Thick, elliptical-planform fin for a water sports board

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.

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.