• Choosing the physics for the Escort

    The gunship escort studied here is a new concept, the centre-line tiltrotor, tailored to the formidable task of escorting the MV-22 throughout its mission.

    On an MV-22 mission to insert or extract troops at a landing zone deep in hostile territory, the escorts must protect the MV-22s every step of the mission and especially at the landing zone. Landing zone duties would be scouting, suppressing hostile fire to clear a window for the troop insertion or extraction, acting as spotter for other providers of air cover, and providing communications or related support. The escort should have a contingency reserve, and speed in hand, so that if diverted it can catch up to rejoin the MV-22 mission. An escort that has the speed but not the range, or has the range but not the speed, will penalise MV-22 operations.

    Once at the landing zone, the escort needs agility and endurance at very low speeds, especially when operating at hover. The physics of the rotary wing is particularly well adapted to this type of duty. Other schemes, successfully used in V/STOL aircraft, achieve hover at the expense of much higher fuel consumption. The reason for this is that fuel efficiency is directly proportional to the diameter of the column of air supporting the aircraft. The large diameter rotor of a helicopter gives it a major advantage in hover efficiency over the relatively small diameters of V/STOL nozzles.

    It is concluded that the escort will have a rotary wing for hover and low speed flight.

    For the cruise portion of the mission, the escort needs speed and range, so the next criterion for choosing the physics for the escort is cruise efficiency, the lowest drag design at MV-22 cruise speed.

    There is a wide range of possible configurations, represented here by three generic concepts:

    • Helicopter
    • Compound helicopter
    • Tiltrotor

    The principal assumptions for their cruise modes are that for the helicopter, all vertical lift and horizontal thrust are provided by the main rotor(s); that for the compound helicopter, lift may be provided in part or wholly by fixed wings and thrust by propeller or other means; and for the tiltrotor that the wings provide all the lift and the tilted rotors all the horizontal thrust.

    In hover, tiltrotors, helicopters and compound helicopters share the same lifting physics: the rotor. For the same aircraft weight and rotor effective areas, the power needed to hover is the same for each concept.

    In cruise, the lifting physics are different. Tiltrotors use fixed wings, helicopters use rotors, and compound helicopters use a combination of rotor, separate propulsion and wings. The difference in the drag of rotors and wings at high forward speeds is a key issue.

    For the same duty in cruise, rotors have much higher drag than wings. This is because the advancing blades face into the wind and so reach Mach number limits sooner. The retreating blades face away from the wind and have to operate closer to stall. Both situations require the blade airfoils to operate away from their optimum and are high drag compared with that of the wing whose airfoil can be designed to operate at the optimum cruise speed.

    The subjective comparison in Table 1 immediately suggests that tiltrotors have a significant advantage over pure helicopters.

    Compound helicopters also have a significant advantage over helicopters by reducing the work of the rotor in cruise, an effective way of reducing their drag.

    Table 1. Sources of drag in Cruise for three escort concepts
    Source Helicopter Compound Tiltrotor
    Fuselage drag Full Full Full
    Rotor drag Full Reduced 0
    Wing drag 0 Full Full

    At present there are advanced compound helicopters in test (Ref. 8, 9) each with a different mix of approaches to make significant performance improvements. In forward flight, the rotor of a helicopter provides lift and the propulsive thrust to maintain speed. Adding an efficient fixed wing to a helicopter allows the rotor lift to be off- loaded. Adding a separate propeller, jet or ducted fan can relieve the rotor of its propulsion duty. Reducing rotor rpm at high forward speed allows advancing blade losses to be reduced. Using two main rotors that contra-rotate achieves torque balance without the losses of a tail-rotor, and if side- by-side or co-axial, allows the use of opposing lateral cyclic to off-load retreating blades to reduce their losses.

    From a subjective point of view, compound helicopters should be able to match the speed of the MV-22 at cruise. However it is difficult to believe that their rotor drag and its penalty on range can be removed entirely.

    At MV-22 mission cruise speeds, all else being equal, the physics of a tiltrotor is assessed as having lower drag than the competing concepts, so that is the chosen physics for the gunship escort studied in this paper.

    This was felt to be a good choice because it means that the basic physics of the MV-22 and its escort are the same. Where the MV-22 goes, so can its escort.

  • Configuration down-select

    Having chosen to stay with the well proven physics of the XV-15, MV-22 and BA609 tiltrotors does not mean that a wing-tip rotor layout suits a gunship. So the study next considered the tiltrotor layout implications for an escort.

    Keeping the proprotors at the wing tips

    For a transport, having the tilting proprotors at the wing tips brings important advantages: efficient use of the proprotors and freedom in designing the fuselage for loading and for airdrop and similar priorities.

    Equally, having the tilting nacelles and proprotors at the wing tips would meet the speed and range needed for escort duties. The downside is that the nacelles and proprotors are relatively bulky. Their presence on the wing tips mean the field of view and fire from the cockpit forward is less good than a helicopter gunship. The blades spread beyond the aircraft′s wing tips so the spot deck area is high. The weight penalty for wing-slew for stowage remains. Also the wing design and its aerodynamics are constrained by carrying the nacelles, and the roll and yaw moments of inertia are high. The high rate of descent Vortex Ring State (VRS) should be the same, including the positive feedback causing un- commanded roll (Ref. 10). The robust strategy of applying forward tilt for recovery from VRS should also apply.

    Moving the proprotors to the centre line of the aircraft

    Assume that the rotors are brought to the centre line of the aircraft in a compact arrangement, as co-axial or as intermeshing rotors.

    It is likely that the effective disk loading may need to be higher, but spot deck area and roll inertia are reduced. Simpler wing fold can be used for stowage, and there are different aerodynamic and structural options for the wing design. The vortex ring state will occur, as in all rotorcraft, but having the rotors compactly together on the aircraft centre-line should reduce or eliminate un-commanded roll.

    These changes move the tilt rotor concept from transport towards an agile gunship.

    Placing the tilting rotors on the fuselage is not new. In 1929 George Lehberger had very similar ideas, see Figure 2

    Discussing a modern version of this approach with a manufacturer, the most telling comment was that tilting the coaxial rotors forwards placed a heavy transmission immediately above the cockpit and placed the rotors into the forward field of view.

    This was seen as a distraction to the crew. It certainly reduces their field of view, denies safe egress in airplane mode, and denies some convenient locations for weapons and sensors.

    flying_mach

    Taking these perceived pros and cons into account, it was decided to survey all "possible" centre-line tiltrotor configurations.

    Survey and down-select of possible centre-line tiltrotor configurations

    The survey and down-select were based on a light aircraft application, which meant that safety issues took a priority as well as having the common interest in range at cruise speed. Nine centre-line tiltrotor configurations were compared with five examples of other rotorcraft and fixed wing configurations. Figure 3 shows cartoon sketches of some of the 9 centre-line concepts.

    One difference between the tiltrotors is the quadrant of tilt: the Osprey is 1st quadrant, 0° to 90°. Option 2 is also 1st quadrant. Options 4B, 6A, 6B and 7 are 2nd quadrant, 90° to 180°, and option 3 is 3rd quadrant, 180° to 270° which was proposed in the Focke-Angelis FA 269 concept. The 4th quadrant, 270° to 360°, was considered of no interest.

    Descriptions, comments and estimates of cruise speed, range and some other parameters were built up as a spreadsheet, and then grouped by topic to be ranked in comparison tables.

    cartoon

    The process was iterative. If a comparison table showed a problem and there were a credible fix, the comparison was updated. If the fix was effectively a new configuration then that was added separately, e.g. configuration 4 became 4A and 4B. In the next iteration 4B was eliminated because it relied on a pusher prop during rotorcraft conversion from helicopter mode to wing mode.

    The process finished with selection of configuration 6B. This concept has intermeshing rotors that are mounted on the aircraft centre line and in the airplane mode are tilted back behind the fuselage to operate as pusher props. For safety, the proprotors are tilted one-at-a-time to make the conversion between helicopter and airplane modes.

    The 6B configuration was sized to the duty of a gunship escort, see Figure 4. The concept appeared novel and was granted US Patent 7,584,923 B2 in Sep. 8, 2009.

    fig4
    Figure 4. The chosen configuration is shown here in airplane mode where the rotors operate as pusher props.

    Thus the configuration shown in Figure 4 is the basis of the following proposed specification for the Escort and the assessment of its potential performance.














  • Escort specification and performance

    Figure 4 shows a side view of the proposed Escort in airplane flight mode; Figure 5 shows a 3-vu of it in hover.

    The specification set out in Table 2 is proposed as the basis for assessing the Escort concept:

    Table 2. Proposed Specification
    Crew: pilot & co-pilot/gunner 2
    Powerplant: 1 turboshaft 6,150 shp
    Length, width 36 ft, 32 ft
    Rotor diameter 24 ft
    Empty weight 13,300 lb
    Max internal fuel 5,150 lb
    Vertical take-off, max weight 19,500 lb
    Service ceiling 25,000 ft
    Hover out of ground effect, max 6,400 ft
    Max cruise, sea level 250 knots
    Mission radius @ 240 knots, 2,500 ordnance payload 285 nm

    To assess this proposed specification, it is helpful to compare the Escort with the assumed characteristics of the MV-22.

    General comparison, see Table 3.

    The Escort should be operated, equipped and armed as a typical gunship, but with the performance advantages of a tiltrotor so that it can escort the MV-22.

    The Escort's two meshing rotors are mounted on the centre-line of the fuselage. They tilt back for cruise, give superb field of view for crew and sensors, and a wide field of fire for weapons and countermeasures. Having meshing rotors that tilt back gives a very compact design.

    The suite of controls available to the Escort′s flight control system is assumed to be similar to the MV-22: cyclic, collective and tilt for rotary wing, primary and secondary controls surfaces for fixed wing mode. An important addition is articulation of the leading portion of the main wings.

    Table 3. Comparison of the Escort and the MV-22**
    MV-22** Escort
    Spot area, ft x ft 83 x 58 36 x 32
    Field of view/fire good superb
    Engines, max hp 2 x 6,150 1 x 6,150
    Max VTO weight, lb 52,600 19,500
    Empty weight, lb 35,300 13,300
    Service ceiling, ft 25,000 25,000
    Hover OGE, max, ft 5,400 6,400
    Max cruise, sea level, kn 250 250
    Mission radius, nm 230 285
    ** Brochure, or author′s estimate not validated by manufacturers

    Blade meshing is required for all relative tilt positions of the rotors. Mechanical meshing is assumed. Slewing the wings for stowage is not needed. Rotor blade stow and wing fold are assumed.

    Take-off in helicopter mode

    The payload achieved depends on the difference between the unloaded weight and the maximum take-off weight (MTOW).

    The unloaded weight of the Escort has been estimated from an example helicopter by taking the weight groups that must change and scaling them according to rotor radius R, first to the AH-1Z and then to the escort duty.

    For example mass of the blades was scaled as R1.3, the hubs as R1.5, and transmission as R1.5 P0.82 (Ref. 11).

    MTOW in turn depends on the lift capability in hover out of ground effect (HOGE), the power requirement of the rotors, and the power actually available. Table 4 shows the estimate of power for MTOW as a percentage of maximum power available, % max hp, plus other parameters: the rotor solidity σ, the percent of rotor lift blocked by the wing/fuselage in the rotor downwash, the effective disk loading, DL, the blade loading Ct/σ, and the figure of merit, FM, estimated from:

    formula1

    Ct is the thrust coefficient, κ = 1.15, and Cd0 = 0.01 (Ref. 12).

    The control power at take-off, that is the margin in lift available to accelerate the aircraft vertically, expressed as a percent of hover lift, was estimated from the maximum engine power available.

    fig5
    Figure 5. Three views of the Escort in the hover mode. The meshing rotors are tiltable about the F-F axis

    The Escort has its two meshing rotors set at 11° relative to the airframe XZ plane, with the hub separation approximately 0.55 R. Solidity and disk loading were estimated using the effective area of the overlapping disks projected onto the XY plane.

    In hover, where the downwash from the rotors meets fuselage or wings, there is some loss of lift by blockage of part of the rotor flow. On the Osprey, the effect is halved by deploying the flaperons (Fig. 1).

    On the Escort, the wing blockage is larger, and greater articulation of the surfaces would be needed. For example, the plan view of the Escort in Fig. 5 shows axes to hinge leading and trailing surfaces. In principle these should achieve the rotor blockage factor shown in Table 4.

    Table 4. Take-off: Escort and the MV-22**
    MV-22** Escort
    MTOW, lb 52,600 19,500
    Blades/rotor 3 3
    Solidity, x 0.12 0.2
    Rotor blockage, % lift 8.9 4.8
    Disk loading, lb/ft² 25.3 34.1
    Blade loading, xx 0.15 0.12
    Rotor figure of merit 0.81 0.80
    Engine(s) % max hp 84 71
    Control power, % lift AH-1Z: 17.1** 21.4
    ** Brochure, or author′s estimate not validated by manufacturers

    Cruise, airplane mode

    The physics of achieving range, devolves into the fuel factor achieved at take-off and the range achieved with that fuel factor at cruise speed.

    Fuel factor, Fuel/MTOW, is taken as fuel available for the mission at take-off, as a proportion of the all up weight at take-off, fully manned, fuelled and equipped with communications, sensors, weapons, stores, counter measures etc to perform its part of the mission.

    Range is estimated using the Breguet formula (Ref. 13)

    formulaBreguet

    This gives a working estimate of range allowing the concepts to be compared.

    As a comparison, assume identical specific fuel consumption, SFC, transmission efficiencies, ζ, and weight of fuel as a proportion of all-up-weight, Fuel/MTOW. Then what separates the designs, is their effective aircraft lift-to- drag ratio, L/D, and their propeller efficiencies.

    Applying these in the Breguet formula, gives an estimate of the capability of the Escort when teamed with the MV-22 on a land assault mission, see Table 5.

    Note that the Escort has been credited worse propulsive efficiency and better aircraft lift to drag ratio L/D. The net effect is better mission radius, but behind these choices is the important design issue of thrust reversal.

    When the Escort's proprotors are tilted back to act as pusher props, their thrust must be reversed. So collective pitch has to be reversed, and if the blades are twisted then twist has to be reversed as well.

    The low risk solution is to use untwisted blades and accept the lower proprotor efficiencies. That is the basis of Table 5.

    A more satisfactory solution would be to use variable twist blades, if feasible. The technology is being researched elsewhere, and should at least be investigated for its potential for the Escort.

    Table 5. Land Assault: Escort mission with the MV-22**
    MV-22** Escort
    Payload, troops or ordnance 24 troops 2,500 lb
    Fuel, lb 5,940 2,685
    TOW, lb 47,000 18,920
    Cruise % max, shp 35 21
    Cruise SFC, lb/shp/hr 0.42 0.42
    Prop. efficiency 0.75 0.65
    Cruise lift/drag, L/D 9 11
    Mission cruise, kn 240 240
    Mission radius, nmi 230 285
    ** Brochure, or author′s estimate not validated by manufacturers

    In designing for hover, careful attention is needed to reduce wing blockage of the rotors, and in cruise, careful attention is needed to wing design to achieve better aircraft L/D.

    Conversion between helicopter and airplane modes

    From a pilot's point of view, it is proposed that the Escort have the same controls and authority as the MV-22.

    On the MV-22, the thumbwheels on the crews' Thrust Control Levers (TCLs) are used to control conversion via proprotor nacelle angle. For each nacelle angle, the aircraft has a viable flight envelope within speed boundaries, part of the tiltrotor's conversion corridor. At any point in the conversion the crew can choose to hold the nacelle angle, reverse or continue to the flight mode that suits.

    For the Escort, it is proposed to use the same approach of thumbwheels on the crews' TCLs: at any point in the conversion the crew can hold, reverse, or continue as required. The Escort's Flight Control Computers (FCCs) must achieve this objective using a different tilting strategy from the MV- 22.

    fig6
    Figure 6. Within the conversion corridor, the rotors can be tilted one-at-a-time between the helicopter and wing models. The transitioning rotor′s thrust is kept substantially zero, while the other rotor maintains the flight thrust.

    First, the conversion from helicopter to airplane mode is tilting backwards to pusher propulsion rather than forwards to tractor propulsion as MV-22. Second, pusher propulsion disallows the proprotor from delivering thrust while tilted between 90° and 180°. Therefore for safety, the proprotors must transit one-at-a-time, so that while one transits, the other provides all the thrust needed, see Figure 6.

    During the one-at-a-time transition the balance of symmetry of the two meshing rotors is lost and so the fixed wing control surfaces (see Figure 5) are sized to trim and control the aircraft. If necessary, control can be augmented by cyclic from the rotor providing aircraft propulsion.

    To match the MV-22 conversion times the Escort, because of its one-at-a-time procedure, needs to tilt the proprotors at twice the speed of the MV-22. As a bench mark, a conversion system capable of tilting the MV-22 proprotors at 8°/sec should be capable of tilting the Escort′s at 16°/sec. A 2-degree freedom (x, z) math model was used to compare speed, wing lift coefficient Cl and rotor blade loading coefficient Ct/σ, during a conversion.

    The point chosen on their flight envelopes was sea level, starting from 60 knots in helicopter mode to about 115 knots in airplane mode, both at minimum operating weights. The math model factors in drag of fuselage, nacelles/masts, weapon stores, wing profile drag, and wing induced drag as a function of wing lift. The rotors are treated as thrust vectors, variable in magnitude and variable in direction by tilting.

    fig7 Figure 7. The Escort and the MV-22** (author′s estimates) transitioning from 60 knots in helicopter mode to about 115 knots in airplane mode.

    Level flight requires that the lift of the wings exactly makes up any deficit in vertical component of lift from the rotors. This allows the math model to be reduced to a single degree of freedom, here expressed in Mathematica® code:

    formulaLevelflight

    The Escort accelerates first then tilts its rotors one-at-a- time over the next 15 seconds to complete the conversion.

    To represent this (Figure 10), piecewise functions of time were used for the pilots/FCCs inputs, flying the aircraft level, while increasing speed and making the conversion.

    Solving for forward velocity v[t] gave the comparison shown in Figure 7.

    This strategy keeps the wing away from stall as shown in Figure 8

    fig8 Figure 8. Wing coefficients of lift Cl, as a % of stall, during the transitions showm in Figure 7 for the Escort and the MV-22** (author′s estimates)

    The range of wing coefficients of lift Cl during the transitions seems an acceptable % of stall. The jagged shape reflects the one-at-a-time tilting of the Escort′s proprotors, and shows even more clearly in Figure 9 where the thrust modulation of the proprotors determines the blade loading Ct/σ throughout the conversion manoeuvre.

    The range of blade loading Ct/σ during the transitions seems acceptable.

    The math model of the Escort′s one-at-a-time conversion shown in Figure 7 used the piecewise functions plotted in Figure 10. Throughout the transitions the meshing rotors must be kept in strict phase to avoid blade interference.

    For the point on the sea level flight envelope chosen for assessing conversion: 60 knots in helicopter mode to 115 knots in airplane mode, it is concluded that stall margins for the wings and blades were comparable with those assessed by the author for the MV-22 performing a similar conversion.

    fig9 Figure 9. Proprotor blade loading Ct/x for the conversion shown in Figure 7 for the Escort (LH rotor shown) and the MV-22** (author′s estimates)
    fig10 Figure 10. Piecewise one-at-a-time tilting as used in the math model for the conversion of Figure 7.

    The above assessments indicate that an Escort designed to the proposed specification would be compact, agile, longer range and as fast as the MV-22, in short, an excellent gunship escort for the MV-22.

  • Meshing Aerodynamics and Mechanics

    Meshing Aerodynamics

    The aerodynamics of fixed meshing rotors has a firm foundation in research, development, manufacture and extensive operational experience. Historically, the Kaman Huskie, and currently, the Kaman K-MAX provide practical benchmarks.

    The principal features that distinguish the Escort from that background are:

    • Rigid proprotors with high loading
    • Cruise thrust reversal as a pusher prop
    • One-at-a-time tilting in transition

    All of these are complex problems in their own right and so to make these studies manageable, blade element theory, vortex theory or CFD were not contemplated. Instead the rotors have been treated as the simple thrust or actuator disks of conventional helicopter momentum theory. Adjustments for blade tip and root losses, blockage by wing and fuselage, and overlap of rotors, were made as seemed appropriate.

    Nevertheless a lot of time was spent thinking through the broad aerodynamics of one-at-a-time tilting in transition. These are the conclusions drawn that give confidence of a successful outcome.

    Firstly, it is important that, in transition, a rotor produces zero net thrust: if there is thrust at least one of the resolved components is in the wrong direction. The other rotor, the one sustaining lift/propulsion, can be visualized as having the flow field of the single rotor on the aircraft but experiencing an additional, local, turbulence generated by the profile drag of the zero lift rotor. The power in that turbulence is significant but unlikely to hazard the sustaining rotor.

    Secondly, achieving zero net lift throughout the range of tilt involved does appear feasible. The rotorcraft is in cruise so the overall flow field is continually swept clean. Aerodynamically the rotor is unaware of its angle of tilt. It sees only the angle of the air flow relative to its tip path plane and in particular its normal component.

    The normal component starts at zero velocity for 90° tilt, growing to full aircraft velocity at 180°. It is always in the direction expected by a rotor climbing "up" the prevailing inflow. Moreover, the induced flows for zero thrust are small compared to the normal inflow component and so the rotor is operating within the regime where momentum theory is a reliable guide.

    It is concluded that zero net thrust should be easily achieved by trimming collective pitch. It will be interesting to see how the transition tests of the 1/10th scale model perform.

    Meshing Mechanics

    At the start of the studies a rotor model had been constructed of two 4-bladed rotors, arranged in tandem, inter-meshing at speed that tilted back and forwards one-at-a-time. It was clear that in helicopter mode, the tandem configuration placed the rear rotor in the wash of the leading rotor, and in airplane mode created a high profile to the aircraft. Placing the intermeshing rotors side-by-side avoided these disadvantages so a mechanical model was constructed (Figure 11) that demonstrated side-by-side one- at-a-time tilting of intermeshing rotors was feasible.

    fig11
    Figure 11. Mechanical model used to demonstrate one-at-a-time tilting of intermeshing rotors to a pusher prop position.

    The mechanical model was also a practical way of showing that thrust reversal was an essential part of this tiltrotor strategy. To go beyond such basic observations, math models were used.

    The next steps were to develop two math models of meshing and tilting: a trigonometry model for a math approach, and a 3D model allowing animation for an interactive parametric approach.

    In its simplest form, the math model of meshing error θ as a function of angle tilt φ reduced to

    formulaAngletilt

    Where gammagamma is twice the angle of cant between the meshing rotors when aligned, as when both are vertical.

    This gave agreement, within measuring errors, of a bench model, see graph of Figure 12, and in its fuller form allowed investigation of the important effects of offsetting the hinge axes about which the rotors tilt.

    fig12 Figure 12. Mesh angle: math and mechanical models compared.

    The math model was used to choose appropriate gearing to minimize the phase errors between the meshing proprotors.

    Visualising the results was difficult, so a 3D animated math model was written to investigate the variables interactively. This gave the meshing process in slow motion and could be frozen at points of interest, to rotate or zoom the 3D image. Figure 13 is a snapshot from an investigation of a pair of two-bladed rotors.

    fig13
    Figure 13. Snapshot from 3D animated math model of blade meshing. Rotors canted 11° to the XZ plane and tilted to 90° vertical. Axis of tilt offset vertically towards the rotor hubs. Projected area is 1.3 times a single disk.


    The conclusion drawn from these differing investigations was that for correctly phased rotors, the minimum clearance occurs with the rotors aligned when each blade overflies the opposing rotor hub. This gave the designer a clear starting point for transmission and tilting systems design. It also provided a practical check on models, pre-test or pre-flight. This was to align the rotors to the same tilt angle, turn a rotor by hand until one of its blades is over the opposing hub, then check the blade to hub clearance and finally check that the opposing blades mesh symmetrical about it.

    This assessment, based on maths and bench tests, suggests that the meshing and tilting mechanics of one-at-a- time transitions are feasible and have a logical pre-flight check discipline.

Nomenclature

A effective disk area of the rotor(s), ft²
cant(°) angle of mast relative to XZ plane
Cd0 section zero-lift drag coefficient
Cl wing lift coefficient
Ct rotor thrust coefficient, T/ρ A (ΩR)²
Ct/ σ blade loading coefficient
DE differential equation
DL disk loading, T/A
FCC flight control computer
FM figure of merit
fusDrag fuselage drag, lbf
HOGE hover out of ground effect
L/D aircraft lift to drag ratio
MTOW maximum TOW, lb
NDSolve a numerical DE solver
P power, hp
propEffic propeller efficiency
R rotor radius, ft
SFC specific fuel consumption
T rotor thrust, lbf
Tilt(°) rotation about x-axis: 0° is full forward, 90° is hover, 180° is fully back for cruise
TCL thrust control lever
TOW take-off weight, lb
gamma(°) twice cant(°)
ζ transmission efficiency
θ mesh angle, or mesh error
κ induced power factor
ρ air density
σ rotor solidity, ratio of total blade area to A
φ mast angle of tilt

Download papers and presentations

Reference Downloads
American Helicopter Society
International, Forum 69, Phoenix AZ, 21-23 May, 2013
Figure of Merit of Meshing Rotors ‐ effects of overlap, blade twist and cant (lateral tilt) AdobeAbstract Forum 69 - pdf 720K
The Aeronautical Journal, April 2013, Volume 117 Enabling technologies for a Centre-line Tiltrotor AdobePaper TAJ No 1190 - pdf 454K
University of Liverpool, November 2012, UK Seminar on Centre-line Tiltrotor concept
University of Liverpool, November 2011, UK Seminar on Centre-line Tiltrotor concept
RAeS Oxford Branch, 20 September 2011, Oxford, UK A Centre-line Tiltrotor - background and progress to Sept. 2011 Adobe Slides RAeS Oxf11 - pdf 6700K
The European Rotorcraft Forum, 13-15 September 2011, Galarate, Italy 10th Scale Model Tests of a Centreline Tiltrotor Adobe Paper ERF37 - pdf 487K

Adobe Slides ERF37 - pdf 3300K

The Future Rotorcraft, 15-16 June 2011, RAeS, London Enabling technologies for a Centre-line Tiltrotor Adobe Paper FTR11 - pdf 705K
International Powered Lift Conference, October 5-7, 2010. Philadelphia, PA, USA Studies of a Gunship Escort concept for the MV-22
(Centre-line Tiltrotor concept)
Adobe Paper IPLC10 - pdf 700K

Adobe Slides IPLC10 - pdf 1200K

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