Integration of Rotor Aerodynamic Optimization with theConceptual Design of a Large Civil Tiltrotor

C. W. Acree, Jr.Cecil.W.Acree@nasa.gov

NASA Ames Research Center, Moffett Field, California 94035, USA

Abstract

Coupling of aeromechanics analysis with vehicle sizing is demonstrated with the CAMRAD II aeromechanicscode and NDARC sizing code. The example is optimization of cruise tip speed with rotor/wing interference forthe Large Civil Tiltrotor (LCTR2) concept design. Free -wake models were used for both rotors and the wing.This report is part of a NASA effort to develop an integrated analytical capability combining rotorcraftaeromechanics, structures, propulsion, mission analysis, and vehicle sizing. The present paper extendsprevious efforts by including rotor/wing interference explicitly in the rotor performance optimization andimplicitly in the sizing.

Notation 1 CRP Contingency Rated Power

A *rotor disk area ISA International Standard Atmosphere

b wing span LCTR Large Civil Tilt Rotor

cd section drag coefficient MCP Maximum Continuous Power

cdo section profile drag coefficient MRP Maximum Rated Power (take-off power)

CT rotor thrust coefficient, T /( AVtip2)NDARC NASA Design and Analysis of RotorcraftOEI One Engine Inoperative

CW rotor weight coefficient, W /( AVtip2) OGE Out of Ground EffectD drag SFC Specific Fuel Consumption

D i induced drag SNI Simultaneous Non-Interfering approach

e Oswald efficiency factor STOL Short Takeoff and Landing

FM figure of merit VTOL Vertical Takeoff and Landing

L liftL/De aircraft lift over equivalent drag, WV/PMtip blade tip Mach numberP power requiredPind induced powerPo profile powerq dynamic pressureR rotor radiusT rotor thrustvi induced velocityV airspeedVbr aircraft best-range speedVtip rotor tip speedW gross weightWE weight empty77 propulsive efficiencyK induced velocity factor

P air densityor rotor solidity (thrust-weighted)

Presented at the AHS Aeromechanics Conference, SanFrancisco, CA, January 20-22, 2010. This material is declared awork of the U. S. Government and is not subject to copyrightprotection.

Introduction: Integration of Aeromechanics andSizing

Increasing demands upon rotorcraft performance andefficiency require more sophisticated analyses to beemployed early in the design process, including deeperintegration of aeromechanics and sizing analyses. Thispaper illustrates the use of aeromechanics analysis forcomponent optimization, and then application of theresults to aircraft sizing and performance analysis with asizing code. This effort is part of a NASA goal to developan integrated analytical capability combining rotorcraftaeromechanics, structures, propulsion, mission analysis,and vehicle sizing.

A new design/sizing code, NDARC, has beendeveloped by NASA to enable exploratory design studiesof advanced rotorcraft. A technical description ofNDARC is given in Ref. 1; the complete theory isdocumented in Ref. 2. The CAMRAD II aeromechanicscode provides a variety of aerodynamic and structuralmodels, applicable to either component (rotor and wing)or total aircraft performance, dynamics, and acousticsanalyses. Reference 3 provides a summary of CAMRAD

https://ntrs.nasa.gov/search.jsp?R=20100036641 2020-04-01T16:04:38+00:00Z

II capabilities; see Ref. 4 for details of the theory andmethods.

In addition to coupling design and aeromechanics, thepresent paper expands and improves upon previous effortsby including rotor/wing interference explicitly in theaeromechanics analysis and implicitly in the sizing.Analysis of the rotor and wing aeromechanics togetherwith CAMRAD II, coupled with simultaneous rotor andwing sizing by NDARC, moves the research effort furthertoward a fully coupled systems design process.

Optimization is extended beyond rotor/wingperformance to vehicle sizing. Neither an aeromechanicsnor a sizing analysis alone will suffice: the two must becoupled to determine the optimum design. The presentstudy is not intended to generate a final, perfect design,but to demonstrate the procedures needed to do so, in theexpectation that further technology advances and designrequirements may be progressively incorporated into theprocess as research progresses.

Methods and Approach

NDARC includes performance and weight models of avariety of rotorcraft components and systems (rotor, wing,engine, fuselage, etc.) that are assembled into a completeaircraft model. NDARC is designed for highcomputational efficiency. Performance is calculated withphysics-based models (e.g. rotor momentum theory), witha wide choice of modeling methods (constant, linear andnonlinear) to best match higher-order analyses or testdata. The weight models are typically based uponhistorical weight trends. Any of the component modelscan be adjusted by technology factors. NDARC alsoincludes a flexible mission model plus point-designperformance analyses for sizing. Given a set ofcomponent models, NDARC calculates vehicle size,weight and power required for the chosen mission modeland performance requirements.

CAMRAD II is a comprehensive rotorcraft analysiscode that includes multibody dynamics, nonlinear finiteelements, and rotorcraft aerodynamics. CAMRAD II canmodel separate rotor and wing free wakes, with or withoutrotor-on-wing, wing-on-rotor, or mutual wing/rotorinterference. Only results with no interference or full,mutual wing/rotor interference are presented here.CAMRAD II is well-suited for rotorcraft designoptimization where efficient aeromechanics analysis isneeded.

The design example used here is the second-generationLarge Civil Tiltrotor (LCTR2, Fig. 1), which has been theobject of NASA research described in Refs. 5-15. In thepresent paper, the emphasis is on aerodynamicperformance of the wing and rotor as a system. Theimmediate objective is to better understand the

aerodynamic phenomena that drive rotor optimization,specifically the effects of cruise tip speed and wing/rotorinterference. Optimization of the complete aircraft canthen proceed with greater confidence that the underlyingrotor behavior is properly modeled.

The aeromechanics analyses are similar to those ofRefs. 11-13. In Refs. 12 and 13, the LCTR2 baselinedesign was determined by an older sizing code, RC (Ref.16), and CAMRAD II was used to investigateperformance for different design variations from thebaseline. Reference 13 reported optimization of LCTR2rotor tip speed, and Ref. 11 reported the effects ofrotor/wing interference for a large military tiltrotor. Thelevel of analysis necessary for proprotor performanceoptimization was explored in Ref. 17.

The major conceptual addition for the present paper isthe coupling of the CAMRAD II aeromechanics analysesto the new NDARC sizing code to determine theminimum vehicle weight over the entire mission, not justbest aerodynamic performance. All hover and cruiseperformance calculations were updated for the presentwork, using CAMRAD II Release 4.7 and NDARCversion 1.1.

The importance of aerodynamic interference onrotor/wing performance has been widely studied.Reference 18 provides a good historical overview of thesubject, with a useful bibliography and examples forhover, transition and cruise. Reference 18 also points outthe need to optimize rotor twist for favorable wing/rotorinterference, not just for isolated rotor performance.Reference 19 discusses optimal wing lift distribution inthe presence of rotor/wing interference. The influence ofrotor advance ratio on wing performance was studied inRef. 20; subsequent studies of the effects of advance ratioinclude Refs. 21 and 22. More recently, Ref. 11 analyzedwing/rotor interference effects for a large tiltrotor.

Outline of sizing procedures

The sizing process can be summarized as follows:

1. An initial design establishes baseline values of emptyweight, rotor radius, tip speed, etc.

A CAMRAD II model of the isolated rotor calculatesrotor performance trades as rotor design parametersare varied. For the LCTR2 example presented here,several performance maps of hover figure of meritversus cruise propulsive efficiency were generated fordifferent cruise tip speeds. The performance curvesrepresent the boundaries of hover/cruise performancetrades as the blade twist distribution is varied.

3. The rotor configurations with the best performance—that is, those falling on the outer boundary of theperformance map—are then analyzed by CAMRAD II

with a full rotor/wing interference model. Thisanalysis generates a detailed performance model,including equivalent rotor hover and cruise efficiencyand wing efficiency in cruise, for each candidateparameter variation.

4. The performance model so generated was supplied tothe NDARC sizing code, which sized the aircraft forthe specified mission model. The results comprisedcurves of empty weight, installed power, fuel burn,etc. versus figure of merit and propulsive efficiency.The LCTR2 rotor/wing performance maps werethereby converted into weight/power tradeoff curvesfor each cruise tip speed.

There are thus three sets of design tradeoffs: cruise vs.hover rotor performance for each cruise tip speed ( VnP);

rotor vs. wing efficiency, as a function of VnP; and vehiclesize, determined by the weight vs. efficiency tradeoff overthe entire mission.

At this point, one can select the best design, determinedas lowest weight, lowest power, or some other criterion.More generally, the process would be repeated byupdating the baseline design, adjusting the rotor modelaccordingly, and recomputing performance, weight, etc.,or else different design parameters (e.g. blade taper orwing span) would be varied. Different technologyassumptions (e.g. engine maps or airfoil decks) might alsobe introduced and the cycle repeated.

The choice of example design parameters analyzed forthis paper is explained in more detail in the section“Sizing Analysis”. The process described here stops shortof a full formal optimization, most obviously because noobjective function is specified (other than weight).Because the focus is on research, it is more useful to“unroll” the process to reveal the aerodynamic effectsthan to terminate with a final design that may obscureimportant technical insights.

Fig. 1. The NASA Large Civil Tiltrotor, LCTR2 baseline version (dimensions in feet).

LCTR2 Concept Design

The Large Civil Tiltrotor (LCTR), was developed aspart of the NASA Heavy Lift Systems Investigation (Ref.5). The concept has since evolved into the second-generation LCTR2, described in detail in Ref. 13. TheLCTR2 design goal is to carry 90 passengers for 1000 nmat 300 knots, with vertical takeoff and landing. Missionspecifications and key design values are summarized inTables 1 and 2 for LCTR2.

Aeroelastic stability (whirl flutter) was examined inRef. 14. The studies reported in Ref. 13 revealed that turnperformance could be a major design driver, withimportant implications for rotor optimization. Reference15 subsequently developed criteria for turn performancemargins.

The LCTR2 design has four engines for good OEIperformance. The engine model assumes advancedengines with a cruise SFC of 0.375 lb/hr/hp. A two-speedtransmission ensures that the turbine speed is heldconstant over different operating conditions for maximumengine efficiency. The combination of a rotor with a widerange of rotational speeds and a multi-speed transmissionwas demonstrated in principle by the XV-3 (Ref. 23).

Evolution of the LCTR2 concept

The LCTR2 is designed to require only helipads locatedwithin existing airport boundaries. The operationalconcept is to move short- and medium-range air traffic offof the main runways, which would free up such runwaysfor use by greater numbers of larger and longer-rangeaircraft. The use of large VTOL aircraft would therebyimprove the capacity of the airspace system as a wholewithout requiring construction of new runways orexpansion of airport boundaries. The basic designrequirements and mission specifications are given inTables 1 and 2.

The LCTR2 variant presented in Ref. 13 was designedwith the RC sizing code; that variant is here designatedLCTR2-01. LCTR2 -01 was designed with fixed fuselagegeometry, dictated by passenger requirements (fourabreast), and fixed wingspan and rotor diameter,determined by gate-space limitations. For the final designiteration presented in Ref. 13, the engine size was fixed at7500 HP. The LCTR2-01 transmission was sized by a2K/97 (2000-ft ISA + 25°C altitude) operating condition.The fixed airframe geometry and engine size did notseriously limit the design, because those specificationsbenefited from several previous design iterations.

In contrast, the LCTR2-02 variant described herein wasdesigned using NDARC (Refs. 1 and 2). NDARC is amore advanced design tool than RC, with a moresophisticated rotor performance model and more flexibleoptions for sizing, among other improvements. Relevant

features of NDARC are discussed in context in thefollowing sections of this paper.

Table 1. LCTR2-02 mission requirements.

Mission summaryTakeoff + 2 min hover OGE 5k ISA+20°CClimb at Vb, (credit distance to cruise segment)Cruise at Vb, for at least 1000 nm range, 28k ISADescend at Vb, (no range credit)1 min hover OGE + landing, 5k ISA+20°CReserve (diversion): 100 nm Vb, , 28k ISAReserve (emergency): 30 min Vb, , 5k ISA+20°C

Operational requirementsOne engine inoperative: Category A at 5k ISA+20°CAll-weather operations: CAT IIIC SNI, Free Flight45-deg banked turn at 80 knots, 5k ISA+20°C, 90% MCP

Table 2. Baseline design values for LCTR2-02.

Design Constraint ValuePayload (90 pax), lb 19,800Cruise speed (90% MCP), knots 300Length, ft 108.9Wing span, ft 107.0Wing sweep —5.0 degRotor radius, ft 32.5Rotor separation, ft 77.0Number of blades 4Precone, deg 6.0Tip speed, hover, ft/sec 650Tip speed, cruise, ft/sec 350

Baseline Design ResultGross weight, lb 103,600Rotor weight, lb (both rotors) 8113Wing weight, lb (zero fuel) 7441Engines and drive train, lb 14,174Fuselage empty weight, lb 12,875Mission fuel, lb 16,092Engine power, hp 47489Rotor solidity 0.128Rotor taper (tip/root chord) 0.70Hover CT / 0.163Cruise CT / 0.0784Wing area, ft2 965Drag D/q, ft2 34.6

NDARC model and sizing of LCTR2-02

The new features of NDARC were freely exploited forthe design of the revised aircraft. The rotor performancemodel was improved, and the rotor sizing (disk loading)was updated to incorporate maneuvering requirementstaken from Ref. 15. The basic airframe geometry was

again fixed, but the transmission was sized to provide a10% torque margin over the worst-case operatingcondition (the 2K/97 transmission sizing condition wasthus made redundant and was deleted). Engine size wasallowed to vary to obtain the best match over all operatingconditions. In practice, engine and transmission size wereset by the sizing condi tions of Table 3, including the 10%margin on the transmission torque. Fuel consumption wascalculated for the entire mission of Table 1. Weightempty, including fuel tank size, wing chord, and rotorsolidity were then iterated along with engine andtransmission size to achieve a converged solution. Thisyielded a new baseline design, the LCTR2-02, which isslightly lighter than the LCTR2-01, largely through areduction in fuel burn. The engines, wing and rotorsolidity are also slightly smaller. Major LCTR2-02 designvalues are summarized in Table 2.

Table 3. LCTR2-02 design constraints for sizing.

Minimum PerformanceMax. takeoff weight at sea level standard, 100% MRPOEI at 5k ISA+20°C, CRP110% [1]Cruise speed 300 knots at 28k ISA, 90% MCP

Key Technology Assumptions

Wing loading, lb/ft2107.4Disk loading, lb/ft215.6Hover CW / 0.133Cruise SFC, lb/hr/hp [2] 0.375Tip speed, hover, ft/sec [3] 650

[1] Approximate OEI trimmed power not at MCP hover[2] Summary of engine model specifications[3] Set by assumed future noise requirements

For the sizing examples presented in this paper, mostdesign values were either held fixed and matched to thoseof the earlier LCTR2-01 design of Ref. 13 (e.g. wingspan), or were determined by underlying technologyassumptions equivalent to those used in Ref. 13 (e.g. wingloading). For example, the LCTR2-02 airframe geometrywas held fixed, with the exception of wing chord, whichwas adjusted during the sizing analysis to maintainconstant wing loading (Table 3).

Mission model

NDARC can analyze a mission as a set of separateflight conditions, specified as individual segments whichare combined into a continuous mission with cumulativefuel burn, or as multiple discrete sizing conditions atwhich one or more performance requirements must bemet, or a combination of both. For a tiltrotor, the rotorsare trimmed to the appropriate collective, and optionallycyclic, settings to match thrust, torque, flapping, etc. tothe current flight condition. The entire aircraft—rotors,

wing, tail, fuselage, nacelles, etc.—is trimmed to total lift,drag, and pitching moment. This is done for each missionsegment and sizing condition, and weight, power, or otherspecified design variables are iterated until a convergedsolution is found.

For this paper, the mission of Ref. 13 was revised toinclude a 100-nm reserve segment (Table 1). Missionreserves are thus a combination of turboprop andhelicopter practice (distance and time, respectively). Therationale is that while a tiltrotor does not need a runwayfor an emergency landing, a routine weather diversionmay require other airport facilities generally equivalent tothose for a turboprop or regional jet, hence the 100-nmsegment. In emergencies, the LCTR2 can be operated likea heli copter, hence a 30-min time reserve is appropriate.

NDARC has options for splitting segments into sub-segments to better account for fuel burnoff during cruiseand performance changes with density altitude duringclimb and descent. The mission model was checked withthe baseline LCTR2 to ensure that the addition orsubtraction of sub-segments did not significantly changethe gross weight. The criteria was that the change in grossweight must be less than one passenger (0.2% grossweight) and the change in required power less than thesame percentage.

In addition to the nominal mission, three sizingconditions were imposed: minimum cruise speed of 300knots at altitude, OEI hover at 5000-ft ISA +20° Caltitude, and maximum gross weight takeoff at sea levelstandard conditions (Table 3). In practice, an enginefailure over the runway or landing pad would result in animmediate vertical landing, and a failure while wing-borne would be treated like any fixed-wing airliner. Thecritical OEI condition is then at low speed departing thelanding site, but not yet converted to airplane mode.Under such conditions, the rotor inflow from even a lowforward speed would reduce rotor power required belowthat for hover. Calculation of the exact worst-casecondition would require much more extensive analyses ofaeromechanics and handling qualities than are warrantedhere. For the present study, a 10% power reduction wasassumed for OEI hover, implemented as a 10% increasein power available as a practical approximation. NominalOEI contingency power is assumed to be 4/3 maximumcontinuous power, so the rotors are trimmed to4/3MCP110% at the design OEI condition.

Sizing Analysis

Determination of optimum cruise tip speed was chosenas the example problem because it strongly and directlyaffects other critical design parameters. The hover/cruisetip-speed ratio may size either the gearbox or engine (andpossibly both) in cruise, depending on flight conditions,rotor performance, and whether a single- or multi-speed

gearbox is used. Hover and cruise tip speeds will alsodrive the choice of rotor airfoils, and will togetherdetermine how rotor twist must be optimized. Cruise tipspeed will also affect aeroelastic stability (whirl flutter)and of course rotor frequency placement. It will alsodetermine airfoil design, especially at the tip.

Other design variables, such as wing twist, span, andchord, are also important, but their affects may cascadethrough the design only weakly or indirectly via fuel burn.For example, wing twist has no direct effect on the rotordesign, and a very small affect (if any) on wing weight.Wing twist affects total vehicle size through fuel burn incruise, not through the direct sizing of any component orsubsystem.

For these reasons, it was highly desirable to choosecruise and hover tip speeds early in the design process.Hover tip speed was limited by noise considerations to650 ft/sec. Previous efforts (Ref. 13) selected a cruise tipspeed of 400 ft/sec based on aerodynamic performance,and examined aeroelastic stability (whirl flutter) usingthat tip speed (Ref. 14). However, those analyses did notutilize a sizing code, so the results did not guarantee anoptimum vehicle size. In order to ensure continuity withthe earlier results generated by the older RC sizing code,the baseline cruise tip speed reverted to 350 ft/sec for theinitial NDARC sizing studies.

For the LCTR2, maximum disk loading is determined2by maneuvering requirements, and was fixed at 15.6 lb/ft

for the present study; the value is derived from Ref. 15.While a fixed disk loading may not yield the trueoptimum design, it guarantees that both the maneuver andengine-out requirements of Table 3 will be met. Once thedesign space has been narrowed by the choice of cruisetip speed, further optimizations of other design variables(e.g. wing twist or disk loading) can proceed withreasonable assurance that the critical requirements willcontinue to be met.

NDARC is not a general-purpose, multi-parameteroptimization code, but a specialized rotorcraft sizing toolspecifically intended to reflect accepted rotorcraft designpractices and technology assumptions. For example, notall rotor parameters —radius, solidity, disk loading, tipspeed, thrust coefficient, etc.—may be varied at once.Some traditional rotor design and performanceparameters, such at CT/o, will be automaticallydetermined by the values of other parameters; a choice ofwhat to vary and what to hold fixed must be made at theoutset. Furthermore, the parameter variations appropriatefor a sizing code are not necessarily the same as for anaeromechanics analysis. For example, Ref. 15 varied rotorsolidity to determine the maneuvering criteria for LCTR2;in that analysis, weight did not vary. For the NDARCanalyses reported here, rotor disk loading was derivedfrom the baseline values of solidity and hover CT/ σ as

adjusted to meet the maneuver requirements of Ref. 15(Table 2), then disk loading was held fixed and radiusvaried as the weight and power were updated during thesizing. Rotor solidity is then a fallout parameterdependent upon the adjusted values of weight and radius.

Rotor radius is limited by airport gate spacing. Radiuswas here allowed to vary because earlier studies hadsettled on a reasonable value as a baseline. A reduction inrotor radius was acceptable, but not an increase (at leastnot without an increase in wing span for rotor/fuselageclearance, with consequent weight increase and otherresulting design changes). Once the aeromechanics andsizing analyses had been coupled and the procedurerefined, the optimization process resulted in low er vehicleweight. Given fixed disk loading, the rotor radius wasautomatically reduced, but only slightly.

CAMRAD II Rotor and Wing Model

The CAMRAD II rotor model of the LCTR2 had fiveelastic beam elements per blade, with full control-systemkinematics, and 15 aerodynamic panels per blade. Bladeaerodynamics were modeled as a lifting line coupled to afree-wake analysis. An isolated-rotor, axisymmetricsolution was used for hover and cruise performanceoptimization. The rotor/wing interference modelincorporated a wake model for the wing in addition to therotor wakes. The rotor/wing wake model was developedfor the work reported in Ref. 11 and is shownschematically in Fig. 2.

Fig. 2. CAMRAD II rotor and wing wake model(Ref. 11).

Blade- and wing-section aerodynamic properties wereread from 2-D airfoil coefficient tables. Rotating, 3-Dstall delay was implemented as modifications to the 2-D

aerodynamic table data, based on the analysis of Ref. 24.Fuselage aerodynamics were modeled with an equivalentdrag D/q, adjusted to match total wing/body dragcomputed by CFD analysis.

To simulate advanced airfoils, the rotor airfoil tableswere constructed based upon projected improvementsbeyond existing airfoil capabilities. These projectionswere based on CFD analysis and modern rotor airfoiltrends. The “virtual airfoils” represented by these tablessimulate performance levels expected of state-of-the-art,purpose-designed airfoils. The tables were constructed tobe generally compatible with XN-series characteristics(Ref. 25), with slight performance improvementsconsistent with more modern airfoils. The tables usedhere are documented in Ref. 13.

The main wing is designed with constant chord and24% thickness, and uses a purpose-designed airfoil (Ref.9). The tip extensions taper to 35% of the main chord andare set to the same incidence angle as the wing (Ref. 13).The wing and extensions are untwisted. The CAMRAD IIwing aerodynamic model used 32 panels, including 7panels for each tip extension.

For calculations of wing/rotor interactions in cruise, thewing incidence angle was allow to vary to match lift tovehicle weight, thereby keeping the fuselage level forminimum drag. The rotor shafts were kept level, and therotors were trimmed to zero flapping with cyclic. Therotors rotate with the lower blades moving inboard,opposite to the swirl in the wing tip vortices.

Twist optimization

The optimum twist distribution varies for differenthover/cruise tip-speed ratios and for different missionmodels. A conventional bilinear twist distribution wasused here, with different values of linear twist over theinner and outer blade span. Performance calculations weremade for different combinations of inboard and outboardtwist for a broad range of cruise tip speeds. CAMRAD IIcalculated isolated rotor performance at the takeoff hoverand long-range cruise conditions of Table 1; the hover tipspeed was held fixed at 650 ft/sec and the cruise tip speedwas varied from 300-550 ft/sec.

The result is a multidimensional performance map withthree independent variables: cruise tip speed ( Vtip) andinboard and outboard twist rate; and two dependentvariables: hover figure of merit (FM) and cruisepropulsive efficiency (q). Figure 3 summarizes theperformance map as a set of lines denoting the outerboundaries of FM and q at each value of cruise Vtip . Foreach tip speed, the optimum twist will lie somewhere onthat line. (The curves in Fig. 3 are slightly different fromthose in Ref. 13 because the older LCTR2-01 model wasupdated and revised to the current LCTR2-02 version, as

discussed earlier in this paper. The range of tip speedsshown in Fig. 3 is also larger.)

A traditional analysis would feed the values along eachboundary into a mission model to compute the lowest fuelburn, hence lowest gross weight. It is immediately evidentthat 300 ft/sec is too low and 500 ft/sec is too high; theoptimum tip speed is 400-450 ft/sec, depending upon therelative importance of hover and cruise performance.However, Fig. 3 alone does not provide enoughinformation to determine the optimum cruise tip speed.Tip speed affects not only performance, but gearboxweight, so a sizing analysis is required.

0.84

0.83 ,y;•' _^^^-^" \^ ^•.^

°—' 0.82 \\

0 0.81CL

Cruise V,1CL t^

Q) (ft/sec) 1A 0.82 300

350400 I

0.79 450500550

0.78 1 1 1 1 1 10.765 0.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 3. Boundaries of isolated rotor twist optimizations fordifferent cruise tip speeds.

Rotor/wing interference

To compute rotor/wing interference, the twistcombinations along the performance boundary for eachtip speed were re-analyzed with CAMRAD II, using a fullwing and rotor aerodynamic model (Fig. 2). With tworotors and a wing, each with a wake model and withmutual wing/rotor interference, the performancecomputations took an order of magnitude longer than forisolated-rotor performance. The large savings in CPUtime were the motivation for splitting the CAMRAD IIanalysis into two series, the first with the isolated rotormodel, and the second with the full wing and rotor model.

The full wing/rotor CAMRAD II analysis was doneonly for cruise; wing/rotor interference in hover wasmodeled in NDARC by an equivalent vertical dragcoefficient, including download. The simpler analysis wasappropriate for hover because the hover tip speed isconstant and the download model can easily be matchedto experimental data or CFD analyses. Equivalent netdownload was 7.9% for the baseline LCTR2 -02.

The performance boundaries shown in Fig. 3 arenonlinear and non-monotonic, as are the variations intwist rates that determine the boundaries. This createschallenges for consistent and unambiguous plotting of theresults. For this paper, the convention was adopted thatpower, weight and other values were usually plottedagainst hover figure of merit. For a given twistdistribution, figure of merit does not vary with cruise tipspeed, nor is it affected by cruise wing/rotor interference.Therefore, using figure of merit as the independentvariable results in plots with fewer ambiguities andclearer trends (at least to this author's eye). However,weight trends are plotted against both FM and tj in theNDARC Sizing Analysis section of this paper forcontrast.

4900

t 4800i

Q

4700

0 4600

3Cruise Vtip4500 (ft/sec)

300 pwr w/o

4400 350¢pwr w/o

400 pwr w/o450 pwr w/o500 pwr w/o550 pwr w/o

4300 i0.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 4. Rotor power in cruise without wing/rotorinterference.

4900

4800ab Cruise Vtip

U(ft/sec)

4700 300350 pwr w/400 pwr w/450 pwr w/

L 4600 - 5003 550 pwr w/

4500

cc 4400

4300 i0.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 5. Rotor power in cruise with wing/rotor interference.

Figures 4 and 5 plot cruise rotor power versus hoverfigure of merit, the first without, and the latter withrotor/wing interference. The figures in this paper plot thepower of only one rotor, not both added together, becausethat makes for more convenient plot scaling. Figure 4suggests that any cruise tip speed between 300 and 450ft/sec will require nearly equal power in cruise. Theimplication is that profile power and induced power tradeoff nearly equally as tip speed changes. Figure 5,however, shows that including interference favors thelower tip speeds. The larger swirl losses at Vtip = 300 -350ft/sec are offset by greater wing efficiency, as shown inFig. 6, which plots the change (delta) in wing powercaused by interference. Wing power is defined here aswing drag times free-stream velocity. Vtip = 350 ft/sec isthe optimum value, although 400 ft/sec is nearly as goodand gives slightly better hover performance. However, theeffects on vehicle sizing have not yet been taken intoaccount.

Figure 6 also plots the change in rotor profile andinduced power components caused by interference. Rotorpropulsive power has been subtracted out because thechange in this power component is equal to the change inwing power. The remaining portion of rotor power ( Po +Pind) is affected much less by interference than wingpower.

100Rotor power,

P0 + Pind

a0b

•-_ ...................... _= _' -` --- --=

UC2 -100 300 300 d w pwr

350 d w pwr350N Cruise Vtip 400 400 d w pwr

(ft/sec) 450 450 d w pwr-200 500 500 d w pwr

a^

v550 550 d w pwr

3 -300$

- ^^----•^ —

% _ _----

0 -400%`Wing power \ %%

-5000.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 6. Changes in wing and rotor power due tointerference.

Plots of traditional rotor and wing power and efficiencycoefficients are problematic, if for no other reason thanthe wing and rotor magnitudes differ enormously in scale.Moreover, rotor/wing interference alters some valuesoutside of their traditional range. Kroo (Ref. 19) pointsout that propeller propulsive efficiency, as traditionallydefined, may be greater than one in the presence of

interference. The wing Oswald efficiency factor can alsobe greater than one because the rotor increases localdynamic pressure above the free-stream value. Theapproach taken here was to avoid nondimensional powercoefficients and plot power components in engineeringunits, retaining only FM and tj as nondimensional valueson the abscissa. The resulting plots are readable atreasonable scales.

The use of an aeromechanics code such as CAMRAD IIallows the rotor and wing drag to be separated intoinduced, profile, and parasite drag components. Thisluxury is not possible for wind-tunnel tests, which arenecessarily limited in the practical installation of separaterotor and wing balances. For the present study, the rotorwas optimized first without interference, and the changein efficiency due to interference was calculated asseparate rotor and wing power components. It isimportant to keep in mind that what matters is theperformance of the total wing/rotor system.

Figure 6 also reveals a strongly non-monotonic trend ofdelta wing power, most evident at Vtip = 450 ft/sec. Ahook in the curve at high figure of merit is present atnearly all tip speeds, but often difficult to discern at thescale of Fig. 6. It does not appear in the rotor powercurves because rotor propulsive power has beensubtracted out (it simply mirrors the wing power trends).The trend is caused by the non-monotonic bilinear twistdistribution along the rotor performance boundaries (Fig.3): at high FM, the inboard twist rate varies rapidly, butthe outboard twist varies slowly or not at all; whereas athigh si, the total twist varies slowly as inboard andoutboard twist rates vary together, but with oppositetrends. The effect can be expected to be different forhigher-order rotor optimizations with nonlinear twistdistributions.

NDARC Sizing Analysis

To determine the true optimum cruise tip speed, theperformance results of Figs. 4-6 were fed into NDARCand the LCTR2 resized. Instead of using only figure ofmerit and propulsive efficiency, the rotor performancewas modeled in NDARC with equivalent profile drag cdo

and induced velocity factor x (the ratio of inducedvelocity to the ideal induced velocity from momentumtheory). The effect of interference on wing performancewas modeled in NDARC by varying the Oswaldefficiency factor e. x and e are defined as follows:

2

v i = x T

/2pA; e =

12 (

L / q) (Ref. 11)jb Di /q

These inputs are, in effect, nondimensional representa-tions of the power variations in Figs. 4-6. The wingincidence angle was also varied to match that calculatedby CAMRAD II. The results are plotted in Figs. 7-10.

66000

65500 \ %` '^^ I

i

E 65000t ^

Cruise Vtip

64500 (ft/sec)

300 450

— 350 500

– 400 550

640000.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 7. Weight empty, without interference.

66000 Cruise Vtip

(ft/sec)300 450

— 350 500\ - 400 55065500 \

65000 %

64500 \ .%•^^

— %

64000 1 1 1 1 10.770 0.775 0.780 0.785 0.790 0.795

Hover figure of merit

Fig. 8. Weight empty, with wing/rotor interference.

Figures 7 and 9 show that the weight-optimized cruisetip speed is somewhat higher than that determined fromrotor power alone (Figs. 3 and 4). Figures 8 and 10 replotweight empty against si. Without interference, theoptimum Vtip is 400-450 ft/sec; with interference, therange extends to 350-450 ft/sec. The optimum value isalso more sensitive to the twist distribution, as is mostevident in Fig. 8, which clearl y shows separate minimafor each tip speed. Contrast with Fig. 4, which showsbroad, nearly flat minima. A proper sizing analysis isneeded to determine the true optimum tip speed andcorresponding twist distribution. Table 4 summarizes theresults of the sizing analysis for those cruise tip speedsyielding the lowest empty weights.

66000

1?

65500

a

"•••-

\\ 1

a65000

m

J.^

.^

Cruise Vtip

(ft/sec)64500 ..... 300 450

— 350 500– – • 400 550

640000.790 0.800 0.810 0.820 0.830 0.840 0.850

Cruise propulsive efficiency

Fig. 9. Weight empty, without interference.

66000 Cruise Vtip 1(ft/sec)300 450

— 350 500 I^400 550

65500

I ^

E 65000 k

64500 - -------------"tip

640000.790 0.800 0.810 0.820 0.830 0.840 0.850

Cruise propulsive efficiency

Fig. 10. Weight empty, with wing/rotor interference.

Table 4. Summary results for minimum empty weight.

Cruise VtiP(ft/sec)

Cruise MtiP FM* * Twist(deg)

WE(lb)

350 0.3488 0.7814 0.8435 36.3 64246400 0.3986 0.7848 0.8430 40.4 64170450 0.4485 0.7866 0.8377 42.6 64242

* Values for isolated rotor (compare Fig. 3)

The most practical choice would favor the cruise VtiP

with the highest FM and , consistent with low weight;Figs. 8 and 10 show this value to be near 400 ft/sec. Thischoice may easily change as new technology, such as

purpose-designed airfoils, is folded into the LCTR2design.

Figure of merit is linked to cruise VtiP through the twistdistribution. A multi-panel twist optimization woulddoubtless have resulted in a more precise end result thanthat reported here for bilinear twist. However, the moreelaborate performance analyses required would havetaken substantially more CPU time. During developmentof the coupled aeromechanics/sizing method, it proveduseful to periodically check the underlying physics of theaeromechanics analysis, notably the circulationdistribution, for reasonable behavior. Use of relativelysimple twist distributions facilitated such checks. Oncethe procedures have been fully developed and a robustbaseline design chosen, it would then be appropriate toperform higher-order optimizations. These would includemore elaborate twist distributions, nonlinear taper, tipextension geometry, etc. for the rotor and airframe, andmay include alternative missions, such as maximum-range ferry, STOL takeoff, etc.

Lessons Learned

During the development of the procedures describedhere, several lessons were learned concerning theappropriate levels of accuracy and other numerical issuesof the aeromechanics analyses. Some of the lessons werealready known, or at least are obvious in retrospect, butthe details of implementation in CAMRAD II had to beworked out for the LCTR2 configuration. Different codeswill have different ways of implementing circulation, trimand wake tolerances, probably with different referencevalues for each. The following observations will have tobe interpreted accordingly.

Circulation in cruise: In cruise, the total inflow anddynamic pressure are so high that tiny changes in trimsettings can cause large changes in thrust. It is not enoughto trim to a small tolerance on thrust: the entire lift (anddrag) distribution must be well-converged, or else theresulting power will be inaccurate. In CAMRAD II, this isbest achieved by imposing a very tight tolerance oncirculation, which must be significantly smaller in cruisethan in hover, typically by a ratio of 1/5.

Rotor and wing trim: Additional constraints areimposed when analyzing the rotors and wing together.The wing lift is much larger than the rotor thrust. Withtwo rotors, the ratio of wing lift to single-rotor thrust istwice the total lift-to-drag ratio. The trim tolerances onwing lift and rotor thrust must each be scaled accordingly.The force tolerances (thrust or lift) may have to be furtheradjusted if rotor/wing interference is included. It isusually more difficult to trim the rotor than the wing,especially if rotor flapping is explicitly trimmed. Forthese reasons, the analysis used a single, global forcetolerance referenced to rotor thrust, based on the

10

observation that if rotor forces are properly trimmed, thentrimming the wing lift to the same tolerance will be morethan adequate.

Wake convergence: In hover, convergence of the wakebecomes an issue. The wake model in CAMRAD II iscomputationally expensive and is, therefore, theoutermost loop of the analysis. Wake distortion andcirculation are converged during inner loops, but there isno internal convergence test for the outer wake loop (Ref.4). For the analyses done here, the critical results werehover figure of merit and cruise propulsive efficiency.Neither of these are trim parameters, nor were theunderlying values of cdo or . There was no metric onwake convergence, referenced to these parameters,equivalent to trim convergence on rotor or airframeforces. The critical trim, wake, and efficiency parametersare computed within different loops, making it difficult todefine a single, global convergence criterion.

In past efforts (e.g. Refs. 13 and 17), this problem wasgreatly alleviated by computing the entire matrix of anygiven parameter variation (twist, taper, etc.). It may seemparadoxical that computing a large set of variations maybe more efficient, and even more accurate, than usingformal optimization to converge on the optimal values.The key is that the path through the parameter matrix maybe chosen in advance to facilitate convergence andthereby reduce total computational time. CAMRAD IIallows the wake geometry and flow solution for one caseto be applied to the next case of rotor variations. For smallchanges in rotor parameters, subsequent cases convergevery quickly. In fact, it was sometimes more efficient tointroduce additional cases to pre -converge the solutionthan to run more wake iterations. Careful checks of wakeconvergence, and of any other global or outer-loopcomputations, must be done in advance of any designoptimizations. This is particularly important whenrunning an automatic optimizer that discards portions ofthe parameter matrix or otherwise shrinks the designspace to save computational time, because important cluesto convergence problems may be lost.

In cruise, the wake converges much faster than inhover, even with rotor/wing interference. The issues justdiscussed for hover were not seen for the cruisecomputations in this study (but that does not guaranteethat they will not occur in future analyses).

Observations and Recommendations

Integrated aeromechanics analysis and vehicle sizing(weight optimization) was demonstrated with theCAMRAD II aeromechanics code and NDARC sizingcode. The example was optimization of cruise tip speed

with rotor/wing interference for the LCTR2 tiltrotorconcept design.

Although a minimum-weight design can be determinedfrom the results presented here, the most telling result isthat optimum weight varies little over a range of cruise tipspeeds, roughly 350-450 ft/sec. The range of acceptabletip speeds is not evident when comparing weight trendscomputed without taking wing/rotor interference intoaccount. Performance trends alone are insufficient, evenwhen interference is included: a sizing analysis is neededto identify the optimum range of tip speeds. Th ese trendswill doubtless change as new technology is included intothe design, or if the mission is revised.

Perhaps a more subtle result is that the process ofchoosing airfoil, planform, twist and other designvariables may benefit from revision. Instead of narrowingthe design space to a single, best cruise tip speed, theresults expand the range of tip speeds at which otherdesign variables must be analyzed. This increases theburden on the designer to investigate a larger matrix ofvariables, but with the payoff of a better design than couldbe obtained otherwise—the classic challenge ofmultidimensional design optimization.

At the least, more sophisticated component designmethods should be applied to determine the true optimumcruise tip speed. An obvious example is that the tradeoffsbetween airfoil performance characteristics—minimumdrag, maximum lift, pitching moment, etc.—willdetermine the optimum cruise tip speed, instead of asingle tip speed determining the airfoil design. In parallel,a nonlinear, multi-segment blade twist distribution may beneeded. There remains the requirement to explicitlyinclude maneuvering flight conditions in the coupledaeromechanics and sizing optimization.

Acknowledgements

The author wishes to acknowledge the assistance of Dr.Hyeonsoo Yeo of the U. S. Army AeroflightdynamicsDirectorate at Ames Research Center, who provided thewing/rotor wake model, and the generous advice of Dr.Wayne Johnson of NASA Ames Research Center, whodeveloped both CAMRAD II and NDARC.

References

1. Johnson, W., “NDARC—NASA Design andAnalysis of Rotorcraft: Theoretical Basis andArchitecture,” AHS Aeromechanics Specialists’Conference, San Francisco, California, January 2010.

2. Johnson, W., “NDARC, NASA Design and Analysisof Rotorcraft,” NASA TP 2009-215402, December 2009.

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3. Johnson, W., Rotorcraft Aerodynamics Models for aComprehensive Analysis, 54th Annual Forum of theAmerican Helicopter Society, Washington, D.C., 1998.

14. Acree, C. W. Jr. and Johnson, W., “AeroelasticStability of the LCTR2 Civil Tiltrotor,” AHS TechnicalSpecialists’ Meeting, Dallas, Texas, October 15-17,2008.

4. Johnson, W., “CAMRAD II ComprehensiveAnalytical Model of Rotorcraft Aerodynamics andDynamics,” Johnson Aeronautics, Palo Alto, California,2005.

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17. Acree, C. W., “Modeling Requirements for Analysisand Optimization of JVX Proprotor Performance,” 64thAnnual Forum of the American Helicopter Society,Montreal, Canada, April 2008; also NASA TM-2008-214581, May 2008.

18. McVeigh, M. A., Grauer, W. K., and Paisley, D. J.,“Rotor/Airframe Interactions on Tiltrotor Aircraft,”Journal of the American Helicopter Society, Vol. 35, No.3, July 1990.

19. Kroo, I., “Propeller-Wing Integration for MinimumInduced Loss,” Journal of Aircraft, Vol. 23, No. 7, July.1986.

20. Snyder, M. H., and Zumwalt, G. W., “Effects ofWingtip-Mounted Propellers on Wing Lift and InducedDrag, Journal of Aircraft, Vol. 6, No. 5, September-Oct.1969.

21. Miranda, L. R., and Brennan, J. E., “AerodynamicEffects of Wingtip-Mounted Propellers and Turbines,”AIAA 86-1802,1986.

22. Witkowski, D. P., Lee, A. K. H., and Sullivan, J. P.,“Aerodynamic Interaction Between Propellers andWings,” Journal of Aircraft, Vol. 26, No. 9, September1989.

23. Deckert, W. H., and Ferry, R. G., “Limited FlightEvaluation of the XV-3 Aircraft,” Air Force Flight TestCenter Report AFFTC-TR-60-4, May 1960.

24. Corrigan, J. J., and Schillings, J.J., “Empirical Modelfor Stall Delay Due to Rotation,” AHS AeromechanicsSpecialists Conference, San Francisco, California,January 1994.

25. Narramore, J. C., “Airfoil Design, Test, andEvaluation for the V-22 Tilt Rotor Vehicle,” 43rd AnnualForum of the American Helicopter Society, St. Louis,Missouri, May 1987.

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