US3008673A - Reciprocating leading edge for airfoils and hydrofoils - Google Patents
Reciprocating leading edge for airfoils and hydrofoils Download PDFInfo
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- US3008673A US3008673A US763361A US76336158A US3008673A US 3008673 A US3008673 A US 3008673A US 763361 A US763361 A US 763361A US 76336158 A US76336158 A US 76336158A US 3008673 A US3008673 A US 3008673A
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 10
- 230000000694 effects Effects 0.000 description 6
- 230000008878 coupling Effects 0.000 description 4
- 238000010168 coupling process Methods 0.000 description 4
- 238000005859 coupling reaction Methods 0.000 description 4
- 239000011888 foil Substances 0.000 description 4
- 235000008429 bread Nutrition 0.000 description 2
- 239000002184 metal Substances 0.000 description 2
- 230000000149 penetrating effect Effects 0.000 description 2
- 230000003014 reinforcing effect Effects 0.000 description 2
- 230000035939 shock Effects 0.000 description 2
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
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- 238000005755 formation reaction Methods 0.000 description 1
- 239000000446 fuel Substances 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 230000003534 oscillatory effect Effects 0.000 description 1
- 230000035515 penetration Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 239000002023 wood Substances 0.000 description 1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64C—AEROPLANES; HELICOPTERS
- B64C23/00—Influencing air flow over aircraft surfaces, not otherwise provided for
Definitions
- the shape of fuselages or boat hulls may be altered to take advantage of such increased speed potential.
- wings When prefaced by dynamic instead of satic leading edges, wings have increased carrying capacity and are capable of achieving exceptionally fast forward flight, while a dynamic hydrofoil fitted to a water craft also offers outstanding advantages to both air and water transportation.
- FIG. 1 is a partial View, looking downward, of the reciprocating leading edges of Wings, showing -a source of power in the form of an electric motor embodied in the body of a craft and twin cams connected thereto, one for reciprocally actuating one leading edge and the other to operate the leading edge off the opposite Wing.
- FIG. 2 is a frontal, partial cross sectional view of the Patented jNov. 14, 1961 o sa leading edges showing their extreme outboard reciprocal travel
- FIG. 3 is a similar view showing their extreme inboard travel.
- the two inner arrows at the bottom thereof depiet the extent of travel of these leading edges, while the two outer arrows indicate the inboard overhang of the leading edges.
- FIG. 4 is a three-quarter view showing part ot an airplane wing and its reciprocating leading edge mounted in position thereupon; also, the top access hole covers of the leading edge and the ball bearings that permit highspeed, anti-frictional reciprocal movement of said leading edges.
- FIG. 5 shows the bow outline of a boat outiittecl with underwater hydrofoils equipped with reciprocating leading edges.
- FIG. 6 is a three-quarter fragmentary view of an airplane showing each of the wing surfaces iitted with a reciprocating edge.
- FIG. 7 is ian enlarged view showing divided stub shaft 14 with its ball construction 14A intermediate coupling 15 for permitting adjustability of the reciprocal travel ofthe leading edges and connection ot this shaft with the slave rings of cams: 9 and 10.
- leading edges are comprised of walls having a shell-like construction consisting of top 1, bottom 2, forward knife-edge 3 and reinforcing sections ⁇ 4, which are integrated with the top and bottom walls on their inner sides as shown particularly in FIG. 4.
- Spar 24 contains several recessed ⁇ areas which carry grooveways 6, as shown in dotted outline in FIGS. 1 and 4. Bearings 5 are mounted in said reinforcing sections, said bearings extending approximately half way into these grooveways. These bearings are also shown in dotted outline in grooves 6, FIG. l. They maintain spatial alignment with the spar and permit anti-frictional reciprocal travel of the shell construction relative to the xed position of the spar.
- a number of openings are formed in the top and bottom walls of said shell construction to permit access to the interior thereof. Removable covers 7 of these openings, illustrated only on the top of the shell, are flushingly secured thereto by a plurality ot' screw bolts 8.
- These shells may be lgiven cutting motion by any conventional means. Obviously, the right and left shells are separate entities and in minimum travel are separated from each other by a space as at 1B.
- cams 9 and 1G which are rotated by motor 11, cause two cutting motions per revolution of shaft 12. Both these cams lare mounted eccentrically, the apexes thereof facing opposite to each other on said shaft, to which they are keyed, as at 13.
- Stub shafts 22, which have a socket construction 22A yfor partially encompassing ball-like structure 14A of rods 14 are secured to walls 20 of the shells, as shown in FIGS. 1, 2, 3 and 7.
- Rods 14 have threads which engage threaded coupling 15, shown in detail in FIG. 7. This permits tine reciprocal travel adjustment ot the leading edges. Locknuts 21 of couplings 15, shown clearly in FIG. 7, secure the settings of rods 14.
- Knife-edge 3 is formed at the extreme forward position of the shell construction by the merging of the top and lbottom walls thereat. Also, the top Iand bottom surfaces have tapering overlapping sections 1A and 2A Irespectively at their trailing edges to minimize drag as the reciprocating edges cut their way through the iluid media.
- Grooveways 6 may be given a polished surface to minimize drag movement of ball bearings 5 therein. These grooveways are secured tospar 24 by a plurality of screw bolts 17, sho-wn in dotted outline in FIGS. 1 and 4.
- the air-foil, or wing, rearwardly of the reciprocating leading adge is indicated by 16, which may be applicable to either airfoil or hydrofoil construction.
- 16 may constitute a sustaining means for either an aircraft or a marine vessel.
- Double-headed arrow 18, shown at the bottom off FIG. 3, indicates the minimum extent of the reciprocal travel of both the shelllike leading edges, while double-headed arrow 19 indicates the maximum extent of travel thereof.
- Double-headed arrow 25 indicates the extent of maximum travel of each shell, double-headed arrow 26 the extent of up-travel and arrow 27 the down-travel of the ca-ms, thereby establishing their eccentric orbit.
- Numeral 23 indicates the hull of a conventional boat riding in the water, the hydrofoils previously mentioned being shown in a cutaway ⁇ section of said Water, and the actuating means therefor being shown in dotted outline at the bottom of the boats hull.
- the operative action'of the bydrolfoils is similar to that of the airfoils.
- powered means ⁇ for moving said body through said media, a forward and a trailing end of said sur-faces and an expanse of surface area therebetween, said forward end having a forwardly projecting spar formed to comprise a top, a bottom yand a tapered forward edge, recesses provided in the top and bottom of said spar and a number of half-circle grooveway ⁇ formations secured therein, walls comprising a cambered shell construction shaped to spatially envelop said spar and to provide a movable leading edge therefor, a trailing edge formed on the top and on the bottom of said shell construction, said trailing edge extending rearward-ly relative to said leading edge and over-hanging said expanse of surface to provide Ia top and bottom extension therefor, said shell having reinforced sections positioned opposite said recesses, a plurality of half-circle formations in said reinforced sections and bearings positioned thenein and protruding therefrom to occupy said groove
Description
Nov. 14, 1961 A. M. CADDELL 3,008,673
RDCIPROCATING LEADING EDGE FDR ARFoILs AND HYDRoFoILs Filed Sept. 25, 1958 1| lll/l l/ Il United States Patent 3,008,673 RECIIROCATING LEADING EDGE FOR AIR- FOILS AND HY DROFOILS Alfred M. Caddell, 1318 W. Hunting Park Ave., Philadelphia 40, Pa. Filed Sept. 25,1958, Ser. N0. 763,361 2 Claims. (Cl. 244-130) This invention aims to speed airfoils and hydrofoils through air and water respectively by minimizing the resistance offered by their passage through these media. By providingreciprocal cutting edges for sustaining surfaces, the shape of fuselages or boat hulls may be altered to take advantage of such increased speed potential. When prefaced by dynamic instead of satic leading edges, wings have increased carrying capacity and are capable of achieving exceptionally fast forward flight, while a dynamic hydrofoil fitted to a water craft also offers outstanding advantages to both air and water transportation.
Clearly, the faster a craft travels through air or water the greater, relatively, lbecomes the density or opposition of the media being penetrated. In water, the effect is increased resistance to its displacement. In air, the compressibility factor resulting from an aircrafts attack against the velocity-created air wall introduces both resistance and shock wave phenomena, the concussionary effects of which often spread to all parts of the craft. Vibrations are set up, resulting in harmonics that generate ever-increasing amplitudes or resonant swings, the
effects of-which may induce metal fatigue and disintegration of a craft,
As a means for attaining present-day speeds, thin wings, swept-back wings which impart a draw-knife effect on the air, or vwings with fixed knife-edge leading edges are relied upon to accomplish the desired effect. Also, rivets have been countersunk, fairings and llets contoured and skin surfacespolished to lessen resistance to travel of a craft through air.
But these developments do not go far enough toward minimizing the resistance or the shock wave problems generated. Both airfoils and hydrofoils perform at only half of their possible elciencies due to the foil itself being inert, motionless and devoid of superior attack ability.l But when altered to impart reciprocal cutting motion, the same airfoil or hydrofoil will penetrate air orwater with practically half the effort otherwise required -torattain a desired speed of travel therethrough.
y In air travel, as a crafts speed increases, the compressibility or solidity of the air likewise increases, not in direct proportion but as the square of the speed. As evidence of this, the table of head yresistances computed on the basis of .0032 pound resistance per square foot of plate set at a right angle to the wind (sea level pressure- Engineers Unit Coefficient) gives a resistance of 32 pounds per square foot when hit by a lOO-mle-per-hour wind; at 500 miles--perhour 800 pounds and at 1,000 miles 3,200v pounds.
In calculatingtheperformance of an aircraft on the drawing boards, engineers reduce 'all frontal dimensions to approximate-the square feet of surface offered to the wind and attempt to arrive at the total resistance in pounds that should be encountered at any specified altitude and speed. On the basis of such calculations, a plane traveling at a speed of 600 miles per hour at sea level and having a total of square feet of penetrating area will be confronted with the enormous drag of 11,520 pounds of head resistance; which drag will of course continue to increase as the square of the speed as forward relative velocities mount higher. This resistance poundage is based, as aforesaid, on resistances offered at an altitude where atmospheric pressure is greatest and accounts for jet planes seeking higher flight altitudes.
In the case of jet powered craft whereinthe faster it travels the more efficient 'jet propulsion becomes, the attainment of supersonic iiight speeds becomes the paramount goal. Whereas the gas being discharged from a jets tail pipe has a speed of approximately 1,227 miles per hour, the highest flight speed attained in level flight at sea level is about 550 or 600 miles per hour or roughly, 50 percent of the `jet or slipstream speed. The lost 50 percent is consumed by resistance offered in the crafts passage through the air. Translated into operating statistics, this means that fully half the crafts possible flight range, pay load and fuel costs are, at present, needlessly sacrificed.
Itis that staggering loss which this invention aims to lessen and thus make possible greater speeds per pound of thrust put out by an engine. Militarily, the value of increased liight eiciency is incalculable.
In wind tunnel tests conducted by this applicant, resistance 'readings of a fixed wing were taken at various angles of mounting and at various air speeds, after which readings were taken on an identically formed wing having a reciprocating leading edge. A D.C. motor was fairedbet-ween a right and a left wing and an adjustable, cam-operated arm permitted controlled reciprocal motion of the leading edge. The travel extended from 1 to 2 inches on each side of center. When the 2-inch motion was employed the motorshaft turned at 1,110 rpm.; at l-inch travel it was operated at 1,850 r.p.m. A scale was installed to measure the differences in drag between the lixed wing and that registered for the wing carrying the reciprocating leading edge.
These tests pointed the way for attaining 40 to 50 percent reductions in drag. The greatest gain occurred with the l-inch travel at a motor shaft speed of between 1,600 and 1,800 r.p.m. With two reciprocal movements per shaft revolution, the cutting motions thus registered between 3,200 and 3,600 per minute. Translated into lift-drag ratios, the results indicate that a Wing having an average 20-1 ratio could be enlivened to nearer a 40-1 ratio if fitted with a leading edge given high reciprocal motion, thus converting the major portion of the thrust now lost in the slipstream to increased forward speed at no further demand of thrust output.
In other fields of activity, when one desires to penetrate or cut anything, such as a log of wood or a loaf of bread, the cutting edge is not just pressed downwardly through the log or bread in the manner that wing surfaces are pushed through the air. Rather the entering edge of the tool is given reciprocal motion. By the name token the same basic cutting law, at present neglected, is extremely applicableV to airfoils and hydrofoils for eflicient air and water penetration.
Considerable experimentation has been conducted in the latter field. Vessels have been equipped with hydrofoils comprised of thin, ladder-like strips of metal attached in vertical tiers to the hull of a boat. During forward motion, the hull rises on the hydrofoils until, virtually free of water drag, it speeds along on the bottommost foils. Reciprocal cutting edges fitted to these same hydrofoils would lessen the resistance they now offer in penetrating the water, thus increasing over-all efliciencyt In the drawings:
FIG. 1 is a partial View, looking downward, of the reciprocating leading edges of Wings, showing -a source of power in the form of an electric motor embodied in the body of a craft and twin cams connected thereto, one for reciprocally actuating one leading edge and the other to operate the leading edge off the opposite Wing.
FIG. 2 is a frontal, partial cross sectional view of the Patented jNov. 14, 1961 o sa leading edges showing their extreme outboard reciprocal travel, while FIG. 3 is a similar view showing their extreme inboard travel. The two inner arrows at the bottom thereof depiet the extent of travel of these leading edges, while the two outer arrows indicate the inboard overhang of the leading edges.
FIG. 4 is a three-quarter view showing part ot an airplane wing and its reciprocating leading edge mounted in position thereupon; also, the top access hole covers of the leading edge and the ball bearings that permit highspeed, anti-frictional reciprocal movement of said leading edges.
FIG. 5 shows the bow outline of a boat outiittecl with underwater hydrofoils equipped with reciprocating leading edges.
FIG. 6 is a three-quarter fragmentary view of an airplane showing each of the wing surfaces iitted with a reciprocating edge.
FIG. 7 is ian enlarged view showing divided stub shaft 14 with its ball construction 14A intermediate coupling 15 for permitting adjustability of the reciprocal travel ofthe leading edges and connection ot this shaft with the slave rings of cams: 9 and 10.
These leading edges are comprised of walls having a shell-like construction consisting of top 1, bottom 2, forward knife-edge 3 and reinforcing sections` 4, which are integrated with the top and bottom walls on their inner sides as shown particularly in FIG. 4. Spar 24 contains several recessed `areas which carry grooveways 6, as shown in dotted outline in FIGS. 1 and 4. Bearings 5 are mounted in said reinforcing sections, said bearings extending approximately half way into these grooveways. These bearings are also shown in dotted outline in grooves 6, FIG. l. They maintain spatial alignment with the spar and permit anti-frictional reciprocal travel of the shell construction relative to the xed position of the spar. A number of openings are formed in the top and bottom walls of said shell construction to permit access to the interior thereof. Removable covers 7 of these openings, illustrated only on the top of the shell, are flushingly secured thereto by a plurality ot' screw bolts 8.
These shells may be lgiven cutting motion by any conventional means. Obviously, the right and left shells are separate entities and in minimum travel are separated from each other by a space as at 1B. As shown herein, cams 9 and 1G, which are rotated by motor 11, cause two cutting motions per revolution of shaft 12. Both these cams lare mounted eccentrically, the apexes thereof facing opposite to each other on said shaft, to which they are keyed, as at 13. Outer slave rings 9A and 10A respectively of these cams lfollow their eccentric motions. Connected to rods 14, these slave rings transmit movements of their respective cams through adjustable couplings 15. Stub shafts 22, which have a socket construction 22A yfor partially encompassing ball-like structure 14A of rods 14 are secured to walls 20 of the shells, as shown in FIGS. 1, 2, 3 and 7.
Knife-edge 3 is formed at the extreme forward position of the shell construction by the merging of the top and lbottom walls thereat. Also, the top Iand bottom surfaces have tapering overlapping sections 1A and 2A Irespectively at their trailing edges to minimize drag as the reciprocating edges cut their way through the iluid media.
The air-foil, or wing, rearwardly of the reciprocating leading adge, is indicated by 16, which may be applicable to either airfoil or hydrofoil construction. In conjunction with spar 24, 16 may constitute a sustaining means for either an aircraft or a marine vessel. Double-headed arrow 18, shown at the bottom off FIG. 3, indicates the minimum extent of the reciprocal travel of both the shelllike leading edges, while double-headed arrow 19 indicates the maximum extent of travel thereof.
Double-headed arrow 25 indicates the extent of maximum travel of each shell, double-headed arrow 26 the extent of up-travel and arrow 27 the down-travel of the ca-ms, thereby establishing their eccentric orbit.
Having described my invention, I claim:
1. In `a craft having a body and sustaining surfaces for supporting said body in fluid media, powered means `for moving said body through said media, a forward and a trailing end of said sur-faces and an expanse of surface area therebetween, said forward end having a forwardly projecting spar formed to comprise a top, a bottom yand a tapered forward edge, recesses provided in the top and bottom of said spar and a number of half-circle grooveway `formations secured therein, walls comprising a cambered shell construction shaped to spatially envelop said spar and to provide a movable leading edge therefor, a trailing edge formed on the top and on the bottom of said shell construction, said trailing edge extending rearward-ly relative to said leading edge and over-hanging said expanse of surface to provide Ia top and bottom extension therefor, said shell having reinforced sections positioned opposite said recesses, a plurality of half-circle formations in said reinforced sections and bearings positioned thenein and protruding therefrom to occupy said grooveways, means for affording access to the interior of said construction, a source of power in said body and means connecting said source with said shell for imparting oscillatory travel motio-n thereto.
2. The strucnlre as described in claim 1 wherein said cambered shell is connected to said source of power by adjustable means for varying the oscillations of said shell and the extent of reciprocal travel thereof relative to the fixed position of said spar.
References Cited in the tile of this patent UNITED STATES PATENTS 1,832,396 Howard Nov. 17, 1931 1,842,656 Carolin Ian. 26, 1932 1,879,594 'Irey Sept. 27, 1932 2,156,110 Brunker Apr. 25, 19.39 2,399,648 Love May 7, 1946 FOREIGN PATENTS 404,149 Great Britain Ian. 11, 1934 749,293, Germany g Nov. 20, 1944
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US763361A US3008673A (en) | 1958-09-25 | 1958-09-25 | Reciprocating leading edge for airfoils and hydrofoils |
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US763361A US3008673A (en) | 1958-09-25 | 1958-09-25 | Reciprocating leading edge for airfoils and hydrofoils |
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Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5052641A (en) * | 1989-04-06 | 1991-10-01 | Coleman Henry L | Method to construct variable area, membrane spar and wing airfoil aircraft and kite wings and suitable aelerons |
US20100124459A1 (en) * | 2008-11-19 | 2010-05-20 | Kelly Slater | Surface Gravity Wave Generator And Wave Pool |
US9476213B2 (en) | 2008-11-19 | 2016-10-25 | Kelly Slater Wave Company, Llc. | Wave generator system and method for free-form bodies of water |
US10597884B2 (en) | 2017-08-30 | 2020-03-24 | Kelly Slater Wave Company, Llc | Wave pool and wave generator for bi-directional and dynamically-shaped surfing waves |
US11619056B2 (en) | 2008-11-19 | 2023-04-04 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
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US1832396A (en) * | 1925-06-05 | 1931-11-17 | Standard Oil Dev Co | Aircraft |
US1842656A (en) * | 1930-05-29 | 1932-01-26 | Carolin Norbert | Aeroplane |
US1879594A (en) * | 1928-07-25 | 1932-09-27 | Trey Serge | Aeroplane wing |
GB404149A (en) * | 1933-02-02 | 1934-01-11 | Fairey Aviat Co Ltd | Improvements in or relating to aerofoil surfaces |
US2156110A (en) * | 1935-09-11 | 1939-04-25 | Waco Aircraft Company | Flush cover access opening |
DE749293C (en) * | 1941-11-27 | 1944-11-20 | Airplane with strongly arrow-shaped wings and partially moving wing covering | |
US2399648A (en) * | 1944-01-28 | 1946-05-07 | Love Harold Norris | Deicing mechanism |
-
1958
- 1958-09-25 US US763361A patent/US3008673A/en not_active Expired - Lifetime
Patent Citations (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US1832396A (en) * | 1925-06-05 | 1931-11-17 | Standard Oil Dev Co | Aircraft |
US1879594A (en) * | 1928-07-25 | 1932-09-27 | Trey Serge | Aeroplane wing |
US1842656A (en) * | 1930-05-29 | 1932-01-26 | Carolin Norbert | Aeroplane |
GB404149A (en) * | 1933-02-02 | 1934-01-11 | Fairey Aviat Co Ltd | Improvements in or relating to aerofoil surfaces |
US2156110A (en) * | 1935-09-11 | 1939-04-25 | Waco Aircraft Company | Flush cover access opening |
DE749293C (en) * | 1941-11-27 | 1944-11-20 | Airplane with strongly arrow-shaped wings and partially moving wing covering | |
US2399648A (en) * | 1944-01-28 | 1946-05-07 | Love Harold Norris | Deicing mechanism |
Cited By (18)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5052641A (en) * | 1989-04-06 | 1991-10-01 | Coleman Henry L | Method to construct variable area, membrane spar and wing airfoil aircraft and kite wings and suitable aelerons |
US10066410B2 (en) | 2008-11-19 | 2018-09-04 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
US9476213B2 (en) | 2008-11-19 | 2016-10-25 | Kelly Slater Wave Company, Llc. | Wave generator system and method for free-form bodies of water |
US10081956B2 (en) | 2008-11-19 | 2018-09-25 | Kelly Slater Wave Company | Wave generator system and method for free-form bodies of water |
US8573887B2 (en) * | 2008-11-19 | 2013-11-05 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
US10221582B2 (en) | 2008-11-19 | 2019-03-05 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
US9546491B2 (en) | 2008-11-19 | 2017-01-17 | Kelly Slater Wave Company, Llc. | Surface gravity wave generator and wave pool |
US9574360B2 (en) | 2008-11-19 | 2017-02-21 | Kelly Slater Wave Company, Llc. | Surface gravity wave generator and wave pool |
US11619056B2 (en) | 2008-11-19 | 2023-04-04 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
US20130036545A1 (en) * | 2008-11-19 | 2013-02-14 | Kelly Slater | Surface Gravity Wave Generator And Wave Pool |
US8262316B2 (en) * | 2008-11-19 | 2012-09-11 | Kelly Slater Wave Company, Llc | Surface gravity wave generator and wave pool |
US20100124459A1 (en) * | 2008-11-19 | 2010-05-20 | Kelly Slater | Surface Gravity Wave Generator And Wave Pool |
US10858851B2 (en) | 2008-11-19 | 2020-12-08 | Kelly Slater Wave Company, Llc | Wave generator system and method for free-form bodies of water |
US10890004B2 (en) | 2008-11-19 | 2021-01-12 | Kelly Slater Wave Company | Surface gravity wave generator and wave pool |
US11441324B2 (en) | 2008-11-19 | 2022-09-13 | Kelly Slater Wave Company, Llc | Wave generator system and method for free-form bodies of water |
US11280100B2 (en) | 2017-08-30 | 2022-03-22 | Kelly Slater Wave Company, Llc | Wave pool and wave generator for bi-directional and dynamically-shaped surfing waves |
US10597884B2 (en) | 2017-08-30 | 2020-03-24 | Kelly Slater Wave Company, Llc | Wave pool and wave generator for bi-directional and dynamically-shaped surfing waves |
US11851906B2 (en) | 2017-08-30 | 2023-12-26 | Kelly Slater Wave Company, Llc | Wave pool and wave generator for bi-directional and dynamically-shaped surfing waves |
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