US3713750A - Circulation control rotor system - Google Patents

Circulation control rotor system Download PDF

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US3713750A
US3713750A US00095643A US3713750DA US3713750A US 3713750 A US3713750 A US 3713750A US 00095643 A US00095643 A US 00095643A US 3713750D A US3713750D A US 3713750DA US 3713750 A US3713750 A US 3713750A
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blade
edge
rotor
slot
chi
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R Williams
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US Department of Navy
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B64AIRCRAFT; AVIATION; COSMONAUTICS
    • B64CAEROPLANES; HELICOPTERS
    • B64C27/00Rotorcraft; Rotors peculiar thereto
    • B64C27/32Rotors
    • B64C27/325Circulation-control rotors

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  • Atl0rrteyR. S. Sciascia and Q, E. Hodges 1 1 ABSTRACT The rotating blades on a helicopter are in the shape of a cambered elliptical airfoil with blunt edges.
  • a plurality of slots are employed on the upper surface of the airfoil to blow a thin sheet of air tangentially across the surface of the foil and around the trailing edge. Circulation control is achieved by the tangential blowing as the sheet of air adheres to the surface and travels around the trailing edge, detaching beneath the trailing edge at a location determined by the intensity of blowing.
  • the effect of the tangential blowing is relocation of the stagnation stream lines producingincreased lift on the foil.
  • the air supplied to the slots is modulated with respect to the azimuth position of the rotor and the speed of the rotating blade so that cyclic control over the lift of the rotor can be accomplished without altering the blade attitude.
  • FIG. 3b
  • the rotating blades in a helicopter are formed from a basic air foil shape selected from potential flow theory calculations and may be cambered elliptical shape, having a blunt or rounded leading and trailing edge.
  • a number of slots are disposed in a line substantially parallel to the edge and adjacent the edge.
  • the thin sheet adheres to the trailing edge and remains attached, by the Coanda effect, until it reaches the separation point on the blade under side, beneath the trailing edge.
  • the point of separation beneath the trailing edge is determined by the intensity of blowing.
  • the effect of the circulation control is to relocate the stagnation stream lines and produce a higher lift on the foil, the lift on the air foil being functionally related to the ratio of the velocity of the blown air to the free stream velocity blowing over the rotating wing.
  • the air blown through the slots and ove the trailing edge is modulated proportionally to the sine and cosine of the rotor azimuth angle and at harmonics thereof to permit the rotor to distribute the lift cyclically in any desired manner, and toreduce power consumption and vibration.
  • Each blade tapers from a predetermined thickness at its root to a more narrow thickness at its tip.
  • the cross-section of the rotor is structured with a plurality of individual plenum chambers to supply air to each of the slots.
  • the plenum chambers supply air to the upper blade surface to produce the tangential flow as needed on leading and trailing edges and to a slot on the underside of the blade, producing a jet flap or blown flap so the effects of the blown flap and circulation control tangential flow may be combined to produce the widest variation in lift on the rotor.
  • FIG. I shows a rotor system according to the principles of this invention, mounted for rotation on a hub, having a slot on the underside of the rotor adjacent its tip to produce the jet flap and tangential slots for circu lation control.
  • FIGS. 2a-2d relate to FIG. 1 and shows cross-sections of the blade of FIG. 1 at various distances along the blade length.
  • FIGS. 3a and 3b are cross-sectional views of the blade showing other possible arrangements of the slots, according to the principles of this invention.
  • FIGS. 4a-4c show the relative wind profile across the blades of FIG. 1.
  • FIG. 5 shows the blade of FIG. 1 with sectioned slots for increasing the control over blade lift.
  • FIG. 6 is a top view of the blade of FIG. 1 with slots arranged to be overlapping on one edge for increasing the control over blade lift.
  • FIG. 1 a blade is shown connected to a hub for rotation and having tangential slots for circulation control blowing as seen.
  • Blade 11 is attached for rotation to hub 13.
  • a second matching rotor 10, partially shown, is attached to hub 13, l out of phase with rotor 11.
  • Conduits 15 within hub 13, supply air for circulation control blowing to blades 10 and 11, respectively.
  • a slot 19 extending from the hub 13 for a portion of the distance along the length of the blade. Slot 19 is substantially parallel to the longitudinal axis of blade 11.
  • a second slot 21 is arranged substantially parallel to the longitudinal axis of the rotor between the trailing edge 20 and slot 19 and below slot 19 relative to the top surface of the blade 11. Slot 21 extends from the hub 13 to the tip of the blade, marked by stage D.
  • a slot 23 substantially parallel to the longitudinal axis of the blade II and on its underside, adjacent to the edge 22 extends from the blade tip a partial distance of the length of rotor 11 towards the hub 13.
  • Additional slots 26 and 27 are arranged substantially parallel to the longitudinal axis of blade 11 and are located on edge 22 of blade I1. Slot 26 extends from the hub a partial distance along the length of blade 11 and slot 27 extends from the hub 13 along the length of edge 22. It can be seen as blade 11 rotates in the direction of arrow 25, slots 21 and 19 will become leading edge slots in relation to the free stream velocity, while slot 27 will become a trailing edge slot. With blade 11, as shown in FIG. 1, edge 20 is trailing and edge 22 is leading with respect to the direction of the free stream velocity.
  • a motor (not shown) is connected to hub 13 to rotate blade 11 and its matching blade 10.
  • This motor can be any suitable type and need not necessarily be attached or drive the rotor through the hub 13 and may be a jet of air blown outward from the rotor along an area adjacent the top of the rotor blade.
  • FIG. 2 cross-sections of the blade 11 at stages A, B, C and D are shown.
  • the cross-sectional shape of the blade 11 at its root at stage A is acambered and substantially elliptical air foil with blunt edges 22 and 20, tangential slots 26 and 27 along one edge and tangential slots 19 and 21 along the other edge and with a typical air foil, being 50 percent thick at stage A and 30 percent at stage B.
  • the section at stage C is shown at FIG. 20, is in the shape of a cambered and substantially elliptical airfoil with slots 27 and 21 disposed on the opposite edges 22 and 20 respectively, and with the thickness of the blade narrowed to approximately 15 percent while FIG. 2d shows the tip of the rotor at stage D narrowed to percent with slot 21 in edge and 27 in the opposite edge 22 with jet slot 23 in the under side of blade 1 1 adjacent edge 22 for producing a jet flap.
  • Plenum chamber 1 supplies air for tangential slot 27.
  • Plenum chamber 2 similarly provides air for tangential slots 19 and 21.
  • Plenum chamber 3 provides air for jet flap slot 23.
  • Air for the three plenum chambers 1, 2 and 3 is provided through conduit 15, mounted within the hub 13 and connected to control box 17.
  • Control box 17 contains a series of valves, is tied in with the pilots controls, and modulates the air supplied to the plenum chambers in a functional relationship to the azimuth position of the blade, as will be explained in the following.
  • Conduit l5 and control box 17, may be any suitable and known means for supplying air to the rotating blade.
  • FIG. 3a shows a blade 31 in cross-section with a double plenum chamber having tangential slots 33 and 35 arranged in each blunt edge and designed to tangentially blow air around each blunt edge.
  • a jet slot 34 may be included in this rotor blade.
  • rotor 37 contains a double plenum chamber with the tangential slot 39 arranged in one blunt edge and the other edge having a jet flap slot arranged in the under side of the rotor.
  • the operation of the blade will be explained in reference to the angular or azimuth position of the blade, relative to the fore-aft line of the helicopter fuselage.
  • the helicopter is in a vector direction, 180 opposite to the free stream velocity direction.
  • Blade 11 is rotating in the direction of arrow and as shown in FIG. 1, is in the retreating position relative to helicopter forward motion.
  • the free stream velocity vector is as shown by the arrow in FIG. 1.
  • the zero azimuth position is designated as the position where blade 11 is aligned in the fore-aft direction of the helicopter fuselage and with rotor 11 extending from the hub towards the aft portion of the helicopter fuselage.
  • the 90 azimuth position of the helicopter rotor 11 would then be with rotor 11,-perpendicular to the fore-aft line of the fuselage and extending from the hub away from the.
  • the 180 position of the rotor blade 11 would be with rotor blade extending from the hub assembly to the forward part of the fuselage and with the tip pointed into the vector of the free stream velocity, the 270 position would be with the rotor 11 perpendicular to the fore-aft line of the fuselage and extending from the hub assembly away from the starboard side of the helicopter fuselage.
  • Air pressure to plenum 2 is cutoff while the air supply to plenum 1 and 3 is pressurized, forcing air out tangential slots 26 and 27, causing it to flow along the trailing edge 22. Pressure within plenum chamber 1 is maintained through 360 of blade rotation. As the free stream velocity is zero at hover, edge 20 will always be the trailing edge.
  • a thin sheet of air will be blown out slots 26 and 27.
  • the thin sheet having a uniform velocity along its length and a uniform density.
  • the thin sheet of air produced by the tangential blowing adheres to the blunt trailing edge 22, curving around the edge and detaching itself from the blade at some point below the trailing edge determined by the intensity of blowing.
  • Circulation control around the trailing edge 22, through tangential blowing results in increased lift on rotor 11.
  • Matching blade 10, arranged to rotate with blade 11 would be similarly ducted and circulation control would be similarly maintained over the trailing edge of blade 10, to balance the lift produced by blade 11.
  • the lift produced is proportional to the velocity of the jet issuing out of the tangential slot.
  • the effect of the tangential blowing is to relocate the stagnation stream lines further aft along the blade and to increase the pressure distribution along the top surface of the blade so that the overall lift along the blade is increased.
  • Air blown out of slot 23 produces ajet flap at the tip of blade 11 and relocates the stagnation stream line further aft, at the tip area.
  • FORWARD FLIGHT In forward flight all plenum chambers are cyclically pressurized. In forward flight, the free stream velocity over the rotors is 'a value greater than zero. In conventional helicopters, the blade 11 produces a greater lift in the first and second quadrants than is produced in the third and fourth quadrants. In the first and second quadrants the relative wind over the advancing blade is in the direction of the free stream velocity and produces a higher lift than when the blade is retreating in the third and fourth quadrant and the relative wind is negative over a portion of the blade.
  • the lift in quadrants 3 and 4 is increased by blowing air out through slots 19 and 21 when edge 20 becomes the trailing edge relative to the free stream velocity.
  • the lift on the rotor in quadrants 3 and 4 will be proportional to the ratio of the tangential slot jet velocity to the free stream velocity.
  • the relative wind across the blade will depend upon the quadrant in which the blade is moving and with the distance along the blade from the hub.
  • the relative velocity along the rotor blades is shown by the envelope 60 connected to the relative wind vectors across the advancing blade 61 and the retreating blade 63.
  • the advancing blade is at the 90 position and the retreating blade is in the 270 position.
  • reverse wind denoted by arrow 69 is being experienced along the retreating blade between points 65 and 67.
  • Point 67 being the axis of rotation with an increase in free stream velocity
  • the distance along the retreating rotor experiencing reverse flow denoted by the distance between points 71 and 67, is increased.
  • FIG. 4c for a maximum free stream velocity and a maximum forward helicopter velocity the reverse flow is experienced along the entire length of the retreating blade 63.
  • the intensity of the blown air through the slots is modulated with respect to the azimuth position of the blade, as expressed by the following relationship.
  • Intensity A Sin x B Cos x A, Sin, x 8,, Cos, A Sin x+B Cos x+. ..A,,Sin,,x+B,,Cos,, Where A 14 ,11 A, and
  • B 8,, I3,, 8,, are constants and x is the azimuth angle of blade 11.
  • the modulated blowing related to the blade angle and its harmonics, reduces vibration and decreases rotational power requirements.
  • the blowing and the blade lift may be further controlled by blowing air only over the length of edge 20, experiencing negative relative flow, while restricting the blowing to over that portion of edge 22, not in negative flow. This can easily be accomplished by utilizing pressure transducers 34 and 36, placed along edge 20, and'dividing slot 27 into two distinct slots 35 and 37, as shown in FIG. 5, separated by stage B by divider 32. Each slot, 35 and 27, is separately supplied with air.
  • the pressure transducers 34 and 36 are placed on edge 20 and are tied into air control 17.
  • the transducer will signal an absence of positive air pressure to control '17.
  • Control 17 responsive to transducer 34 then will cut off the supply of air to slot 26 and slot section 35 and supply air'to slot 19.
  • the portion of blade 11 experiencing negative relative wind extends to transducer 36, itwill signal an absence of positive air pressure to control 17, causing control 17 to cut off the supply of air to slot section 37 and to supply air to slot 21.
  • the lift on the blade in quadrants 3 and 4 can be more precisely controlled by blowing air over the portion of edge 20 experiencing negative relative flow while supplying air to the portion of edge 22 not in negative relative flow.
  • FIG. 6 it is shown how this control concept can be extended by increasing the number of slots on edge 20, each slot extending from hub 13, a unique distance along the length of the blade 11 and sectioning the slots on edge 22 to correspond to the lengths of each slot on edge 20.
  • blade 11 is shown in a top view as having slots 41, 43 and 45, each slot extending for a unique length along edge 20.
  • One slot 47 is shown on edge 22, sectioned by dividers 55 and 57 into distinct slot sections 49, 51 and 53.
  • dividers 55 and 57 are opposite the ends of slots 41 and 43, respectively, so the length of slot 49 corresponds to the length of slot 41, the combined length of slot 49 and 51 corresponds to the length of slot 43 and the combined length of slots 49, 51 and 53 corresponds to the length of slot 45.
  • Pressure transducers 61, 63 and 65 are tied to control box 17 and sense an absence of positive air pressure corresponding to negative relative wind. The control box 17, in response to the signals received from the pressure transducers controls the air to the slots.
  • transducer 61 When the negative relative wind extends along a small length of blade 11, as in FIG. 40, only transducer 61 will sense an absence of positive air pressure. Control 17, is response to the transducer signal, will cut off the supply of air to slot 49 and supply air to slot 41. When the portion of blade 11 experiencing negative relative wind increases, as shown in FIG. 4b, transducer 63, will sense an absence of positive air pressure causing air to be cut off from slots 49 andSl and causing air to be supplied to slots 41 and 43. Similarly, when the length of blade 11 is experiencing negative relative wind, as shown in FIG.
  • transducer 65 senses an absence of positive air pressure and causes air to be cut off slots 49, 51 and 53 and causes air to be supplied to slots 41, 43 and 45. As slots 41, 43 and 45 overlap, causing the air flow to combine in the overlapped portions, the intensity of blowing will be proportional to the intensity of the negative relative wind along the length of blade 11.
  • plenum chambers 1 and 2 are shown, for the helicopter rotor 11, additional slots of varying length can be added and plenum chambers 1 and 2 can be additionally subdivided to separately maintain air supplies to the additional slots as may be desirable to more accurately control the lift along the blades.
  • the pressure transducers can be used which can sense the magnitude of the negative relative wind and control 17,. responsive to the magnitude sensed, can proportionally control the intensity of blowing.
  • a circulation control helicopter -rotor blade system for varying blade lift through a cycle of rotation, comprising:
  • a rotor blade having a cambered and substantially elliptical air foil shape and blunt edges;
  • one of said blunt edges being a leading edge relative to blade rotation and the other blunt edge being a trailing edge relative to blade rotation;
  • said trailing edge having at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge;
  • control means connected to said rotor blade to control the intensity of blown fluid from said slot for varying the blade lift through a cycle of rotation;
  • control means including a first means for modulating the intensity of said blown fluid at a first fundamental frequency equal to the frequency of rotor rotation and at harmonic frequencies of the fundamental frequency;
  • I is the unmodulated blowing intensity
  • a A A, and 8,, B B, are constants
  • x is the azimuth angle of rotation with the blade zero azimuth angle position being the polistion where the blade is parallel with the fore-aft line of the helicopterand with the blade extending aft from the root.
  • said leading edge has at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge; said tangentially blown fluid adhering to the leading edge curving down and around said blunt edge and detaching from the rotor at a point on its underside I functionally related to the intensity of the blowing;- said control means blows fluid outisaid slot during the interval within a cycle of rotation when said blade is in a retreating position relative to the freestream velocity; and 7 said control means includes means for deriving said fluid blown out said leading edge slot, from said modulated fluid flow supply for said trailing edge 3.
  • l li system of claim 2 including:
  • control means including means for shutting off the modulated fluid flow to said trailing edge and connecting the modulated fluid flow to said leading edge in response to said sensing means sensing negative relative wind.
  • said means for connecting the fluid flow to said leading edge controls the intensity of said blowing from said leading edge slot in proportion to the magnitude of the relative wind component sensed by said sensing means.

Abstract

The rotating blades on a helicopter are in the shape of a cambered elliptical airfoil with blunt edges. A plurality of slots are employed on the upper surface of the air foil to blow a thin sheet of air tangentially across the surface of the foil and around the trailing edge. Circulation control is achieved by the tangential blowing as the sheet of air adheres to the surface and travels around the trailing edge, detaching beneath the trailing edge at a location determined by the intensity of blowing. The effect of the tangential blowing is relocation of the stagnation stream lines producing increased lift on the foil. The air supplied to the slots is modulated with respect to the azimuth position of the rotor and the speed of the rotating blade so that cyclic control over the lift of the rotor can be accomplished without altering the blade attitude.

Description

Williams n 1 3,713,750 1 Jan. 30, 1973 CIRCULATION CONTROL ROTOR SYSTEM [75] Inventor: Robert M. Williams, Chantilly, Va.
[73]- Assignee: The United States of America as represented by the Secretary of the Navy [22] Filed: Dec. 7,1970
[21] Appl. No.: 95,643
[52] US. Cl ..4l6/20, 416/90 [51] Int. Cl ..B64c 27/72 [58] Field of Search ..4l6/20, 90
[56] References Cited UNITED STATES PATENTS 2,759,548 8/1956 Yuan et al. ..416/20 3,062,483 11/1962 Davidson ..416/90 A 3,139,936 7/1964 Davidson et al. ..416/90 A 2,925,129 2/1960 Yuan et al. ..416/90 A 3,524,711 8/1970 Cheeseman et al. ..4l6/20 3,567,332 3/1971 Seed ..4l6/90 FOWARD PORT STAR BORD AFT 3,588,273 6/1971 Kizilos ..416/20 Primary Examiner-Everette A. Powell, Jr.
Atl0rrteyR. S. Sciascia and Q, E. Hodges 1 1 ABSTRACT The rotating blades on a helicopter are in the shape of a cambered elliptical airfoil with blunt edges. A plurality of slots are employed on the upper surface of the airfoil to blow a thin sheet of air tangentially across the surface of the foil and around the trailing edge. Circulation control is achieved by the tangential blowing as the sheet of air adheres to the surface and travels around the trailing edge, detaching beneath the trailing edge at a location determined by the intensity of blowing. The effect of the tangential blowing is relocation of the stagnation stream lines producingincreased lift on the foil. The air supplied to the slots is modulated with respect to the azimuth position of the rotor and the speed of the rotating blade so that cyclic control over the lift of the rotor can be accomplished without altering the blade attitude.
4 Claims, 12 Drawing Figures PATENTEDJAN 30 I975 SHEET 1 OF 3 u HF I HHUI L .rmOm
INVENTOR. ROBERT M. WILL/4M5 A 'r ran/v5 r WIND - RELATIVE PAIENIEnmaoms 3.713.750 sum 2 OF 5 FIG. 3a.
FIG. 3b;
DIRECTION OF ROTATION e7 ADVANCING BLADE 4a RETREATING BLADE IN V EN TOR. ROBE T M. W/L L IAMS [WWW ATTORNEY CIRCULATION CONTROL ROTOR SYSTEM The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
DESCRIPTION OF THE PRIOR'ART The conventional means for altering the lift of helicopter blade is to cyclically alter the blade angle of attack and the blade speed. This has been accomplished by mechanical means, introducing extreme mechanical complexity and increased dynamic weight. Other methods use cylindrical air foils with circulation control or lifting foils combined with a blown jet flap. However, the cylindrical foil and jet flap concepts are limited and cannot attain the efficiency of the circulation control rotor which is capable of higher lift coefficients and higher lift to drag ratios.
SUMMARY OF THE INVENTION The rotating blades in a helicopter are formed from a basic air foil shape selected from potential flow theory calculations and may be cambered elliptical shape, having a blunt or rounded leading and trailing edge. A number of slots are disposed in a line substantially parallel to the edge and adjacent the edge. As the blade is rotated air is blown out these slots in a thin sheet. The thin sheet adheres to the trailing edge and remains attached, by the Coanda effect, until it reaches the separation point on the blade under side, beneath the trailing edge. The point of separation beneath the trailing edge is determined by the intensity of blowing. The effect of the circulation control is to relocate the stagnation stream lines and produce a higher lift on the foil, the lift on the air foil being functionally related to the ratio of the velocity of the blown air to the free stream velocity blowing over the rotating wing.
In addition, the air blown through the slots and ove the trailing edge is modulated proportionally to the sine and cosine of the rotor azimuth angle and at harmonics thereof to permit the rotor to distribute the lift cyclically in any desired manner, and toreduce power consumption and vibration.
Each blade tapers from a predetermined thickness at its root to a more narrow thickness at its tip. In addition, the cross-section of the rotor is structured with a plurality of individual plenum chambers to supply air to each of the slots. The plenum chambers supply air to the upper blade surface to produce the tangential flow as needed on leading and trailing edges and to a slot on the underside of the blade, producing a jet flap or blown flap so the effects of the blown flap and circulation control tangential flow may be combined to produce the widest variation in lift on the rotor.
DESCRIPTION OF THE DRAWINGS FIG. I shows a rotor system according to the principles of this invention, mounted for rotation on a hub, having a slot on the underside of the rotor adjacent its tip to produce the jet flap and tangential slots for circu lation control.
FIGS. 2a-2d relate to FIG. 1 and shows cross-sections of the blade of FIG. 1 at various distances along the blade length.
FIGS. 3a and 3b are cross-sectional views of the blade showing other possible arrangements of the slots, according to the principles of this invention.
FIGS. 4a-4c show the relative wind profile across the blades of FIG. 1.
FIG. 5 shows the blade of FIG. 1 with sectioned slots for increasing the control over blade lift.
FIG. 6 is a top view of the blade of FIG. 1 with slots arranged to be overlapping on one edge for increasing the control over blade lift.
DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to FIG. 1, a blade is shown connected to a hub for rotation and having tangential slots for circulation control blowing as seen.
Blade 11 is attached for rotation to hub 13. A second matching rotor 10, partially shown, is attached to hub 13, l out of phase with rotor 11. Conduits 15 within hub 13, supply air for circulation control blowing to blades 10 and 11, respectively. Arranged on blade 11 is a slot 19 extending from the hub 13 for a portion of the distance along the length of the blade. Slot 19 is substantially parallel to the longitudinal axis of blade 11. A second slot 21 is arranged substantially parallel to the longitudinal axis of the rotor between the trailing edge 20 and slot 19 and below slot 19 relative to the top surface of the blade 11. Slot 21 extends from the hub 13 to the tip of the blade, marked by stage D. A slot 23 substantially parallel to the longitudinal axis of the blade II and on its underside, adjacent to the edge 22 extends from the blade tip a partial distance of the length of rotor 11 towards the hub 13. Slot 23, connected to conduit 15, produces a jet flap when air is expelled through it. Additional slots 26 and 27 are arranged substantially parallel to the longitudinal axis of blade 11 and are located on edge 22 of blade I1. Slot 26 extends from the hub a partial distance along the length of blade 11 and slot 27 extends from the hub 13 along the length of edge 22. It can be seen as blade 11 rotates in the direction of arrow 25, slots 21 and 19 will become leading edge slots in relation to the free stream velocity, while slot 27 will become a trailing edge slot. With blade 11, as shown in FIG. 1, edge 20 is trailing and edge 22 is leading with respect to the direction of the free stream velocity.
A motor (not shown) is connected to hub 13 to rotate blade 11 and its matching blade 10. This motor can be any suitable type and need not necessarily be attached or drive the rotor through the hub 13 and may be a jet of air blown outward from the rotor along an area adjacent the top of the rotor blade.
Referring now to FIG. 2, cross-sections of the blade 11 at stages A, B, C and D are shown. As shown in FIGS. 2a and 2b, the cross-sectional shape of the blade 11 at its root at stage A is acambered and substantially elliptical air foil with blunt edges 22 and 20, tangential slots 26 and 27 along one edge and tangential slots 19 and 21 along the other edge and with a typical air foil, being 50 percent thick at stage A and 30 percent at stage B. The section at stage C is shown at FIG. 20, is in the shape of a cambered and substantially elliptical airfoil with slots 27 and 21 disposed on the opposite edges 22 and 20 respectively, and with the thickness of the blade narrowed to approximately 15 percent while FIG. 2d shows the tip of the rotor at stage D narrowed to percent with slot 21 in edge and 27 in the opposite edge 22 with jet slot 23 in the under side of blade 1 1 adjacent edge 22 for producing a jet flap.
Extending the length of rotor 11 and dividing it into three plenum chambers is a continuous divider struc' ture 29. Plenum chamber 1 supplies air for tangential slot 27. Plenum chamber 2 similarly provides air for tangential slots 19 and 21. Plenum chamber 3 provides air for jet flap slot 23. Air for the three plenum chambers 1, 2 and 3 is provided through conduit 15, mounted within the hub 13 and connected to control box 17. Control box 17 contains a series of valves, is tied in with the pilots controls, and modulates the air supplied to the plenum chambers in a functional relationship to the azimuth position of the blade, as will be explained in the following. Conduit l5 and control box 17, may be any suitable and known means for supplying air to the rotating blade.
Referring now to FIG. 3, wherein is shown other possible arrangements of slots and plenum chambers within the rotor. FIG. 3a shows a blade 31 in cross-section with a double plenum chamber having tangential slots 33 and 35 arranged in each blunt edge and designed to tangentially blow air around each blunt edge. In addition, a jet slot 34 may be included in this rotor blade. In FIG. 3b, rotor 37 contains a double plenum chamber with the tangential slot 39 arranged in one blunt edge and the other edge having a jet flap slot arranged in the under side of the rotor.
OPERATION The operation of the blade will be explained in reference to the angular or azimuth position of the blade, relative to the fore-aft line of the helicopter fuselage. For explanation purposes, it is assumed the helicopter is in a vector direction, 180 opposite to the free stream velocity direction. Blade 11 is rotating in the direction of arrow and as shown in FIG. 1, is in the retreating position relative to helicopter forward motion. The free stream velocity vector is as shown by the arrow in FIG. 1. The zero azimuth position is designated as the position where blade 11 is aligned in the fore-aft direction of the helicopter fuselage and with rotor 11 extending from the hub towards the aft portion of the helicopter fuselage. The 90 azimuth position of the helicopter rotor 11 would then be with rotor 11,-perpendicular to the fore-aft line of the fuselage and extending from the hub away from the.
port side of the helicopter, the 180 position of the rotor blade 11 would be with rotor blade extending from the hub assembly to the forward part of the fuselage and with the tip pointed into the vector of the free stream velocity, the 270 position would be with the rotor 11 perpendicular to the fore-aft line of the fuselage and extending from the hub assembly away from the starboard side of the helicopter fuselage.
HOVER OPERATION First, the operation of the blades will be explained in reference to a hovering condition where the free stream velocity is zero. In hovering, the free stream is equal to zero, the relative wind velocity over the helicopter blade 11 in each quadrant is constant, the first quadrant being zero to 90, the second quadrant being to the third quadrant being 180 to 270 and the fourth quadrant being 270 to 360 of rotor 11 rotation.
Air pressure to plenum 2 is cutoff while the air supply to plenum 1 and 3 is pressurized, forcing air out tangential slots 26 and 27, causing it to flow along the trailing edge 22. Pressure within plenum chamber 1 is maintained through 360 of blade rotation. As the free stream velocity is zero at hover, edge 20 will always be the trailing edge. I
In the hover condition, a thin sheet of air will be blown out slots 26 and 27. The thin sheet having a uniform velocity along its length and a uniform density. The thin sheet of air produced by the tangential blowing adheres to the blunt trailing edge 22, curving around the edge and detaching itself from the blade at some point below the trailing edge determined by the intensity of blowing.
Circulation control around the trailing edge 22, through tangential blowing results in increased lift on rotor 11. Matching blade 10, arranged to rotate with blade 11 would be similarly ducted and circulation control would be similarly maintained over the trailing edge of blade 10, to balance the lift produced by blade 11. The lift produced is proportional to the velocity of the jet issuing out of the tangential slot. The effect of the tangential blowing is to relocate the stagnation stream lines further aft along the blade and to increase the pressure distribution along the top surface of the blade so that the overall lift along the blade is increased.
Air blown out of slot 23 produces ajet flap at the tip of blade 11 and relocates the stagnation stream line further aft, at the tip area.
FORWARD FLIGHT In forward flight all plenum chambers are cyclically pressurized. In forward flight, the free stream velocity over the rotors is 'a value greater than zero. In conventional helicopters, the blade 11 produces a greater lift in the first and second quadrants than is produced in the third and fourth quadrants. In the first and second quadrants the relative wind over the advancing blade is in the direction of the free stream velocity and produces a higher lift than when the blade is retreating in the third and fourth quadrant and the relative wind is negative over a portion of the blade. In this forward flight condition to equalize the higher lifting forces produced when the blade is in quadrants l and 2 with the lower lifting forces produced when the blade is in quadrants 3 and 4, the lift in quadrants 3 and 4 is increased by blowing air out through slots 19 and 21 when edge 20 becomes the trailing edge relative to the free stream velocity. The lift on the rotor in quadrants 3 and 4 will be proportional to the ratio of the tangential slot jet velocity to the free stream velocity.
As shown in FIG. 4, the relative wind across the blade will depend upon the quadrant in which the blade is moving and with the distance along the blade from the hub.
As shown in FIG. 4a, the relative velocity along the rotor blades is shown by the envelope 60 connected to the relative wind vectors across the advancing blade 61 and the retreating blade 63. The advancing blade is at the 90 position and the retreating blade is in the 270 position. As shown, reverse wind denoted by arrow 69 is being experienced along the retreating blade between points 65 and 67. Point 67 being the axis of rotation with an increase in free stream velocity, as shown in FIG. 4b, the distance along the retreating rotor experiencing reverse flow, denoted by the distance between points 71 and 67, is increased. While as shown in FIG. 4c, for a maximum free stream velocity and a maximum forward helicopter velocity the reverse flow is experienced along the entire length of the retreating blade 63. Where reverse flow occurs, the lift along the blade will be decreased proportionally to the distance along the blade experiencing reverse flow. As this condition of reverse flow becomes excessive, the lift in quadrants 3 and 4 of blade 11 will be reduced to the point where a couple develops to rotate the helicopter about its longitudinal center line resulting in a flipping of the helicopter. However, with circulation control through tangential blowing, lift is increased on the blade, in quadrants 3 and 4 by blowing along the blade approximately where the reverse flow is occuring. Where the free stream velocity is relatively low as shown in FIG. 4a and the reverse flow occurs between the rotating hub and a point short distance from the rotating hub, the slot 19 is used independently to blow over the inside portion of the rotor and increase the lift over that portion. As the free stream velocity increases, the reverse flow at any point along the retreating blade will be an increasing function of the free stream velocity and will be inversely propor tional to its distance from the hub 13. As shown in FIG. 4c, where a relative wind across the retreating blade causes the retreating blade to be completely in reverse flow, the reverse flow will be maximum at the hub and in this condition, tangential slots 19 and 21 are used together to increase the lift on the retreating blade, the flow from slots 19 and 21 combine to maximize the blowing intensity when the reverse flow magnitude is greatest. In forward flight, to maximize the lift on the blade through a full cycle of rotation, air is cyclically blown through slots 26, 27 and 23 when the blade 11 is in the first and second quadrants and air is cyclically blown through slots 19 and 21, where the blade is experiencing reverse flow in the third and fourth quadrants.
The intensity of the blown air through the slots, is modulated with respect to the azimuth position of the blade, as expressed by the following relationship. Intensity A, Sin x B Cos x A, Sin, x 8,, Cos, A Sin x+B Cos x+. ..A,,Sin,,x+B,,Cos,, Where A 14 ,11 A, and
B 8,, I3,, 8,, are constants and x is the azimuth angle of blade 11.
The modulated blowing, related to the blade angle and its harmonics, reduces vibration and decreases rotational power requirements.
The blowing and the blade lift may be further controlled by blowing air only over the length of edge 20, experiencing negative relative flow, while restricting the blowing to over that portion of edge 22, not in negative flow. This can easily be accomplished by utilizing pressure transducers 34 and 36, placed along edge 20, and'dividing slot 27 into two distinct slots 35 and 37, as shown in FIG. 5, separated by stage B by divider 32. Each slot, 35 and 27, is separately supplied with air.
The pressure transducers 34 and 36, are placed on edge 20 and are tied into air control 17. When blade 11 experiences negative relative wind at transducer 34, the transducer will signal an absence of positive air pressure to control '17. Control 17 responsive to transducer 34 then will cut off the supply of air to slot 26 and slot section 35 and supply air'to slot 19. When the portion of blade 11 experiencing negative relative wind extends to transducer 36, itwill signal an absence of positive air pressure to control 17, causing control 17 to cut off the supply of air to slot section 37 and to supply air to slot 21. In this described manner, the lift on the blade in quadrants 3 and 4 can be more precisely controlled by blowing air over the portion of edge 20 experiencing negative relative flow while supplying air to the portion of edge 22 not in negative relative flow. Referring now to FIG. 6, it is shown how this control concept can be extended by increasing the number of slots on edge 20, each slot extending from hub 13, a unique distance along the length of the blade 11 and sectioning the slots on edge 22 to correspond to the lengths of each slot on edge 20. In FIG. 6, blade 11 is shown in a top view as having slots 41, 43 and 45, each slot extending for a unique length along edge 20. One slot 47 is shown on edge 22, sectioned by dividers 55 and 57 into distinct slot sections 49, 51 and 53. The position of dividers 55 and 57 are opposite the ends of slots 41 and 43, respectively, so the length of slot 49 corresponds to the length of slot 41, the combined length of slot 49 and 51 corresponds to the length of slot 43 and the combined length of slots 49, 51 and 53 corresponds to the length of slot 45. Pressure transducers 61, 63 and 65 are tied to control box 17 and sense an absence of positive air pressure corresponding to negative relative wind. The control box 17, in response to the signals received from the pressure transducers controls the air to the slots.
Referring now to FIG. 4, the control of tangential blowing along the length of blade 11 is described. When the negative relative wind extends along a small length of blade 11, as in FIG. 40, only transducer 61 will sense an absence of positive air pressure. Control 17, is response to the transducer signal, will cut off the supply of air to slot 49 and supply air to slot 41. When the portion of blade 11 experiencing negative relative wind increases, as shown in FIG. 4b, transducer 63, will sense an absence of positive air pressure causing air to be cut off from slots 49 andSl and causing air to be supplied to slots 41 and 43. Similarly, when the length of blade 11 is experiencing negative relative wind, as shown in FIG. 40, transducer 65 senses an absence of positive air pressure and causes air to be cut off slots 49, 51 and 53 and causes air to be supplied to slots 41, 43 and 45. As slots 41, 43 and 45 overlap, causing the air flow to combine in the overlapped portions, the intensity of blowing will be proportional to the intensity of the negative relative wind along the length of blade 11.
Although three slots and three plenum chambers are shown, for the helicopter rotor 11, additional slots of varying length can be added and plenum chambers 1 and 2 can be additionally subdivided to separately maintain air supplies to the additional slots as may be desirable to more accurately control the lift along the blades.
In addition, the pressure transducers can be used which can sense the magnitude of the negative relative wind and control 17,. responsive to the magnitude sensed, can proportionally control the intensity of blowing.
Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.
What is claimed is:
1. A circulation control helicopter -rotor blade system, for varying blade lift through a cycle of rotation, comprising:
a rotor blade having a cambered and substantially elliptical air foil shape and blunt edges;
one of said blunt edges being a leading edge relative to blade rotation and the other blunt edge being a trailing edge relative to blade rotation;
said trailing edge having at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge;
said tangentially blown fluid adhering to said trailing edge, cu'rving'down and around said blunt edge and detaching from the rotor at a point on its un-. derside functionally related to the intensity of the blowing;
control means connected to said rotor blade to control the intensity of blown fluid from said slot for varying the blade lift through a cycle of rotation;
said control means including a first means for modulating the intensity of said blown fluid at a first fundamental frequency equal to the frequency of rotor rotation and at harmonic frequencies of the fundamental frequency;
second means for combining the blown fluid modulated at the fundamental frequency with the blown fluid modulated at harmonics of the fundamental, to produce a resultant blown fluid flow from said slot, described by the relationship:
l(A,sin x B cos X A sin 2x'+ B cos 2x A,,sin nx B cos nx).
where I is the unmodulated blowing intensity; A A A, and 8,, B B, are constants; and x is the azimuth angle of rotation with the blade zero azimuth angle position being the polistion where the blade is parallel with the fore-aft line of the helicopterand with the blade extending aft from the root. 2. The system of claim 1 wherein:
said leading edge has at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge; said tangentially blown fluid adhering to the leading edge curving down and around said blunt edge and detaching from the rotor at a point on its underside I functionally related to the intensity of the blowing;- said control means blows fluid outisaid slot during the interval within a cycle of rotation when said blade is in a retreating position relative to the freestream velocity; and 7 said control means includes means for deriving said fluid blown out said leading edge slot, from said modulated fluid flow supply for said trailing edge 3. l li system of claim 2 including:
means to sense negative relative wind, mounted on said blade and connected to said control means; and
said control means including means for shutting off the modulated fluid flow to said trailing edge and connecting the modulated fluid flow to said leading edge in response to said sensing means sensing negative relative wind.
4. The-system of claim 3 wherein:
said means for connecting the fluid flow to said leading edge controls the intensity of said blowing from said leading edge slot in proportion to the magnitude of the relative wind component sensed by said sensing means.

Claims (4)

1. A circulation control helicopter rotor blade system, for varying blade lift through a cycle of rotation, comprising: a rotor blade having a cambered and substantially elliptical air foil shape and blunt edges; one of said blunt edges being a leading edge relative to blade rotation and the other blunt edge being a trailing edge relative to blade rotation; said trailing edge having at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge; said tangentially blown fluid adhering to said trailing edge, curving down and around said blunt edge and detaching from the rotor at a point on its underside functionally related to the intensity of the blowing; control means connected to said rotor blade to control the intensity of blown fluid from said slot for varying the blade lift through a cycle of rotation; said control means including a first means for modulating the intensity of said blown fluid at a first fundamental frequency equal to the frequency of rotor rotation and at harmonic frequencies of the fundamental frequency; second means for combining the blown fluid modulated at the fundamental frequency with the blown fluid modulated at harmonics of the fundamental, to produce a resultant blown fluid flow from said slot, described by the relationship: I(A1sin Chi + B1cos Chi + A2sin 2 Chi + B2cos 2 Chi + . . . Ansin n Chi + Bncos n Chi ). where I is the unmodulated blowing intensity; A1, A2, . . . An and B1, B2, . . . Bn are constants; and Chi is the azimuth angle of rotation with the blade zero azimuth angle position being the polistion where the blade is parallel with the fore-aft line of the helicopter and with the blade extending aft from the root.
1. A circulation control helicopter rotor blade system, for varying blade lift through a cycle of rotation, comprising: a rotor blade having a cambered and substantially elliptical air foil shape and blunt edges; one of said blunt edges being a leading edge relative to blade rotation and the other blunt edge being a trailing edge relative to blade rotation; said trailing edge having at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge; said tangentially blown fluid adhering to said trailing edge, curving down and around said blunt edge and detaching from the rotor at a point on its underside functionally related to the intensity of the blowing; control means connected to said rotor blade to control the intensity of blown fluid from said slot for varying the blade lift through a cycle of rotation; said control means including a first means for modulating the intensity of said blown fluid at a first fundamental frequency equal to the frequency of rotor rotation and at harmonic frequencies of the fundamental frequency; second means for combining the blown fluid modulated at the fundamental frequency with the blown fluid modulated at harmonics of the fundamental, to produce a resultant blown fluid flow from said slot, described by the relationship: I(A1sin Chi + B1cos Chi + A2sin 2 Chi + B2cos 2 Chi + . . . Ansin n Chi + Bncos n Chi ). where I is the unmodulated blowing intensity; A1, A2, . . . An and B1, B2, . . . Bn are constants; and Chi is the azimuth angle of rotation with the blade zero azimuth angle position being the polistion where the blade is parallel with the fore-aft line of the helicopter and with the blade extending aft from the root.
2. The system of claim 1 wherein: said leading edge has at least one slot adjacent to said edge and shaped to tangentially blow fluid over said edge; said tangentially blown fluid adhering to the leading edge curving down and around said blunt edge and detaching from the rotor at a point on its underside functionally related to the intensity of the blowing; said control means blows fluid out said slot during the interval within a cycle of rotation when said blade is in a retreating position relative to the free-stream velocity; and said control means includes means for deriving said fluid blown out said leading edge slot, from said modulated fluid flow supply for said trailing edge slot.
3. The system of claim 2 including: means to sense negative relative wind, mounted on said blade and connected to said control means; and said control means including means for shutting off the modulated fluid flow to said trailing edge and connecting the modulated fluid flow to said leading edge in response to said sensing means sensing negative relative wind.
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Cited By (24)

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US3883266A (en) * 1973-09-24 1975-05-13 Jr Herman A Soulant Differential lift control by synchronous resonant excitation of air column in helicopter rotor
US3904313A (en) * 1973-11-05 1975-09-09 Henry J Bernaerts Higher harmonics hub valve
US3917435A (en) * 1974-01-11 1975-11-04 Joseph B Wilkerson Cam and nozzle control valve for fluid flow modulation
US3918833A (en) * 1974-01-11 1975-11-11 Warren H Eilertson Circulation control rotor hub using teacup cam and pushrod valves
US3990811A (en) * 1975-02-26 1976-11-09 The United States Of America As Represented By The Secretary Of The Navy Circulation controlled rotary wing aircraft and control system therefor
US4519563A (en) * 1974-12-13 1985-05-28 Tamura Raymond M Pollution reducing aircraft propulsion
US4555079A (en) * 1983-12-28 1985-11-26 The United States Of America As Represented By The Secretary Of The Air Force Multiple jet blowing around the blunt trailing edge of a circulation controlled airfoil
US4630997A (en) * 1981-11-24 1986-12-23 Fondation Cousteau Apparatus for producing a force when in a moving fluid
US4799859A (en) * 1985-11-06 1989-01-24 Dornier Gmbh Helicopter rotor blade control
US4966526A (en) * 1989-07-13 1990-10-30 United Technologies Corporation Mechanically actuated slot for circulation control rotor
US5281084A (en) * 1990-07-13 1994-01-25 General Electric Company Curved film cooling holes for gas turbine engine vanes
ES2074010A2 (en) * 1993-07-14 1995-08-16 Univ Pais Vasco Aerodynamic profiles of simple geometry
US5813625A (en) * 1996-10-09 1998-09-29 Mcdonnell Douglas Helicopter Company Active blowing system for rotorcraft vortex interaction noise reduction
US6234751B1 (en) 1997-06-05 2001-05-22 Mcdonnell Douglas Helicopter Co. Oscillating air jets for reducing HSI noise
US6478541B1 (en) 2001-08-16 2002-11-12 The Boeing Company Tapered/segmented flaps for rotor blade-vortex interaction (BVI) noise and vibration reduction
US6543719B1 (en) 1997-06-05 2003-04-08 Mcdonnell Douglas Helicopter Co. Oscillating air jets for implementing blade variable twist, enhancing engine and blade efficiency, and reducing drag, vibration, download and ir signature
US20080145219A1 (en) * 2006-12-13 2008-06-19 The Boeing Company Vortex generators on rotor blades to delay an onset of large oscillatory pitching moments and increase maximum lift
US20110211952A1 (en) * 2011-02-10 2011-09-01 General Electric Company Rotor blade for wind turbine
US20130168491A1 (en) * 2010-09-09 2013-07-04 Groen Brothers Aviation, Inc Mission-adaptive rotor blade with circulation control
US9120567B2 (en) * 2012-06-11 2015-09-01 Sikorsky Aircraft Corporation High speed compound rotary wing aircraft
US20160001881A1 (en) * 2011-07-11 2016-01-07 Groen Brothers Aviation, Inc Mission-adaptive rotor blade with circulation control
US9505492B2 (en) 2012-02-23 2016-11-29 Sikorsky Aircraft Corporation Mission adaptive rotor blade
US10703468B2 (en) 2015-09-17 2020-07-07 Sikorsky Aircraft Corporation Stress reducing holes
US11014661B2 (en) * 2016-10-24 2021-05-25 Sikorsky Aircraft Corporation Tip jet orifice for aircraft brown out mitigation

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Cited By (27)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3883266A (en) * 1973-09-24 1975-05-13 Jr Herman A Soulant Differential lift control by synchronous resonant excitation of air column in helicopter rotor
US3904313A (en) * 1973-11-05 1975-09-09 Henry J Bernaerts Higher harmonics hub valve
US3917435A (en) * 1974-01-11 1975-11-04 Joseph B Wilkerson Cam and nozzle control valve for fluid flow modulation
US3918833A (en) * 1974-01-11 1975-11-11 Warren H Eilertson Circulation control rotor hub using teacup cam and pushrod valves
US4519563A (en) * 1974-12-13 1985-05-28 Tamura Raymond M Pollution reducing aircraft propulsion
US3990811A (en) * 1975-02-26 1976-11-09 The United States Of America As Represented By The Secretary Of The Navy Circulation controlled rotary wing aircraft and control system therefor
US4630997A (en) * 1981-11-24 1986-12-23 Fondation Cousteau Apparatus for producing a force when in a moving fluid
US4555079A (en) * 1983-12-28 1985-11-26 The United States Of America As Represented By The Secretary Of The Air Force Multiple jet blowing around the blunt trailing edge of a circulation controlled airfoil
US4799859A (en) * 1985-11-06 1989-01-24 Dornier Gmbh Helicopter rotor blade control
US4966526A (en) * 1989-07-13 1990-10-30 United Technologies Corporation Mechanically actuated slot for circulation control rotor
US5281084A (en) * 1990-07-13 1994-01-25 General Electric Company Curved film cooling holes for gas turbine engine vanes
ES2074010A2 (en) * 1993-07-14 1995-08-16 Univ Pais Vasco Aerodynamic profiles of simple geometry
US5813625A (en) * 1996-10-09 1998-09-29 Mcdonnell Douglas Helicopter Company Active blowing system for rotorcraft vortex interaction noise reduction
US6234751B1 (en) 1997-06-05 2001-05-22 Mcdonnell Douglas Helicopter Co. Oscillating air jets for reducing HSI noise
US6543719B1 (en) 1997-06-05 2003-04-08 Mcdonnell Douglas Helicopter Co. Oscillating air jets for implementing blade variable twist, enhancing engine and blade efficiency, and reducing drag, vibration, download and ir signature
US6478541B1 (en) 2001-08-16 2002-11-12 The Boeing Company Tapered/segmented flaps for rotor blade-vortex interaction (BVI) noise and vibration reduction
US20080145219A1 (en) * 2006-12-13 2008-06-19 The Boeing Company Vortex generators on rotor blades to delay an onset of large oscillatory pitching moments and increase maximum lift
US7748958B2 (en) * 2006-12-13 2010-07-06 The Boeing Company Vortex generators on rotor blades to delay an onset of large oscillatory pitching moments and increase maximum lift
US20130168491A1 (en) * 2010-09-09 2013-07-04 Groen Brothers Aviation, Inc Mission-adaptive rotor blade with circulation control
US9004394B2 (en) * 2010-09-09 2015-04-14 Groen Brothers Aviation, Inc. Mission-adaptive rotor blade with circulation control
US20110211952A1 (en) * 2011-02-10 2011-09-01 General Electric Company Rotor blade for wind turbine
US20160001881A1 (en) * 2011-07-11 2016-01-07 Groen Brothers Aviation, Inc Mission-adaptive rotor blade with circulation control
US9637229B2 (en) * 2011-07-11 2017-05-02 Groen Aeronautics Corporation Mission-adaptive rotor blade with circulation control
US9505492B2 (en) 2012-02-23 2016-11-29 Sikorsky Aircraft Corporation Mission adaptive rotor blade
US9120567B2 (en) * 2012-06-11 2015-09-01 Sikorsky Aircraft Corporation High speed compound rotary wing aircraft
US10703468B2 (en) 2015-09-17 2020-07-07 Sikorsky Aircraft Corporation Stress reducing holes
US11014661B2 (en) * 2016-10-24 2021-05-25 Sikorsky Aircraft Corporation Tip jet orifice for aircraft brown out mitigation

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