flow 51 can become partly inwardly directed towards the longitudinal center line of the vessel 1.
[0285] If the aft body 4 is placed between the hull sides 2′,2″, as shown in FIG. 9C, FIG. 9D, FIG. 15A drawing (b) and FIG. 15B drawing (c), it might be advantageous to round the lowest part of the inward facing hull sides 2′,2″ in order to make a streamlined inlet at the sides for a water flow 51 to enter the passage 50.
[0286] FIG. 9A shows the aft body 4 fixed to the hull 2 by two vertical support plates 8. The number of support plates 8 are decided according to the demand for structural integrity. Each support plate 8 is preferably orientated according to the local direction of water flow 51.
[0287] Alternatively, the aft body 4 may be fixed to the transom 7 of the hull 2. In FIG. 9B such a configuration is exemplified by two triangular support 8 plates, where the curved horizontal edge is fixed to the top surface 45 of the aft body 4, and the vertical edge is fixed to the transom 7.
[0288] In order to prevent a rise of the water flow surface level 53 at the outer side of the hull sides 2′,2″ at the aft hull section 3 that might accrue during forward motion, and further to prevent this rise of the water flow surface level 53 to be deflected outward as stern wave 9 from the hull sides 2′,2″, it might be advantageous to taper the hull sides 2′,2″ of the aft hull section 3 inward towards the longitudinal center line of the vessel 1. An example of such a tapering of the hull sides 2′, 2″ is shown in FIG. 9D.
[0289] Adaption to Variation in Draft
[0290] Some vessels 1 experience a significant variation in draft DV when being operated due to different load conditions. To optimise the vessel 1 for such draft variations it would be advantageous to be able to adjust the amount of water passing over the aft body 4 (i.e. altering H1) according to the vessel's 1 draft DV, as well as the height H2 from the trailing edge 42 of the aft body 4 to the water surface 5.
[0291] By making the aft body 4 adjustable in a horizontal longitudinal direction of the vessel 1, an optimal water flow 51 can be led over the aft body 4 at different drafts DV of the hull 2. At shallow draft DV of the hull 2, the leading edge 41 can be arranged close to the hull 2, for example vertically below the separation line 6. As the vessel 1 is operated at a deeper draft DV of the hull 2, the leading edge area A.sub.le can be increased by moving the aft body 4 horizontally further downstream the separation line 6.
[0292] Alternatively, or in addition, the front part of the aft body 4, or the entire aft body 4, can be made tiltable with a rotational axis parallel to the transverse direction of the vessel 1 and parallel to the water surface 5. When the leading edge 41 is tilted down, a larger water flow 51 is allowed to pass over the top surface 45. If the entire aft body 4 is tilted around said rotational axis close to aft body's 4 centre line, the trailing edge 42 will approach the water surface 5 while the leading edge 41 will become deeper as the chord line 43 of the aft body 4 is tilted downward (i.e. a smaller or more negative chord angel γ). This will contribute to a larger leading edge area A.sub.le and a reduced trailing edge area A.sub.te. However, to tilt the aft body 4 downward has the disadvantage of creating a non-desired upward direction of a water flow 51 downstream the trailing edge 42.
[0293] If the aft body 4 is fixed and the hull 2 is to be operated at different drafts DV, a compromise has to be found. An advantageous compromise could be to adapt the leading edge area A.sub.le in view of the trailing edge area A.sub.te for a draft DV corresponding to the deepest draft DV of the hull 2, or at least deeper than minimum operational draft DV of the hull 2.
[0294] Although the aft body 4 counteracts a stern down trim, the vessel 1 might experience some increased stern down trim as the speed rises, thereby increasing the distance from the trailing edge 42 to the water surface 5 at high speed. With this in mind, it might be advantageous to allow the leading edge area A.sub.le to be greater than the trailing edge area A.sub.te when the vessel 1 is floating motionless in a body of water. Alternatively, the leading edge area A.sub.le can be increased as mentioned above as the speed of the vessel 1 increases. Also the geometry of the aft hull section 3 can be made with a flap or similar to make the leading edge area A.sub.le adjustable.
[0295] Location of Propeller
[0296] The vessel's 1 propeller 12 can be located upstream/in front of the aft body 4 as shown in one embodiment in FIG. 26. Furthermore, the propeller 12 can be located vertically under the aft body 4 or vertically above the aft body 4. Note that positions vertically under or above the aft body 4 include any positions along a horizontal plane.
[0297] Initial testing performed indicates that a location of the propeller 12 under the aft body 4 can be advantageous as the same thrust force [N] is generated from the propeller with a smaller power consumption [W] from the propulsion engine.
[0298] A Vessel Having Both an Aft Body and a Bow Body
[0299] The arrangement of an aft body 4 according to the invention as described will reduce the total resistance R.sub.t for a vessel 1 above a certain speed of the vessel 1. Further, the inventive vessel 1 will counteract a stern down trim of the vessel 1 if the vessel 1 is being operated at higher speeds, for example above F.sub.N=0.3. As a negative consequence, the inventive vessel 1 can experience a larger bow down trim than a prior art vessel 1 not fitted with an aft body 4. Even if the total resistance R.sub.t of the inventive vessel 1 is lower, the bow down trim of the inventive vessel 1 will result in an increased bow wave 22 and thereby an increased wave resistance R.sub.w from the bow area 21.
[0300] The invention disclosed in patent publication EP3247620B1 concerns a bow design with a bow body 10 that counteracts creation of a bow wave 22, thereby reducing the wave resistance R.sub.w from the bow area 21 and the total resistance R.sub.t for the vessel 1. However, this particular bow design suffers the disadvantage that such a vessel 1 can experiences an increased stern down trim during forward propulsion, thereby creating greater wave resistance R.sub.w from the stern. In other words, by reducing the formation of waves at one end of the vessel 1, the formation of waves at the other end of the vessel 1 is often increased.
[0301] By combining these two inventions (i.e. an aft body 4 and a bow body 10) on the same vessel 1 as shown in FIG. 11, model tests have shown that a significant synergy effect is achieved. I.e. the reduction in total resistance R.sub.t becomes greater than adding the individual contribution from each invention one at the time on the same vessel 1.
[0302] Numerous model tests measuring the total resistance R.sub.t has been performed and an overview picture of these tests are shown in FIG. 12. The solid line marked Rt(A) is the total resistance R.sub.t for a prior art displacement vessel 1. The stippled line Rt(B) is the total resistance R.sub.t for an inventive displacement vessel 1 having an aft body 4 and the dotted line marked Rt(C) is the total resistance R.sub.t for an inventive displacement vessel 1 having both an aft body 4 and a bow body 10. As can be seen from the graph the displacement vessel 1 having both an aft body 4 and a bow body 10 has superior performance above F.sub.N of about 0.26, while the vessel 1 has somewhat higher total resistance R.sub.t under that speed.
[0303] A prior art planing hull 2, as shown in FIG. 3, relies upon reaching planing speed to obtain reasonable good resistance/speed ratio. The speed needed to obtain sufficient dynamic lift depends to a large degree on the weight of the vessel 1. This highly limits the load capacity of a prior planing vessel 1. In contrast, an inventive vessel 1 as disclosed in FIG. 11 does not rely on lifting the hull 2 out of the water to achieve a reasonable good resistance/speed ratio. Since there is no need to lift the inventive vessel 1 out of the water, the resistance of the vessel 1 is far less depended on the weight of the vessel 1. The inventive vessel 1 described herein combined with a bow body 10 thus makes it possible to operate a vessel 1 even at heavy load conditions throughout a wide speed range with far better fuel economy than a prior art vessel 1.
[0304] Also for planning vessels 1 numerous model tests has been performed. FIG. 13 gives an overview based on these model tests, where the solid line marked Rt(A) is the total resistance R.sub.t for a prior art planing vessel 1. The stippled line Rt(B) is the total resistance R.sub.t for an inventive planing vessel 1 having an aft body 4 and the dotted line marked Rt(C) is the total resistance R.sub.t for an inventive planing vessel 1 having both an aft body 4 and a bow body 10. From this can be seen that the inventive vessel 1 having both an aft body 4 and a bow body 10 has better performance than a prior art planning vessel 1 above F.sub.N of about 0.25.
Detailed Description of a First Embodiment
[0305] FIG. 14A and FIG. 14B shows an aft hull section 3 of a vessel 1 according to a first embodiment.
[0306] FIG. 14A drawing (a) shows a vertical longitudinal plane of the aft hull section 3 when the vessel 1 is floating motionless in a body of water. The vessel 1 comprising a hull 2, hull sides 2′,2″ and a transom 7. The separation line 6 is located slightly above the water surface 5. The vessel 1 comprises an aft body 4 having an underside 46 oriented parallel with the water surface 5 and located at approximately 50% of the draft DV of the hull 2. The aft hull section 3 has decreasing cross sectional area towards the stern of the vessel 1. The angel between the tangent line TH of the aft hull section 3 immediately upstream/in front of the separation line 6 and the water surface 5 is marked β. The aft body 4 is located at a distance to the hull 2 making a passage 50 between the aft hull section 3 and the top surface 45 of the aft body 4. The minimum distance between the top surface 45 and the aft hull section 3 is kept constant upstream/in front of the separation line 6 in order to achieve a constant velocity of a water flow 51 in the passage 50 when the vessel 1 is at operational speed. The minimum distance H1 between the leading edge 41 and the aft hull section 3 is equal to the distance H2 being the distance from the trailing edge 42 to the water surface 5.
[0307] FIG. 14A drawing (b) is the aft hull section 3 shown in FIG. 14A drawing (a) seen from behind. FIG. 14A drawing (b) is showing the hull 2 having draft DV and a transom 7. The separation line 6 is located slightly above the water surface 5. The aft body 4 is attached to the vessel 1 by two supports 8. The supports 8 are placed with equal offsets to the longitudinal centre axis of the vessel 1. The outer ends of the aft body 4 in transverse direction of the vessel 1 have downward tapered top surface 45 to reduce turbulence. The two imaginary vertical planes 49 in the longitudinal direction of the vessel 1 intersecting the two points defining the maximum width (W) of the aft body 4 are marked with stippled lines.
[0308] FIG. 14B drawing (c) shows the aft hull section 3 of FIG. 14A seen from below. The hull 2, hull sides 2′,2″ and the underside 46 of the aft body 4 is shown with solid lines. The two streamlined supports 8 fixing the aft body 4 to the hull 2 are shown with stippled lines. The supports 8 are orientated in the direction of travel of the vessel 1. The separation line 6 is shown in the transverse direction of the vessel 1 with a stippled line. Also the two imaginary vertical planes 49 are shown with stippled lines. The outer ends in the transverse direction of the aft body 4 have rounded shape when seen from below to reduce turbulence. The leading edge 41 and the trailing edge 42 is extending all the way out to the two points defining the maximum width (W) of the aft body 4 (i.e. all the way out to the hull sides 2′ and 2″.
[0309] FIG. 14B drawing (d) is the same vertical longitudinal plane of the aft hull section 3 of the inventive vessel 1 as shown in FIG. 14A drawing (a) and having the same draft DV. But here the working principle and the water flow 51 indicated by arrows at the aft hull section 3 and around the aft body 4 at operational speed is illustrated. The water flow 51 direction upstream the leading edge 41 has a partly upward direction due to the tapered design of the aft hull section 3. This partly upwardly directed water flow 51 entering over the leading edge 41 of the aft body 4 is redirected by the shape of the top surface 45 from partly upward to a horizontal (or slightly downward) direction immediately downstream the trailing edge 42. The horizontally orientated underside 46 of the aft body 4 will redirect the upwardly directed water flow 51 upstream the aft body 4 that passes under the leading edge 41 to a horizontal (or almost horizontal) direction immediately downstream the trailing edge 42, thus achieving a resulting horizontal direction of the combined water flow 51 passing over and under the aft body 4 merging downstream the trailing edge 42. (As a water flow 51 passing under the trailing edge 42 may still have a slightly upwardly direction it can be advantageous that a water flow 51 passing over the trailing edge 42 has a slightly downwardly direction to ensure that the merged water flow 51 downstream the trailing edge 42 has a horizontal direction). The constant minimum distance between the aft hull section 3 and the top surface 45 upstream the separation line 6 contributes to a constant speed of the water flow 51 through the passage 50. The water flow surface level 53 is elevated slightly above the surrounding water surface 5 over a part of the top surface 45 as indicated. The height of the water flow 51 over the leading edge 41 is marked H1 and is equal to the height of the water flow 51 over the trailing edge 42 marked H2. Since the water flow surface level 53 passing over the trailing edge 42 is at the same level as the surrounding water surface 5, a state of equilibrium in the water mass downstream the trailing edge 42 is obtained. The creation of a stern wave 9 is thereby greatly reduced.
Detailed Description of a Second Embodiment
[0310] FIG. 15A and FIG. 15B shows an aft hull section 3 of a vessel 1 according to a second embodiment. This vessel 1 is similar to the vessel 1 of the first embodiment, with the following main exceptions:
[0311] As best shown in FIG. 15A drawing (a) (showing a longitudinal vertical plane of an aft hull section 3), the separation line 6 is arranged upstream/in front of the leading edge 41. The separation line 6 is further located slightly below the water surface 5 when the vessel 1 is floating motionless in a body of water having a draft DV. The angel β between the tangent line TH and the water surface 5 is shown. As the separation line 6 is located upstream/in front of the leading edge 41, the distance H1 is here defined by the minimum distance between the tangent line TH and a line parallel with TH intersecting the leading edge 41 marked TF.
[0312] As best shown in FIG. 15A drawing (b) (being the aft hull section 3 shown in FIG. 15A drawing (a) seen from behind), the hull sides 2′,2″ are used as supports 8 for the aft body 4.
[0313] As best shown in FIG. 15B drawing (c) (showing the aft hull section 3 of FIG. 15A seen from below) the transverse ends of the aft body 4 are straight and oriented along the longitudinal direction of the vessel 1 and are fixed directly to the hull 2. Each hull side 2′,2″ at the aft hull section 3 below the water surface 5 are tapered towards the longitudinal centre axis of the vessel 1 shown with stippled lines.
[0314] FIG. 15B drawing (d) (showing the same vertical longitudinal plane of the aft hull section 3 of the vessel 1 as shown in FIG. 15A drawing (a)) has the same draft DV, but here the working principle and a water flow 51 indicated by arrows at the aft hull section 3 and around the aft body 4 at operational speed is illustrated. The working principle for this second embodiment is the same as for the first embodiment, and the text explaining the working principle of FIG. 14B drawing (d) could be duplicated except for: “The constant minimum distance between the aft hull section 3 and the top surface 45 upstream/in front of the separation line 6 contributes to a constant speed of a water flow 51 through the passage 50.” which is not relevant for this second embodiment.
Detailed Description of a Third Embodiment
[0315] In a third embodiment, the inventive vessel 1 comprises both an aft body 4 as described herein and a bow body 10 as described in patent publication EP3247620B1, the contents of which are incorporated herein by reference, in particular the FIGS. 10-15 and its related text in EP3247620B1.
[0316] As a specific example of the third embodiment, reference is made to FIG. 11 showing a bow body 10 arranged at the bow area 21 of the vessel 1 and an aft body 4. A water flow 51 around the bow body 10 and a water flow 51 around the aft body 4 are shown with arrows.
[0317] Model Tests—Total Resistance of Model Vessels
[0318] To document the mode of operation of the inventive vessel 1 and to verify a reduction in total resistance R.sub.t, the inventor has carried out model tests on the model vessels shown in FIG. 16, FIG. 20 and FIG. 22.
[0319] To be able to monitor thrust from a propeller 12, all model vessels 1 (except for the planning model vessels 1 shown in FIG. 22) are equipped with powertrain set up as shown in FIG. 17. The propeller 12 is connected to an electrical motor 14 by a propeller shaft 11. Around the propeller shaft 11 there is a propeller sleeve 13 with brass bearings to support the propeller shaft 11. The propeller sleeve 13 does not absorb any thrust from the propeller 12. The electrical motor 14 is directly attached to the motor housing 15. The motor housing 15 is attached to four mounting brackets 18 through four motor suspension systems 16 which are configured to absorb torsional moment but not thrust from the propeller. The four mounting brackets 18 are directly connected to the base plate 19. The motor suspension system 16 makes the motor housing 15 hover over the base plate 19 without restricting movement for the motor housing 15 in longitudinal direction of the propeller shaft 11. The base plate 19 and the propeller sleeve 13 are attached to the model vessel 1. In front of the motor housing 15 there is a high precision load cell 17 attached to the base plate 19 that limits the forward movement of the propeller 12, the propeller shaft 11, the electrical motor 14 and the motor housing 15. The propeller shaft 11 is mounted close to horizontal when the model vessel 1 is laying still and floating in a body of water.
[0320] During operation, the motor housing 15 applies pressure onto the load cell 17 and all thrust from the propeller 12 is transferred to the load cell 17. Consequently, the propeller thrust in Newton [N] is monitored and logged during operation of the model vessel 1. When the model vessels 1 is operated at constant speed the propeller thrust is equal to the total resistance Rt for the model vessel 1.
[0321] The speed of all model vessels 1 is measured with high accuracy Doppler GPS. The speed in meters per second [m/s] is converted to Froude number (F.sub.N) for each model vessel 1.
[0322] The measured results of the total resistance R.sub.t for the model vessels 1 shown in FIG. 16 and FIG. 20 measured in Newton [N] as function of speed (F.sub.N) are logged and plotted in FIG. 19 and FIG. 21 respectively, using the test setup as described above.
[0323] In FIG. 19, and in all other graphs, Poly. ( . . . ) means interpolation of measurement points.
[0324] For the planing model vessels 1 shown in FIG. 22, the power consumption [W] of an electric brushless motor attached to a Z-drive and corresponding speed (F.sub.N) is logged using the same high accuracy Doppler GPS. The result is and plotted in FIG. 24.
[0325] All model vessels 1 are radio-controlled.
[0326] Model Test 1—Double Propelled Slender Displacement Hull
[0327] FIG. 16 shows an upside down perspective illustrations of a prior art model vessel 1 with a slender displacement hull marked as Model 16A. Model 16B is the same model vessel 1 as Model 16A but fitted with an aft body 4 according to the invention. The model vessel 1 is equipped with two propulsion systems for measuring thrust as described above.
[0328] The length, width and draft DV of both model hulls 2 are 270 cm, 42 cm and 11 cm, respectively. The full-scale vessel 1 of this model vessel 1 has the separation line 6 located at the water line 5 and so has the model vessel 1. Consequently, in order to apply an aft body 4 as described above, there is no need to do any cut-out of the aft hull section 3 in order to make A.sub.le equal to A.sub.te.
[0329] With reference to the Model 16B, the length of the chord line 43 of the aft body 4 is 10 cm. The aft body 4 is attached to the aft hull section 3 such that the leading edge 41 is located 1 cm upstream/in front of the separation line 6. Further, the maximum (W) of the aft body 4 in the transvers direction (w) of the hull 2 is 42 cm, which is equal to the width of the model vessel 1. The underside 43 of the aft body 4 is placed 2.7 cm below the water surface 5 and the cord angel γ is orientated parallel to the water surface 5 when the model vessel 1 is floating motionless in a mass of water. The maximum vertical thickness of the aft body 4 is 1.0 cm. The aft hull section 3 has a double curvature in the longitudinal vertical plane of the model vessel 1 and the angel β between the tangent line TH and the water surface 5 is 0 degrees (i.e. parallel with the water surface 5).
[0330] During test runs of the prior art Model 16A maintained close to neutral trim throughout the entire speed range of the test. However, the model vessel 1 experiences some degree of increasing draft DV as speed increased.
[0331] Model 16B according to the invention obtained some bow down trim and increased draft for the bow area 21 as speed increased, leading to an increased bow wave 22 compared to the prior art model vessel 1 at comparable speeds.
[0332] As clearly seen from the pictures in FIG. 18A and FIG. 18B there is a significant reduction of the stern wave 9 for the inventive Model 16B compared to the prior art Model 16A at both speeds (i.e. F.sub.N=0.30 and 0.36).
[0333] FIG. 19 shows the results from the model testing, logged as total resistance R.sub.t [N] as a function of speed (F.sub.N). As clearly seen, even if Model 16B generates a larger bow wave 22 than Model 16A at comparable speeds, Model 16B experiences a reduction in the total resistance R.sub.t compared to Model 16A in the full speed range from about F.sub.N=0.19 and up to about F.sub.N=0.37. Above F.sub.N=0.3 Model 16B experiences about 8% lower total resistance R.sub.t than the prior art Model 16A. (For a full-scale vessel 1, the reduction in total resistance R.sub.t will be even greater).
[0334] Model Test 2—Single Propelled Displacement Hull
[0335] FIG. 20 shows upside down perspective illustrations of three displacement model vessels 1, where Model 20A shows a prior art model vessel 1, Model 20B shows a prior art model vessel 1 with a bow body 10 and Model 20C shows an inventive model vessel 1 with both a bow body 10 and an aft body 4.
[0336] The bow body 10 on Model 20B is in accordance with the patent publication EP3247620B1. Further, the configuration of the bow body 10 and bow area 21 is similar to the bow configuration shown in FIG. 11.
[0337] Model 20C has the same bow body 10 and bow area 21 as Model 20B, but with an aft hull section 3 similar to the aft hull section 3 shown in FIG. 11.
[0338] All three model vessels 1 have a hull length of 184 cm. The width for Model 20A is 36 cm and 34 cm for both Model 20B and Model 20C. Further, all three model vessels 1 have the same weight and thereby the same displacement volume, resulting in a draft DV of 14 cm for Model 20A, 15 cm for Model 20B and 15.2 cm for Model 20C.
[0339] The separation line 6 for Model 20A and Model 20B is located respectively 2.0 cm and 1.5 cm under the water surface 5 and for Model 20C at the water surface 5 when the model vessels 1 are floating motionless in a body of water.
[0340] Moreover, the length of the chord line 43 of the aft body 4 of Model 20C is 11 cm, and the maximum width (W) of the aft body 4 in the transvers direction (w) of the hull 2 is 33 cm. The chord angel γ is oriented parallel to the water surface 5 and the underside 46 of the aft body 4 is located 7 cm under the water surface 5 when the model vessel 1 is floating motionless in a body of water. The separation line 6 is located 5 cm upstream/in front of the transom 7 and the leading edge 41 of the aft body 4 is located vertically below the separation line 6. The maximum vertical thickness of the aft body 4 is 1.1 cm. The angel β between the tangent line TH and the water surface 5 is 8.5 degrees.
[0341] During model tests, all three model vessels 1 have a neutral trim when floating motionless in a body of water.
[0342] In order to compare the inventive Model 20C having an aft body 4 with a prior art Model 20B (without an aft body 4), and to exclude the tendency of the inventive Model 20C to generate a bow down trim of the vessel 1 due to the aft body 4, thereby preventing a stern down trim, the angel of attach of the bow body 10 for Model 20B and Model 20C are adjusted separately to obtain close to neutral trim and unchanged draft for their bow area 21 when they are in motion throughout the testing speed range. The wave making from the bow area 21 is then similar for the Model 20B and Model 20C. The bow body 10 contributes to a great reduction of wave resistance R.sub.w from the bow area 21. The main differences in total resistance R.sub.t between the Model 20B and the inventive Model 20C is thus isolated to be the difference between an aft hull section 3 without and with an aft body 4.
[0343] FIG. 21 shows the results from the model testing, logged as total resistance R.sub.t[N] as a function of speed (F.sub.N). As clearly shown in the graphs, the total resistance R.sub.t of the prior art Model 20A is significantly higher at a speed above F.sub.N=0.3. In the speed range from F.sub.N=0.3 to F.sub.N=0.4 the total resistance R.sub.t of Model 20B and Model 20C are almost the same and the aft body 4 does not have a significant effect for this embodiment in this speed range. Above F.sub.N=0.4, wave resistance R.sub.w from the aft hull section 3 becomes more crucial. Model 20C is seen to have a significantly lower total resistance R.sub.t compared to the prior art Model 20B at a speed above F.sub.N=0.4. The reason for the lower total resistance R.sub.t is the decrease in wave resistance R.sub.w from the aft hull section 3 of the inventive Model 20C. Hence, it is possible to design an inventive model vessel 1 (Model 20C) having the same total resistance R.sub.t as a prior art displacement model vessel 1 (Model 20A) at F.sub.N=0.3 but with 46% lower total resistance R.sub.t at F.sub.N=0.45. (For a full-scale vessel 1 the reduction in total resistance R.sub.t will be even greater).
[0344] Model Test 3—Planing Hull
[0345] FIG. 22 shows upside down perspective illustrations of two model vessels 1, where Model 22A is a “flat bottomed” prior art planing hull and Model 22B is an inventive model vessel 1 with a bow body 10 and an aft body 4. The bow area 21 of Model 22B is modified with a bow body 10 according to patent publication EP3247620B1 and the aft hull section 3 is modified with an aft body 4 as described herein.
[0346] Both model vessels 1 have a length of 120 cm and a width of 40 cm. Further, the weight, and accordingly the displacement volume, is the same for the two model vessels 1, giving a corresponding draft DV of 5.5 cm for Model 22A and 6 cm for Model 22B when the model vessels 1 are floating motionless in a body of water.
[0347] The separation line 6 of Model 22A is located 5.5 cm under the water surface 5 and for Model 22B the separation line 6 is located at the water surface 5 when the model vessels 1 are floating motionless in a body of water.
[0348] The angel β between the tangent line TH and the water surface 5 is 20 degrees for Model 22B. The aft hull section 3 of Model 22B has a similar layout as shown in FIG. 7C. The length of the cord line 43 is 14 cm and the chord angle γ is parallel to the water surface 5. The underside 46 of the aft body 4 is located at the base line 58. The trailing edge 42 is arranged 3 cm downstream/aft of the separation line 6. The maximum vertical thickness of the aft body 4 is 1.8 cm.
[0349] During testing, both prior art Model 22A and inventive Model 22B are trimmed to neutral when floating motionless in a body of water.
[0350] FIG. 23A, FIG. 23B and FIG. 23C show pictures of prior art Model 22A and inventive Model 22B at speed corresponding to F.sub.N=0.4, F.sub.N=0.5 and F.sub.N=0.65 respectively. At low speed, F.sub.N=0.4, the trim and wave making appears to be almost the same for both model vessels 1. At higher speed, F.sub.N=0.5, the prior art Model 22A gains an increasing positive trim with a significant increase in wave making. At a speed of F.sub.N=0.65, the bow area 21 of prior art Model 22A is lifted out of the water and the aft hull section 3 of the hull 2 causes a significant stern wave compared to the inventive Model 22B. The pictures hence demonstrate that the inventive model vessel 1 with a bow body 10 and an aft body 4 counteracts increasing sinkage of the aft hull section 3 as speed increases, while the trim and wave making stays almost the same regardless of speed.
[0351] FIG. 24 shows the results from the model testing logged as required power [W] for the brushless electrical propulsion engine versus speed (F.sub.N) for Model 22A and Model 22B. The required power [W] for the inventive Model 22B is lower than for the prior art Model 22A throughout the entire speed range tested. Particularly in the speed range from F.sub.N=0.4 to F.sub.N, =0.7. At F.sub.N, =0.6 the inventive Model 22B requires 40% less power [W] than the prior art Modell 22A. (For a full-scale vessel 1 the reduction in power [W] will be even greater).
[0352] Model Tests—Horizontal Forces Provided by an Aft Body
[0353] To document how the configuration of an aft hull section 3 and an aft body 4 effects the horizontal forces provided by an aft body 4 in a longitudinal direction of a model vessel 1, a series of model tests have been conducted. The model tests are performed on a model vessel 1 with configurations according to the invention and configuration according to prior art, where the aft body 4 is providing a continuous propulsion force on the model vessel 1 (i.e. a continuous forwardly directed horizontal forces in the longitudinal direction of the model vessel 1).
[0354] Model Vessel—Testing Set Up
[0355] FIG. 25 shows an upside-down perspective illustration of the model vessel 1 having a test setup to measure the horizontal forces in the longitudinal direction of the model vessel 1 from the aft body 4 acting on the model vessel 1. The same model vessel 1 is used for all the model tests. The model vessel 1 is configured with a hard chine bow area 21 to prevent a bow down trim of the model vessel 1 during testing (i.e. increased sinkage for the bow area 21).
[0356] Dimensions of the model vessel 1: [0357] Length: 185 cm [0358] Width: 34 cm [0359] Draft DV: 8-10 cm [0360] Maximum width (W) of all aft bodies 4: 34 cm
[0361] Maximum vertical thickness of all aft bodies 4: 1.1 cm, except for aft body 4 marked (B) in FIG. 31 which is 1.4 cm thick.
[0362] FIG. 26 shows a side view of the aft hull section 3 of the model vessel 1 in FIG. 25 where the aft body 4 and the two supports 8 are attached to the vessel 1 via two ball bearing slides 20 oriented in a horizontal longitudinal direction of the model vessel 1 when the model vessel 1 is floating motionless in a mass of water. The ball bearing slides 20 are separated by 18 cm in the transvers direction of the hull 2. The setup enables the aft body 4 to move freely in the horizontal longitudinal direction of the model vessel 1. A high precision load cell 17 is mounted to the vessel 1 and is further attached to the support 8 arrangement in order to measure the horizontal forces generated by the aft body 4 in the longitudinal direction of the model vessel 1. A compression force measured in the load cell 17 gives a positive value reading corresponding to the aft body 4 providing a resistance force on the model vessel 1 (i.e. a backwardly directed horizontal forces in the longitudinal direction of the model vessel 1). While a tension/stretch force measured in the load cell 17 gives a negative value reading corresponding to the aft body 4 providing a propulsion force on the model vessel 1 (i.e. a forwardly directed horizontal forces in the longitudinal direction of the model vessel 1).
[0363] The model vessel 1 shown in FIG. 25 and FIG. 26 is fitted with an interchangeable aft hull section 3 below the water surface 5 in order to compare different geometries of the aft hull section 3 and accordingly different angels β between TH and the water surface 5. It is further possible to alter the chord angel γ, the draft DV of the hull 2, the depth of the aft body 4 in relation to the base line 58 and changing to an aft body 4 with a longer chord line 43. The different configurations tested are shown in FIGS. 27-32.
[0364] During all model tests the leading edge 41 of the aft body 4 was located 10 mm downstream/aft of the separation line 6, the chord angel γ is 0 degree unless otherwise stated and the trim angel of the model vessel 1 was kept neutral when floating motionless in a body of water.
[0365] Results from Model Tests
[0366] FIG. 33 is showing the test results for a model vessel 1 having a configuration as shown in FIG. 27 with a chord angle γ of 0 degrees marked (A), a chord angle γ of −2 degrees marked (B) and a chord angle γ of −3 degrees marked (C). As seen from FIG. 33 the aft body 4 having a chord angel γ of 0 degrees (graph (A)) is providing a backwardly directed force (i.e. resistance) throughout the entire speed range. Also, a chord angel γ of −2 degrees (graph (B)) is providing a backwardly directed force throughout the entire speed range. As seen for graph (B) the resistance is decreasing from about F.sub.N=0.23 to F.sub.N=0.44 and increasing thereafter. At a chord angel γ of −3 degrees (graph (C)) there is a forwardly directed force (i.e. propulsion) in the speed range from about F.sub.N=0.36 to F.sub.N=0.51. Outside this speed range there is a backwardly directed force also for a chord angel of −3 degrees. It should be noted that none of the graphs (A), (B) or (C) in FIG. 33 provides a continuous forwardly directed propulsion.
[0367] FIG. 34 shows the effect of altering the ratio of the leading-edge area divided by the trailing edge area (i.e. A.sub.le/A.sub.te ratio). This is achieved by varying the draft DV of the model vessel 1 from 80 mm to 90 mm and to 100 mm as shown in FIG. 28. Since the width in the transverse direction of the hull 2 of the leading edge 41 is the same as the width of the trailing edge 42, the A.sub.le/A.sub.te ratio equals the H1/H2 ratio. As seen from graph (A) showing A.sub.le=1.0×A.sub.te, the aft body 4 is providing a backwardly directed force (i.e. resistance) throughout the entire speed range. Also for A.sub.le=0.83×A.sub.te (graph (B)) the aft body 4 is providing a backwardly directed force throughout the entire speed range. At A.sub.le=0.71×A.sub.te there is a very small forwardly directed force (i.e. propulsion) present in the speed range from about F.sub.N=0.22 to F.sub.N=0.34. Outside this speed range there is a backwardly directed force also for A.sub.le=0.71×A.sub.te. As can be seen from FIG. 34, a reduction of the A.sub.le/A.sub.te ratios (from graph (A) to graph (C)) leads to a reduction in resistance from the aft body 4 throughout the entire speed range and especially at the lower end of the speed range. Such a low ratio is hence important for achieving a propulsion from the aft body 4. It should however be noted, that none of the graphs (A) or (B) in FIG. 34 provides a continuous forwardly directed propulsion.
[0368] FIG. 35 shows the effect of altering the configuration of the aft hull section 3 by changing the angle β of the tangent line TH immediately upstream/in front of the separation line 6 as shown in FIG. 29. As seen from graph (A), showing a TH angel β of 4.5 degrees, the aft body 4 is providing a backwardly directed force (i.e. resistance) throughout the entire speed range. From graph (B), showing a TH angel β of 11.0 degrees, there is a very small forwardly directed force (i.e. propulsion) present in the speed range from about F.sub.N=0.34 to F.sub.N=0.45. Outside this speed range there is a backwardly directed force also for a TH angel β of 11.0 degrees. It is hence concluded that an increasing angle β of the aft hull tangent TH reduces the resistance from the aft body 4 and may contribute to forward propulsion, while a lower angle β will increase the resistance from the aft body 4. It should be noted that none of the graphs (A), (B) or (C) in FIG. 35 provides a continuous forwardly directed propulsion.
[0369] FIG. 36 shows the effect of altering the depth of the aft body 4 in relation to the base line 58 as shown in FIG. 30, where graph (A) is showing the resistance for a deep aft body 4 located 30 mm above base line 58 and where graph (B) is showing the resistance for a shallow aft body 4 located 50 mm above the base line 58. As seen in FIG. 36, both the deep (graph (A)) and the shallow (graph (B)) aft body 4 is providing a backwardly directed force (i.e. resistance) throughout the entire speed range, but the shallow aft body 4 (graph (B)) has a lower resistance than the deep aft body 4 (graph (A)) at a speed above F.sub.N=0.18.
[0370] FIG. 37 shows the effect of altering the length of the chord line 43 of the aft body 4 as shown in FIG. 31, where graph (A) is showing the resistance for a chord length of 105 mm (having a maximum vertical thickness of 1.1 cm) and graph (B) is showing the resistance for a chord length of 145 mm (having a maximum vertical thickness of 1.4 cm). As seen in FIG. 37, both the smaller (graph (A)) and the larger (graph (B)) aft body 4 is providing a backwardly directed force (i.e. resistance) throughout the entire speed range, but the smaller aft body 4 (graph (A)) has a lower resistance than the larger aft body 4 (graph (B)) throughout the speed range.
[0371] FIG. 38 is showing the test results for a model vessel 1 with aft hull sections 3 as shown in FIG. 32 for a configuration according to an inventive model vessel 1 marked (A) and for a configuration according to a prior art model vessel 1 marked (B).
[0372] The geometry of the inventive model vessel 1 (A) is configured to minimize the wave resistance R.sub.w from the aft hull section 3. Hence, the inventive model vessel 1 (A) has a draft DV(A) of 80 mm, which entails A.sub.le=1.0*A.sub.te, an angle β(A) for the tangent line TH of 4.5 degrees and a chord angel γ(A) of 0 degree.
[0373] In order to obtain a continuous forward propulsion from the aft body 4 the configuration of the prior art model vessel 1 (B) is based upon a combination of the configurations found through the model testing to contribute to a forward propulsion. The prior art model vessel 1 (B) hence has a draft DV(B) of 100 mm, which entails A.sub.le=0.71*A.sub.te, an angle β(B) for the tangent line TH of 11.0 degrees and a chord angel γ(B) of −2 degrees.
[0374] From FIG. 38 graph (A) it can be seen that the aft body 4 of the inventive model vessel 1 (A) is providing a continuous backwardly directed force (i.e. resistance) throughout the speed range. The resistance graph (A) is kept relatively steady from F.sub.N=0.2 to F.sub.N=0.4. Above F.sub.N=0.4 the resistance from the aft body 4 of the inventive model vessel 1 (A) is increasing with increasing speed. This is in clear contrast to graph (B), showing a continuous forwardly directed force (i.e. propulsion) throughout the speed range of the prior art model vessel 1 (B) and increasing as the speed increases.
[0375] Conclusion from Model Testing
[0376] When measuring the horizontal forces from the aft body 4 of a model vessel 1 according to the invention, it was revealed that the aft body 4 itself applied a backwardly directed force (i.e. resistance) on the model vessel 1. When the configuration of the aft body 4 and the geometry of the aft hull section 3 was altered, creating a vessel 1 beyond the scope of the invention, a forwardly directed force (i.e. propulsion) from the aft body 4 occurred under certain conditions.
[0377] A low A.sub.le/A.sub.te ratio, a high angel β of the tangent line TH and a downward tilted chord angel γ are important parameters to achieve a propulsion force from the aft body 4. Furthermore, a reduction of the chord length of the aft body 4 and an arrangement of the aft body 4 closer to the water surface 5 will also contribute to possibly achieve forward propulsion from the aft body 4.
[0378] The model tests demonstrate that a configuration seeking to achieve forward propulsion from the aft body 4 are contrary to a configuration seeking to achieve a reduction of the stern wave 9.
[0379] Hence a prior art vessel 1 will benefit from a low A.sub.le/A.sub.te ratio to achieve forward propulsion from the aft body 4. This is in clear contrast to the inventive vessel 1 which will benefit of a ratio of A.sub.le/A.sub.te≈1.0 to achieve equilibrium in the water mass downstream the aft body 4.
[0380] A prior art vessel 1 will benefit from a larger angel β of the tangent line TH to achieve forward propulsion from the aft body 4. This is also in clear contrast to the inventive vessel 1 which will benefit of small angel β of the tangent line TH to achieve a horizontal direction of a water flow 51 downstream the aft body 4.
[0381] A prior art vessel 1 will benefit from a negative chord angel γ to achieve forward propulsion from the aft body 4. Again, this is in clear contrast to the inventive vessel 1 which will benefit of horizontal, or near horizontal, chord angel γ to achieve a horizontal direction of a water flow 51 downstream the aft body 4.
[0382] A prior art vessel 1 having a larger angel β of the tangent line TH would also benefit from an even more negative chord angel γ. However, both a higher angel β of the tangent line TH and an increased negative chord angel γ will contribute to an increasing stern wave 9.
[0383] A prior art vessel 1 will benefit from a shorter chord length of the aft body 4 as a shorter chord length results in larger forward propulsion. In contrast, an inventive vessel 1 would need a longer chord length of the aft body 4 to be able redirect the upwardly directed water flow 51 upstream/in front of the aft body 4 to a horizontal water flow 51 downstream the aft body 4 without causing turbulence.
[0384] A visual comparison of models tested of the inventive vessel 1 described above and the prior art vessels 1 providing forward propulsion from an aft body 4 shows that the inventive vessel 1 generates a smaller stern wave 9 and has less sinkage at the stern relative to the prior art vessel 1. It is further observed through model tests, not included in this paper, that an inventive vessel 1 seeking to obtain a reduced stern wave 9 contributes to a larger reduction in total resistance R.sub.t for the vessel 1 than a design according to the prior art seeking to obtain forward propulsion from the aft body 4.
[0385] In the preceding description, various aspects of the vessel 1 according to the invention have been described with reference to the illustrative embodiment. For purposes of explanation, specific numbers, systems and configurations were set forth in order to provide a thorough understanding of the vessel 1 and its workings. However, this description is not intended to be construed in a limiting sense. Various modifications and variations of the illustrative embodiments, as well as other embodiments of the vessel 1, which are apparent to persons skilled in the art to which the disclosed subject matter pertains, are deemed to lie within the scope of the present invention.
