_____________________________________

Presented at the AHS Aeromechanics Specialists' Meeting, November 13-15, 2000, Atlanta, Georgia.

DESIGN OF THE ACTIVE ELEVON ROTOR FOR LOW VIBRATION

Mark V. FultonResearch Scientist

Army/NASA Rotorcraft DivisionAeroflightdynamics Directorate (AMRDEC)US Army Aviation and Missile Command

Ames Research Center, Moffett Field, California

Introduction

Helicopter fuselages vibrate more thandesired, and traditional solutions have limitedeffectiveness and can impose an appreciableweight penalty. Alternative methods ofcombating high vibration, including HigherHarmonic Control (HHC) via harmonicswashplate motion and Individual Blade Control(IBC) via active pitch links, have been studied forseveral decades. HHC via an on-blade controlsurface was tested in 1977 on a full scale rotorusing a secondary active swashplate and amechanical control system (Ref. 1).

Recent smart material advances haveprompted new research into the use of on-bladecontrol concepts. Recent analytical studies (Refs.2-3) have indicated that the use of on-blade controlsurfaces produces vibration reduction comparableto swashplate-based HHC but for less power.Furthermore, smart materials (such aspiezoceramics) have been shown to providesufficient control authority for preliminary rotorexperiments. These experiments were initiallyperformed at small scale for reduced tip speeds(Refs. 4-8). More recent experiments have beenconducted at or near full tip speeds (Refs. 9-10),and a full-scale active rotor is under developmentby Boeing (Ref. 11) with Eurocopter et al. (Ref. 12)pursuing a similarly advanced full-scaleimplementation.

The US Army Aeroflightdynamics Directoratehas undertaken a new research program called theActive Elevon Rotor (AER) Focus Demo. Thisprogram includes the design, fabrication, andwind tunnel testing of a four-bladed, 12.96 ft

diameter rotor with one or two on-blade elevonsper blade. The rotor, which will be Mach scaled,will use 2-5/rev elevon motion for closed-loopcontrol and will be tested in late 2001. Theprimary goal of the AER Focus Demo is thereduction of vibratory hub loads by 80% and thereduction of vibratory blade structural loads. Asecondary goal is the reduction of rotor power.The third priority is the measurement andpossible reduction of Blade Vortex Interaction(BVI) noise.

The present study is focused on elevoneffectiveness, that is, the elevon's ability to reduceall six components of the nonrotating 4/rev hubloads. Some design parameters have been keptfixed in this study, while others have been variedto determine their influence on elevoneffectiveness. The fixed parameters include allblade structural properties except for torsionstiffness; the varied parameters include torsionstiffness, elevon aerodynamic location, and thenumber and individual authority of elevonaerodynamic surfaces. This paper describes thepreliminary design process being used for theAER, and describes and quantifies the emergingactive rotor characteristics.

Rotor Description

The Active Elevon Rotor (AER) will be a four-bladed articulated rotor with a 12.96 ft diameter, arectangular planform, and linear twist. One airfoil(the VR-18 with a 0.04 c tab at -3 deg, Ref. 13) willbe used for the entire blade aerodynamic crosssection. Blade properties will be uniform (exceptfor inherent differences at the blade root and,

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possibly, in the active section). Structuralproperties for the baseline AER will be those usedfor the 27% Apache rotor (Ref. 14). The nominalrotor speed will be 1,070 RPM (17.83 Hz). Rotorproperties are given in Table 1. The rotor radius,chord, and tip speed match the ideally scaled 27%Apache (Ref. 14) and are compatible with theArmy Rotorcraft Test Stand (ARTS) to be used forthe AER.

Blade structural properties are varied from abaseline during preliminary design. The baselineblade properties are taken from the ideally scaled27% Apache properties (Ref. 14) and are listed inTable 2 for the uniform section. Structuralvariations from the baseline will be discussedlater.

Elevon Sizing and Aerodynamics

The elevon is a plain trailing-edge controlsurface, which indicates that there is noaerodynamic balance; specifically, the elevon isassumed to pivot about the airfoil mid thicknessand to have a semi-circular shape forward of thehinge point. Two-dimensional (2-D) thin-airfoiltheory indicates that elevons are more efficient forsmaller elevon chords. That is, more lift andmoment are produced for a given amount ofelevon work for smaller elevons. It was believedthat an elevon size of 0.15 c or 0.20 c would beoptimum for the present investigation. Since thin-airfoil theory is not sufficiently accurate forcalculating elevon aerodynamic coefficients, a 2-DCFD (Computational Fluid Dynamics) study wasperformed by Ray Wong and C.P. van Dam (UCDavis) using MSES (a viscous/inviscid interaction,integral boundary layer code, Ref. 15).Preliminary results from their study indicated thatthe 0.15 c elevon would be significantly moreefficient (than a 0.20 c elevon) for representativecombinations of angle of attack and Mach number(Ref. 16). Because of these preliminary CFDresults and since a 0.15 c actuator configurationwas under investigation by Domzalski Machine asdescribed in the next section, the 0.15 c elevon wasselected for the present preliminary rotor bladedesign study. Elevon aerodynamic coefficientsused in the study were clδ = 2.29/rad and cmδ =-0.427/rad (Ref. 16).

Actuation

The actuator used for the AER is part of theDomzalski CAT (Conformal Actuator Technology)series (Ref. 17). This actuator uses a piezoceramicmaterial and has been sized to provide ±5 degdeflection of a 0.15 c elevon operating at 463 lb/ft2,the dynamic pressure at 0.86 R in hover. Theactuator is radially co-located with the elevon.Domzalski conceptual sizing for the AER providesa minimum elevon span of 3.1 in (or 0.04 R), withmultiples of this minimum size available asrequired. This minimum span will be referred toas a "single-wide" actuator; a total of four suchsingle-wide actuators have been anticipated, or atotal span of 0.16 R, although the preliminarydesign will need to determine the adequacy of thisestimate. The total actuator weight used for thisstudy was fixed at 0.52 lb, which corresponds to a12.4 in span, including balance weights for achord-wise center of gravity at 0.263 c. Thisweight was assumed to be evenly distributedbetween .68 and .84 R. The actuator weight andgeneral configuration may remain unchanged forvarious elevon positions, although appropriatemodifications can be made to keep the actuatorstiffness equal to the aerodynamic stiffness tomaximize work output. Thus, as the elevonaerodynamic location was varied in this study, themaximum elevon angle was varied in proportionto 1/rδ , where rδ is the radial position of theelevon mid-span.

Modeling

All calculations were performed usingCAMRAD II (Ref. 18) with a common structuraldefinition. This model consisted of eleven (11)structural elements for the blade, and severalelements defining the articulating portions of thehub, with the non-articulating portion of the huband the control system assumed rigid.

The aerodynamic surface of the blade wasmodeled as a lifting line with twenty (20)aerodynamic panels. The blade aerodynamicloads were calculated using table look-up toaccount for static nonlinearities due to angle ofattack and Mach number; dynamic stall wasneglected. The airfoil table was developed byBoeing for a variant of the VR-12 similar to theversion being used for the AER, with CAMRAD IIadjustment for zero-lift angle and a momentcoefficient increment to account for a tab angle

3

change. Unsteady aerodynamics was representedby the thin airfoil model.

Wake modeling varied with the analysis beingperformed. For all hover calculations, uniforminflow was used. For forward flight calculations,a free wake model was used.

Elevon aerodynamics was modeled using thelinear coefficients given in a previous section.

Trim was calculated for the nonlinearstructural elements in hover (without modalanalysis), but 8 trim blade modes were used whencalculating harmonic balance in forward flight.Forward flight trim targets were CT/σ = 0.10 (T =1,534 lb), a propulsive force of 2.0 ft2 times thedynamic pressure, and zero 1/rev flapping; trimcontrols were collective, longitudinal shaft tilt(positive aft), and cyclic pitch angles. The fuselageequivalent flat plate area of 2.0 ft2 is 0.015 timesthe rotor area and yields -4.0 deg shaft tilt for thebaseline model at an advance ratio of 0.30. Hovertrim was calculated for a fixed collective pitch of9.5 deg, zero shaft tilt, and zero cyclic pitch angles,yielding CT/σ = 0.10 for the baseline model usinguniform inflow.

Frequency response functions were onlycalculated in hover and were based on a fluttersolution which approximates the control (i.e. theelevon) as a quasi-static variable, although theother degrees of freedom are treated as dynamicvariables. Calculations were made for 4/rev hubload response to 4/rev elevon modes, all in thenonrotating frame. Both 4/rev thrust (T) and4/rev torque (Q) loads are affected by the 4/revelevon collective mode (δo), and the in-plane hubloads (shears and moments) are affected by the4/rev elevon cyclic modes (δ 1s and δ 1 c). Thesymmetry of hover means that the response of thelateral force to longitudinal elevon cyclic (Y/δ1c) isequal to the response of the longitudinal force tolateral elevon cyclic (-H/δ1s); similarly, Y/δ1s =H/δ1c . Analogous relations exist between the rollmoment (Mx) and pitch moment (My). Thus, thenonrotating hover transfer functions are governedby six unique relations, T/δo , Q /δo , H/δ1c , H/δ1s ,Mx/δ1c , and Mx/δ1s , for each elevon radial location.Of the two longitudinal responses, H/δ1c and H/δ1s ,one will generally be larger than the other,suggesting a preferred control (either δ1s or δ1 c)when circumstances permit; likewise for Mx/δ1cand Mx/δ 1s . The elevon cyclic mode whichmaximizes a given in-plane response will bedenoted as δ1x . This simplification will be usedduring some of the following analysis when itappears advantageous and reasonable.

Natural Frequencies

The natural frequencies of the baselinestructural model are shown in Figure 1 as solidlines, with alternative solutions shown for the 1sttorsion natural frequency at the nominal rotorspeed; all frequencies were calculated in hover, at9.5 deg collective pitch, in a vacuum. Thealternative torsion frequencies were achieved bymeans of changes of the torsion stiffness of theblade; the 1st torsion natural frequency is shownto vary between 2.5 and 5.5/rev in roughly0.2/rev increments.

Steady-State Vibratory Hub Loads

The steady-state, 4/rev hub loads werecalculated for the baseline model and arepresented in Figure 2 and Figure 3 for advanceratios between 0.125 and 0.32. The two verticallines indicate two advance ratios which will befurther considered during the remainder of thepaper – transition at µ = .125 and cruise at µ = .25.Transition is simply the lowest advance ratiocalculated, and it yields the maximum 4/rev hubloads, both for the shears (Figure 2) and for themoments (Figure 3). Cruise is defined as theadvance ratio for maximum range of the baselineconfiguration. Since the 4/rev vibratory hubloads have not increased significantly by µ = .32,further calculations will be required before highspeed flight can be considered during the design;the use of a dynamic stall model and a higherpropulsive force will be considered for futurecalculations.

Elevon Effectiveness

Elevon effectiveness was calculated in hoverfor the six unique transfer functions previouslydescribed, T/δo , Q/δo , H/δ1c , H/δ1s , Mx/δ1c , andMx/δ1s . Of these six unique relations, the mostsignificant four were retained, T/δo , Q/δo , H/δ1x ,and Mx/δ1x . Plots of two of these functions, H/δ1xand T/δo , are given in Figure 4 and Figure 5 as afunction of torsion natural frequency for variousradial locations of a single-wide elevon. Thetransfer functions represented by these twofigures have been normalized by theircorresponding 4/rev hub load for the baselinemodel in transition (µ = .125); H / δ 1 x wasnormalized by the 4/rev longitudinal force to

4

create Figure 4, and T/δo was normalized by the4/rev thrust to create Figure 5.

These two normalized transfer functions aregiven because they are representative and inconflict. They are representative because Mx/δ1xfollows somewhat similar trends to H/δ1x , andQ/δo is very similar to T/δo . The two functions arein conflict in that the H/δ1x effectiveness (Figure 4)peaks at torsion frequencies lower than thosefound for the T/δo effectiveness (Figure 5). Inaddition, H/δ1x and T/δo differ in the range ofpeaks displayed for elevon locations between 0.62and 0.94 R – T/δo has a range of peaks double thatof H/δ1x . Finally, note that two torsion frequencieshave been labeled. The "baseline" vertical linesimply marks the torsion frequency of the baselinemodel, or 4.79/rev; the "alternate" vertical lineindicates a tentative design choice (of ω φ1 =3.3/rev) based largely on Figure 4. This alternatedesign appreciably improves the H/δ1xeffectiveness (relative to the baseline) for allelevon locations. Although the alternate generallylowers the T/δo effectiveness, a later section willdemonstrate that this is a reasonable compromisesince normalized elevon effectiveness is higher forT/δo and Q/δo than for the remaining hubresponses.

Importance of Elevon Location

Another way to explore the design space is toselect a few structural configurations and to thenplot the elevon effectiveness ratios versus single-wide (.04 R) elevon radial position. Two sets ofsuch plots have been created, one set for thebaseline (Figure 6 and Figure 7), and the other forthe alternate (Figure 8 and Figure 9). Each setincludes two plots, with the first plot emphasizingthrust and yaw (or torque), and the secondfocussing on the in-plane loads (longitudinal andlateral forces, and pitch and roll moments).

In the figures to be discussed, six elevon radiallocations have been selected, and each single-wide(.04 R) elevon has been assigned a unique primaryhub load target. (In the next section, elevonsecondary and tertiary hub load targets will bediscussed.) The use of six elevon locations is asimplification which will likely be abandonedduring future work – a design goal for the AER isthat only one or two independently controlledelevons be used on each blade. Towards this goal,the positioning of single-wide elevons isaddressed in this section, with control authority

(of single-wide elevons) being addressed in thenext section.

As an example, consider the baseline results ofFigure 6 and Figure 7. Both figures include sixvertical lines which mark the span-wise center ofsix different single-wide (.04 R) elevon locations.Each of these lines intersects one (and only one)transfer function (curve) in a special place denotedby a circle and number. The second figure (Figure7) reveals four such intersections, while the firstfigure (Figure 6) indicates two specialintersections. These markings reveal a simplistic,first-order approach – use six elevons to controlsix hub loads and assign each elevon as theprimary control for one (and only one) hub load.The numerical order reveals the selection order;thus the circle labeled "1" in Figure 7 indicates thatthe elevon at 0.74 R was chosen first and that itwas assigned the primary responsibility forcontrolling the hub lateral force. The sequence ofselections progresses from 1 to 6 as the elevoneffectiveness ratio increases. This is an attempt totreat all hub loads as equally important and,therefore, to give preferential treatment for thosenondimensional hub loads which are moredifficult to reduce. Figure 6 and Figure 7 revealthat there is a significant variation in elevoneffectiveness for each hub load, and that thrustand yaw moment are more easily reduced thanthe in-plane loads.

Results for the alternate design are shown inFigure 8-Figure 9. Note that the alternate in-planetransfer functions (Figure 9) are significantlylarger than the corresponding baseline transferfunctions (Figure 7). Also note that the preferredelevon locations for the alternate are .04 R fartheroutboard than for the baseline design, and that theelevon primary control assignments have beenredistributed to better match the alternate transferfunction characteristics.

Elevon Sizing

The elevon locations selected in the previoussection, and other selections made using similartechniques, were used to calculate the number andindividual authority of the elevon aerodynamicsurfaces required to achieve significant vibratoryhub load reduction. Four sizing cases arepresented in Table 3-Table 6, and a summary of allcases is presented in Table 7 and Table 8.

Table 3-Table 6 use the standard, single-wideelevon described previously; namely, the elevon

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chord is cδ = .15 c , and the magnitude of themaximum, local elevon deflection is|δr| = (.86R/rδ) 5 deg. Primary and secondary elevonmotions are designated as δp and δs , respectively,with their sum constrained to be less than or equalto δr for the standard elevon. The elevon-inducedhub loads are calculated from the transferfunctions multiplied by the elevon deflection.(The hub load symbols are defined in Table 7 andTable 8.) Finally, the controlled hub load iscalculated by invoking superposition; namely, thecontrolled hub load equals the uncontrolled hubload (Figure 2 and Figure 3) minus the sum of theelevon-induced hub loads.

Consider the most demanding case –transition vibratory hub load reduction using thebaseline elevon effectiveness for a total of sixelevon locations (using the locations andassignments previously shown in Figure 6 andFigure 7). Because the transition loads are so highrelative to the elevon-to-hub transfer functions,the approach is very simple – start by letting eachelevon work on its primary responsibility with100% of the maximum elevon deflection availablefor its radial location. This case is detailed inTable 3. The first four elevons (rδ = 0.62 to 0.74 R)use 100% of their available elevon deflection, yettheir targets (Y , Mx, M y, and H, respectively) arenot significantly reduced (as can be seen in the lastcolumn). If the two most outboard of this six-elevon set (i.e. rδ = 0.78 and 0.82 R) were allowedto contribute 100% towards their primary targets,then the Thrust (T) and Torque (Q ) would besignificantly reduced. Instead, the two outboardelevons have been assigned only about 1/4 oftheir deflection towards their primary duty, withthe balance being assigned to secondary loads inan attempt to reduce all loads to a similar fractionof their uncontrolled values. (Secondarycontributions are italicized, while tertiarycontributions are italicized and underlined as inTable 4.)

Table 7 (ωφ1 = 4.79/rev) and Table 8 (ω φ 1 =3.3/rev) summarize all of the sizing cases studiedto date. Table 7 (ωφ1 = 4.79/rev) repeats thecontrolled/uncontrolled ratios previously given inTable 3 for each of the six 4/rev hub loads attransition (µ = .125), resulting in an averagecontrolled response of 0.77 times the uncontrolledvalue. Note that this limited effectiveness wasachieved using six standard single-wide elevonsworking at their full capacity. For cruise (µ = .25),Table 7 indicates that these same six elevonsreduced the average controlled response to 0.53times the uncontrolled value, and that ten elevonsare able to reduce this fraction to 0.27. The final

column in Table 7 achieves a final fraction of 0.19using "big" elevons equivalent (on a work basis) to10.3 standard elevons concentrated in sixlocations, with the biggest elevon having 2-1/2times the effectiveness of the standard 0.15 celevon (moving ±5 deg at 0.86 R). The big elevonsare able to be more effective since the elevons areallowed to work hardest where they are mosteffective; that is, the peaks evident in Figure 7 canbe best exploited with highly concentratedaerodynamic effectiveness.

A comparison of Table 8 (ωφ1 = 3.3/rev) withTable 7 (ωφ1 = 4.79/rev) indicates a significantlyenhanced effectiveness with the reduced torsionfrequency. For the alternate design, a standard setof six elevons reduces the 4/rev hub loads to 0.59times the uncontrolled value for transition; 3.7elevons produces a fraction of 0.20 for cruise; and4.8 elevons essentially nulls cruise 4/rev hubloads. Thus, significant improvements arepredicted for the reduced torsion frequency of3.3/rev.

Effect of Torsion on Uncontrolled Hub Loads

The total vibratory hub loads are affected bythe elevon-to-hub-load transfer functions(previously described) and the uncontrolledvibratory hub loads. The promise of an alteredtorsion frequency must, therefore, be weighedagainst any potential increases in the uncontrolledvibratory loads. Figure 10-Figure 13 address thisissue by showing the variation of the 4/rev hubloads with torsion natural frequency for transitionand cruise. These plots reveal that the 4/rev hubloads are generally reduced for the alternatedesign.

Concluding Remarks

The preliminary design of the Active ElevonRotor (AER) has begun and initial procedures andresults were described in this paper. The primaryconclusion to date is that enhanced elevoneffectiveness is achieved at a reduced torsionnatural frequency of 3.3/rev. While vibratory hubload alleviation is the primary goal, otherconsiderations must eventually be taken intoaccount, including blade structural loads and rotorpower.

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References

1. McCloud, J.L., III and Weisbrich, A.L., “WindTunnel Test Results of a Full-Scale MulticyclicControllable Twist Rotor,” American HelicopterSociety 34th Annual Forum, Washington, DC,May 1978.

2. Millott, T.A. and Friedmann, P.P., “VibrationReduction in Helicopter Rotors Using an ActivelyControlled Partial Span Trailing Edge FlapLocated on the Blade,” NASA CR 4611, June 1994.

3. Milgram, J. and Chopra, I., “HelicopterVibration Reduction with Trailing Edge Flaps,”American Helicopter Society Northeast RegionAeromechanics Specialists' Meeting, Stratford,Connecticut, October 1995.

4. Samak, D.K. and Chopra, I., “A FeasibilityStudy to Build a Smart Rotor: Trailing Edge FlapActuation,” SPIE Smart Structures and MaterialsConference, Albuquerque, New Mexico, February1993.

5. Ben-Zeev, O. and Chopra, I., “Advances in theDevelopment of an Intelligent Helicopter RotorEmploying Smart Trailing-Edge Flaps,” SmartMaterials & Structures, Vol. 5, (1), 1996.

6. Koratkar, N.A. and Chopra, I., “Analysis andTesting of a Froude Scaled Helicopter Rotor withPiezoelectric Bender Actuated Trailing EdgeFlaps,” Journal of Intelligent Material Systems andStructures, Vol. 8, (7), 1997.

7. Fulton, M.V. and Ormiston, R.A., “HoverTesting of a Small-Scale Rotor with On-BladeElevons,” American Helicopter Society 53rdAnnual Forum, Virginia Beach, Virginia, April-May 1997.

8. Fulton, M.V. and Ormiston, R.A., “Small-ScaleRotor Experiments with On-Blade Elevons toReduce Blade Vibratory Loads in Forward Flight,”American Helicopter Society 54th Annual Forum,Washington, DC, May 1998.

9. Prechtl, E.F. and Hall, S.R., “Hover Testing ofa Mach-Scaled Rotor with an Active Trailing EdgeFlap,” Eighth ARO Workshop on theAeroelasticity of Rotorcraft Systems, State College,Pennsylvania, October 1999.

10. Koratkar, N.A. and Chopra, I., “Wind TunnelTesting of a Mach-Scaled Rotor Model withTrailing-Edge Flaps,” American Helicopter Society

56th Annual Forum, Virginia Beach, Virginia, May2000.

11. Straub, F.K., “Development of a Full ScaleSmart Rotor System,” Eighth ARO Workshop onthe Aeroelasticity of Rotorcraft Systems, StateCollege, Pennsylvania, October 1999.

12. Schimke, D., Jänker, P., Blaas, A., Kube, R.,Schewe, G., and Keßler, Ch., “Individual BladeControl by Servo-Flap and Blade Root Control: ACollaborative Research and DevelopmentProgramme,” 23rd European Rotorcraft Forum,Dresden, Germany, September 1997.

13. Poling, D.R., “1/5th Scale Model 360 DNWRotor Blade Structural Properties and AirfoilTables,” Boeing Document 8-1160-0215, June 1992.

14. Straub, F.K. and Johnston, R.A.,“Aeroelasticity and Mechanical Stability Report,0.27 Mach Scale Model of the YAH-64 AdvancedAttack Helicopter,” NASA CR 178284, May 1987.

15. Drela, M., “Newton Solution of CoupledViscous/Inviscid Multielement Airfoil Flows,”AIAA Paper 90-1470, June 1990.

16. Wong, Raymond and van Dam, C.P., privatecommunication, September 2000.

17. Domzalski Machine, “Deformable TrailingEdges and Smart Material Actuation for ActiveControl of Rotor Blades,” Phase II SBIR, ContractDAAH10-99-C-0022, private communication.

18. Johnson, Wayne, “Technology Drivers in theDevelopment of CAMRAD II ,” AHSAeromechanics Specialists' Conference, SanFrancisco, California, January 1994.

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Table 1. Rotor Characteristics.

Description Variable Value

No. of Blades b 4Rotor Radius R 6.48 ft = 77.76 inAirfoil Chord c 5.670 inPlanform RectangularSolidity σ=bc/π R 0.0928Twist, Linear θpt -10°Airfoil VR-18 with

.04 c –3 deg tabFeathering & Twist Axes 0.27 cBlade Elastic Axis 0.20 cBlade Center of Gravity 0.263 cBlade Tensile Axis 0.263 c

Lag-Flap Hinge Location e 3.50 in (4.50% R)Blade Grip Location rg 10.530 in (13.54% R)

Root Cutout Location rc 22.2 in (28.55% R)

Kinematic Couplings 0Lag Damping Dζ 8.48 ft-lb/(rad/s)

Elevon Chord, Plain cδ 0.850 in (15% c)Elevon Motion δ ±5.0 deg at rδ=.86R

Density, Air ρo 0.002377 slug/ftTemperature, Air τ 59 deg FSpeed of Sound, Air cso 1,116.45 ft/s

Viscosity, Air µo 3.7372 E-7 slug/ft-s

Weight, Passive Blade 2.96 lb

Nominal Rotor Speed Ωo 1,070 RPM (17.83 Hz)Tipspeed, hover Vtip 726.1 ft/s

Mach Number, hover Mtip 0.6504

Reynolds Number, hover Retip 2.182 E6

Table 2. Uniform blade sectionproperties (r = 22.2 to 77.76 in),baseline.

Property Value

EIFlap, lb-in2 1.095 E5

EIChord, lb-in2 4.55 E6

GJ, lb-in2 1.010 E5m, lb/in 0.0368Iθ, lb-in 0.0684

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Table 3. Fraction of maximum elevon deflection (Primary and Secondary), resulting elevon-induced hubloads, and fraction of controlled to uncontrolled hub loads, baseline (ωφ1 = 4.79/rev), µ = .125.

rδ/R 0.62 0.66 0.70 0.74 0.78 0.82 0.86 Total|δp|/|δr| 1.00 1.00 1.00 1.00 0.28 0.25 4.53|δs|/|δr| 0.72 0.75 1.47

6.00

Elevon-Induced Hub Load (lb or ft-lb) TotalControlled/Uncontrolled

T from δo 40 40 0.77Q from δo 5 5 0.75H from δ1x 14 14 0.81Y from δ1x 12 10 22 0.77Mx from δ1x 13 13 0.79My from δ1x 11 9 20 0.74

AVG 0.77

Table 4. Fraction of maximum elevon deflection (Primary and Secondary), resulting elevon-induced hubloads, and fraction of controlled to uncontrolled hub loads, baseline (ωφ1 = 4.79), µ = .25.

rδ/R 0.62 0.66 0.70 0.74 0.78 0.82 0.86 Total|δp|/|δr| 1.00 1.00 1.00 1.00 0.16 0.16 4.32|δs|/|δr| 0.84 0.84 1.68

6.00

Elevon-Induced Hub Load (lb or ft-lb) TotalControlled/Uncontrolled

T from δo 23 23 0.52Q from δo 3 3 0.54H from δ1x 14 14 0.53Y from δ1x 12 11 23 0.56Mx from δ1x 13 3 15 0.50My from δ1x 11 6 17 0.52

AVG 0.53

Table 5. Fraction of maximum elevon deflection (Primary and Secondary), resulting elevon-induced hubloads, and fraction of controlled to uncontrolled hub loads, alternate (ωφ1 = 3.3/rev), µ = .125.

rδ/R 0.62 0.66 0.70 0.74 0.78 0.82 0.86 Total|δp|/|δr| 0.79 0.54 1.00 1.00 1.00 1.00 5.33|δs|/|δr| 0.21 0.46 0.67

6.00

Elevon-Induced Hub Load (lb or ft-lb) TotalControlled/Uncontrolled

T from δo 65 65 0.61Q from δo 8 8 0.56H from δ1x 33 33 0.55Y from δ1x 33 33 0.65Mx from δ1x 3 21 25 0.61My from δ1x 9 23 32 0.55

AVG 0.59

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Table 6. Fraction of maximum elevon deflection (Primary and Secondary), resulting elevon-induced hubloads, and fraction of controlled to uncontrolled hub loads, alternate (ωφ1 = 3.3/rev), µ = .25.

rδ/R 0.62 0.66 0.70 0.74 0.78 0.82 0.86 Total|δp|/|δr| 0.44 0.50 0.85 1.00 1.00 0.76 4.55|δs|/|δr| 0.00 0.00 0.00 0.24 0.24

4.79

Elevon-Induced Hub Load (lb or ft-lb) TotalControlled/Uncontrolled

T from δo 36 36 0.00Q from δo 8 8 0.00H from δ1x 25 25 0.00Y from δ1x 33 6 39 0.04Mx from δ1x 18 18 0.00My from δ1x 23 23 0.03

AVG 0.01

Table 7. Total fraction of all elevon deflections (equivalent number of standard elevons) andresulting fraction of controlled to uncontrolled hub loads, baseline (ωφ1 = 4.79/rev).

µ = .125 µ = .25Type of Elevons Standard Standard Big

Equiv. No. of Std. Elevons 6.00 6.00 10.00 10.30

T (Thrust) 0.77 0.52 0.31 0.19Q (Torque) 0.75 0.54 0.31 0.19H (Longitudinal Force) 0.81 0.53 0.31 0.18Y (Lateral Force) 0.77 0.56 0.28 0.19Mx (Roll Moment) 0.79 0.50 0.26 0.20My (Pitch Moment) 0.74 0.52 0.27 0.20

AVG 0.77 0.53 0.29 0.19

Table 8. Total fraction of all elevon deflections (equivalent number of standardelevons) and resulting fraction of controlled to uncontrolled hub loads, alternate(ωφ1 = 3.3/rev).

µ = .125 µ = .25Type of Elevons Standard Standard

Equiv. No. of Std. Elevons 6.00 3.70 4.79

T (Thrust) 0.61 0.20 0.00Q (Torque) 0.56 0.20 0.00H (Longitudinal Force) 0.55 0.20 0.00Y (Lateral Force) 0.65 0.20 0.04Mx (Roll Moment) 0.61 0.20 0.00My (Pitch Moment) 0.55 0.20 0.03

AVG 0.59 0.20 0.01

10

φ1, alt

0

25

50

75

100

125

150

0.0 0.2 0.4 0.6 0.8 1.0 1.20

1

2

3

4

5

6

7F

req

uen

cy (

Hz)

Rotor Speed

ζ1

β1

β2

φ1

β3

ζ2

β4

Figure 1. Rotor blade frequencies in a vacuum, 9.5deg collective pitch, including effect of torsionstiffness on first torsion natural frequency at thenominal rotor speed of 1,070 RPM; β = Flap, ζ =Chord, φ = torsion, and subscripts indicate modenumber.

0

20

40

60

80

100

120

140

160

180

0.0 0.1 0.2 0.3

Vib

rato

ry H

ub

Fo

rces

, 4P

(lb

)

Advance Ratio

Tra

ns

itio

n

Cru

ise

Vertical

Lateral

Longitudinal

Figure 2. Steady-state 4/rev vibratory hub forces(nonrotating frame).

0

10

20

30

40

50

60

70

80

0.0 0.1 0.2 0.3

Vib

rato

ry H

ub

Mo

men

ts,

4P (

ft-l

b)

Advance Ratio

Tra

ns

itio

n Cru

ise

Pitch

Roll

Yaw

Figure 3. Steady-state 4/rev vibratory hub moments(nonrotating frame).

11

0.0

0.1

0.2

0.3

0.4

0.5

2 3 4 5 6

Ele

von

Eff

ecti

ven

ess

Rat

io,

Lo

ng

itu

din

al

Torsion Natural Frequency (/rev)

rδ=.94

Peak

.86

.78

.70

.62

Ba

se

lin

e

Range of Peaks

Alt

ern

ate

Figure 4. Effect of torsion natural frequency onelevon 4/rev longitudinal force effectiveness forvarious elevon radial positions, normalized bybaseline (ωφ1 = 4.79/rev) steady-state 4/revlongitudinal force at µ = 0.125.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

2 3 4 5 6

Ele

von

Eff

ecti

ven

ess

Rat

io,

Th

rust

Torsion Natural Frequency (/rev)

rδ=.94

Peak

.86.78

.70

.62

Ba

se

lin

e

Range of PeaksAlt

ern

ate

Figure 5. Effect of torsion natural frequency onelevon 4/rev thrust force effectiveness for variouselevon radial positions, normalized by baseline (ωφ1= 4.79/rev) steady-state 4/rev thrust at µ = 0.125.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.5 0.6 0.7 0.8 0.9 1.0

Ele

von

Eff

ecti

ven

ess

Rat

io

Elevon Mid-Span Radial Position

Pitch

Longitudinal Roll

Lateral

Thrust

Yaw 56

Figure 6. Effect of elevon radial position on elevoneffectiveness for reducing 4/rev hub loads for thebaseline (ωφ1 = 4.79/rev); each hub load isnormalized by its corresponding (ωφ1 = 4.79/rev)steady-state vibratory load at µ = 0.25.

0.0

0.1

0.2

0.3

0.4

0.5

0.5 0.6 0.7 0.8 0.9 1.0

Ele

von

Eff

ecti

ven

ess

Rat

io

Elevon Mid-Span Radial Position

Pitch

Longitudinal

Roll

Lateral

1

2

3

4

Figure 7. Same data as Figure 6 but with differentordinate scale.

12

0

1

2

3

4

5

0.5 0.6 0.7 0.8 0.9 1.0

Ele

von

Eff

ecti

ven

ess

Rat

io

Elevon Mid-Span Radial Position

Pitch

LongitudinalRoll

Lateral

Thrust

Yaw

5

6

Figure 8. Effect of elevon radial position on elevoneffectiveness for reducing 4/rev hub loads for thealternate (ωφ1 = 3.3/rev); each hub load isnormalized by its corresponding (ωφ1 = 3.3/rev)steady-state vibratory load at µ = 0.25.

0.0

0.5

1.0

1.5

0.5 0.6 0.7 0.8 0.9 1.0

Ele

von

Eff

ecti

ven

ess

Rat

io

Elevon Mid-Span Radial Position

Pitch

Longitudinal

Roll

Lateral

1

2

3

4

Figure 9. Same data as Figure 8 but with differentordinate scale.

0

20

40

60

80

100

120

140

160

180

2 3 4 5 6

Vib

rato

ry H

ub

Fo

rces

, 4P

(lb

)

Torsion Natural Frequency (/rev)

Alt

ern

ate

Ba

se

lin

e

Vertical

Lateral

Longitudinal

Figure 10. Effect of torsion natural frequency onsteady-state 4/rev vibratory hub forces, µ = .125.

0

10

20

30

40

50

60

70

80

2 3 4 5 6

Vib

rato

ry H

ub

Mo

men

ts,

4P (

ft-l

b)

Torsion Natural Frequency (/rev)

Alt

ern

ate

Ba

se

lin

e

Pitch

Roll

Yaw

Figure 11. Effect of torsion natural frequency onsteady-state 4/rev vibratory hub moments, µ = .125.

13

0

20

40

60

80

100

120

140

160

180

2 3 4 5 6

Vib

rato

ry H

ub

Fo

rces

, 4P

(lb

)

Torsion Natural Frequency (/rev)

Alt

ern

ate

Ba

se

lin

eVertical

Lateral

Longitudinal

Figure 12. Effect of torsion natural frequency onsteady-state 4/rev vibratory hub forces, µ = .25.

0

10

20

30

40

50

60

70

80

2 3 4 5 6

Vib

rato

ry H

ub

Mo

men

ts,

4P (

ft-l

b)

Torsion Natural Frequency (/rev)

Alt

ern

ate

Ba

se

lin

e

Pitch

Roll

Yaw

Figure 13. Effect of torsion natural frequency onsteady-state 4/rev vibratory hub moments, µ = .25.