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GATC Presentation

Derivation of an
Optimized Configuration
for Aerobatics

A summary of lines of reasoning presented
at the SAE General Aviation Technology Conference,
Wichita, Kansas, 10 May 2000

Philip Carter, 2000
ESOTEC Developments
P.O. Box 1396, Kaslo, B.C.
Canada V0G 1M0


The Generalized Aerobatic Mission

In generalized terms, aerobatics could be defined as the precise control of attitude and velocity on three axes in three dimensional space, relying solely on inertias and aerodynamic interaction with the atmosphere.

Qualifications

  • To satisfy competition requirements and focus the mission as a performing art we define "three dimensional space" as a kilometer cube (the aerobatic box).
  • The aircraft should be able to fly the complete Aresti system as a subset of its flight envelope.
  • Control of velocity is more important than maximum velocity. Maximum airspeeds need not be greater than that required to pull 10-12 G (human bodily limitations). In practice, speeds greater than 200 mph are of little use in the aerobatic box - particularly if the aircraft can climb vertically without relying on stored energy (speed).
  • Since control of airspeed is more important than maximum airspeed, a lower wing loading allows aerobatic figures to be performed at lower speeds and with lower G forces, or with similar G forces in a smaller airspace, in contact with spectators.

Maneuverability, mobility, and symmetry

Precise control of attitude and velocity facilitates three key aerobatic qualities:

Maneuverability: The ability to change attitude and direction on three axes. This involves the generation of forces and moments on each axis. A truly maneuverable aircraft would retain the ability to change attitude and direction at zero airspeed, and even at negative airspeeds.

Mobility: The ability to move from any location directly to any other location (within the aerobatic box). Mobility is an extension of maneuverability. To be fully mobile an airplane must be able to fly straight up and straight down (and fly at zero airspeed, or hover, with 3 axis control).

Symmetry: For every maneuver there is a geometrically opposite (mirror) maneuver.

Key Symmetries

The ideal aerobatic aircraft would demonstrate symmetrical flight characteristics on each axis. In practice, some asymmetries are unavoidable. An optimized aerodynamic device will always favor a particular direction of motion, for instance, and gravity is aways pointing straight down.

Vertical Symmetry (up/down, positive G/negative G, inside/outside maneuvers).
This is well demonstrated by all modern aerobatic aircraft, with symmetrical wings and sometimes 0,0,0 rigging (0 degrees wing incidence, tail incidence, dihedral).

Lateral Symmetry (left/right).
The natural lateral aerodynamic symmetry of a bird and most aircraft yields symmetrical flight characteristics left/right. Adding a single engine/propeller destroys this natural symmetry.

Vertical/Lateral Symmetry (side-flight, knife-edge).
Vertical/lateral symmetry requires the aircraft to perform all basic aerobatic maneuvers laterally - on its side. Aerodynamically demanding maneuvers such as loops should be flyable in side-flight (knife-edge), preferably power off. In practice this will be a qualitative symmetry; practical constraints on vertical span ensure that side-flight aerodynamic performance will always fall short of upright/inverted aerodynamic performance.

Longitudinal Symmetry (forward/aft, thrust/drag).
As with lateral aerodynamics, the goal here is to achieve a qualitative symmetry, which implies the ability to fly backwards at some low but significant (negative) airspeed under full control.
Available thrust and drag forces would ideally be comparable at a given airspeed, thus providing similar acceleration/deceleration. (In practice, thrust levels will be higher at low speeds, while more drag will be available at high speeds.)

Propulsive Symmetry

  • Asymmetric gyroscopic forces generated by a rotating engine and propeller are required to complete some tumbling maneuvers. The symmetry principle requires the ability to perform the mirror image maneuver (in yaw or pitch), impossible with a single propeller.
  • Counter-rotating coaxial propellers can provide propulsive symmetry, which creates symmetrical flight behavior right/left but precludes asymmetrical gyroscopic maneuvers.
  • Providing the ability to power down one such propeller in flight allows the option of performing gyroscopic maneuvers right and left, thus restoring symmetry while affording optimal control for torque-related maneuvering.
  • Counter-rotating coaxial propellers can provide a minimum-energy wake and thus optimal propulsive efficiency, particularly at low and zero airspeeds. (The program XROTOR predicts counter-rotating propellers in this application can produce 4-5% more static thrust than a single propeller of the same diameter absorbing the same total power.)
  • Propulsive symmetry permits a balanced hover with symmetrical roll control.

Required Accelerations

Control of velocity on three axes requires control of acceleration on three axes, and thus, control of aerodynamic and propulsive forces.

Vertical Axis( inside/outside maneuvers)
Aircraft must be capable of exceeding human limitations.
10-12G positive/negative acceleration (achieved currently).

Lateral Axis (side-flight, knife-edge maneuvers)
Side-flight loops tending towards square loops. (See Lateral Lift, below.)
4-5G left/right acceleration.

Longitudinal Axis (thrust/drag)
In order to fly vertically up and down the aircraft must be capable of producing more thrust and drag than aircraft weight. (See Propulsion System, below.)
In excess of 1G (+/-) longitudinal acceleration.
(In practice, available drag forces will be substantially less than thrust forces at low airspeeds - unless beta thrust can be employed. )

Specifications

We can thus list some specifications for our aerobatic aircraft optimized for the generalized aerobatic mission:

  • Three-axis control available at all airspeeds, including zero airspeed and some significant negative airspeed (qualitative symmetry).
  • Static thrust greater than aerobatic weight (@ 5000 ft altitude).
  • Maximum level airspeed no less than 200 mph.
  • Available drag equal to aerobatic weight at no more than 200 mph
  • Lateral acceleration capability 4-5G at 200 mph
  • Counter-rotating engines and propellers for propulsive symmetry.

Lifting System

Lateral Lift

  • A vertical planar wing of sufficient area and span to permit 5G lateral accelerations within our 200 mph speed range would, for an aircraft of average weight, quickly become ungainly and impractical. Furthermore, such surfaces would obstruct the pilot's view on standard configurations. Vertical surfaces could be added outboard but only at the expense of increased roll inertias.
  • To bring vertical span to a practical range, we require a lateral lifting system of high span efficiency. The annular wing has perhaps the highest span efficiency of any practical non-planar wing, with a theoretical maximum span efficiency of 2.
  • The annular wing is ideally suited for the aerobatic mission due to its symmetry about the roll axis, unique lift curve, high span efficiency, and structural rigidity.
  • Annular wing (duct) camber (defined here as inlet area/outlet area) should be slightly greater than one for optimal stall development. (This is not the same as duct airfoil camber, which will be close to zero for symmetry.)

Vertical Lift

  • Horizontal wing area must be appended to the annular wing to fulfill design objectives of 10-12G vertical accelerations.
  • Longitudinally distributed lifting systems (tandem, canard, etc.) are discarded since they cannot safely stall asymmetrically (snap roll, etc.).
  • A planar wing passing horizontally through the axis of the annular wing creates 90 degree intersections everywhere and structurally braces the annular wing.
  • Other configurations are possible (biplane and joined-wing variations, for instance) but none approach the overall efficiencies of the simple annular/planar wing combination.
  • Small vertical surfaces at the planar wing tips (winglets) would further increase span efficiency during upright/inverted flight. These, in addition to the ventral fins vertically supporting the annular wing, contribute further to lateral lift.
  • The ratio planar wing span/annular wing span is predominantly driven by the 12G/5G vertical/lateral acceleration requirements, and sets the relative power of the inboard and outboard lifting systems.
  • Since the annular wing and planar wing have very different lift curves, it is important to avoid stability and control complications by placing them close together longitudinally. In this way they function as an integrated lifting system rather than as isolated surfaces. Consequently the duct is nested into the trailing edge of the wing as far as possible, while considering airfoil design and structural implications.

Inboard and Outboard Lifting Systems

  • The inboard wings combine with the annular wing and ventral fins (and under some conditions the stators) to form the inboard lifting system. The outboard wings (and optional winglets) form the outboard lifting system.
  • The outboard lifting system consists of a thin, efficient airfoil with a high CLmax and sharp, deep stall break. By contrast, the inboard lifting system has a very soft stall curve, especially power on, and will keep generating lift at very high angles of attack.
  • It follows that the annular wing must be located at the correct location relative to the planar wing for proper handling through stall development of the lifting system (snap rolls, spins, etc.).

Planforms

  • Duct (annular wing) diameter is determined by lateral lift and propulsion requirements.
  • Duct chord will be larger than aerodynamic optimum in order to accommodate propellers plus clearances plus attach structures. Detail design therefore must address minimizing duct chord, and therefore aircraft length.
  • Duct trailing edge coincides with wing trailing edge. This nests the duct into the wing as far as practical, while being visually clean and structurally viable.
  • Wing chord at the wing/duct intersection is determined by duct chord, duct/wing overlap (a structural consideration), and the relative thickness/chord of the two blended airfoils at the wing chordbreak. This relative airfoil thickness is an important parameter implicit in the configuration.
  • Wing root chord is constrained by spar root location, which coincides with the fuselage attach bulkhead and the ventral fin leading edges. Thus, sweep is constrained by the bulkhead position, which is in turn constrained by engine and sump tank dimensions.
  • Wing sweep is desirable to bring wing surface area closer longitudinally to duct area. Aerodynamic sweep of the configuration will be lower than the geometric sweep of the wing, due to the duct's powerful contribution to lift.
  • Curved leading edges are optional. Double-taper wing/tailplane planforms would be aerodynamically similar (and look like. . .).
  • Straight, zero-sweep trailing edges provide clean geometric references for judging and allow suitable aerodynamic sweep.
  • Stall development over outboard wing is tailored by both planform and airfoil parameters.
  • Tail surfaces mimic lifting surface planforms for visual harmony.

Propulsion

  • It is possible to size an aircraft where propeller diameter required to achieve thrust objectives coincides with a suitable annular wing diameter to achieve lateral acceleration objectives. Therefore the propellers can be accommodated within the annular wing, bringing about a natural aerodynamic coupling between the lifting system and propulsion system. The annular wing is both a wing and a shroud, or duct.
  • Engines of high power/weight ratio are required to meet thrust/weight objectives.
  • Independently powered counter-rotating coaxial propellers provide the choice of propulsive symmetry or asymmetry right/left, while reducing energy losses at low speeds.
  • Engines must be located forward and aft of propellers to satisfy CG requirements. To be practical as both thrust and drag producing devices, the propellers must be variable pitch, featherable, programmable.
  • Engines are geared to turn propellers at appropriate RPM to optimize blade area for blade rigidity, thrust, and drag capability.

Aerodynamic coupling between propulsion and lifting systems

  • The inboard lifting system is integrated with the propulsion system and can generate significant forces at low airspeeds and high angles of attack. The magnitude of this effect has yet to be determined.
  • No assumptions are made concerning the propulsive contribution of the "duct". While a net thrust contribution is possible, this is not required by the design to fulfill its mission.

Why an aerobatic aircraft's propulsion system should be near the CG

  • Minimizes aircraft mass moments of inertia.
  • Places propellers immediately forward of the tail surfaces, thus enhancing control at low/zero/negative airspeeds.
  • Provides the opportunity to aerodynamically couple the propulsion system and lifting system.
  • Provides the opportunity to increase propeller drag levels beyond those possible with a forward propeller (unproven).
  • Forces cockpit forward (ergonomically optimum).

The Hummingbird Configuration

The lifting system and propulsion system together form the heart of the configuration. Pilot accommodations, tail surfaces, and landing gear complete it.

  • Cockpit is located forward, attached to the duct through the inboard wings and ventral fins.
  • Since an engine must be located aft of the propellers (to achieve correct CG), structure must exist connecting this aft engine/propeller to the duct. This structure also supports the aft fuselage; thus all fuselage loads go through the duct, and not through the propellers.
  • Propellers rotate on a fixed tubular axle suspended between the forward and aft fuselages. There are no cantilevered propeller shafts.
  • Access between forward and aft fuselages is through the propeller axis. This forces the engines off-axis. Engine access on the ground is optimized if the aft engine is above the axis, the forward engine below.
  • Tail surfaces are cruciform, placed centrally in the propeller wash for positive control at low/negative airspeeds. Upper/lower fin/rudder planforms are as symmetrical as possible to ensure good yaw authority in any spin.
  • Narrow-chord control surfaces (statorons) inhabit the stator trailing edges. These surfaces are connected to the ailerons for roll control at low/zero/negative airspeeds (power on).
  • Taildragger type main landing gear attaches to forward fuselage, tailwheel to lower fin.

Structural System

  • The annular wing (duct) is the heart of the structural system. The inboard wings and ventral fins connect the forward fuselage to the duct leading edge at four points. Four "stators", rotated 45 degrees from square, connect the aft engine and fuselage to the duct aft spar. Thus all fuselage loads go through the duct.
  • The inboard wings, fins, stators, and duct together form an offset octagonal truss. For this to work, the duct must resist the torsional loads resulting from the offset geometry (possible with a thick airfoil).
  • The wing trailing edges brace the duct at two further points, bringing the total to 10. If necessary, structural stiffness can be further enhanced by adding two vertical struts bracing the top and bottom aft duct spar to the aft fuselage. This would effectively create an octagonal truss at the aft duct spar.
  • The wing connects into the forward fuselage and is pinned to the duct forward and aft shear webs. Thus the wing is braced in both bending and torsion and is free to flex under load while putting only point loads into the duct.

Conclusion

I conclude my simplified derivation of the Hummingbird Configuration for Aerobatics. While not addressing every corner of the Generalized Aerobatic Mission, the configuration promises to demonstrate a wider aerobatic envelope than any preceding aircraft.

Philip Carter
May 15, 2000

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