Note: Descriptions are shown in the official language in which they were submitted.
CA 02662592 2009-04-15
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 manoeuvrability
of the surfboard.
The initial goal was to make longboards, surfboards longer than 9 feet in
length,
more manoeuvrable 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.
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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
manoeuvring 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
manoeuvring. 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 3/8
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 manoeuvring, 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 outetmost
fins are experiencing positive angles of attack. When the surfer shifts his
weight forward so
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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 3/8 inch thick
piece of fibreglass that is cut to the desired planfonn 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 manoeuvring 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.
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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 foi- use on a
water sport board such as a surfboard. The fin provides for improved stability
and
manoeuvrability 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 Figure 1, with
a maximum thickness at 30 percent of chord length, a blunter leading edge, and
a short
elliptical planfonn 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.
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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
planfonn,
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
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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.
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The linear slope component and said elliptical sweep component may be
applied to a substantially 30 percent chord line corresponding to said
maxiinu.m
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.
Figure 1 is a prior art fin, viewed in planform, and mounted onto the tail end
of
a surfboard.
Figure 2 illustrates one fin cross-section according to the present invention,
normalized from 0 to 1.
Figure 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.
Figure 3 a 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.
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Figures 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.
Figure 5 illustrates an underneath view of a longboard showing typical fin
placement and using fins according to the present invention.
Figure 6a illustrates an elliptical planform having no slope or sweep.
Figure 6b illustrates an elliptical planform having no linear slope coinponent
and a forward elliptical sweep component.
Figure 6c illustrates an elliptical planform having a rearward linear slope
component and forward elliptical sweep component.
Figure 6d illustrates an eIliptical planform having a rearward linear slope
component and a rearward elliptical sweep component.
Figure 7 is a plot of planform area of a fin according to one embodiment of
the
presentinvention
Figure 8 is a plot of a chord slope, linear component of the fin of Figure 7.
Figure 9 is a plot of a chord slope, elliptical component for the embodiment
of
Figure 8.
Figure 10 is a plot of the fin profile for the embodiment of Figure 8.
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Figures 1la 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.
Figure 1 illustrates a prior art fin. Figure 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. Figure 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
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CA 02662592 2009-04-15
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.
Figure 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 Figure 5. The height dimension 24 (also
referred to
herein as the length) of the fin 10 is measured as seen in Figure 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 fm 10
uses a constant
relative dimension cross-sectional shape such as seen in Figure 2 applied
along the entire
height of the fin.
Figure 3a illustrates a tilted perspective view of the thick, elliptical-
planform
fin without tang or mounting base, to show the symmetrical shape from Figure 2
extending
from root 18 to tip 16.
Figures 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'g (FCS) fin plugs of Figure 4a, and the Future." fin box of
Figure 4b.
CA 02662592 2009-04-15
Figure 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
tai128c. 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 Figure 3 is installed. Smaller fins 10' as depicted in
Figures 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 Figure
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 fm), at any fm 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.
Figures 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 Figures 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.
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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 fm base). A corresponding surface map of the desired fm 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. Zon.gboards
with 2+1 setups
typically have one larger center fin, and two smaller "side bitter" fins.
These side biter fms 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.
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Based on the equation of an ellipse, the height of the fm 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
conaplete 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 Figure 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 Figure 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 Figure 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 figures 6a - 6d) planform
area. Figure 9
shows in particular a rearward elliptical component to sweep, i.e. the fin
curves slightly
rearward as seen by way of example in Figure 6d.
The combination of both the linear and elliptical component of slope and sweep
respectively yield the planform projection as seen in Figure 10.
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The combination of linear slope and elliptical sweep offer a wide variety of
options for the projection of the planform. The ellipiical 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 Figures 11 a and 11b is that the elliptical
component of
Figure 11a can be applied to the 30 percent chord line 32 of Figure 11b, such
that the 30
percent chord line forms a straight line. An example of this also seen in
Figure 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 Figures 12a and 12b the fin. of Figure 12b has a rearward
linear slope, but a
forward elliptical sweep as a result of the elliptical coinponent adjustments
of Figure 12a.
Figure 12a as seen in Figures 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 forins 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 fitlly 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
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until the bottom of the tang seats. Different boxes sometimes have different
depth slots. The
boxes 22 are typically 3/8 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 1/4 inch (0.75 inch) so as to substantially overhang the lip of slot
22a. Fins 10 may have
maximum thickness in the range of %z inch to one ineb..
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 weigh.t polyethylene (UHMW), and poly vinyl chloride (PVC).
Larger scale
production methods could employ plastic injection molding, or composite (e.g.,
fiberglass,
carbon fiber, Kevlar.TM) 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.
