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WO1992013758A1 - Profile aerodynamique elastique souple module - Google Patents

Profile aerodynamique elastique souple module Download PDF

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Publication number
WO1992013758A1
WO1992013758A1 PCT/US1992/000835 US9200835W WO9213758A1 WO 1992013758 A1 WO1992013758 A1 WO 1992013758A1 US 9200835 W US9200835 W US 9200835W WO 9213758 A1 WO9213758 A1 WO 9213758A1
Authority
WO
WIPO (PCT)
Prior art keywords
airfoil
wing
pivot axis
trailing edge
leading edge
Prior art date
Application number
PCT/US1992/000835
Other languages
English (en)
Inventor
Sheila E. Widnall
William S. Widnall
Jeffrey T. Evernham
William E. Gorgen
Original Assignee
Flex Foil Technology, Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Flex Foil Technology, Inc. filed Critical Flex Foil Technology, Inc.
Publication of WO1992013758A1 publication Critical patent/WO1992013758A1/fr

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C3/00—Wings
    • B64C3/38—Adjustment of complete wings or parts thereof
    • B64C3/44—Varying camber
    • B64C3/48—Varying camber by relatively-movable parts of wing structures
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B41/00—Drop keels, e.g. centre boards or side boards ; Collapsible keels, or the like, e.g. telescopically; Longitudinally split hinged keels
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C11/00—Propellers, e.g. of ducted type; Features common to propellers and rotors for rotorcraft
    • B64C11/30—Blade pitch-changing mechanisms
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B39/00—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude
    • B63B39/06—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude to decrease vessel movements by using foils acting on ambient water
    • B63B2039/063—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude to decrease vessel movements by using foils acting on ambient water the foils comprising flexible portions
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T50/00—Aeronautics or air transport
    • Y02T50/10—Drag reduction

Definitions

  • the present invention provides a flexible elastic airfoil section that adapts its shape to loading requirements, and a finite wing or blade made up of such airfoil sections, that obtains a substantial portion of its lift from cambered deflections.
  • Such an airfoil section has application in a variety of subsonic aerodynamic and hydrodynamic applications whenever a wing or blade is required to produce both positive and negative loads as well as to generate a wide range of forces with good aerodynamic efficiency.
  • the invention can be used to stabilize or control the direction of travel of an aircraft or a watercraft. It can be used to provide lift for an aircraft or sideforce for a sailing craft . It has application in the design of a wide variety of aircraft components and of various aerodynamic devices for fluid machinery. 2. Description of the Prior Art.
  • the present invention deals with the design of airfoil sections and wings for a variety of applications.
  • the principles of design of airfoils and wings for operation in a subsonic flow of a gas such as air are the same principles used to design foil sections for application to incompressible fluids such as water. Therefore the present disclosure will deal with the design and operation of airfoil sections and wings in both gases and incompressible fluids and the application of these devices to aircraft, watercraft and fluid machinery.
  • the general term fluid will be used to refer to either a gas or a liquid.
  • airfoil or its equivalents, airfoil section and foil will be used to describe a streamlined shaped profile designed for operation in either a gas or a liquid.
  • wing will be used to describe a structure of finite span whose cross-sections are airfoil sections designed for operation in a gas such as air, where it may serve as an aircraft wing, a vertical stabilizer or other aircraft control surfaces, or such a structure designed for operation in a liquid such as water where it may serve as a keel, centerboard or rudder for a watercraft, or a fin for a sailboard.
  • the present invention may also be applied in the design of blades for rotating machinery in air, such as a fan, a wind turbine or a helicopter rotor, or for rotating machinery in a liquid, such as a propeller in water or for general applications in the design of fluid machiner .
  • Airfoil sections have a wide variety of applications: providing lift to an aircraft, providing sideforce to a stabilizing device such as the centerboard of a watercraft, and obtaining thrust and transferring power to or from a blade in a fan, wind turbine or propeller. In all of these applications, the forces provided by the various devices, the wing, the centerboard, and the blade are derived from the lift and drag of the individual airfoil sections. Therefore, in the disclosed invention, we will refer to the forces generated by the airfoil sections as lift and drag forces even though in application these give rise to sideforce and thrust as well as lift and drag depending on the geometry of the application.
  • airfoil sections should be designed with a combination of camber (curvature of the airfoil centerline) and angle of attack (attitude to the wind) .
  • camber curvature of the airfoil centerline
  • angle of attack attitude to the wind
  • both of these devices snap through to a predetermined fixed non-symmetric aerodynamic shape, providing some load due to the curvature or camber of this excess material or non- symmetric shape.
  • additional increments of load are provided primarily by changes in angle of attack and this load is accompanied by strong negative pressure peaks near the leading edge of the airfoil. If operation at high lift coefficients is required, such airfoils are prone to stall and, for operation in water, to ventilation and cavitation. It is an aspect of the present invention to provide devices which are resistant to stall and ventilation.
  • Such snap-through airfoil section designs operate poorly at zero angle of attack where the lift force is not sufficient to force them to take their designed cambered shape.
  • operation at low angles of attack produces flutter and vibration; for a flexible airfoil section with internal linkages, it is likely that low lift will be accompanied by vibration leading to high drag and fatiguing of mechanical structures.
  • Aircraft wings are designed with a plurality of rigid sections, such as leading and trailing edge flaps, which are deployed as required to increase the effective camber of the airfoil, thereby providing increased lift.
  • Most airfoil sections designed for aircraft are not required to operate symmetrically at both positive and negative angles of attack producing positive and negative loads.
  • Rigid airfoils for aircraft wings can be designed with initially cambered centerlines. Additional changes in camber can be accomplished with actuating machinery, say by lowering the leading and trailing edge flaps. This requires intervention of the pilot or an active control system.
  • variable camber devices For watercraft, several designs for variable camber devices have been proposed wherein the effective camber shape is adjusted by pumping fluid or causing fluid to be pumped into flexible reservoirs on either side of a rigid central surface, or otherwise deploying flexible surfaces on either side of a rigid support structure, often with a variety of internal linkages. Such designs are extremely complex and limit the benefits of camber that can be achieve because of the rigid central section which constrains the travel of the foil centerline.
  • variable-camber devices share several of the following characteristics that differ from the present invention: the flexible surface is deployed about a central rigid structure located on the undeformed centerline of the airfoil section, limiting the deflection of the airfoil under load; the deflection of the airfoil is not proportional to load over a substantial range of load, so that it deflects to a fixed limiting shape at small loads; the surface of the airfoil is discontinuous, with layers of the skin free to slide, forming discontinuities in the surface slope; the flexibility of the airfoil is not chosen with a relationship to the dynamic pressure of the flow. It is an aspect of the present invention to overcome these limitations of prior art devices.
  • the present invention also has application in the design of various aircraft components such as helicopter, wind turbine and fan blades. These blades are currently designed with rigid airfoil sections. The performance range of such devices is limited by the stall of the blade sections.
  • the airfoils described here postpone stall to higher loadings while having good aerodynamic performance at light loading where the blade camber will be small.
  • Other applications include aircraft horizontal stabilizer and rudder surfaces; application of these airfoils leads to enhanced aircraft stability and control authority in comparison to the current rigid control surfaces. Alternatively, smaller control surfaces of the same effectiveness as larger rigid surfaces can be used resulting in reduced drag.
  • the present invention provides a flexible, elastic airfoil section for a wing or blade such that the lift force on the wing is obtained with a cambered deflection of the airfoil centerline that increases proportionately to the lifting load due to the elasticity of the airfoil.
  • the wing is ideally designed to be pivotably mounted to a supporting structure by means providing pivot axes for the airfoil sections near their leading and trailing edges, and incorporating means to permit the airfoil to slide in a direction along its undeformed centerline.
  • An elastically deformable airfoil section for a wing or a blade is disclosed with a streamlined shaped profile section chosen for a specific application using considerations such as those outlined in Ref 1.
  • a flexible wing or blade constructed utilizing the disclosed elastic airfoil sections has a critical dynamic pressure qcrit.
  • U the fluid velocity.
  • U C rit and qcrit are referred to as properties of the airfoil section.
  • Operation of the flexible wing or blade at dynamic pressures at or above qcrit results in full cambered deflection of its airfoil sections in response to the smallest non-zero angle of attack with respect to the flow. In this condition, the airfoil acquires some of the undesirable characteristics of the prior-art snap- through airfoils previously discussed, with degraded aerodynamic performance.
  • Airfoils designed according to the present invention are designed to operate at speeds near but below their critical, for which they will obtain the benefits of lift due to camber in a proportional, controlled manner.
  • the critical speed is determined by the static aeroelastic divergence boundary, at which condition the airfoil camber in the presence of flow grows until the geometric stop of the sliding means is reached or until large mid-plane tensions are created.
  • the relative proportions of lift on the airfoil section obtained from both camber and angle of attack are roughly constant.
  • increased lift requirements can be met with smaller changes in angle of attack to the oncoming flow than is required for a rigid airfoil section with.a fixed camber.
  • a sailing craft can achieve the required lateral resistance from a centerboard at lower values of leeway angle than using a rigid foil, a definite benefit to the efficiency of the craft.
  • the pressure distribution on the airfoil has a favorable shape. For a rigid airfoil section with fixed camber, the pressure distribution is determined in part by camber and in part by the angle of attack.
  • the part due to camber is essentially fixed and independent of angle of attack changes. Additional lift is generated by increases in that part of the pressure distribution ascribed to changes in angle of attack.
  • This pressure distribution has a large negative peak near the leading edge of the airfoil section. Such a pressure peak (and the adverse pressure gradient that accompanies it) leads to flow separation, stall and, for operation in water, can trigger ventilation or cavitation.
  • the pressure distribution of a cambered airfoil section is more resistant to separation, ventilation and cavitation. If desired, the details of the pressure distribution can be controlled by tailoring the stiffness distribution along the chord of the airfoil section so as to control the cambered shape.
  • the required stiffness of the airfoil section for a specific application may be achieved in many ways.
  • a single material of specific elastic properties for example a plastic or rubber elastomer, with properties chosen for the specific application (size, speed, fluid medium) is molded or otherwise shaped to take on an airfoil shape.
  • Another possibility would be to construct a central spine of a relatively stiff material and surround it with a more flexible material such that the resulting composite structure has the desired stiffness distribution and magnitude as well as an efficient aerodynamic shape.
  • a flexible airfoil body is surrounded by a skin of greater stiffness, which could be integral with the flexible body or could be fastened at the trailing edge and allowed to slide over the flexible body of the airfoil.
  • an airfoil section may be made of elastic material in which a void or cavity of a specific shape is formed for the purposed of achieving both an efficient exterior aerodynamic shape and a desired stiffness distribution.
  • This void may contain ribs or other structural elements.
  • this void or cavity could be filled with a material of elastic properties different from the airfoil body.
  • a series of rigid sections joined together at axes between the sections to produce a single articulated airfoil section, and optionally incorporating torsion springs to provide a restoring force proportional to relative rotation between the sections can also be employed as an elastic airfoil.
  • various combination of rigid and elastic sections, joined together solidly or at axes between the sections, mounted to a supporting structure by means providing pivot axes, the axes between the sections and the mounting at the pivot axes being constructed with or without torsion springs can be employed.
  • the stiffness of the resulting structure and its mounting can be chosen in such a way as to fulfil the purpose of the present invention.
  • a control surface flap of conventional design is incorporated into a wing made of elastic material.
  • the axle of the control surface can serve as one of the pivot axis for the flexible airfoil section.
  • the present invention has application to the design of a wide variety of force-generating appendages for watercraft.
  • Devices such as centerboards and fins benefit from the enhanced side force and reduced leeway angle. Rudders benefit from the enhanced control effectiveness and the reduced drag.
  • the present device can be incorporated into a keel for a yacht, and may also serve as a keel incorporating a control surface such as an attached rudder or tab.
  • the present invention may be employed in the design of rotating blades for a fan, wind turbine or helicopter rotor.
  • the dynamic pressure of the flow at each blade section is a function of blade radial position.
  • the stiffness distribution along the span should be tailored so that ideally all of the sections operate below their critical speeds by the same proportion.
  • leading and trailing edge pivot attachments can be mounted to the central blade supporting structure by conventional means and the elastic airfoil sections employed for the blade.
  • a partial span elastic blade may be employed for a portion of the blade span, as for example the tip region.
  • Application of the present invention will both enhance the high lift performance of the blades, which is currently limited by stall, and provide good aerodynamic performance at low lift coefficients.
  • the present invention may be employed for conventional aerodynamic surfaces such as aircraft wings and vertical stabilizers. It has particular application where the high lift performance of a configuration needs enhancement without the complexity of pilot intervention or an active control system, as in various sport aeroplanes such as ultralights, hang gliders and man- powered vehicles. It may also be used in combination with a conventional aerodynamic control surface such as a trailing edge flap, for enhanced control and increased lift.
  • the flexible airfoils, wings and blades disclosed herein can also be used as components in fluid machinery such as internal fins, guide vanes, and turning vanes.
  • Fig. 1 Shows a preferred embodiment of a flexible elastic wing containing a trailing edge slot mounted to a support structure on two rigid axles;
  • Fig 2. Shows a finite wing with leading and trailing edge attachments inserted into cavities in a support structure;
  • Fig 3 Shows a finite wing mounted in a shaped cavity in a support structure;
  • Fig 4 is a cross-section through the support cavity of Fig 3;
  • Fig. 5 Shows the principle of operation of the foil with camber produced in operation at an angle of attack to the flow
  • FIG. 6 shows the aerodynamic performance of a family of prior art rigid airfoils of varying camber
  • FIG. 7 is a cross-section of an embodiment of the invention showing an airfoil shaped out of flexible material
  • Fig. 8 is an embodiment showing a stiff central spine surrounded by flexible material
  • Fig. 9 is an additional embodiment showing a stiff skin surrounding a core of flexible material
  • Fig 10 is a preferred embodiment of a flexible elastic airfoil showing a part chord spine, a stiff trailing edge, and a flexible airfoil body;
  • Fig. 11 is an additional embodiment containing a cavity and showing a leading and trailing edge of alternate materials
  • Fig 12 shows shaping of the spine in the spanwise direction
  • Fig 13 shows a detail of a spine unit
  • Fig 14 shows an embodiment wherein rigid sections are elastically joined to form an embodiment of the invention
  • Fig 15 shows a flexible airfoil with a conventional flap
  • Fig 16 shows the deflection of a flexible airfoil by a static load p
  • Fig 17 shows deflection of a flexible wing by a static load P distributed along the span
  • Fig 18 shows deflection response w to load p;
  • Fig 19 shows various stiffness distributions along the airfoil chord;
  • Fig 20 shows a flexible airfoil with a part chord spine with critical dynamic pressures given in Table 2;
  • Fig 21 shows a wing of finite span mounted to a support structure showing the image effect which doubles the aspect ratio;
  • Fig 22 shows the increased lift of a flexible foil ratioed to that of a rigid foil at the same angle of attack as a function of the ratio of flow speed to critical speed;
  • Fig 23 shows an application of the present invention to a wing of general planform mounted to a support structure;
  • Fig 24 shows a detail of a leading edge axle and axle cavity
  • Fig. 25 shows an alternate detail of a leading edge axle and cavity
  • Fig 26 shows an alternate leading edge cavity and axle with an additional structural member
  • Fig. 27 shows a detail of a trailing edge axle and cavity
  • Fig 28 Shows a sailboard in combination with a flexible fin
  • Fig 29 shows a design for the fin of a sailboard
  • Fig. 30 shows the application to the centerboard of a catamaran
  • Fig 31 shows the stiffness curves for the foil of Fig 32
  • Fig 32 shows the foil cross-section for the foil of Fig 29;
  • Fig 33 shows the application to the rudder of a watercraft;
  • Fig 34 shows a detail of the rudder of Fig 33;
  • Fig 35 show an application of the present invention to the aerodynamic surfaces of an aircraft;
  • Fig 36 shows an aircraft incorporating an aerodynamic surface according to the present invention;
  • Fig 37 shows an application of the invention to a fan or wind turbine; and
  • Fig 38 shows an application of the invention to the rotor blades of a helicopter.
  • finite span wings which incorporate the principles of the present invention and show pivotable mounting of a flexible wing 102 to a supporting structure 104 incorporated into an aircraft, watercraft or other device employing the present invention by means providing pivot axes near the leading and trailing edges .
  • one or both of the pivot axes must incorporate means to permit the wing to slide in a direction generally aligned along the centerline 105 of the undeformed profile. For typical operation, the travel of this sliding means should be about 3% of the chord of the airfoil.
  • the pivot axis mounting means is provided by two axles, the leading edge axle 106 and the trailing edge axle 108, on which the wing 102 is mounted at axle cavities in the wing permitting rotation about the axles, a leading edge cavity 110 and a trailing edge cavity 112.
  • the sliding means is realized by extending one cavity in the direction of the airfoil centerline 105 to permit deflection of the airfoil centerline without strong resistance from the axles.
  • Fig. 1 shows an elongated trailing edge cavity 112 incorporating a slot to serve this function.
  • axles 106, 108 are rigid; another embodiment would employ axles rigid in bending in the direction perpendicular to the undeflected airfoil centerline 105 but flexible in bending along this centerline; the sliding means would then be provided by this flexibility.
  • Fig.2 an embodiment is shown where the pivot axis mounting means for the wing 102 are provided by rigid axle attachments 114 and 116 integral with the leading edge 118 and trailing edge 120 respectively of wing 102 which are made of relatively stiff material to resist bending deformations in the direction perpendicular to the wing under load. These axles are then inserted into a leading edge cavity 122 and a trailing edge cavity 124 in the supporting structure 104.
  • the sliding means is provided by a slot in the supporting axle cavity at the trailing edge 124.
  • the axles are fastened in the support structure 104 by conventional means not shown in a manner permitting their rotation.
  • Fig. 3 illustrates a further embodiment in which the leading and trailing edge pivot mounting means and the sliding means are provided by mounting wing 102 of span s in a shaped cavity 126 in the support structure 104.
  • the wing so mounted has an effective span Seff exposed to the flow. In its deflected position the wing would bear against the cavity 126 at positions near its leading and trailing edges for structural support, which positions then provide pivot axes 128 and 130 about which the wing can rotate.
  • the leading edge 118 and the trailing edge 120 of the wing should be made of relatively stiff material.
  • Fig 4 shows a cross-section through the cavity showing the airfoil section 132 mounted in the cavity.
  • the pivot axes for airfoil rotation are provided by the internal shape of the support cavity 126: the leading edge pivot axis 128 is substantially at the center of curvature of the leading edge section of the cavity; and the trailing edge pivot axis 130 is essentially at the trailing edge of the foil.
  • the wing is supported in the cavity by conventional means appropriate to the application; these are not shown.
  • Such mounting means can also incorporate the axles of Fig 1 or 2 to provide rigid support and fixed axis locations. For example, it may be desired to mount the wing so as to fix the location of the leading edge pivot axis.
  • the cavity 126 may contain a flexible material 134 to provide a smooth surface for contact with the flow.
  • Fig. 1,2,3 illustrate but do not limit the possible pivot axis mounting means that may be used for the present invention.
  • the concepts shown may be combined together in several ways to fulfil the purposes of the invention, such as utilizing an axle mounted to the support structure as the leading edge pivot mounting means while using an axle integral to the wing trailing edge as the trailing edge pivot mounting means.
  • Typical examples of materials suitable for construction of flexible wings according to the present invention include but are not limited to: urethanes and other synthetic rubbers, flexible plastics, elastomers, nylon, foam rubber and foam urethanes, and thin metal sheets such as aluminium.
  • Various suggestions for airfoil design using materials of this type appear below.
  • the principle of operation of the invention is shown in Fig. 5.
  • the flexible airfoil cross- section 132, of thickness t (x) and chord c, mounted at pivot axes near the leading and trailing edges 128 and 130 respectively, is placed at an angle of attack 136 to a flowing medium 138, the resulting aero/hydrodynamic load will deform its surface contour from its undisturbed position 140 to an equilibrium deflected position 142.
  • the camber deflection w(x) 143 is the distance between the undeflected centerline of the airfoil 105 and the deflected centerline 144.
  • the magnitude of the deflection is determined by the foil stiffness, flow dynamic pressure, and pivot axis locations.
  • the distance between the pivot axes is d*c, the distance between the leading edge and the leading edge pivot axis is d ⁇ *c; the distance between the trailing edge and the trailing edge pivot axis is d2*c.
  • the sliding means shown as a slot in the trailing edge cavity 112, acts to insure that the deflection of the airfoil takes place in proportion to the load without substantial mid-plane tension.
  • the aerodynamic load will be greater than that of the undeformed section for the same angle of attack, flow speed, and flowing medium. A substantial portion of this load will be provided by the airfoil camber. Because the camber increases in proportion to the load, the airfoils disclosed in the present invention have a lift curve slope greater than that of a rigid foil. (Lift curve slope for an airfoil or a wing is the rate of increase in lift for an increase in angle of attack to the flow.)
  • Fig 6 presents a family of curves showing typical behavior of the drag coefficient Cd vs the lift coefficient Ci for a family of rigid airfoils with the same thickness distribution but differing amounts of camber.
  • Curve 146 is for an airfoil with no cair er; curve 148 for a small camber; curve 150 for more camber; with airfoil camber continuing to increase to curves 152 and 154.
  • each rigid airfoil section has a region of low drag (called a "drag bucket") which occurs at a Ci that increases with camber.
  • the center of this low drag region can be considered to be the optimum design point of the airfoil section.
  • Each cambered airfoil section has a region of higher drag for Ci's both lower and higher than its design point .
  • a camber can be selected which minimizes the drag. Consequently, cambered airfoils can provide lift at lower drag than symmetric airfoils especially as the required lift coefficient increases.
  • a preferred embodiment of the present invention is to mount a flexible wing or blade to a supporting structure by means of two rigid pivot attachments, located near the leading and trailing edges of the foil.
  • the airfoil sections of the wing or blade are constructed primarily of a flexible, elastic material so as to provide a deflection of the wing surface in proportion to the load which in combination with rotation about the pivot axes provides an efficient cambered airfoil section.
  • the external shape of the airfoil can take a variety of forms consistent with the principles of airfoil design as outlined in Ref. 1.
  • the exterior profile of the airfoil shape of the present invention forms a smooth continuous curve such that points on the surface initially adjacent remain in contact.
  • Fig. 7,8,9,10,11,14 and 15 illustrate airfoils which incorporate the principles of the present invention.
  • Fig. 7 shows an embodiment of the present invention in which the airfoil cross-section 132 of thickness t(x) is molded out of a uniform flexible material such as a urethane or other elastomer.
  • the airfoil is mounted on two rigid axles providing pivot axes mounting means, a leading edge axle 106 and a trailing edge axle 108, said axles being inserted into leading and trailing edge cavities, 110 and 112 respectively, molded into the airfoil cross-section, the trailing edge cavity 112 incorporating a slot to provide the sliding means.
  • Fig. 7 shows an embodiment of the present invention in which the airfoil cross-section 132 of thickness t(x) is molded out of a uniform flexible material such as a urethane or other elastomer.
  • the airfoil is mounted on two rigid axles providing pivot axes mounting means
  • an airfoil section 132 incorporates a spine 156 to provided some of the required stiffness, a leading edge 118 and a trailing edge 120 of relatively stiff material, incorporating axle cavities for the leading and trailing edge axles 110, 112 surrounded by a flexible material 158 to form the profile shape.
  • the airfoil shown here is mounted on leading and trailing edge axles 106, 108 to provide the pivot axis mounting means.
  • the spine 156 would be manufactured of a stiffer material than the airfoil body 158.
  • Fig 9 shows an embodiment in which the flexible material 158 of the airfoil section 132 is surrounded with a skin of stiffer material 160 which may be free to slide over the flexible body except at the trailing edge.
  • ribs 162 can be incorporated into the airfoil to provide additional structural stability.
  • the region between the skin and the ribs may be a void 164.
  • the pivot axis mounting means (not explicitly shown) is provided by axles integral to the airfoil 114, 116 incorporated into the wing leading and trailing edges 118 and 120.
  • Fig. 10 shows a flexible airfoil section 132 of thickness t (x) made primarily of flexible material 158 incorporating a spine unit 166 with a trailing edge section 120 and a central spine 156 of thickness ti (x) that extends over part of the chord.
  • the pivot axis mounting means are provided by incorporating cavities 110, 112 into the airfoil at its leading and trailing edges and pivotably mounting the airfoil on leading and trailing edge axles 106, 108.
  • Fig 11 shows an additional embodiment in which the central portion of the flexible airfoil 158 contains a cavity 164 designed to tailor the stiffness distribution to a desired form, and also incorporating the spine unit 166 of Fig. 10.
  • the cavity 164 may be empty or filled with elastic material differing from that of the airfoil body 158 and may incorporate ribs 162.
  • the airfoil is mounted at pivot axis 128 and pivot axis 130 incorporating a sliding means in the form of a trailing edge cavity slot 112.
  • Fig.12 shows the wing 102 containing a spine unit 166 incorporating a trailing edge 120 and discloses shaping the planform of the spine unit to achieve a desired stiffness distribution.
  • Fig 13 shows a detail of the spine unit 166. The spine at its leading edge occupies a fraction so and at its trailing edge occupies a fraction sf of the total width of the spine st.
  • Fig. 14 shows an embodiment of the elastic airfoil in which the airfoil is constructed of rigid sections 168 which are joined together to form a single articulate unit at axes 170 allowing relative rotation between the sections. Shown is a three segment airfoil consisting of a leading edge section 172, a trailing edge section 174 and a center section 168, mounted on leading and trailing edge axles 106 and 110 enclosed in axle cavities 110 and 112.
  • the required elastic restoring forces are provided by torsion springs 176 of which there must be a number at least equal to the number of axes joining the sections.
  • Fig 15 shows a flexible airfoil section 132 in combination with a control surface of conventional design 178 having a axis 180 and an actuating means 182.
  • the airfoil is mounted at a leading edge pivot axis 128, and at a trailing edge pivot axis 130 which may be incorporated into the control surface axis 180.
  • the elastic airfoil section deflects from its initially undeformed position 140 to its deformed position 142.
  • the deflection w, 188, at the point Q is then determined.
  • w is substantially proportional to p for small deflections w/c ⁇ .1 where c is the chord of the airfoil: that is w increases monotonically with increases in p such that w/p is substantially constant.
  • the ratio p /w is defined as the effective section stiffness Ss of a given airfoil.
  • a total load P is uniformly distributed along a line 190 located midway between the leading edge pivot axis 128, and the trailing edge pivot axis 130 (or their linear extensions) .
  • This loaded line extends from the root to the tip of the wing along the effective span, defined as that portion of the span exposed to the flow s e ff.
  • the load per unit span is P/s e ff.
  • the deflection w 188 is taken at the point Q, 186, located along this line midway along the span Seff ⁇
  • the ratio P/(Seff w) so determined is defined as the effective stiffness of the wing, S w .
  • Fig 18 The deflection of the airfoil according to the present invention as a function of load P in comparison to several prior art flexible wings is shown in Fig 18.
  • These prior art devices are designed to easily deflect under load until their deflection is limited by contact with a central support structure or other geometric stop, after which load the deflection w remains constant. This is shown by curve 192 of Fig 18.
  • the present invention has a proportional deflection over a much larger range than prior art devices and in particular is not limited by contact with a central support structure. This is shown by curve 194 of Fig 18 which also shows that the curve of deflection is close to a straight line of best fit 196. c) .
  • N d ,(s(x) a (x)) qD ,(x;w(x)/c;M;AR,a) dx 2 dx 2 ⁇
  • w(x) is the deflection of the airfoil centerline
  • D Cp(x; w(x)/c; , AR,a) is the distributed lifting pressure coefficient across the airfoil, which has a known dependence on the deflected shape of the airfoil relative to the chord length w(x)/c, the Mach number M, the aspect ratio AR, and the angle of attack a
  • N is the local bending stiffness of the midchord section of the airfoil
  • s(x) the stiffness shape function.
  • this equation may be used to design desirable airfoil section stiffness distributions to achieve a desired camber shape w(x) for given operating conditions.
  • this equation can be solved to determine the required stiffness shape function s (x) .
  • stiffnesses are characterized as: 198 constant; 200 stiff midchord (MC) and 202 stiff trailing edge (TE) . They are representative of various stiffness shape functions that can be employed for the present invention.
  • the camber shape under load can be controlled by selecting the stiffness shape function s (x) so as to produce the desired camber deflection w(x) in response to the load distribution naturally occurring on the elastic airfoil.
  • the external shape of the airfoil section can take a variety of forms such as the many airfoil shapes given in Theory of Wing Sections by Abbott and Van Doenhoff which gives suggestions for the choice of airfoil section for a given application.
  • t(x) c (.34 Sqrt(x/c) -.097 x/c+.142 (x/c) 2 -.53
  • the desired stiffness shape function s(x) cannot be obtained with a solid elastic airfoil section formed from material of uniform properties.
  • the airfoil section design, shown in Fig 20 was designed to have a resulting s(x) that approximates the desired s(x) .
  • a family of urethane material was chosen for airfoil construction; these materials have a Poison's ratio of .49.
  • Materials with a variety of elastic (Young's) moduli as listed in Table 2 are used for the airfoil elastic body to vary qcrit- A material (ROYAL Cast 3101 from UniRoyal Inc.) with a modulus of 210,000 psi was chosen for the trailing edge and for the central spine attached to the trailing edge.
  • qcrit- A material ROYAL Cast 3101 from UniRoyal Inc.
  • a modulus of 210,000 psi was chosen for the trailing edge and for the central spine attached to the trailing edge.
  • a shaping of the spine in the spanwise direction as shown in Figs. 12 and 13, was also included to better tailor the stiffness distribution along the chord.
  • these values are expressed as the percentage of the spine present across the span at these two points.
  • the critical dynamic pressure of a given elastic airfoil is a function only of thickness ratio, tmax/C r and pivot axis location relative to chord length, therefor elastic airfoils of any desired chord length may be made using these materials and geometry.
  • these airfoil sections or equivalently stiff sections made of alternate materials may also be used for a wing or blade operating in air at subsonic Mach numbers below the critical Mach number of the section (see Ref 1.) .
  • Desirable elastic airfoil sections can be designed with any streamlined airfoil shape and for a range of stiffness distributions such as the specific example given herein or any similar shape.
  • the description above demonstrates how the stiffness distribution may be chosen independently of the airfoil shape by suitable layers of materials with different elastic moduli. These methods of calculating the stiffness distribution of a structure and designing a structure to have desired properties are well known in the art .
  • the teaching of the present invention demonstrates how airfoils of desired properties may be constructed with desired stiffness distribution and the critical dynamic pressure may be predicted from the elastic properties of the airfoil.
  • an elastic airfoil section for a wing or blade of finite span requires analysis of the effects of finite aspect ratio on the airfoil section behavior described above.
  • SA the projected surface area of the wing.
  • the results of this analysis is governed not only by the actual aspect ratio of the wing or blade but also by the details of its application.
  • the aspect ratio is effectively doubled by the imaging effect, shown in Fig. 21 in which the presence of the wall 104 is equivalent to that of a image wing 204.
  • Fig 21 shows the geometry of a finite wing 102 mounted to a supporting structure 104 such that the span s is effectively doubled to 2 s by the image wing.
  • the effective aspect ratio is twice the actual aspect ratio.
  • the aspect ratio referred to will be the effective aspect ratio.
  • the aspect ratio referred to will be the actual aspect ratio of the fin.
  • This formula can be combined with the previously presented results for q crit and Ucrit for the specific airfoil section of table 2 or to any airfoil section constructed using the principles disclosed herein to design a finite wing according to the present invention.
  • the critical dynamic pressure is a function of the ratio of the total span stotal to the span exposed to the flow Seff• Also, pulling the wing into the cavity changes the aspect ratio. Both effects can be combined into a single formula to predict the critical dynamic pressure for such a wing as a function of the critical dynamic pressure of its airfoil section qcrit airfoil.
  • the critical dynamic pressures given above for airfoil sections and wings of finite span is determined by the aeroelastic divergence speed for an airfoil section or a wing of finite span pivoted about points close to the leading and trailing edges.
  • Prior art wings are not mounted in this manner.
  • the stiffness is so distributed that the airfoil sections are free to twist and the wing bends in the spanwise direction. Aeroelastic deflections of such wing do not provide the benefits of the present invention since the increased lift comes primarily from increases in local angle of attack to the flow due to elastic twisting of the airfoil sections.
  • the essence of the present invention is that airfoil sections and wings of finite span are so constructed and mounted that aeroelastic deformation, rather than having detrimental effects on airfoil aerodynamic performance, is to actually be employed to obtain an unexpected benefit, namely, that of obtaining lift due to camber in a controlled manner.
  • the formulae presented herein instruct how do do this for specific examples. More generally, methods of aeroelastic analysis to predict the aeroelastic divergence speed are available to the designer of a wing more complex than those described herein.
  • the teaching of the present invention is that a flexible wing mounted at leading and trailing edge pivot axes incorporating a sliding means can be used to obtain the beneficial effect of providing lift due to camber.
  • Fig. 22 shows the ratio of the lift coefficient for a flexible airfoil or wing to that for a rigid airfoil at the same angle of attack (C /C rigid) as a function of ratio the speed of operation U to the critical speed ⁇ rit of the airfoil or wing. For low U/Ucrit the airfoil behaves as a rigid foil and the ratio of lift to that of a rigid foil becomes 1.
  • the lift is increased by a factor 1.5; for a speed 76% of critical, lift is doubled; for a speed 85% of critical, lift is tripled. Therefore, at speeds 80% of critical, roughly equal portions of lift come from angle of attack to the flow and camber deformations. For the airfoils examined, this proportion provided the lowest drag for a given lift in the sense of curve 155 of Fig. 6. Therefore, the design speed should be chosen to be roughly 80% of the critical speed. However, substantial benefits are still obtained if the design speed ranges from 60% to 95% of the critical speed.
  • the design Mach number and speed should be determined for the application.
  • the geometry of the wing, and thus its aspect ratio should chosen by conventional criteria.
  • the designer should assume a lift curve slope for the airfoil sections roughly twice that for a rigid foil in determining the required planform area for a specific application.
  • the shape of the airfoil should be chosen according to known aerodynamic principles.
  • the ratio of design speed to critical speed should be selected; 80% is suggested as an optimum.
  • the desired critical speed of the wing is determined and also its critical dynamic pressure.
  • the design of the elastic properties of the sections may proceed by the techniques disclosed herein. In most applications the airfoil sections along the span of the wing or blade should have the same critical dynamic pressure.
  • the area, span and thus the effective aspect ratio of the wing is determined by the required lift force, the desire to minimize induced drag, issues of operability and maneuverability and possibly by class rules in the case of competing yachts.
  • the effective aspect ratio is twice the actual aspect ratio due to the image effect of the mounting surface.
  • sweepback of the leading edge is thought to be important for maneuverability and for clearing weeds that may become attached to the leading edge. This leads to either sweeping back the pivot axes or to some compromise of pivot axis placement relative to the leading edge at the root.
  • the pivot locations should be placed as close as possible to the leading and trailing edges of the airfoil sections.
  • the mechanical embodiment of the pivot axis mounting means incorporating a sliding means is selected according to the application.
  • the airfoil sections are designed so that substantially all of the airfoil sections operate below their critical dynamic pressure. (It is straightforward to design all sections to have the same critical dynamic pressure; this should normally be done.) Two methods are presented herein to accomplish this purpose: first, the elastic structure is designed so that the effective airfoil section stiffness Ss, define by the point-load method, is that required to achieve the desired critical dynamic pressure for the airfoil section. Alternatively, the formulae presented relating critical dynamic pressure, airfoil stiffness magnitude and stiffness distribution, and axes location for the specific stiffness shape functions considered may be used to design the elastic properties of an airfoil section for a specific application.
  • Fig. 23 shows an embodiment of the present invention in which the flexible airfoil sections are employed to form a wing of finite span of general planform shown here mounted by means unspecified to a support structure 104 which is not part of the invention.
  • the wing is pivotably mounted by means forming pivot axes at the leading edge, 128, and at the trailing edge 130, at least one pivot axis incorporating sliding means.
  • the design, location and embodiment of the pivot axes is an important part of the design of a system utilizing the present invention. For many applications, transmitting the lift forces to the support structures will cause large bending moments in the pivot attachments and related structures. This requires that the strength of these structures be sufficient for the anticipated loads.
  • axle diameter or cross-section dimensions such as related to details of the support structures.
  • axles it is not necessary that the axles be round. Elongated axle shapes may be employed to increase the sustainable root bending moment with less impact on the airfoil section thickness. These axles can be accommodated in the foil structure by suitable shaping of the axle cavities to permit airfoil section rotation about the axle. If required, additional structural members can be employed within suitably shaped cavities to provide additional load carrying capability at large deflections.
  • Fig. 24 through 26 show a variety of possible designs for leading edge axles and cavities that employ non-circular axles 106 and shaped cavities 110 in the airfoil section 132 to support increased bending moments without corresponding increases in thickness. Additionally Fig 26 shows a structural member 218 which is placed in a shaped cavity 220 to carry a portion of the load at large deflections. A spring could also be included in cavity 220 to carry load over a wider range of deflections. Fig. 27 shows an alternate trailing edge axle 108 and shaped cavity 112 that permit rotation of the airfoil 132 and transmission of the load to the axle. i) application to the design of a fin for a sailboard
  • the disclosed invention has application to the design of a fin or blade for a sailboard.
  • the benefits of the present invention in this application are several: reduced leeway angle; reduced tendency to stall or ventilate leading to a reduced tendency to spinout (loss of control) ; as well as lower profile drag relative to a rigid foil.
  • the airfoil section is taken as the laminar flow section shown in Fig 20.
  • the elastic design of the airfoil section is that previously discussed with its critical dynamic pressure and speed given in table 2: an airfoil with a spine unit whose thickness and planform are adjusted so that a single elastic material may be used to design a family of fins for the desired speed range, in this case between 7 and 35 kts.
  • FIG. 28 shows the fin 222 mounted to a sailboard 224.
  • One possibility is to construct a cavity for mounting.
  • the section through 4-4 of Fig 28 would be as shown in Fig 4.
  • Fig. 29 shows the fin 222 mounted to the sailboard 224 by conventional means employing a standardized mounting structure 226 with mounting fastener 228 to the fin box of the sailboard 224 in Fig. 28.
  • the root chord 230 is 6.5"; the tip chord 232 is 4.5"; the span is 10", giving an aspect ratio for the foil of 1.8; this is effectively doubled in the mounting to the board to 3.6.
  • the critical speed increases by a factor 1.25 above the critical speed for this airfoil section given in Table 2.
  • the operating speed U was chosen as .8 U C rit/ at this condition the lift comes equally from camber and angle of attack and the pressure distribution has a favorable shape.
  • the tip of the fin 210 forms a body of revolution having the shape of the airfoil section at the tip chord 232.
  • the wing incorporates a spine unit 166.
  • the pivot axis mounting means incorporating a sliding means are realized by mounting the wing on rigid axles 106, 108 inserted into cavities 110, 112 moulded into the wing leading and trailing edges.
  • the trailing edge cavity incorporates a slot to provide the sliding means.
  • the axles are made of stainless steel and are integral with a stainless steel mounting structure 226 that fits into a conventional fin box. This member is made in two parts, joined by an adjustable fitting 227 to permit assembly.
  • the fin is fastened to the axles by conventional fastening means 228 such as screws at the axle ips.
  • the centerboard is designed to obtain benefit from its flexibility in the range from 15 to 25 knots.
  • the planform of the centerboard 234 is designed to have an effective aspect ratio of 8, including the image effect but operated with at least 25% of the span retracted into the supporting cavity to provide structural support and pivot axis means.
  • the maximum effective aspect ratio is 6.
  • the critical dynamic pressure of the airfoil section should be chosen as 14.3 knots. This insure that the design speed of 15 knots will be reached with the foil extended to 75% of its span while a design speed of 30 knots will be reached if the foil is retracted to 30% of its length.
  • the desired stiffness shape function is chosen as the stiff mid-chord (MC) previously presented; this function is shown in Fig 31 as curve 200.
  • the critical value of K for this stiffness shape function is 1.45.
  • the stiffness shape function for a solid material made into the airfoil shape chosen above with a modulus of 5800 psi is also shown as curve 238 in Fig. 31 in comparison to the desired curve 200 of Fig. 31.
  • the stiffness shape function given by the solid airfoil differs considerably from the desired shape and the design will therefore be modified by the addition of a part chord spine.
  • the final design incorporates a part chord spine, attached to the stiff trailing edge to form a spine unit 166 which has a thickness of .029c and begins at the 25% c.
  • the flexible airfoil body has an elastic modulus of 3300psi, the spine unit a modulus of 210,000 psi.
  • the resulting composite structure stiffness curve 240 of Fig 31 is a good fit to the desired stiffness curve 200.
  • the resulting airfoil cross-section is shown in Fig. 32 showing the leading edge 118, the trailing edge 120 the spine unit 166 and the flexible body of the airfoil 158.
  • the leading edge 118 should be stiff or can be stiffened with an internal structural member which can also serve as an adjustable attachment means, to support the centerboard in the watercraft and permit its adjustment.
  • a rudder for a watercraft.
  • An example is shown in Fig. 33 showing a watercraft 236 with a centerboard 234 which may be of conventional design or may incorporate the principles of the present invention.
  • the watercraft is adapted to utilize the present invention.
  • a rudder 242 is shown constructed according to the present invention. In this example only the rudder near and below the water surface is flexible, the remainder of the rudder is rigid and serves as the mounting structure.
  • Fig 34 shows a detail of the rudder showing a flexible wing section 102, a stiff leading edge, 118 with a rigid axle integral 114, a stiff trailing edge 120, with a rigid axle integral 116, shown pivotable mounted to a support structure 104, in this case the rigid portion of the rudder 104 by conventional fasteners 228 in cavities 122 and 124.
  • the sliding means is provided by an elongated trailing edge axle cavity
  • this rudder can be made out of the foil described in Fig 31 with a spine thickness .008c having a modulus of 210,000 and a flexible body 102 having a modulus of 100 psi. k) other applications
  • the present invention can also be applied to the improvement of aerodynamic surfaces such as sketched in Fig 35 showing a vertical tail with rudder.
  • the aerodynamic surface 244 with its control surface 246 is mounted to the aircraft 248 on rigid axles 106 and 108 attached to the aircraft, the aerodynamic surface pivotable mounted at its leading and trailing edge by means of leading and trailing edge cavities in the aerodynamic surface 244.
  • the trailing edge axle can also serve as the axle 250 for the control surface 246 incorporating the control surface actuator 252.
  • the elastic properties of this wing may be designed for a desired speed and Mach number using the formulae presented here.
  • Fig 36 shows an aircraft adapted to utilize the present invention. In this case a mounting is incorporated into the aircraft at the base of the vertical stabilizer to contain the pivotable axle mounting means.
  • the present invention can be used to design flexible airfoils for rotating machinery such as fans, propellers, wind turbines, and helicopter rotors operating in air and propellers operating in water. These devices fall into two categories: axial low devices such as propellers, fans and wind turbines that operate with their axis of rotation substantially along the flow direction; and helicopters which operate with the flow substantially perpendicular to the axis of rotation.
  • the local dynamic pressure at the airfoil section is a function of airfoil radial position r along the blade, flow velocity and rotation speed.
  • the airfoils should be designed so that each airfoil section operates at the same ratio of local flow dynamic pressure to airfoil section critical dynamic pressure.
  • FIG 37 A typical axial flow device is shown in Fig 37 showing a central rotating hub structure 254 with flexible blades 256 attached by pivot axis mounting means incorporating a sliding means as specified in the present invention forming pivot axes 128 and 130.
  • the rotating device is attached to a vehicle or other support structure 104.
  • the flow velocity is V
  • the rotation velocity is W.
  • the airfoil sections should be designed so that q ⁇ qcrit • A value qblade 31 .64 qcrit will provide a velocity at the blade section equal to .8 Ucrit• F o r a blade operating in air at speed of sound a, the local Mach number is
  • Mp Sqrt( (V 2 +(Wr) 2 )/a.
  • qcritical A p/w /(1-1.3/AR) with .09 ⁇ A ⁇ .12.
  • Fig 38 shows a flexible rotor blade 258 rotating about an axis 260 with rotation speed W and moving at a speed V in the flight direction.
  • the blades are attached by means providing pivot axes to a conventional rotor hub which is incorporated into the vehicle 262 by conventional means.
  • the local dynamic pressure varies around the azimuth of the rotor disk but is maximum when the blade is perpendicular to the flight direction.
  • the blade sections should be designed to operate below their critical dynamic pressure.

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  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Mechanical Engineering (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Ocean & Marine Engineering (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

Profilé aérodynamique souple pour une aile (102) ou une pale (258) présentant une forme fuselée et une structure élastique dont la répartition de la rigidité le long de sa corde et de son envergure est adaptée spécialement pour assurer un profil cambré souhaitable dont la cambrure augmente proportionnellement avec la sustentation, monté sur une structure de support (104) de telle sorte que les profilés aérodynamiques (102) soient libres de pivoter autour d'axes (106, 108) à proximité de leurs bords d'attaque et de fuite. En service, le profilé (102) tire une grande partie de sa sustentation de la déformation élastique en flexion de sa forme souple, réalisant ainsi une sustentation supérieure à un profilé aérodynamique symétrique avec le même angle d'attaque tout en différant le début de la séparation du flux et du décrochement et, pour le fonctionnement dans l'eau, de la ventilation et de la cavitation. Une aile (102) ou une pale (258) de forme en plan habituelle comprenant des profilés aérodynamiques élastiques souples s'utilisant pour stabiliser, ou commander le sens de marche de, ainsi que pour fournir la force pour, une embarcation telle qu'un bateau à voile (236) ou une planche à voile (224), ou pour application à une grande variété de composants (104) et de configurations aéronautiques pour fournir la force sustentatrice et la force latérale, peuvent également servir de surfaces aérodynamiques de divers types d'engins fluidiques, notamment ventilateurs, rotors d'hélicoptères et turbines éoliennes travaillant dans un courant subsonique.
PCT/US1992/000835 1991-02-04 1992-02-03 Profile aerodynamique elastique souple module WO1992013758A1 (fr)

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Cited By (4)

* Cited by examiner, † Cited by third party
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WO1998021091A1 (fr) * 1996-11-14 1998-05-22 Philippe Arribi Corps d'ecoulement
WO2002070890A1 (fr) * 2001-03-02 2002-09-12 Robert Lipp Turbine hydraulique immergee omnidirectionnelle a axe perpendiculaire au courant d'eau et applications
WO2017048140A1 (fr) * 2015-09-15 2017-03-23 Politechnika Rzeszowska Dérive hydro-élastique
CN116611175A (zh) * 2023-07-18 2023-08-18 北京航空航天大学 一种大展弦比飞机体自由度颤振的预测方法

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US1341758A (en) * 1919-07-17 1920-06-01 Parker Humphrey Francis Variable-camber rib for aeroplane-wings
US3332383A (en) * 1965-06-24 1967-07-25 Wright Edward Morris Variable camber airfoil
US3275083A (en) * 1965-10-15 1966-09-27 Bradley A Kendis Variable pitch propeller
US3753415A (en) * 1971-11-30 1973-08-21 S Burtis Hydrofoil-shaped stabilizing or attitude-affecting means for boats
US3954230A (en) * 1973-09-26 1976-05-04 Dornier System Gmbh Flow elements for influencing flowing media
US3999886A (en) * 1974-10-10 1976-12-28 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Hingeless helicopter rotor with improved stability
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US4235397A (en) * 1978-04-29 1980-11-25 British Aerospace Flow deflector blades
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Publication number Priority date Publication date Assignee Title
WO1998021091A1 (fr) * 1996-11-14 1998-05-22 Philippe Arribi Corps d'ecoulement
WO2002070890A1 (fr) * 2001-03-02 2002-09-12 Robert Lipp Turbine hydraulique immergee omnidirectionnelle a axe perpendiculaire au courant d'eau et applications
WO2017048140A1 (fr) * 2015-09-15 2017-03-23 Politechnika Rzeszowska Dérive hydro-élastique
CN116611175A (zh) * 2023-07-18 2023-08-18 北京航空航天大学 一种大展弦比飞机体自由度颤振的预测方法
CN116611175B (zh) * 2023-07-18 2023-09-12 北京航空航天大学 一种大展弦比飞机体自由度颤振的预测方法

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