Fins with improved fluid dynamic properties
11679846 · 2023-06-20
Inventors
Cpc classification
B63B34/26
PERFORMING OPERATIONS; TRANSPORTING
B63B32/66
PERFORMING OPERATIONS; TRANSPORTING
B63B2035/009
PERFORMING OPERATIONS; TRANSPORTING
International classification
Abstract
A fin for use on a surfboard, the fin comprising: a leading edge, a trailing edge, and a base, the base comprising at least one mount for mounting the fin onto a surfboard; a first and a second outer fin surface which meet along the leading edge and the trailing edge and abut the base; and a first ridge protruding laterally from the first outer fin surface, and/or a second ridge protruding laterally from the second outer fin surface; wherein the shape and configuration of the fin creates an area of lower water pressure around and in front of the fin, as well as disrupting and/or reducing the size of trailing vortices, resulting in additional forward thrust for the board on which the fin is mounted.
Claims
1. A fin for use on a propeller or impeller, the fin comprising: a leading edge, a trailing edge, and a base, the base comprising at least one mount for mounting the fin onto a propeller or impeller; a first and a second outer fin surface which meet along the leading edge and the trailing edge and abut the base; a first ridge protruding laterally from the first outer fin surface, and a second ridge protruding laterally from the second outer fin surface, a third ridge protruding laterally from the first outer fin surface, and a fourth ridge protruding laterally from the second outer fin surface; wherein the third ridge and the fourth ridge are smaller and located further from the base than the first ridge and the second ridge.
2. A fin according to claim 1, wherein the distance of the first ridgeline or the second ridgeline to the base is between approximately 4% and 8% of the distance of the base to the tip of the fin.
3. A fin according to claim 1 wherein the first ridge protrudes laterally from the first outer fin surface, or the second ridge protrudes laterally from the second outer fin surface, to a maximum distance from the centreplane of between 2 to 4.5 times greater than the maximum distance of the centreplane to a non-ridged portion of the first outer fin surface, wherein the centreplane passes through the leading edge and trailing edge of the fin.
4. A fin according to claim 1, wherein the first ridge and the second ridge are located equidistant from the base.
5. A fin according to claim 1, wherein the first ridge comprises a first ridgeline, and the second ridge comprises a second ridgeline, and the first and second ridgelines are on a plane substantially parallel to the base and/or on adjacent surface of the propeller or impeller to which the fin is mounted.
6. A fin according to claim 1, wherein the first ridge comprises first ridge sides, and the second ridge comprises second ridge sides, and the third ridge comprises third ridge sides, and the fourth ridge comprises fourth ridge sides, and at least a portion of the first ridge sides or second ridge sides or third ridge sides or fourth ridge sides comprise concave, convex, and/or flat portions.
7. A fin according to claim 5, wherein the first ridgeline or second ridgeline end at the leading edge.
8. A fin according to claim 1, wherein the third or fourth ridges are on a plane that is substantially parallel to the base, or a plane that is substantially parallel to an adjacent surface of the propeller or impeller.
9. A fin according to claim 1, wherein the third ridge protrudes laterally from the first outer fin surface, or the fourth ridge protrudes laterally from the second outer fin surface, to a maximum distance from the centreplane of between 1.5 to 6 times greater than the maximum distance of the centreplane to a non-ridged portion of the first outer fin surface, wherein the centreplane passes through the leading edge and trailing edge of the fin.
10. A fin according to claim 1, wherein the third ridge and the fourth ridge are located equidistant from the base.
11. A fin according to claim 1, wherein the fin is an adjustable fin comprising: a base comprising: a mount for attaching the fin to a propeller or impeller; and an insert member extending in a direction contrary to the mount; a fin section comprising: two outer fin surfaces which meet at a leading edge and a trailing edge comprising the first and the second outer fin surfaces; an underside surface comprising an opening to an internal cavity within the fin section, the internal cavity within the fin section configured to house the insert member of the base and enable slidable movement of the insert member in a direction towards the leading edge or the trailing edge; and a lock that is manipulable, wherein the lock can releasably couple to the insert member at one of two or more locking positions thereby preventing slidable movement of the insert member; wherein the fin section is configured to adjust relative to the base by manipulating the lock to uncouple the lock from the insert member at a first locking position, slidably moving the insert member through the internal cavity, and releasably coupling the lock to the insert member at a second locking position.
12. A fin according to claim 1, wherein the fin is a detachable fin comprising: a base comprising: a mount for attaching the fin to a propeller or impeller; and an insert member extending in a direction contrary to the mount; a fin section comprising: two outer fin surfaces which meet at a leading edge and a trailing edge comprising the first and the second outer fin surfaces; an underside surface comprising an opening to an internal cavity within the fin section, the internal cavity within the fin section configured to house the insert member of the base; and a lock that is manipulable, wherein the lock can releasably couple to the insert member thereby preventing movement of the fin section relative to the base; wherein the fin section is uncoupled and detached from the base by manipulating the lock to uncouple the lock from the insert member.
13. A fin according to claim 5, wherein the distance of the first ridgeline or the second ridgeline to the base is between approximately 1% and 15% of the distance of the base to the tip of the fin.
14. A fin according to claim 5, wherein the first ridgeline or second ridgeline end at the trailing edge.
15. A fin for use on a propeller or impeller, the fin comprising: a leading edge, a trailing edge, and a base, the base comprising at least one mount for mounting the fin onto a propeller or impeller; a first and a second outer fin surface which meet along the leading edge and the trailing edge and abut the base; a first ridge protruding laterally from the first outer fin surface, or a second ridge protruding laterally from the second outer fin surface, and a third ridge protruding laterally from the first outer fin surface, or a fourth ridge protruding laterally from the second outer fin surface; wherein the third ridge or the fourth ridge is smaller and located further from the base than the first ridge or the second ridge.
Description
BRIEF DESCRIPTION OF DRAWINGS
(1) The present invention will now be described, by way of example, with reference to the accompanying drawings, in which:
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DESCRIPTION OF PREFERRED EMBODIMENTS
(33) Those skilled in the art will appreciate that the invention described herein is susceptible to variations and modifications other than those specifically described. It is to be understood that the invention includes all such variations and modifications. The invention also includes all of the steps, features, compositions and compounds referred to or indicated in the specification, individually or collectively and any and all combinations or any two or more of the steps or features.
(34) The present invention is not to be limited in scope by the specific embodiments described herein, which are intended for the purpose of exemplification only. Functionally equivalent products, compositions and methods are clearly within the scope of the invention as described herein.
(35) Throughout this specification, unless the context requires otherwise, the word “comprise”, or variations such as “comprises” or “comprising”, will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.
(36) Other definitions for selected terms used herein may be found within the detailed description of the invention and apply throughout. Unless otherwise defined, all other scientific and technical terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which the invention belongs.
(37) Features of the invention will now be discussed with reference to the following preferred embodiments.
(38) Surfboard Fins
(39) A preferred embodiment of a fin according to the invention is shown in a variety of views in
(40) The fin further comprises a first outer fin surface on the ‘port’ or ‘left’ side of the fin (the port side outer fin surface 610), and a second outer fin surface on the ‘starboard’ or ‘right’ side of the fin (the starboard side outer fin surface 612), when considered from the rear or trailing edge 604 of the fin looking towards the front or leading edge 602. The port side outer fin surface 610 meets the starboard side outer fin surface 612 along the leading edge 602 and the trailing edge 604. Both the port side outer fin surface 610 and the starboard side outer fin surface 612 abut the base 606 by meeting along separate edges of the base 606 as shown in
(41) Protruding laterally from the port side outer fin surface 610 adjacent the base 606 is a port side main ridge 614 (i.e. a “first ridge”) from leading edge 602 to trailing edge 604. This may also be considered a port side main protrusion. Protruding laterally from the starboard side outer fin surface 612 adjacent the base 606 is a starboard side main ridge 616 (i.e. a “second ridge”) from leading edge 602 to trailing edge 604. This may also be considered a starboard side main protrusion. The port side main ridge 614 and starboard side main ridge 616 lie substantially parallel to the base 606 and equidistant to the base 606. When the fin is mounted to a surfboard with mounting blocks 608 secured in FCS® plugs in the board, the port side main ridge 614 and starboard side main ridge 616 also lie substantially parallel to the bottom surface of the surfboard, at least at the location the fin is mounted.
(42) The port side main ridge 614 and starboard side main ridge 616 produce a kite or diamond shape when viewing the front of the fin or through a cross-sectional front view. The kite or diamond shape having a truncated base at the fin base 606, and an elongated port side main ridge upper side 618 and starboard side main ridge upper side 622.
(43) The main ridges in the fin of the invention do not comprise sections of a standard fin attached or protruding from either or both sides of the fin.
(44) In alternative embodiment, the kite or diamond shape is instead a bulbous shape, torpedo-like shape, or tear-drop shape, with a truncated base and an elongated top, when viewing the front of the fin or through a cross-sectional front view where the ridge sides comprise convex surfaces.
(45) In another means for describing the shape produced by the port side main ridge 614 and starboard side main ridge 616 of the fin of the invention, the front view or a cross-sectional front view shows the port side main ridge 614 and starboard side main ridge 616 protruding from the sides of the fin. The port side main ridgeline 615 and starboard side main ridgeline 617 at the crest of each ridge are at substantially right angles or at right angle planes to the centreplane 603 of the fin (shown with a symbol for a right angle superimposed over the illustration of the fin in
(46) The port side main ridgeline 615 and starboard side main ridgeline 617 meet at the leading edge 602 and at the trailing edge 604.
(47) The port side outer fin surface 610 either side of the port side main ridge 614 comprises a port side main ridge upper side 618 and a port side main ridge lower side 620.
(48) The starboard side outer fin surface 612 either side of the starboard side main ridge 616 comprises a starboard side main ridge upper side 622 and a starboard side main ridge lower side 624.
(49) In this embodiment, the port side main ridge lower side 620 and starboard side main ridge lower side 624 comprise a slight curve; however, they may also comprise more curvature, or less curvature, or comprise at least a portion that is flat.
(50) In this embodiment, the port side main ridge upper side 618 and starboard side main ridge upper side 622 comprise flat and curved portions; however, they may also comprise curved portions with no flat portions, and the curved portions may have more or less curvature.
(51) The ends of the port side main ridge 614 and starboard side main ridge 616 meet at the leading edge 602 and trailing edge 604.
(52) A port side minor ridge 626 (i.e. a “third ridge”) protrudes laterally from the port side outer fin surface 610 above the port side main ridge 614. The port side minor ridge 626 is smaller than the port side main ridge 614 and is positioned further from the base 606. The port side minor ridge 626 does not extend to the leading edge 602 or the trailing edge 604. In the embodiments of the fin that are adjustable and contain a knob, the port side minor ridge 626 can comprise the knob.
(53) A starboard side minor ridge 628 (i.e. a “fourth ridge”) protrudes laterally from the starboard side outer fin surface 612 above the starboard side main ridge 616. The starboard side minor ridge 628 is smaller than the starboard side main ridge 616 and is positioned further from the base 606. The starboard side minor ridge 628 does not extend to the leading edge 602 or the trailing edge 604 though may in other embodiments. In the embodiments of the fin that are adjustable and contain a knob, the starboard side minor ridge 628 can comprise the knob.
(54) The port side minor ridge 626 and starboard side minor ridge 628 may be parallel to the main ridges, but in this embodiment, the port side minor ridge 626 and starboard side minor ridge 628 have a slight angle of attack towards the base at the ends closest the leading edge 602 as shown in
(55) In another preferred embodiment, the fin according to the invention may not comprise one or more port side minor ridge and/or starboard side minor ridge. Alternatively, the fin according to the invention may comprise additional minor or major ridges on one or both sides of the fin, similar or different to the ridges shown in these preferred embodiments.
(56) This embodiment of the non-adjustable fin is made in a mould constructed in one part, though could be constructed from more than one part.
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(60) The distance between the main ridgeline and base (where the fin meets the mount) is approximately 7 mm. Thus, the distance of the main ridgeline to the base is approximately 6% of the distance of the base to the tip of the fin.
(61) The maximum thickness of the minor ridges at 19.29 mm, when compared to the maximum thickness of the (non-ridged portion of the) fin at 6.38 mm, equals a factor of approximately 3 (i.e. 19.29/6.38=3.33). The distance between the minor ridge and base (where the fin meets the mount) is approximately 18.31 mm. Thus, the distance of the minor ridge to the base is approximately 16% of the distance of the base to the tip of the fin.
(62) The distance between the front of the fin where the leading edge meets the base and mount, and the front end of the minor ridge is 31.74 mm. Thus, the minor ridge starts approximately one third of the distance of the total fin behind the front of the fin. The distance between the rear of the fin where the trailing edge meets the base and mount, and the rear end of the minor ridge is 40.12 mm. Thus, the minor ridge ends approximately one third (approximately 36%) of the distance of the total fin from the end of the fin.
(63) The shape of the minor ridge is of
(64) The distance from the base to where the upper ridge sides merge into, meet, or become, the outer fin surface is approximately 30 mm. Thus, the portion of the height of the outer fin surfaces of the fin comprising ridges is approximately one quarter (approximately 26.5%) of the height of the fin from base to tip.
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(66) The portion of the fin relative to the base attachment surface 642 may be created at a specific cant for use as side fins in a thruster set up.
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(69) Support plates 645 have been attached in this embodiment to the port side main ridge lower side 620 and starboard side main ridge lower side 624 to provide additional strength to this portion of the fin. Such support plates 645 may, or may not be part of the fins of the invention. Support plates 645 may be a metal or metal alloy including those already described herein. In a preferred embodiment, the support plates are made from titanium alloy.
(70) Gaps are produced between the support plate 645 and the surfboard onto which the fin in this embodiment is mounted, between the mounting blocks 608 and the front and rear of the fin where the leading edge 602 and the trailing edge 604 meet the bottom surface of the surfboard. These gaps assist to provide additional beneficial effects on the vortices created as water passes the fin according to the invention during use on a wave as shown in the modelling and analysis below.
(71) In this respect, the fin according to the invention can comprise one or more gaps between the base of the fin and the surfboard onto which it is mounted. These gaps may vary in shape, size, and height between surfboard and base, according to the desired vortices to be created around the fin as water passes the fin according to the invention.
(72) Without wanting to be limited by any one theory, a benefit of elevating a fin section from the outer surface of a surfboard on which it is mounted is to allow creation of additional vortices, when compared to a fin section which abuts or aligns flush with the outer surface of a surfboard.
(73) A starboard side fin (not shown in
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(76) Initially, the inventor introduced the main ridges either side of the fin of the invention to increase the width of the fin to accommodate an internal mechanism for adjusting a fin section relative to a base. The minor ridge was formed to accommodate the locking mechanism in order to reduce drag created by the protruding locking knob. However, during testing of the fins by expert surfers, surfing waves on surfboards to which fins according to these embodiments of the invention were mounted, additional velocity was experienced by the surfers on waves, particularly during turns, when compared to standard flat fins. Upon further analysis, it was considered that the shape of the fins was causing the increase of speed due to reduction of drag forces. This was predicted to be taking place through affecting vortices adjacent where the fin is mounted onto the board. It is understood that where large vortices are created behind an object moving through water, or air, these large vortices create drag or a ‘sucking’ effect, therein reducing velocity. Disruption of the formation of large vortices by instead creating smaller vortices around the base of the fin either sides of the main ridges, resulting in a reduction of drag forces behind the fins was predicted to be causing the observed effect. Thus, computational fluid dynamics modelling and analysis was performed to confirm the benefits provided by these fin configurations when compared to standard flat fins.
(77) Computational Fluid Dynamics Modelling and Analysis
(78) Background
(79) Comparative computational fluid dynamics (CFD) modelling of a three-fin ‘thruster’ arrangement of: fins of the invention (the “Inventive fins” or “INV”), compared to standard, commercially available flat fins (the “Standard fins” or “STD”) as shown in
(80) The geometries modelled are shown graphically in
(81) TABLE-US-00001 TABLE 1 Flow velocity combinations modelled. INV Fins STD Fins Waterline 1 10 m/s 10 m/s Waterline 2 7 m/s 7 m/s 4 m/s 4 m/s
(82) The numerical model of the fluid flow was constructed using a rectangular domain containing the relevant board and fin sections as shown in
(83) Results
(84) The analysis of the results focuses on investigation and identification of the flow fields around the different fin systems and differentiation of their resulting performance.
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(86) The effect of flow past the rear central fin is shown in
(87) Differentiation of the flow behaviour between the inventive and Standard fins is also investigated by considering a cut-plane parallel to and slightly below the board surface as shown in
(88) To further assist in understanding the response of the flow to the presence of the key design elements of the Inventive fin, streamlines are generated down either side of each fin system as illustrated in
(89) Forces in Tables
(90) The hydrodynamic forces extracted from the CFD model for each of the fins are presented in Table 2.
(91) TABLE-US-00002 TABLE 2 The ratios of change in lateral forces of inventive fins compared to Standard fins. Note: The sign convention is that the forces are the water force on the fin, which is oriented so that (for 4 and 7 m/s) the forces are towards the inner side of the board as shown in Figure 16. Board Lateral Force on Fin Speed Waterline f(x) [N] [m/s] (Figure 9A) Fin INV STD Δf(x) 4 2 Port −2.71 −3.98 −32% Centre 0.09 0.18 −50% Starboard 2.63 4.55 −42% 7 2 Port −17.86 −12.03 48% Centre 0.24 0.52 −54% Starboard 17.87 13.72 30% 10 1 Port −11.84 6.72 −276% Centre −0.54 1.65 −133% Starboard 13.27 −3.76 −453%
(92) The key observations from this are that: The lateral fin forces are considered as giving the best indication of how much of an effect the fins are having on the flow over the board; The centre fins have very low forces and therefore are expected to have very little effect since they are aligned with the flow; The lateral fins (both types and at all speeds) produce roughly equal and opposite forces—this is expected since the board is travelling straight ahead. There are subtle differences in the geometries which can be seen in the differences between left and right forces; and The lateral forces increase as speed increases for waterline 2, but the change in waterline and velocity results in a change in the direction of the forces on the Standard fins.
(93) In general, lateral forces increase greatly on the Inventive fins, compared to the Standard fins, which is anticipated to be important in the observed speed increase with Inventive fins. It will also be very important in the performance and stability of the board during turning manoeuvres, one of the most frequent actions needed to be taken during surfing.
(94) Conclusions
(95) The results of the CFD modelling show a significant change in the flow of water immediately adjacent to the board and downstream of the fins of the invention when compared to the standard fins in a thruster arrangement. These flow changes are potential causes for the observed speed and stability increases observed for boards using the fins of the invention.
(96) Prior to the modelling, the additional thrust was predicted to be due to the disruption of the formation of large vortices by instead creating smaller vortices around the base of the fin either sides of the main ridges, resulting in a reduction of drag forces behind the fins. However, the results of the modelling showed that while part of the additional forward thrust experienced was due to the effect of disruption or reduction of trailing vortices which reduced the negative ‘sucking’ effects (but maintained the area of high pressure), the main effect was that the ridges created a vortex as a result of the combination of the surfaces of (i) the lower surface of the surfboard adjacent to the fin, (ii) the lower main ridge surface adjacent the board, and (iii) the minor ridge. This vortex created a measurable area of lower pressure surrounding the lower portion of the fin and in front of the fin when compared to surrounding water and the high pressure measured behind the fin. Incredibly, an area of low pressure created in front of the fin was shown (video not able to be included) to be up to 500 mm long beneath the surfboard. This effect is believed to be the cause of the additional thrust (towards the area of lower pressure) experienced by surfers using fins according to the invention when compared to standard fins without the major or minor ridges.
(97) Detachable and Adjustable Fin
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(99) Removing the screws 652 also enables the fin section 648 to be removed and separated from the base portion 646. This can be beneficial for transporting a surfboard to which the base portion 646 is permanently attached so that the fin section 648 is not damaged or in the way when stacking boards or other equipment on top of the surfboard. It also allows a fin section 648 to be replaced by a fin section of, for example, a different shape, size, colour, material, amongst others as the user requires or if the fin section 648 on the board becomes damaged.
(100) A detachable fin according to the invention may or may not also be adjustable in a direction towards the leading edge or trailing edge of the fin. Likewise, an adjustable fin according to the invention may or may not be detachable in the fin section being separable from the base.
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(102) This embodiment further comprises an upper fin section attached to the bottom portion of the fin section, the upper fin section comprising a titanium alloy (comprising approximately 4% vanadium and approximately 6% aluminium) upper fin 500 covered with an overmolding 510 of protective safety polymer. The titanium alloy upper fin section is up to approximately 2 mm to 2.5 mm thick in the widest section 505.
(103) The upper fin 500 shown in
(104) The upper fin 500 shown in
(105) Across the profile of the upper fin section is varying thickness to create a single or double sided fin foil as is known in the art and common to the shapes of surfboard fins, with a thicker section 505 toward the leading edge of the fin section which decreases in thickness with closer proximity to the trailing edge.
(106) In the embodiment of the detachable and adjustable fin shown in
(107) A further detachable and adjustable version on an embodiment of a fin according to the invention is shown in a collapsed form in
(108) The underside of the base plate is shown in
(109) When mounted to a surfboard, the base of the embodiment of the detachable and adjustable fin of
(110) A further detachable and adjustable version of a preferred embodiment of a fin according to the invention is shown in
(111) An exploded view of the parts of the lock used in some adjustable versions of preferred embodiments described herein is shown in
(112) Propeller for Watercraft Propulsion
(113) A preferred embodiment of a propeller 700 for providing propulsion through water is shown in
(114) An aperture 706 through the hub 702 comprises impeller blades 708 that rotate with the revolving of the hub 702 to create a sucking force to draw water through the aperture therein increasing the pressure of the fluid and thus its flow through the aperture 706.
(115) The combined forward thrust provided by the rotating propeller blades 704 and impeller blades 708 forces the propeller 700 of the invention through the water and the vessel to which it is attached.
(116) The rotational force applied to the propeller 700 of this preferred embodiment is via a motor which turns a sprocket 710 interlocking with a first end of a loop of roller chain 712. At a second end, the loop of roller chain 712 interlocks with teeth 714 on the hub 702, and the turning of the sprocket 710 by the motor therein rotates the loop of roller chain causing the propeller 700 to also rotate.
(117) The propeller blades 704 comprise outer blade surfaces 716. A ridge 718 protrudes generally laterally from each outer blade surface 716 as shown in the cross-sections of
(118) The inner surfaces 722 of the lateral ridges 716, and the ridgeline 720 comprise a similar curve to the curved shape of the hub 702. The end of the ridgelines 720 meet at the blade edge 726. The blade edges 726 and ridgelines 720 are relatively sharp edges which assist in cutting through the water.
(119) The impeller blades 708 are relatively short blades compared to the propeller blades 704. The impeller blades 708 on the inner aperture surface 728 of the hub 702 are curved (spirally similarly to rifling in a barrel) assists to cause water passing through the aperture 706 and the impeller blades 708 to spiral in the direction of the revolving hub 702. A cross-section of the impeller blades 708 as shown in
(120) Keels
(121) A preferred embodiment of a keel of a boat (or yacht) according to the invention is shown in
(122) The keel 800 comprises two main ridges 808 protruding laterally from the sides of the keel 800 adjacent where the keel 800 meets the vessel hull 804. An upper minor ridge 810 protrudes laterally from each side of the keel 800 just above the main ridges 808. A lower minor ridge 810 protrudes laterally from each side of the keel 800 just below the main ridges 808.
(123) The rear 818 of the keel in
(124) Each side of the ridge 808 between the ridgeline 814 and where the ridge 808 protrudes from the outer keel surface 820 is a curved sloped ridge surface 822. These sloped ridge surfaces 822 may comprise curved portions, substantially flat portions, and steeper curves near the ridgelines 814 and/or where main ridge 808 meets the outer keel surfaces 820.
(125) The ridgelines 814 of the main ridges 808 are at substantially right angles or at right angle planes to the centreplane 826 of the keel 800 (see, for example,
(126) The upper minor ridge as shown in
(127) The lower minor ridge 812, is a similar shape and configuration to the upper minor ridge 810 except the flat foil shape of the lower minor ridge has the flat side facing down away from the vessel hull 804.
(128) The upper minor ridge 810 and lower minor ridge 812 extend only part way between front 816 and rear 818 of the keel 800.
(129) While these upper minor ridges 810 and lower minor ridges 812 of the preferred embodiment comprise a configuration of a flat foil, the upper and lower minor ridges may be differently shaped or not even present in other embodiments of the keel of the invention. For example, the upper and lower ridges may not be present; or one or both of the upper or lower ridges may be present; the upper and/or lower ridges may extend from the front 816 of the keel 800 to the rear 818; or the upper and/or lower ridges may comprise more evenly shaped ridges similar to, though smaller, than the main ridges 808. The upper minor ridges and/or lower minor ridges may comprise relatively sharp ridgelines at their crest, or they may comprise rounded, or even squared edges, or a combination of both or other shapes at their ridgelines. The upper minor ridges and/or lower minor ridges may also not comprise flat foil shapes, but comprise more even configurations with similar or the same sloped sides either side of straight or (curved) ridgelines on the upper minor ridges and/or lower minor ridges. The upper minor ridges and/or lower minor ridges may be similarly shaped or may comprise different shapes.
(130) While a fin keel according to the invention is shown in
(131) A catamaran or trimaran may use the keel according to the invention on the bottom of one or more hulls as shown in