Title:
Thick, elliptical-planform fin for a water sports board
Kind Code:
A1


Abstract:
A thick, elliptical-planform fin for use on a water sport board such as a surfboard. One set of attributes of the fins according to the present invention is the use of a substantially thick cross-section which, at its maximum thickness, overhangs the receiver slot, typically a 12 to 15 percent thickness ratio, with a maximum thickness at 30 percent of chord length, a blunter leading edge, and a short elliptical planform of constant relative dimension cross-section along its length.



Inventors:
Leek, Derek Robert (Honolulu, HI, US)
Application Number:
12/385654
Publication Date:
10/15/2009
Filing Date:
04/15/2009
Primary Class:
International Classes:
B63B35/79
View Patent Images:
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Primary Examiner:
SWINEHART, EDWIN L
Attorney, Agent or Firm:
Antony C. Edwards (Calgary, AB, CA)
Claims:
What is claimed is:

1. A surfboard fin for mounting into a slot in a receiver box in the underside of a surfboard, said fin comprising: an elliptical planform having a root and an opposite tip, said root and said tip separated by a longitudinally extending length defining a height of the fin, a leading edge and an opposite trailing edge extending from said root to said tip along opposite edge of said planform, said planform having a thickness defined by cross-sections of said planform, wherein said cross sections are substantially orthogonal to said length, and extend along corresponding chords of said cross sections between said opposite edges so as to extend from said leading edge to said trailing edge, a ratio of said thickness and said chord of each of said cross sections defining a corresponding thickness-to-chord ratio, and wherein substantially all of said thickness-to-chord ratios are substantially equal to one another, and are greater than substantially a thickness-to-chord ratio of twelve, and wherein a ratio of a square of said longitudinally extending length and a planform area of said planform define a corresponding aspect ratio, and wherein said aspect ratio is less than three, and wherein said each of said cross sections has a nose section at a forward end thereof corresponding to said leading edge, a curved mid section including a maximum thickness position, and a tapered rear section corresponding to said trailing edge, and wherein said nose section, mid section and rear section of said each of said cross sections is defined by a curvature which is substantially that of a non-cambered NACA four digit airfoil shape so as to have a substantially parabolic nose section and a continuously smoothly substantially convexly curved mid section, where said nose section, said mid section and said rear section form a single smoothly continuously curved foil section which is symmetric on opposites sides of said chord, and wherein said maximum thickness position is located substantially at 30 percent of said chord on said each of said cross sections, and wherein said length has a linear slope component relative to said root chosen from forward slope, no slope, rearward slope, and wherein said length has an elliptical sweep component relative to said root chosen from forward sweep, no sweep, rearward sweep, and wherein irrespective of said sweep said planform is substantially elliptical and its corresponding lift distribution is also substantially elliptical and has a surface area which is substantially constant for a particular said aspect ratio and for particular said cross section and corresponding said thickness-to-chord ratio and corresponding said maximum thickness position, and wherein said planform does not have winglets or auxiliary foils protruding therefrom.

2. The fin of claim 1 further comprising a tang depending from said root, wherein a maximum root thickness, defined as said thickness of said root at said maximum thickness position, is greater than a width of the opening in the slot of the receiver box so as to overhang said root from the slot when said tang is mounted in the slot.

3. The fin of claim 2 wherein said maximum root thickness is in the range of substantially one half inch to one inch for use with a receiver box having slot width of less than three eighths of an inch.

4. The fin of claim 3 wherein said maximum root thickness is substantially three quarters of an inch.

5. The fin of claim 1 wherein said linear slope component and said elliptical sweep component is applied to a substantially 30 percent chord line corresponding to said maximum thickness positions.

6. The fin of claim 5 wherein said slope is forward and said sweep is forward.

7. The fin of claim 5 wherein said slope is forward and said sweep is rearward.

8. The fin of claim 5 wherein said slope is rearward and said sweep is forward.

9. The fin of claim 5 wherein said slope is rearward and said sweep is rearward.

10. A method for making a surfboard fin for mounting into a slot in a receiver box in the underside of a surfboard, said method comprising the steps of. a) an elliptical planform having a root and an opposite tip, said root and said tip separated by a longitudinally extending length defining a height of the fin, a leading edge and an opposite trailing edge extending from said root to said tip along opposite edge of said planform, said planform having a thickness defined by cross-sections of said planform, wherein said cross sections are substantially orthogonal to said length, and extend along corresponding chords of said cross sections between said opposite edges so as to extend from said leading edge to said trailing edge, a ratio of said thickness and said chord of each of said cross sections defining a corresponding thickness-to-chord ratio, and wherein substantially all of said thickness-to-chord ratios are substantially equal to one another, and are greater than substantially a thickness-to-chord ratio of twelve, and wherein a ratio of a square of said longitudinally extending length and a planform area of said planform define a corresponding aspect ratio, and wherein said aspect ratio is less than three, and wherein said each of said cross sections has a nose section at a forward end thereof corresponding to said leading edge, a curved mid section including a maximum thickness position, and a tapered rear section corresponding to said trailing edge, and wherein said nose section, mid section and rear section of said each of said cross sections is defined by a curvature which is substantially that of a non-cambered NACA four digit airfoil shape so as to have a substantially parabolic nose section and a continuously smoothly substantially convexly curved mid section, where said nose section, said mid section and said rear section form a single smoothly continuously curved foil section which is symmetric on opposites sides of said chord, and wherein said maximum thickness position is located substantially at 30 percent of said chord on said each of said cross sections, b) choosing length has a linear slope component of said length from forward slope, no slope, rearward slope, and choosing an elliptical sweep component of said length chosen from forward sweep, no sweep, rearward sweep, c) irrespective of said sweep, maintaining said planform substantially elliptical so that its corresponding lift distribution is also substantially elliptical and maintaining a surface area of said planform which is substantially constant for a particular said aspect ratio and for particular said cross section and corresponding said thickness-to-chord ratio and corresponding said maximum thickness position.

11. The method of claim 10 further comprising the steps of providing a tang depending from said root, and making a maximum root thickness, defined as said thickness of said root at said maximum thickness position, greater than a width of the opening in the slot of the receiver box so that said root overhangs from the slot when said tang is mounted in the slot.

12. The method of claim 10 wherein said maximum root thickness is chosen from the range of substantially one half inch to one inch for use with a receiver box having a slot width of less than three eighths of an inch.

13. The method of claim 12 wherein said maximum root thickness is substantially three quarters of an inch.

14. The method of claim 10 wherein said linear slope component and said elliptical sweep component is applied to a substantially 30 percent chord line corresponding to said maximum thickness positions.

15. The method of claim 14 wherein said slope is forward and said sweep is forward.

16. The method of claim 14 wherein said slope is forward and said sweep is rearward.

17. The method of claim 14 wherein said slope is rearward and said sweep is forward.

18. The method of claim 14 wherein said slope is rearward and said sweep is rearward.

Description:

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. Provisional Patent Application No. 61/071,152 filed Apr. 15, 2008 entitled A Thick, Elliptical-Planform Fin for a Water Sports Board.

FIELD OF THE INVENTION

This invention relates to the field of water sports boards such as surfboards and in particular to an improved design of fin for such boards.

BACKGROUND OF THE INVENTION

Surfing is a popular sport, enjoyed throughout many parts of the world today. Surfing generally involves a surfer riding a wave while upright on a surfboard. The surfer controls the surfboard by positioning himself at different locations on the surfboard and by varying his center of gravity. The surfboard (and other types of water sport boards) typically has one or more fins, located on the underside of the surfboard that help direct the flow of water and have a substantial effect on the stability and the maneuverability of the surfboard.

The initial goal was to make longboards, surfboards longer than 9 feet in length, more maneuverable and turn better. Due to their larger displacement, longboards paddle faster and are better able to catch smaller waves than shorter surfboards. However due to their longer lengths and heavier weight, longboards don't turn or manoeuvre as well as shorter surfboards. The intent was to improve the performance of surfboards, specifically long boards, by applying aerodynamic theory to increase the performance of the surfboard fins.

Surfboards originally did not have a fin. Originally surfboards were heavy long planks of wood that had no fin. A surfer dragged his foot in the water to turn the surfboard.

In the 1950's the construction of surfboards changed with the introduction of foam core construction and the incorporation of a large keel-like fin at the tail of the surfboard. The fin helped the board track straight. The intent to riding was to drop into a wave, control the stall rate to set up for the tube ride, and drive the board straight. There was no maneuvering such as seen today.

Modern surf fins have been patterned after the planform shape of fins found on fish. These fins allowed development of a new style of surfing that involved considerable maneuvering. These smaller fins, coupled with smaller boards gave birth to the style of surfing people are accustomed to today. The planform was cut to match a desired shape and the leading and trailing edges were ground by hand.

In the early 1970's multi fin arrangements started to emerge. Twin fin setups were the first to gain market dominance. The twin fin setup has removable fins that were spaced apart on opposite sides of the rear of the board and each fin could be adjusted in its receiver box that was mounted in the board. A male tang protruding from the base or root of the fin mated into a female slot in the receiver box. Because of variations found in the depth of the slots between different types of receiver boxes, and because fins were often fashioned from plate-like material, such as of fibreglass, having a thickness of less than or equal to ⅜ inch and then hand ground into the desired platform and thickness profile, the thickness of a fin was kept to no more than the width of the slot opening. This allowed the fin root to be pushed into the slot if the tang was otherwise too short to properly seat against the base, i.e. bottom, of the slot.

A three fin “thruster” setup emerged in the early 1980's and has been dominant in the short board market until today. Typically the outermost fins have flat inner surfaces with curved outer surfaces. Additionally the fins toe slightly inward pointing toward the nose of the board. During maneuvering, when the surfer shifts his weight toward the rear of the board, the flow off the tail of the surfboard tends to be more radial, meaning that the outermost fins are experiencing positive angles of attack. When the surfer shifts his weight forward so the surfboard rides flatter in the water for speed, the flow tends to come more straight off the tail of the board, meaning that the toed-in outer fins are experiencing negative angles of attack. The sharp leading edge and thin thickness ratio of conventional fins encourages flow separation around the fin and noticeable drag. A variation on the thruster setup is the 2+1 setup, with two smaller outer fins and a larger central fin, this arrangement is common on longboards. The fins typically still retain the rearwardly raked planform shape mimicking fish fins.

Typically the chord length of such conventional fins, where the fin rakes back, is longer that the chord length of the base of the fin. The fin is thinner at the tip than at the base. While the base is typically 8% thick, towards the tip of the fin where the chord is longer and the fin thinner, the fin may be only 5% thick. Most longboard fins start as a ⅜ inch thick piece of fibreglass that is cut to the desired planform profile and shaped by hand using a grinder.

The resulting cross section of popular longboard cutaway style fins are often unintentionally non-symmetrical about their center line, have a flat middle section that extends to roughly 60% of chord length, and have a sharp leading edge. Most fin manufacturers focus on the planform shape with almost no emphasis or analysis of the cross-sectional shape. This is especially the case with longboard fins.

The most common fin shape for outside fins for Thruster and 2+1 setups are flat on inside surface and have a large flat section through most of the middle of upper surface of the fin, and have a sharp leading edge. During aggressive maneuvering the fins are subject to alternating positive and negative angles of attack. The sharp leading edges and flat bottom surfaces of the fin encourage separation of low angles of attack and an increase in the resultant drag.

Surfboard fins with thin cross-sections (typically 6 to 8% in thickness), sharp leading edges, surfaces that have abrupt changes in the radius of curvature (referred to as curve incontinuity), and fins where the thickest part of the fin is located more rearward (40 to 50% of chord length), are common designs found throughout the surfing industry today.

It is an object of the present invention to provide fins for water sports boards which are more responsive, cause less drag, and enable the surfboard to run faster in the water than conventional fins.

SUMMARY OF THE INVENTION

The thick, elliptical-planform fin apparatus described herein is for use on a water sport board such as a surfboard. The fin provides for improved stability and maneuverability for the water sport board. The fin has a tang portion which attaches the base or root of the fin to the water sport board to transfer the forces of the fin to the board. The fin has a hydrodynamic portion that extends into the water that interacts and directs the flow of water to provide stability and steering for the water sport board. The tang attaches to a receiver mounted into the water sports board such that the fin is removable. Any of several different conventional styles of tang can be used which are compatible with receivers commonly found in water sports boards. One set of attributes of the fins according to the present invention is the use of a substantially thick cross-section which, at its maximum overhangs the receiver slot, typically 12 to 15 percent thickness ratio as seen in FIG. 1, with a maximum thickness at 30 percent of chord length, a blunter leading edge, and a short elliptical planform of constant relative dimension cross-section along its length. These attributes combine to provide substantial hydrodynamic benefit when compared with available surfboard fins on the market today.

The present invention may be characterized as a surfboard fin for mounting into a slot in a receiver box in the underside of a surfboard, where the fin includes:

    • an elliptical planform having a root and an opposite tip, said root and said tip separated by a longitudinally extending length defining a height of the fin, a leading edge and an opposite trailing edge extending from said root to said tip along opposite edge of said planform,
    • said planform having a thickness defined by cross-sections of said planform, wherein said cross sections are substantially orthogonal to said length, and extend along corresponding chords of said cross sections between said opposite edges so as to extend from said leading edge to said trailing edge, a ratio of said thickness and said chord of each of said cross sections defining a corresponding thickness-to-chord ratio,
    • and wherein substantially all of said thickness-to-chord ratios are substantially equal to one another, and are greater than substantially a thickness-to-chord ratio of twelve,
    • and wherein a ratio of a square of said longitudinally extending length and a planform area of said planform define a corresponding aspect ratio, and wherein said aspect ratio is less than three,
    • and wherein said each of said cross sections has a nose section at a forward end thereof corresponding to said leading edge, a curved mid section including a maximum thickness position, and a tapered rear section corresponding to said trailing edge, and wherein said nose section, mid section and rear section of said each of said cross sections is defined by a curvature which is substantially that of a non-cambered NACA four digit airfoil shape so as to have a substantially parabolic nose section and a continuously smoothly substantially convexly curved mid section, where said nose section, said mid section and said rear section form a single smoothly continuously curved foil section which is symmetric on opposites sides of said chord, and wherein said maximum thickness position is located substantially at 30 percent of said chord on said each of said cross sections,
    • and wherein said length has a linear slope component relative to said root chosen from forward slope, no slope, rearward slope, and wherein said length has an elliptical sweep component relative to said root chosen from forward sweep, no sweep, rearward sweep,
    • and wherein irrespective of said sweep said planform is substantially elliptical and its corresponding lift distribution is also substantially elliptical and has a surface area which is substantially constant for a particular said aspect ratio and for particular said cross section and corresponding said thickness-to-chord ratio and corresponding said maximum thickness position,
    • and wherein said planform does not have winglets or auxiliary foils protruding therefrom.
      • The fin may further include a tang depending from said root, wherein a maximum root thickness, defined as said thickness of said root at said maximum thickness position, is greater than a width of the opening in the slot of the receiver box so as to overhang said root from the slot when said tang is mounted in the slot.
      • The maximum root thickness may be in the range of substantially one half inch to one inch for use with a receiver box having slot width of less than three eighths of an inch. The maximum root thickness may be substantially three quarters of an inch.
      • The linear slope component and said elliptical sweep component may be applied to a substantially 30 percent chord line corresponding to said maximum thickness positions. The slope is forward and said sweep may forward or rearward.
      • The slope may be rearward and said sweep is forward or rearward.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be further understood by reference to the following description and attached drawings that illustrate aspects of the invention. Other features and advantages will be apparent from the following detailed description of the invention, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the present invention. In the drawings like characters of reference denote corresponding parts in each view.

FIG. 1 is a prior art fin, viewed in planform, and mounted onto the tail end of a surfboard.

FIG. 2 illustrates one fin cross-section according to the present invention, normalized from 0 to 1.

FIG. 3 illustrates an example of a planform view of the fin according to the present invention with tang suitable for mounting in 10.5 fin receiver box.

FIG. 3a illustrates perspective view of a fin according to the present invention showing its constant cross-section symmetrical shape extending from the fin root to the tip of the fin.

FIGS. 4a and 4b illustrate an example planform view of the fin according to the present invention with tangs suitable for mounting in other types of receivers commonly found on water sport boards.

FIG. 5 illustrates an underneath view of a longboard showing typical fin placement and using fins according to the present invention.

FIG. 6a illustrates an elliptical planform having no slope or sweep.

FIG. 6b illustrates an elliptical planform having no linear slope component and a forward elliptical sweep component.

FIG. 6c illustrates an elliptical planform having a rearward linear slope component and forward elliptical sweep component.

FIG. 6d illustrates an elliptical planform having a rearward linear slope component and a rearward elliptical sweep component.

FIG. 7 is a plot of planform area of a fin according to one embodiment of the present invention

FIG. 8 is a plot of a chord slope, linear component of the fin of FIG. 7.

FIG. 9 is a plot of a chord slope, elliptical component for the embodiment of FIG. 8.

FIG. 10 is a plot of the fin profile for the embodiment of FIG. 8.

FIGS. 11a and 11b, 12a and 12b, 13a and 13b are plots of the chord slope elliptical component and fin profile respectively for three further embodiments of the fin according to the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention relates in general to a fin apparatus and method of making same, where the fin is for use on a water sport board such as a surfboard, and, more particularly, relates to a thick, short or low aspect ratio elliptical planform fin having substantially thick cross-section (typically 12-15% thickness ratio) which overhangs the receiver box slot, and having a maximum thickness position at 30% of chord length, and a blunter leading edge.

In the following description of the invention, reference is made to the accompanying drawings, which form a part thereof, and in which is shown by way of illustration a specific example whereby the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. The thick, elliptical planform fin structure and method described herein is designed to operate on a water sport board.

FIG. 1 illustrates a prior art fin. FIG. 2 illustrates an example cross section of fin 10 according to the present invention normalized from 0 to 1. Fin 10 provides a reaction force when in motion relative to the surrounding water. FIG. 2 illustrates a symmetrical foil shape with a 15% thickness ratio. The shape is symmetrical about the center line with 0% camber, or no arching of the shape. The shape has a 15% thickness to chord length ratio, or it is 15% as thick as it is long. The chord is the imaginary straight line through the cross-section that connects the leading edge to the trailing edge. The maximum thickness of the example fin is located at 30% of chord length, the leading edge is rounded and blunt, the trailing edge comes to a sharp point, and the upper and lower surface form a smooth curve with no “flat spots” or abrupt changes in curve continuity.

FIG. 3 illustrates a planform view of an example longboard center fin according to the present invention suitable for mounting in a surfing industry standard 10.5 inch fin receiver box 22. The fin 10 has a leading edge 12 (0% of chord length), a trailing edge 14 (100% of chord length), a fin tip 16, and a fin root 18 that is attached to the fin tang 20 which is removably securable into a fin receiver box 22. Receiver box 22 is permanently mounted into a surfboard 24 as seen in FIG. 5. The height dimension 24 (also referred to herein as the length) of the fin 10 is measured as seen in FIG. 3 perpendicularly from the root 18 to the tip 16. The vertically extending lines 26 represent lines of constant chord percentage. The chord percentage is the ratio of the distance from the leading edge 12 to a given point (at a constant fin height), to that point's associated chord length. Surfboard fin 10 uses a constant relative dimension cross-sectional shape such as seen in FIG. 2 applied along the entire height of the fin.

FIG. 3a illustrates a tilted perspective view of the thick, elliptical-planform fin without tang or mounting base, to show the symmetrical shape from FIG. 2 extending from root 18 to tip 16.

FIGS. 4a and 4b illustrate a planform view of a shorter, thick, elliptical planform fin that may be used on shorter surf boards and on surfboards with multiple fin arrangements. This style of fin can be manufactured with different tangs to be compatible with different fin mounting systems that are commonly found on water sports boards, such as the Fin Control System™ (FCS) fin plugs of FIG. 4a, and the Future™ fin box of FIG. 4b.

FIG. 5 illustrates a thick, elliptical planform fin 10 installed into a longboard 28. The underneath side 28a of surfboard 28 extends from the nose 28b to the tail 28c. A 10.5 inch fin receiver box 22 is mounted in the board, towards the rear of the board, into which the center fin 10 from FIG. 3 is installed. Smaller fins 10′ as depicted in FIGS. 4a and 4b, commonly called side biters, are installed into receivers forward of center fin 10, close to either edge of the surfboard. Center fin 10 stands perpendicular to underside 28a of the surfboard on the centerline 28d. The side biter fins 10′ are turned in slightly such that they each fall on a corresponding line 28e of a pair of such lines converging to a vertex at nose 28b. The side biter fins are typically not perpendicular to the underside of the surfboard but canted away from the center of the board by a few degrees.

For these fins, an elliptical area distribution is used. Referring to FIG. 3, the overall height 24 is measured perpendicularly from the plane of root 18 to tip 16. The chord length, measured from leading edge 12 to trailing edge 14 parallel to the fin root (i.e. parallel to the direction of the flow of water past the fin), at any fin height, can be calculated using the mathematical equations of an ellipse. The fin can be angled backward or forward at a constant linear slope, or swept backward or forward with an elliptical contribution to that slope, or some combination of both.

FIGS. 6a-6d illustrate some examples of various elliptical planform projections showing the effect of different amounts of constant slope and elliptical sweep. Regardless of how much the fin is sloped or swept backward or forward, the length of the foil chord at a given height along the overall height or length 24 would be the same for all fins with the same root chord length and height dimensions. The intent is to preserve the elliptical area distribution and to ensure that the chord length, and subsequently the foil thickness, decreases from root 18 toward tip 16. All of the fins pictured in FIGS. 6a-6d have the same root chord length and fin height, and as such have the same planform surface area. The differences between the fins lie in the amount of constant linear slope or elliptical sweep.

Fins are designed using the desired characteristics of the fin (fin height, fin root length, constant and elliptical slope parameters, fin cant, fin thickness in percentage, and style of fin base). A corresponding surface map of the desired fin is then generated. Corresponding CNC machine computer code provides for automated machining of the fins. By changing these various input parameters, the fin can be tailored for a specific fin application or for the preferences of its intended user. For example, moving the center of pressure of the fin forward relative to the receiver box makes for a “looser”, that is, more maneuverable board; the fin acting more like a heel and less like a rudder. This may be accomplished using forward slope and/or sweep components to adjust the trajectory of the 30 percent chord line when designing the fin.

When designing a fin, its intended surfboard and use are initially taken into mind. Some determination of the desired size and planform area of the fin needs to be made. Surfboards with thruster setups typically have three identically sized fins. Twin fin setups have two fins that are larger than the fins for thruster setups. Longboards with 2+1 setups typically have one larger center fin, and two smaller “side bitter” fins. These side biter fins are smaller than fins for thruster setups. Larger/heavier surfers typically use bigger fins. Bigger surfboards typically have bigger fins. Larger fins, enable the surfer to pump the board to build more speed (referred to as drive), but may reduce the maneuverability of the surfboard in certain conditions. Larger fins work better on bigger waves, when the surfboard is traveling faster and the rider can move rearward on the board with more of his weight over the fins. On smaller waves, smaller fins work better to loosen up the surfboard and make it more maneuverable when the rider tends to be more forward on the surfboard, so the board rides flatter in the water. The total area of all the fins on the board, and the placement of those fins on the board (forward or rearward on the surfboard), determine a number of characteristics about the board, including its stability and maneuverability.

Based on the equation of an ellipse, the height of the fin and the length of the base or root of the fin determine the area. The semi major axis is the height 24 of the fin (variable A in the following equation), the semi minor axis is half the length of the base or root 18 of the fin (variable B in the following equation). The area of an ellipse is given by the equation, Area=(3.14) A*B. The area of the fin is half the area of the complete ellipse.

Once the determination of the fin size has been made, specifically the height of the fin and length of the base, the parameters can be chosen to control the projection of the fin as determined by the trajectory of the 30 percent chord line. The fin depicted in FIG. 7 stands 8.5 inches tall, and has a base length of 4 inches. 30 percent chord line 32 is the projection of the 30 percent point, or the thickest portion of the fin. This fin is half of a standard ellipse as it has not been sloped or swept.

The fin can be sloped forward, or rearward with a constant linear contribution to its slope as illustrated graphically in FIG. 8. This cord slope is applied to the 30 percent chord line 32 or the thickest portion of the fin. The leading and trailing edges of the fin adjust accordingly to maintain the desired planform area.

The fin can be swept forward or rearward with an elliptical contribution to its slope as illustrated graphically in FIG. 9. This sweep is applied to the 30 percent chord line 32 or the thickest portion of the fin. The leading and trailing edges of the fin again adjust accordingly to maintain the desired (constant in FIGS. 6a-6d) planform area. FIG. 9 shows in particular a rearward elliptical component to sweep, i.e. the fin curves slightly rearward as seen by way of example in FIG. 6d.

The combination of both the linear and elliptical component of slope and sweep respectively yield the planform projection as seen in FIG. 10.

The combination of linear slope and elliptical sweep offer a wide variety of options for the projection of the planform. The elliptical component can be used to make the curvature of the fin increase exponentially along the length of the fin, both forward or rearward. One example as seen in FIGS. 11a and 11b is that the elliptical component of FIG. 11a can be applied to the 30 percent chord line 32 of FIG. 11b, such that the 30 percent chord line forms a straight line. An example of this also seen in FIG. 6b

The platform profile adjustment by use of the elliptical component applied to the 30 percent chord, may be done such that the leading edge of the fin forms a straight line. In the example of FIGS. 12a and 12b the fin of FIG. 12b has a rearward linear slope, but a forward elliptical sweep as a result of the elliptical component adjustments of FIG. 12a.

FIG. 12a as seen in FIGS. 13a and 13b, the elliptical components may also be applied to the 30 percent chord line 32, such that the trailing edge of the fin forms a straight line.

The combination of linear slope and elliptical sweep offer a great deal of control over the projection or planform of the fin, but do not change the characteristics of the fin's size or area.

Taking the fin height, fin root length, constant and elliptical slope and sweep, fin cant, fin thickness in percentage, and style of fin base characteristics into account, a variety of fins can be produced for different surfing applications. In all of the fins according to the present invention the maximum thickness at the root is substantially thicker than conventional, and overlaps the opening of the slot 22a in receiver box 22, that is broader than the slot 22a. This is counter intuitive as the fin is usually not wider than the slot in the box so that the fin will seat properly and fully if the tang is too short for the box slot receiver depth. That is, conventionally the whole tang and some of the root will slide into the slot if the slot is too deep until the bottom of the tang seats. Different boxes sometimes have different depth slots. The boxes 22 are typically ⅜ inch wide (0.375 inch). Slots 22a are typically 0.365 inch wide. The fins of the present invention may typically have an average maximum thickness at the root of the ¾ inch (0.75 inch) so as to substantially overhang the lip of slot 22a. Fins 10 may have maximum thickness in the range of ½ inch to one inch.

In addition to forward or rearward slope or sweep, the fin may be canted to the side when viewed from the front (looking down the chord line from leading edge to trailing edge). The outermost fins in multi-fin arrangements are commonly canted away from the centerline of the surfboard.

These fins may be manufactured using any combination of method or material that yields the desired shape with sufficient strength to perform their function. Prototype versions of these fins were manufactured on a computer numerically Controlled (CNC) milling machine out of thick sheets of fiberglass, clear acrylic (commonly called Plexiglas™), clear polycarbonate (typically used as bullet proof glass), high density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMW), and poly vinyl chloride (PVC). Larger scale production methods could employ plastic injection molding, or composite (e.g., fiberglass, carbon fiber, Kevlar™) molding techniques.

As will be apparent to those skilled in the art in the light of the foregoing disclosure, many alterations and modifications are possible in the practice of this invention without departing from the spirit or scope thereof. Accordingly, the scope of the invention is to be construed in accordance with the substance defined by the following claims.