Experimental Investigation and Fundamental Understanding of a … · 2013-04-10 · Experimental...

Experimental Investigation and Fundamental

Understanding of a Slowed UH-60A Rotor at High

Advance Ratios

Anubhav Datta

Science and Technology Corporation

Hyeonsoo Yeo

Aeroflightdynamics Directorate (AMRDEC)

U.S. Army Research Development and Engineering Center

Thomas R. Norman

Aeromechanics Branch, NASA

NASA Ames Research Center, Moffett Field, CA

ABSTRACT

This paper describes and analyzes the measurements from a full-scale, slowed RPM, UH-60A rotortested at the National Full-Scale Aerodynamics Complex 40- by 80- ft wind tunnel up to an advance ratioof 1.0. A comprehensive set of measurements, that includes performance, blade loads, hub loads andpressures/airloads makes this data set unique. The measurements reveal new and rich aeromechanicalphenomena that are special to this exotic regime. These include reverse chord dynamic stall, retreatingside impulse in pitch-link load, large inboard-outboard elastic twist differential, supersonic flow at lowsubsonic advancing tip Mach numbers, diminishing rotor forces yet dramatic build up of blade loads,and dramatic blade loads yet benign levels of vibratory hub loads. The objective of this research isthe fundamental understanding of these unique aeromechanical phenomena. The intent is to provideuseful knowledge for the design of high speed, high efficiency, slowed RPM rotors of the future and achallenging database for advanced analyses validation.

NOMENCLATURE

CD,A,H rotor drag; nondim. by ρπR2(ΩR)2

CL,N,T rotor thrust; nondim. by ρπR2(ΩR)2

CDE effective drag coeff.CDE = (CPi + CPo)/µ = CP /µ− CX

CDE = −CX in autorotationCHo profile H-force coeff.CP power coeff. = P/ρA(ΩR)3 = CQ

CP = CPi + CPo + µCX

CPi induced power coeff.CPo profile power coeff. = CQo + µCHo

CQ torque coeff. = Q/ρπR2(ΩR)2R = CP

Presented at the American Helicopter Society 66th AnnualForum, Virginia Beach, VA, May 3–5, 2011. This is a work ofthe U.S. Government and is not subject to copyright protection.

CQo profile torque coeff.CX propulsive force coeff.= −CD

Cp pressure coeff. = 2(p− p∞)/ρU2∞

C∗p sonic pressure coeff.

CP = C∗P when Ml = 1.0

D,A,H rotor drag in wind, horiz. and shaft axesL,N, T rotor thrust in wind, vert. and shaft axesL/DE lift-to-drag ratio = CL/CDE

MA advancing tip Mach numberMT tip Mach number = ΩR/aMl surface Mach number

M2cc chord force distributionnondim. by 1

2ρa2c

M2cm 1/4-c pitch. mom. distributionnondim. by 1

2ρa2c2

M2cn normal force distributionnondim. by 1

2ρa2c

P,Q rotor power, torque; P = ΩQ

1

https://ntrs.nasa.gov/search.jsp?R=20110014334 2020-04-25T05:59:43+00:00Z

R rotor radius

V tunnel speed

X propulsive force = −Da speed of soundc local chordcl, cd sectional lift and drag coeffs.r radial station

Ω rotor RPM

∆α tunnel correction angle, +ve in up washαS shaft angle, +ve aftµ advance ratio V/ΩRρ densityγ heat capacity; 1.4 for air at 20Cσ rotor solidity; 0.0826θ75 collective angle at 75% R, degreeθ1S , θ1C longitudinal and lateral cyclics, degree

INTRODUCTION

Slowed rotors are recognized as technology en-ablers for higher speeds in edgewise rotors and highercruise efficiencies in tiltrotors. Even at low speeds,optimal use of rotor speed can offer significant ef-ficiency gains, assuming a required thrust level canbe maintained. As a result, considerable attentionis devoted today towards the development of widespeed-range power turbines and continuously variablemultiple-speed transmissions for rotorcraft [1,2]. Someof these technologies are already available today in lim-ited form, and have found application on advanced ro-torcraft. For instance, a 15-20% reduction in engineRPM is deliverable by today’s commercial power tur-bines with no more than 5-10% penalty in specific fuelconsumption [3]. The Sikorsky X2 Technology Demon-strator slows its rotor by 20% from 446 to 360 rev-olutions per minute (RPM) to fly at 250 kt using asimilar technology [4,5]. The Bell/Boeing V-22 Ospreyslows its rotor by 19% from 412 to 333 RPM to flyin cruise using a similar technology. Two-speed trans-missions, with innovative gear-boxes and clutches forchanging gears in flight, have also been demonstrated.Frontier System’s optimum speed rotor – now part ofBoeing’s 6500 lb A160 unmanned air vehicle (UAV) –uses a similar technology on edgewise rotors for high ef-ficiency low speed flight [6]. It is now being pursued ontiltrotors for high efficiency high speed flight [7]. Eventhough the underlying technology of RPM reductionremains the same in both edgewise rotors and tiltro-tors, the aeromechanics of their operations is entirelydifferent. An edgewise rotor, when slowed down for thepurposes of high speed, begins to operate at very high,non-conventional advance ratios (µ= 0.7 – 1.0 and be-yond). About 80% or more of its retreating side nowremains immersed in reverse flow. The objective of thisresearch is to understand the aeromechanics of such aslowed rotor.

High advance ratios are traditionally associated

with autogiros [8] or innovative helicopter-autogiro hy-brids [9, 10]. For a helicopter to achieve high speeds(200-300 kt) and yet remain efficient and maneuver-able, it is desired that the rotor be powered and remainscontrolled. The word slowed rotor refers to such rotors.By definition, slowed rotors generate lower forces andmoments, and are therefore intended primarily for usein compound helicopters (with the exception of light-weight UAVs). The decades of 1960s - 70s saw exten-sive research, development and flight testing of a widevariety of compound helicopters [11, 12]. The develop-ments spurred significant research on high advance ra-tio slowed rotors, yet, none actually found a place on anaircraft at the time. Some of the aircraft, like the U.S.Army XH-51A (Lockheed), experimented with RPMreduction but only down to 95% nominal, below whichstructural resonance problems were encountered [13].Eventually, none of these aircraft entered regular pro-duction. Today, with advances in materials, controls,and engine/drivetrain technologies, compounds haveonce again emerged as potential contenders for high-speed heavy lift rotorcraft [14] – this time, envisionedto be equipped with slowed rotors. One vision for thefuture is a 50% or more reduced RPM slowed rotor thatis applicable to heavy lift, high speed, high efficiencyrotorcraft.

Extensive analytical investigations of slowed rotorswere performed in the last decade [15–19]. Successfulflight demonstrations of three modern compound he-licopters were also carried out, namely: the SikorskyX2 with a coaxial rotor and pusher prop [20], the Eu-rocopter X3 with a wing and two wing mounted pro-pellers [21,22], and the Piasecki X-49A with a wing anda Vectored Thrust Ducted Propeller [23]. The coaxialX2 flew at advance ratio of µ = 0.8 at 80% nominalRPM (hover) to demonstrate successful flight at 250 kt.The single rotor X3 demonstrated 180 kt with the even-tual goal of reaching 220 kt at advance ratio of µ = 0.66at 78% nominal RPM. Additionally, CarterCopter’ssuccessful demonstration of the first ever µ = 1.0 flightin 2005 with 50% reduced RPM, even though as an au-togiro, contributed further to growing interest in highadvance ratio slowed rotors [24].

A slowed rotor must operate as a conventional ro-tor in hover and yet all but disappear – in drag, loadsand vibration – at high speeds. Understanding theirfundamental dynamics is important to address thistechnical challenge efficiently (minimum vehicle power)and safely (control reversal, loads and vibration, sta-bility). Unlike conventional rotors, there is a scarcityof experimental data and a lack in the fundamentalunderstanding of the aerodynamic and dynamic envi-ronment of high advance ratio slowed rotors. Histor-ically, only four full-scale high advance ratio tests aredocumented: the Pitcairn PCA-2 Autogiro tests in theNACA Langley 30- by 60- ft wind tunnel [25], a two-bladed teetering rotor test at the same tunnel [26, 27],

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the Sikorsky H-34 tests in the NASA Ames 40- by 80-ft wind tunnel [28], and the Bell UH-1 tests in the samewind tunnel [29]. All of these tests, conducted duringthe 1960s (the autogiro test was in 1930s), provide onlyrotor performance and blade root motions and limitedflow visualization (tufts). Recently, a comprehensivestudy was conducted on correlating these data withanalyses [30]. The study highlighted the discrepanciesin current analyses – both lifting-line and CFD based– in predicting high advance ratio performance. Thesediscrepancies have not been addressed systematicallydue to the scarcity of reliable and comprehensive testdata. Several researchers are carrying out model-scaletests in recent years to address the above technical chal-lenges [31, 32]. The focus of the present research is onfull-scale testing.

In an effort to address the lack of fundamental un-derstanding as well as comprehensive data, a full-scaleUH-60A rotor (26.83 ft radius, 4-bladed, fully artic-ulated) was tested at the U. S. Air Forces’ NationalFull-Scale Aerodynamics Complex (NFAC) 40- by 80-ft wind tunnel at slowed rotational speeds - 65% and40% of nominal – with resultant advance ratios reach-ing up to 1.0. A comprehensive set of measurementsincluding performance, blade loads, hub loads and pres-sures/airloads make this data set unique. The test waspart of a broader UH-60A airloads test program [33].The program was divided into six test phases. The firstfive phases involved conventional operations: 1-g levelflight speed sweeps, parametric sweeps, reproductionof earlier flight test and DNW tunnel test points, andParticle Image Velocimetry (PIV) tests. The fifth phasewas the high advance ratio Slowed Rotor Test (SRT) –the subject matter of this paper. The objective was toexplore the aeromechanics of a conventional (edgewise)rotor in a non-conventional (large reverse flow) regimein anticipation of the next generation of high speed,high efficiency, variable RPM rotors.

Finally, note that the UH-60A rotor was not de-signed to operate in a high advance ratio regime. It isprecisely for this same reason, however, that it is ex-pected to reveal many of the critical, limiting aerome-chanical phenomena that will constrain the design andoperation of future slowed rotors in this regime.

Scope of Paper

The present test differs from those conducted ear-lier in that it acquires a more complete set of mea-surements: performance, motions, structural loads, hubloads and pressures/airloads under slowed RPM highadvance ratio conditions. The emphasis of this paperis on the fundamental understanding of aeromechanicsin this unique regime by connecting flow phenomena torotor performance and structural loads. The first sec-tion provides a brief description of the experiment, em-phasizing the special considerations of the slowed rotor

test. The second section describes the test points. Thefollowing three sections examine specific results fromthis test: performance, structural loads and hub loads,and pressure and airloads.

Figure 1: Full-scale UH-60A rotor installed onthe Large Rotor Test Apparatus in the NFAC40- by 80- ft wind tunnel.

WT Horizontal

WT

Ver

tica

l

T

H

N

Velocity (nominal)

Velocity (corrected)

D

L

αS

∆α

∆α

AX

Figure 2: Model shaft angle αS, wall correction∆α, and rotor forces in tunnel axes (N and A),shaft axes (T and H), and corrected wind axes(L and D), and the propulsive force (X = -D).

DESCRIPTION OF EXPERIMENT

The hardware, measurement systems, data acqui-sition systems, data reduction procedures, and pre-testactivities common to all six test phases are described indetail in Ref. [33]. A brief summary is provided here,with details relevant to and considerations specific tothis test.

Model : The UH-60A rotor mounted on the NFACLarge Rotor Test Apparatus (LRTA) is shown in Fig. 1.A schematic of the model defining the force conventionsis given in Fig. 2. The tunnel wall correction ∆α, basedon the rotor diameter to tunnel width ratio, model off-set from center-line (10.9 inches up), and rotor disk areato tunnel area (79 ft x 39 ft, 1 ft reduced for acoustic

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lining) ratio, is given by

∆α = 8.6101(CN/µ2

)deg (1)

Instrumentation : The blades are exactly the samefour blades flown during the 1993 Airloads Pro-gram [34], but refurbished and re-calibrated with newinstrumentation. A total of 332 rotor and hub mea-surements and 124 LRTA and wind tunnel measure-ments were acquired during the test. The rotor and hubmeasurements included: a total of at least 160 workingpressure transducers (down from 215 functional trans-ducers at the beginning of test, out of 235) arrangedchordwise and spanwise in Gaussian spacing over ninestations (22.5, 40, 55, 67.5, 77.5, 86.5, 92, 96.5, and99% R) and several additional intermediate stations; atotal of 26 two- or four-leg strain-gage bridges on a sec-ond instrumented blade for structural loads at the root(11.3%R) and eight uniformly distributed stations from20% to 90%R; two independent blade motion hardware– a set of three Rotary Variable Differential Transform-ers (RVDTs) mounted on each blade hinge points anda set of three laser distance transducers mounted oneach blade hub arm; 8 strain gage bridges on the shaft– 4 to measure shaft stresses and 4 to measure shaftbending moments; and 10 four-leg strain-gage bridgesto measure axial loads on the pitch links (4), damper(4), and rotating scissors (2). The LRTA and windtunnel measurements included: a five-component rotorbalance – four flexures instrumented with 12 primaryand 12 back-up gages for three forces and pitching androlling moments, and an in-line flex-coupling for torque;8 strain-gage bridges to measure non-rotating controlsystem forces and moments (3 bridges on stationarypushrods, one bridge on stationary scissor, and 4 onthe swashplate guide); 6 displacement measurementsof the primary (3) and dynamic (3) actuators; 6 loadcells between LRTA fairing and chassis for steady fuse-lage loads; and 31 tunnel pressure/temperature mea-surements, 3 model angle measurements and a rotorRPM measurement. The blade pressure data were ac-quired at 2048 per revolution (/rev). The motions andloads data were acquired at 256/rev.

Independent measurements: In addition to theabove, two independent data sets were acquired: span-wise blade deformations, using 8 CCD progressive scancameras, 16 high-power xenon flash-lamp strobes on thetest section floor cavities and 48 retro-reflective targetson the blade lower surfaces [35]; and density gradientsdownstream of the advancing blade to track tip vorticeswith retro-reflective background oriented schlieren, us-ing 2 cameras synchronized to rotor 1/rev, a retro-reflective light source, and a speckled background puton the tunnel wall [36]. Data from these measurementsare part of ongoing investigation and beyond scope ofthis paper.

Motion and loads allowables: Several special stepswere taken for the slowed rotor test including thosebased on Sikorsky’s review of the motions and loadsallowables at reduced RPM. The main rotor dynamicflap and droop stop mechanisms were modified to al-low adequate flapping at the reduced RPM. The lagdisplacement was monitored for instabilities in case 1–3/rev motions significantly decreased damping at thelag frequency. Trailing edge strains (vibratory and pos-itive/negative peaks) at 50% R and 68% R were addedas safety of flight parameters in case decreased centrifu-gal forcing led to compression from edgewise bending.The lug stress at the blade cuff was confirmed not tobe a concern.

Test plan and procedure : The test plan was con-structed as a parametric sweep with tip Mach numberMT as the primary variable. The MT settings were0.65 at 100% nominal RPM (NR) of 258, 0.42 at 65%NR and 0.26 at 40%NR. The maximum model speedwas limited to 182 kt (maximum tunnel speed is 300kt). The minimum RPM (40% NR) and the maximummodel speed were set by safety of flight considerations.These limits determined the maximum advance ratio.All RPM changes were carried out after bringing thetunnel speed down to zero or a very low value (nominalhover), to prevent resonance due to changing blade fre-quencies. Similarly, all shaft angle changes were carriedout after bringing the tunnel speed down, to avoid largetransient blade flapping. The emergency shut downprocedure was to reduce the tunnel speed first. Thetest procedure was: (1) set RPM (i.e., MT ); (2) setshaft angle αS ; (3) vary tunnel speed for intended µ;(4) at each µ, acquire data over a range of collective an-gles with the maximum limited by cyclic control limitsor load limits whichever was encountered first (usuallythe latter); and (5) after completion of the collectivesweeps at all µ, bring tunnel speed down, and go to nextαS . Each collective setting was a test point. At eachtest point, the rotor was trimmed to minimize flappingmanually.

PERFORMANCE MEASURES

The following definitions are used for interpreta-tion of performance.

Rotor power CP equals rotor torque CQ in coeffi-cient form. Torque includes induced (cl contribution)and profile (cd contribution) components.

CP = CQ = CQi + CQo (2)

Adding and subtracting µCH = µ(CHi + CHo), rec-ognizing CQi + µCHi =

∫λdCT , and defining profile

power as CPo = CQo + µCHo, Eq. 2 takes the form

CP =

∫λdCT + CPo − µCH (3)

4

Table 1: Slowed rotor test runs; NR: NominalRPM (258), αS: shaft angle (deg), V: speed (kt),µ: advance ratio, MA: advancing tip Mach no.,θ75: collective angle (deg).

Run % NR αS V µ MA θ75

R66 100 0.0 130 0.3 0.85 -0.1–10.02.0 0.0–9.94.0 -0.1–5.9

R69 0.0 172 0.4 0.91 0.4–8.02.0 -0.1–8.04.0 0.0–5.9

R87 65 0.0 83 0.3 0.55 -0.1–7.9111 0.4 0.59 -0.1–7.9139 0.5 0.63 -0.1–7.9167 0.6 0.67 0.0–7.9

R91 40 0.0 52 0.3 0.34 0.0–8.069 0.4 0.36 -0.1–8.087 0.5 0.39 0.0–8.0104 0.6 0.42 0.0–7.9121 0.7 0.44 0.0–8.0139 0.8 0.47 -0.1–8.0157 0.9 0.49 0.0–4.0174 1.0 0.52 -0.8–1.8

R93 4.0 52 0.3 0.34 0.0–8.070 0.4 0.36 0.0–8.087 0.5 0.39 -0.1–8.0104 0.6 0.42 0.0–8.0

R95 52 0.3 0.34 0.9,1.1104 0.6 0.36 2.8,5.1,6.2121 0.7 0.44 -0.1–7.7138 0.8 0.47 -0.1–7.7156 0.9 0.49 -0.1–6.2173 1.0 0.52 0.0–2.0

R96 2.0 52 0.3 0.34 1.7,1.970 0.4 0.36 1.987 0.5 0.39 1.9104 0.6 0.42 2.0121 0.7 0.44 1.9139 0.8 0.47 1.9156 0.9 0.49 1.9174 1.0 0.52 0.9

Separating inflow into induced and forward speed com-ponents as λ = λi − µ(αs + ∆α), where αs is pos-itive for tilt back as per test convention, recognizing(αs + ∆α)CT + CH = CD = −CX (see Fig. 2 andassume small angles), and defining induced power asCPi =

∫λidCT , leads to the energy balance expression

CP = CPi + CPo + µCX (4)

µCX is power for propulsion. Because the remainderis power associated entirely with lift generation, it isrepresented as an effective drag CDE where µCDE =CPi + CPo. Thus effective drag is

CDE = CP /µ− CX (5)

Rotor efficiency (lift to drag ratio) follows

L/DE =CL

CP /µ− CX(6)

In autorotation, CP = 0, hence (from Eq. 5)

CDE = −CX . (7)

SLOWED ROTOR TEST MATRIX

The slowed rotor test points are summarized inTable 1. There are a total of 232 points; 47 of theseare a set of 100% NR points carried out at three shaftangles 0, 2, and 4; 36 are a set of 65% NR pointscarried out at a single shaft angle of 0; and 149 are aset of 40% NR points carried out at three shaft angles0, 2, and 4.

The 40% NR points constitute the more compre-hensive of the two slowed RPM sets. The maximumadvance ratio of µ = 1.0 was achieved during this set.The points at shaft angle 2 were obtained only at asingle collective, nominally 2, except for the highestadvance ratio of µ = 1.0, where it was obtained ad-ditionally at 1. The points at shaft angle 4 wereobtained over two separate runs, 93 and 95. The firsttwo points of run 95 (shown in grey) were check pointsrepeating the first and last points from run 93.

The advance ratios and advancing tip Mach num-bers matrix of the test points, Fig. 3, indicate a usefulseparation of high compressibility and high reverse flowphysics. The largest variation of µ (i.e. extent of re-verse flow) from 0.3 to 1.0 is contained entirely withinthe subsonic regime. Additional features of the testmatrix design is described in Fig. 4 which presents asummary of all the test points in a power-speed enve-lope. There are two sets of points that have commonspeeds at different RPM. The speed 139 kt is a com-mon speed between 65% and 40% NR (with µ = 0.5and 0.8 respectively). Similarly, the speed 174 kt iscommon between 100% and 40% NR (with µ = 0.4 and1.0 respectively). In other words, the nominal rotor atµ = 0.4 flies at the same speed as the 40% NR rotor

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at µ = 1.0. The 65% NR rotor at µ = 0.5 flies at thesame speed as the 40% NR rotor at µ = 0.8. There is apair of points that represents a common advancing tipMach number but widely different advance ratios – the65% NR, µ=0.3 point and the 40% NR, µ=1.0 point.

The thrust-speed envelope is shown in Fig. 5.Thrust is minimal for the slowed rotor, as expected,but not insignificant (2000-3000 lb) at µ = 1.0. Eventhough the dimensional thrust is low, the collectivesweeps up to load limit ensured high non-dimensionalthrust levels. The non-dimensional thrust-speed en-velopes for shaft angles of 0 and 4 are shown inFigs. 6 and 7 respectively. The rotor generated dragat all points, but never operated in autorotation. Theproximity of the test points to autorotation is shownin Fig. 8 where the effective drag coefficient is plottedalong with the value expected during autorotation. Itcame closest to autorotation for the 40% NR case witha shaft angle of 4 at the highest advance ratios.

From the test matrix, test points for parametricsweeps are identified for the purposes of studying struc-tural loads, hub loads and airloads. The first two digitsof each test point identify the run number. Table 2shows two RPM sweeps (i.e., MT sweeps), at advanceratios of 0.3 and 0.4. These sweeps isolate the effects ofslowing the rotor while keeping the reverse flow area thesame. Table 3 shows two advance ratio sweeps at shaftangles 0 and 4. The thrust level is the same betweenthe two so that the two sets can also be used to studythe effect of shaft angle variation. These sweeps isolatethe effects of increasing reverse flow area. Note thatthe advance ratio sweep is also a speed sweep since allpoints are at the same RPM (40% NR). Table 4 showssix thrust sweeps – two sets each for shaft angles 0 and4, and each set constituting three collective sweeps atadvance ratios 0.8, 0.9, and 1.0. The sweeps isolatethe effects of reverse flow stall. Selected subsets of theabove sweeps are used in this paper to illustrate thespecial aeromechanical phenomena of the high advanceratio regime.

Table 2: Slowed rotor test points for RPM (i.e.MT ) sweeps at two different advance ratios; Pt:test point number, CT /σ: nondim. thrust, θ1Cand θ1S: nominal lateral and longitudinal cyclicangles (deg).

Point MT αS µ θ75 CT /σ θ1C θ1S

µ = 0.36619 0.65 0.0 0.3 6.0 0.082 0.4 -4.68716 0.42 0.0 0.3 5.9 0.081 -0.7 -5.39117 0.26 0.0 0.3 5.9 0.082 -1.6 -5.7

µ = 0.46912 0.65 0.0 0.4 6.0 0.071 1.9 -4.58724 0.42 0.0 0.4 5.9 0.070 0.6 -6.39125 0.26 0.0 0.4 6.0 0.072 -0.6 -6.7

0 0.5 1 1.5 2 2.5 3 3.50.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Advance ratio, µ

Adv

anci

ng ti

p M

ach

num

ber,

M A

100%NR65%NR40%NR

0k / 70°F100% NR = 258 RPM

280 kt240 kt

200 kt160 kt

120 kt80 kt

100% NR

80%

65%

50%

40%30%

20%

Figure 3: Advancing tip Mach number vs. ad-vance ratio of all slowed rotor test points.

40 60 80 100 120 140 160 1800

200

400

600

800

1000

1200

1400

1600

1800

Speed, kt

Pow

er, H

P

100% NR65% NR40% NR

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.3 0.4 0.5 0.6

0.3 0.4µ at 100% NR

µ at 65% NR

µ at 40% NR

Figure 4: Power vs. speed envelope of all slowedrotor test points.

40 60 80 100 120 140 160 1800

5,000

10,000

15,000

20,000

25,000

30,000

Speed, kt

Thr

ust,

lb

100% NR65% NR40% NR

Figure 5: Thrust vs. speed envelope of all slowedrotor test points.

6

0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Advance ratio, µ

Thr

ust,

CT /

σ

100% NR65% NR40% NR

Figure 6: Non-dimensional thrust vs. speed at 0

shaft angle.

0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Advance ratio, µ

Thr

ust,

CT /

σ

100% NR40% NR

Figure 7: Non-dimensional thrust vs. speed at 4

shaft angle (tilt back).

−0.025 −0.02 −0.015 −0.01 −0.005 00

0.005

0.01

0.015

0.02

0.025

Propulsive force, CX / σ

Effe

ctiv

e dr

ag, C

DE /

σ

Shaft αS = 0°

Shaft αS = 2°

Shaft αS = 4°

Autorotation lineC

DE = − C

X

Dragging rotor

Figure 8: Operation relative to autorotation; 40%NR.

Table 3: Slowed rotor test points for advance ra-tio (speed) sweeps at two different shaft angles.


αS = 0

9116 0.26 0.0 0.3 4.0 0.062 -0.8 -4.29133 0.26 0.0 0.4 6.0 0.063 0.4 -7.49145 0.26 0.0 0.5 7.9 0.062 1.4 -10.0

αS = 4

9318 0.26 4.0 0.4 2.0 0.063 0.0 -4.19325 0.26 4.0 0.5 2.0 0.063 0.7 -4.89518 0.26 4.0 0.7 3.0 0.062 2.0 -6.69528 0.26 4.0 0.9 6.2 0.063 5.0 -10.9

Table 4: Slowed rotor test points for thrust (col-lective) sweeps at two shaft angles and threeadvance ratios.


αS = 0

µ = 0.8;9155 0.26 0.0 0.8 -0.1 0.020 2.8 0.09156 0.26 0.0 0.8 2.0 0.033 3.3 -2.59157 0.26 0.0 0.8 4.0 0.034 3.9 -5.39158 0.26 0.0 0.8 6.0 0.040 4.3 -7.79159 0.26 0.0 0.8 8.0 0.045 4.4 -10.2

µ = 0.99162 0.26 0.0 0.9 0.0 0.021 3.6 0.39163 0.26 0.0 0.9 2.0 0.024 4.4 -2.39164 0.26 0.0 0.9 4.0 0.026 5.3 -5.2

µ = 1.09168 0.26 0.0 1.0 -0.1 0.019 4.7 0.89175 0.26 0.0 1.0 1.9 0.022 5.5 -1.8

αS = 4

µ = 0.8;9520 0.26 4.0 0.8 -0.1 0.047 2.7 -3.19521 0.26 4.0 0.8 1.9 0.056 2.9 -5.59522 0.26 4.0 0.8 5.9 0.069 3.5 -10.59523 0.26 4.0 0.8 7.7 0.076 3.6 -12.6

µ = 0.99526 0.26 4.0 0.9 -0.1 0.058 3.6 -2.79527 0.26 4.0 0.9 2.0 0.060 4.4 -5.59528 0.26 4.0 0.9 6.2 0.063 5.0 -10.9

µ = 1.09531 0.26 4.0 1.0 0.0 0.061 4.5 -2.69530 0.26 4.0 1.0 2.0 0.059 5.6 -5.5

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ROTOR PERFORMANCE

This section analyzes the measured rotor perfor-mance. The 40% NR case is studied in detail as thiscase extends up to µ = 1.0. The 65% NR case (up toµ = 0.6) and 100% NR case (up to µ = 0.4) are usedfor comparison purposes. For all of the test points,thrust almost equals lift (CT ≈ CL), but not used in-terchangeably to maintain consistency of nomenclature.In addition, for the case of 0 shaft angle, drag almostequals H-force (CD ≈ CH).

The thrust variation with collective at 0 shaft an-gle at 40% NR is shown in Fig. 9. The sensitivity isreduced to almost zero at µ = 1.0. The thrust variationwith collective at 4 shaft angle is shown in Fig. 10. Thesensitivity reverses slightly at µ = 1.0. The thrust sen-sitivities at the two shaft angles are plotted in Fig. 11as a function of advance ratio. Also plotted in the samefigure is the thrust sensitivity to shaft angle at 0 col-lective. This sensitivity shows a slight increase at thelower and higher advance ratios (µ = 0.3 to 0.4 andµ = 0.7 to 1.0) with a dip in between, but remainsnominally constant compared to the sensitivity to col-lective.

This thrust behavior under high advance ratios(near µ = 1.0) was first reported in 1965 by Jenk-ins [27], and attributed to the sensitivity of longitudinalflapping (i.e. longitudinal cyclic, under trim condition)to collective being greater than its sensitivity to shaftangle. The sensitivities of the longitudinal cyclic to col-lective and to shaft angle, shown in Fig. 12, confirm thistrend. An increase in collective makes the reverse flowregime more severe at high advance ratios, results ina progressively higher longitudinal cyclic requirementfor trim, and consequently begins to offset the effect ofthrust increase with collective (Fig. 11). An increasein shaft angle makes the reverse flow less severe, andbecause a greater reverse flow area (i.e. advance ratio)leads to a greater benefit, generally augments the effectof thrust increase with shaft angle (Fig. 11). However,an increase in collective at a higher shaft angle (4 ver-sus 0) appears to be detrimental to thrust beyond anadvance ratio of 0.5. It is shown later that an addi-tional mechanism which contributes significantly to thethrust behavior is the large elastic twist deformation ofthe blades that drives the advancing blade inboard andoutboard stations to produce a differential airloading.

The power variation with thrust at 0 shaft angle isshown in Fig. 13. Each symbol represents one collectivesetting. Beyond µ = 0.7 power reduces with increasingthrust as the rotor begins to absorb energy and gener-ate increasingly greater propulsive force in the negativedirection (drag). This is seen in Fig. 14 where the dragforce is plotted versus lift. The drag sensitivity to col-lective increases with advance ratio, unlike thrust, andshows a steep increase beyond µ = 0.7. The H-force isexpected to be same as drag force at 0 shaft angle, the

−1 0 1 2 3 4 5 6 7 80

0.02

0.04

0.06

0.08

0.1

0.12

Collective, θ75

, deg

Thr

ust,

CT /

σ

µ = 0.3µ = 0.4µ = 0.5µ = 0.6µ = 0.7µ = 0.8µ = 0.9µ = 1.0

Figure 9: Thrust vs. collective for advance ratiosup to 1.0; 0 shaft; 40% NR.

−1 0 1 2 3 4 5 6 7 80.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

Collective, θ75

, deg

Thr

ust,

CT /

σ

µ = 0.3µ = 0.4µ = 0.5µ = 0.6µ = 0.7µ = 0.8µ = 0.9µ = 1.0

Figure 10: Thrust vs. collective for advance ra-tios up to 1.0; 4 shaft; 40% NR.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−4

−2

0

2

4

6

8

10

12

14x 10

−3

Advance ratio, µ

∂ (C

T /

σ) /

∂ θ 75

, ∂

(C

T /

σ) /

∂ α S

∂ (CT/σ) / ∂ θ

75

αS = 4°

αS =0°

∂ (CT/σ) / ∂ α

S

θ = 0°

Figure 11: Thrust sensitivity to collective at twoshaft angles (0 and 4), and to shaft angle at 0

collective; 40% NR.

8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−1.5

−1.25

−1

−0.75

−0.5

−0.25

0

Advance ratio, µ

∂ θ 1S

/ ∂

θ 75,

∂ θ

1S /

∂ α S

αS=4°

αS=0°

θ75

= 0°

∂ θ1S

/ ∂ αS

∂ θ1S

/ ∂ θ75

Figure 12: Longitudinal cyclic sensitivity to col-lective at two shaft angles (0 and 4), and toshaft angle at 0 collective; 40% NR.

0 0.02 0.04 0.06 0.08 0.1 0.120

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Thrust, CT / σ

Pow

er, C

P /

σ

µ = 0.3µ = 0.4µ = 0.5µ = 0.6µ = 0.7µ = 0.8µ = 0.9µ = 1.0

Figure 13: Power vs. thrust for advance ratios upto 1.0; 0 shaft; 40% NR.

0 0.02 0.04 0.06 0.08 0.1 0.120

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Lift, CL / σ

Dra

g, C

D /

σ

Shaft = 0 deg

µ = 0.3µ = 0.4µ = 0.5µ = 0.6µ = 0.7µ = 0.8µ = 0.9µ = 1.0

CH / σ

Figure 14: Drag (= −X ≈ H) vs. lift for advanceratios up to 1.0; 0 shaft; 40% NR.

0 0.02 0.04 0.06 0.08 0.1 0.120

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Lift, CL / σ

Indu

ced

+ p

rofil

e po

wer

, (C

Pi+

Cpo

) / σ

1.0

0.9

0.8

0.7

0.6

0.5

0.4

µ = 0.3

Figure 15: Induced and profile power vs. lift foradvance ratios up to 1.0; 0 shaft; 40% NR.

0 0.02 0.04 0.06 0.08 0.1 0.120

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Lift, CL / σ

Effe

ctiv

e dr

ag, C

DE /

σ

µ = 0.3

0.4

0.5

0.6

0.70.80.91.0

Figure 16: Effective drag vs. lift for advance ra-tios up to 1.0; 0 shaft; 40% NR.

0 0.02 0.04 0.06 0.08 0.1 0.120

1

2

3

4

5

6

7

8

9

Lift, CL / σ

Lift

to d

rag

ratio

, L/D

E

µ = 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Figure 17: Lift to drag ratio for advance ratios upto 1.0; Shaft=0, 40% NR.

9

0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Thrust, CT / σ

Pow

er, C

P /

σ

µ = 0.3µ = 0.4µ = 0.5µ = 0.7µ = 0.8µ = 0.9µ = 1.0

Figure 18: Power vs. thrust for advance ratios upto 1.0; 4 shaft; 40% NR.

0 0.02 0.04 0.06 0.08 0.10

1

2

3

4

5

6

7

Lift, CL / σ

Lift

to d

rag

ratio

, L/D

E

µ = 0.6

µ = 0.7

µ = 0.8µ = 0.9µ = 1.0

µ = 1.0µ = 0.9

µ = 0.8

µ = 0.7µ = 0.6

Shaft αS= 4°

Shaft αS = 0°

Decreasing θ75

increasing CL

increasing L / DE

Figure 19: Lift to drag ratio compared at zeroand positive shaft angles; 40% NR.

deviation found at the lower advance ratios and higherlift are due to the tunnel correction ∆α becoming moresignificant (Eq. 1).

If the propulsive power (µCX) is removed from to-tal power (Fig. 13), then the reduction with increas-ing thrust at the higher advance ratios vanish andthe remaining induced and profile power components(CPi + CPo = CP − µCX), plotted in Fig. 15, showa continuous increase as expected. The effective drag(CDE , where µCDE = CPi + CPo), shown in Fig. 16,follows the same trend, except that the lower advanceratios (µ = 0.3 and 0.4) collapse to a single curve. Therotor efficiency (lift-to-drag ratio L/DE) is shown inFig. 17. Even though the rotor power reduces withthrust at the high advance ratios, the dragging rotorhas a poor efficiency, with L/DE ≈ 1− 3. At a highershaft angle of 4 the power variation with thrust is asshown in Fig. 18. The curves show a more distinct op-

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9

Advance ratio, µ

Max

imum

L/D

E

0.2 0.4 0.6 0.8 10123456789

Advancing tip Mach number, MA

40% NR; αS = 0°

100% NR

65% NR

40% NR

40% NR; αS = 4°

65% NR; αS = 0°

100% NR; αS = 0°

Figure 20: Maximum lift to drag ratios.

timum (around CT /σ = 0.06) compared to the 0 shaftangle case (Fig. 13). The L/DE values at the two shaftangles are compared in Fig. 19 for the high advanceratios. A positive shaft angle increasing efficiency istypical of rotors, what is different for the slowed rotor,is that the efficiency is maximized by a decrease in col-lective when operating beyond thrust reversal. This isthe case for µ = 1.0 at αS = 4 in Fig. 19.

The maximum efficiencies are plotted in Fig. 20.At any given advance ratio, i.e. a given reverse flowarea, the maximum is higher for the slowed rotor. Thisis most likely the result of lower profile drag at a lowertip speed. The reduction with advance ratio is clearly afunction of reverse flow alone as the advancing tip Machnumbers appear far from drag divergence (see subplot).However, it is shown later in the section on pressuresand airloads that for the high advance ratios, largeswaths of supersonic flow exist on the lower surface ofthe advancing side. Thus, even though the advancingtip Mach number is low, high wave drag penalty fromlocal supersonic flow is a significant contributor to thereduction shown in Fig. 20.

The increase in rotor efficiency with a positiveshaft angle is produced at the cost of an increase indrag, which implies an increase in propulsive power re-quired from auxiliary sources and hence a decrease invehicle efficiency. This trade-off is illustrated in Fig. 21.Here, the rotor power is re-plotted versus its propul-sive force multiplied by speed. The latter is the powerfor propulsion: available, if propulsive force is positive(propelling rotor), or required, if propulsive force is neg-ative (dragging rotor). This power is represented by thestraight line CP = µCX in the plot. The test data cor-respond to the collective angle sweeps carried out ateach advance ratio. At the lower advance ratios (up toµ = 0.7 for αS = 0 and up to µ = 0.8 for αS = 4) anincrease in collective increases both propulsive powerand rotor power. At the higher advance ratios, an in-

10

−0.02 −0.015 −0.01 −0.005 0 0.005−0.001

0

0.001

0.002

0.003

0.004

Propulsive power, µ CX/σ

Pow

er, C

P/σ

Auxiliary powerneeded forpropulsionDragging Propelling

CP = µ C

X1.0

0.9

0.8

0.7

0.6

0.50.4

µ = 0.3

(a) Shaft angle αS = 0

−0.02 −0.015 −0.01 −0.005 0 0.005−0.001

0

0.001

0.002

0.003

0.004

Ideal propulsive power coeff, µ CX/σ

Pow

er c

oeff,

CP/σ

Auxiliary powerneeded forpropulsionDragging Propelling

CP = µ C

X

1.0

0.9

0.8

0.7

0.60.5 0.4

µ = 0.3

(b) Shaft angle αS = 4

Figure 21: Total power vs. propulsive power showing auxiliary power needed to overcome drag atshaft angles 0 and 4; 40% NR.

−4500 −4000 −3500 −3000 −2500 −2000 −15000

50

100

150

200

250

300

350

400

Propulsive power, VX (HP)

Pow

er (

HP

) αS = 0°

αS = 4°

µ = 0.8

αS = 0°

αS = 4°

µ=1.0

Figure 22: Total power vs. propulsive power(HP) for advance ratios µ = 0.8 (green), 0.9(blue) and 1.0 (red) at shaft angles 0 (opensymbols) and 4 (solid symbols); arrows markdirection of increasing collective.

crease in collective decreases rotor power but increasespropulsive power. A comparison of Figs. 21(a) and21(b) shows that for operations at the highest advanceratios (µ = 0.9 and µ = 1.0), a shaft angle of αS = 0,even though inefficient for the rotor alone (Fig. 19),appears more suitable as it requires significantly lesspropulsive power. The trade-off is more clearly illus-trated in Fig. 22 where the curves corresponding toµ = 0.8 and 1.0 are re-drawn at the two shaft angles interms of dimensional power (HP). It shows, at µ = 0.8,increasing shaft angle at the lowest collective, increasespropulsive power and decreases rotor power by com-parable amounts. Thus the higher shaft angle – with

0 0.2 0.4 0.6 0.8 1−0.005

0

0.005

0.01

0.015

0.02

0.025

Advance ratio, µ

Rot

or fo

rces

100% NR65% NR40% NR

CT / σ

CH / σ

CY / σ

Symbols

Figure 23: Rotor forces at 0 shaft and 0 collec-tive; Conventional vs. slowed RPM.

better rotor efficiency (greater L/DE) – is the preferredmode of operation. But at µ = 1.0, where the increasein propulsive power and decrease in rotor power are+400 HP and -25 HP respectively, the lower shaft an-gle – with worse rotor efficiency – is the preferred modeof operation. The price to pay for carrying an inefficientrotor is a loss in lift that must be compensated for byother means.

From considerations of propulsive power, mini-mum collective operations are of interest at high ad-vance ratios. The rotor forces from a nominally zerocollective angle sweep is shown in Fig. 23. The sweepalso represents the closest approach to a zero thrustsweep – useful for analyses validation of profile com-ponents. Because of the high built-in twist, the thrustproduced is still non-zero, but the rotor forces are near-

11

est to their profile contributions (CHo and CY o).In summary, the performance measurements were

consistent with previous test data. A drop off in thrustsensitivity to collective at high advance ratios, alongwith a reversal at 1.0, was observed as expected. Adramatic drop off in efficiency was observed at the highadvance ratios. The efficiency was higher at a positiveshaft angle but at the expense of greater drag.

BLADE LOADS AND HUB LOADS

In this section, the blade structural loads and hubloads are compared between the nominal and slowedrotors. As before, the 40% NR case is studied in detail,the others used for comparison. The oscillatory (1Pand higher) and vibratory (3P and higher) harmonicsof blade loads and first blade passage (4P) hub loadsare considered. The steady loads are ignored.

The structural loads are examined in dimensionalform, as these are directly relevant to blade design.The parametric comparison of flight conditions andbreak down into harmonics are still carried out in non-dimensional form. That is, thrust variation is in termsof CT /σ, speed in terms of µ, and harmonic content rel-ative to operating RPM (/rev, P). This is appropriatebecause these non-dimensional parameters are directindicators of proximity to stall, extent of reverse flow,and blade dynamic response. For purposes of plotting,every other azimuthal data is plotted (128 points perrev). Flap bending is positive for upper surface in com-pression, chord bending is positive for trailing edge incompression, and torsion moment is positive for nose-up. Pitch link load is positive in extension (nose-up).

The rotor frequencies, shown in Table 5, are verydifferent for the slowed rotor beyond the third mode.Even though the rotor is generally stiffer (relative to

Table 5: Predicted slowed rotor frequencies com-pared to nominal.

100%NR 65%NR 40%NR Mode/rev /rev /rev

0.276 0.287 0.318 Lag1.037 1.040 1.048 Flap2.83 2.98 3.33 Flap4.39 5.66 7.33 Torsion4.69 6.70 10.54 Lag

its reduced rotational frequency), the second flap fre-quency still lies near 3/rev and remains the dominantdriver of blade loads. A notable difference at 40%NRis the large frequency gap between the second flap andfirst torsion modes. The absence of any mode near5/rev has important ramifications on vibratory hubloads, as shown later.

Consider as the baseline, the flap bending momentson the nominal rotor (100%NR) in a high speed con-

0.2

0.4

0.6

0.8

1

090

180270

360

−2,000

0

2,000

r/R

Azimuth, deg

Fla

p be

ndin

g m

omen

t, ft−

lb

Figure 24: Flap bending moment at 100% NR;µ = 0.4, CT /σ = 0.07 (T=15885 lb), αS = 0.

0.2

0.4

0.6

0.8

1

090

180270

360

−2,000

0

2,000

r/R

Azimuth, deg

Fla

p be

ndin

g m

omen

t, ft−

lb

Loading shiftedinboard

Figure 25: Flap bending moment at 40% NR; µ =0.9, CT /σ = 0.063 (T=2280 lb), αS = 4.

0.2

0.4

0.6

0.8

1

090

180270

360

−2,000

0

2,000

r/R

Azimuth, deg

Fla

p be

ndin

g m

omen

t, ft−

lb

Steeper valleyStronger 2nd ridge

Figure 26: Flap bending moment at 40% NR; µ =1.0, CT /σ = 0.022 (T=780 lb), αS = 0.

12

0 0.2 0.4 0.6 0.8 10

250

500

r/R0 0.2 0.4 0.6 0.8 1

0

250

500

r/R

5P (

ft−lb

)

0 0.2 0.4 0.6 0.8 10

250

500

0 0.2 0.4 0.6 0.8 10

250

500

4P (

ft−lb

)

0 0.2 0.4 0.6 0.8 10

500

1000

0 0.2 0.4 0.6 0.8 10

500

1000

3P (

ft−lb

)

0 0.2 0.4 0.6 0.8 10

500

1000

0 0.2 0.4 0.6 0.8 10

500

1000

2P (

ft−lb

)

0 0.2 0.4 0.6 0.8 10

1250

2500

0 0.2 0.4 0.6 0.8 10

1250

2500

1P (

ft−lb

)

µ=0.4; CT/σ=0.06

µ=0.7; CT/σ=0.06

µ=0.9; CT/σ=0.06

µ=0.9; CT/σ=0.06

µ=1.0; CT/σ=0.02

100% NR (µ=0.4) 100% NR (µ=0.4)

Figure 27: Flap bending moment harmonics fornominal and 40% NR slowed rotor; nominal:µ = 0.4, CT /σ = 0.07, αS = 0 (shown as symbols-); slowed: µ = 0.4–0.9, CT /σ = 0.06, αS = 4 andµ = 1.0, CT /σ = 0.02, αS = 0 (shown as lines).

0.2

0.4

0.6

0.8

1

090

180270

360

−500

0

500

r/R

Azimuth, deg

Tor

sion

mom

ent,

ft−lb

Figure 28: Torsion moment at 100% NR; µ = 0.4,CT /σ = 0.07, αS = 0.

0.2

0.4

0.6

0.8

1

090

180270

360

−500

0

500

r/R

Azimuth, deg

Tor

sion

mom

ent,

ft−lb

Figure 29: Torsion moment at 40% NR; µ = 0.9,CT /σ = 0.063, αS = 4.

0 0.2 0.4 0.6 0.8 10

100

200

300MAGNITUDE (ft−lb)

1P

0 0.2 0.4 0.6 0.8 1−180

0

180PHASE (degrees)

0 0.2 0.4 0.6 0.8 10

100

200

2P

0 0.2 0.4 0.6 0.8 1−180

0

180

0 0.2 0.4 0.6 0.8 10

50

100

150

3P

0 0.2 0.4 0.6 0.8 1−180

0

180

0 0.2 0.4 0.6 0.8 10

50

100

150

4P

0 0.2 0.4 0.6 0.8 1−180

0

180

0 0.2 0.4 0.6 0.8 10

50

100

150

r/R

5P

0 0.2 0.4 0.6 0.8 1−180

0

180

r/R

100% NR; µ=0.4

40% NR; µ=0.9

40%NR (µ = 0.9)

100%NR (µ = 0.4)

Figure 30: Torsion moment harmonics for nomi-nal and 40% NR slowed rotor; nominal: µ = 0.4,CT /σ = 0.07, αS = 0; slowed: µ = 0.9, CT /σ =0.06, αS = 4.

13

0 90 180 270 360−500

−250

0

250

500

750

Azimuth, deg

Tor

sion

mom

ent,

ft−lb

100% NR; µ=0.4; CT / σ=0.07; α

S=0° (6912)

40% NR; µ=0.9; CT / σ=0.06; α

S=4° (9528)

µ = 0.9slowed rotor

µ = 0.4nominal rotor

Figure 31: Torsion moment at 30% R for nominaland 40% NR slowed rotor; nominal: µ = 0.4,CT /σ = 0.07, αS = 0; slowed: µ = 0.9, CT /σ =0.06, αS = 4.

0 90 180 270 360−500

−400

−300

−200

−100

0

100

200

300

400

500

Azimuth, deg

Tor

sion

mom

ent,

ft−lb

low θ75

= 0°

high θ75

= 2°

high θ

75 = 2°

lowθ

75 = 0°

Shaft αS = 0°

Shaft αS = 0°

Figure 32: Study of retreating side impulse intorsion moment (30% R) at µ = 1.0 for a 40%NR slowed rotor showing increased severity atlower shaft angle and higher collective.

0 0.2 0.4 0.6 0.8 10

100

200

300

1P

Magnitude (ft−lb) αS = 0 deg

0 0.2 0.4 0.6 0.8 10

100

200

300

Magnitude (ft−lb) αS = 4 deg

0 0.2 0.4 0.6 0.8 10

50

100

150

2P

0 0.2 0.4 0.6 0.8 10

50

100

150

0 0.2 0.4 0.6 0.8 10

50

100

r/R3P

0 0.2 0.4 0.6 0.8 10

50

100

r/R

Coll=0°

Coll=2°Coll=0°

Coll=2°

Figure 33: Effect of collective increase on 1-3/revtorsion moments at µ = 1.0 for two differentshaft angles; αS = 0 (θ75=0 and 2 producesCT /σ = 0.019 and 0.022) and αS = 4 ( θ75=0 and2 produces CT /σ = 0.061 and 0.059 – reversal);40% NR.

dition: µ = 0.4, CT /σ = 0.071 and αS = 0, Point6912 (P6912) in Table 2. The azimuthal variations ofthe oscillatory bending moments are plotted for all ra-dial stations from the root to the tip (20%–90%R) ina 3-dimensional plot in Fig. 24. If RPM is swept downto 40%NR keeping advance ratio constant, along thepoints in Table 2, the peak-to-peak bending momentsreduce by about 50% (not shown). But as advance ratioincreases, with RPM constant at 40% NR, the bendingmoments build up again, eventually reaching the base-line level and then higher. To study the variation withadvance ratio, consider the sweep at αS = 4 in Table 3.The thrust level is closest to the baseline. The bendingmoments at the end of this sweep, at µ = 0.9, are shownin Fig. 25. Even though the thrust level is lower thanthe baseline, the moments are higher. The loading pat-tern is also qualitatively different. The second modeis still dominant but the peak loading is now shiftedinboard. The bending moments at µ = 1.0, shown inFig. 26, corresponding to a point with an even lowerthrust level of CT /σ = 0.022 (P9175, Table 4), showeven greater magnitudes. The advancing side drop issteeper and the fourth quadrant oscillation stronger.Note that the dimensional thrusts for both the highadvance ratio points are very low, 2,280 lb and 780 lb,compared to a thrust of 15,885 lb for the baseline.

14

0 90 180 270 360−1500

−1000

−500

0

500

1000

1500

Azimuth, degrees

Pitc

h lin

k lo

ad, l

b

0 2 4 6 8 100

100

200

300

400

500

600

700

Harmonics, /rev (P)

Pitc

h lin

k lo

ad, l

b

µ = 0.4

µ = 0.5

µ = 0.7

µ = 0.9

µ = 0.4µ = 0.5µ = 0.7µ = 0.9

(a)

(b)

Reverseimpulse

Figure 34: Pitch link load variation with advanceratio; µ = 0.4 − 0.9, CT /σ ≈ 0.06, αS = 4; 40%NR.

The bending moment harmonics are shown inFig. 27. The left hand side column of plots showsthe variation with increasing advance ratio at the samethrust level. The right hand side column of plots com-pares two highest advance ratio cases at high and lowthrust levels. The baseline is plotted in both for com-parison. The left hand side plots show that the 5Pharmonic is negligible for the slowed rotor, regardless ofadvance ratio. The 4P harmonic increases dramaticallybeyond µ = 0.7. The 3P harmonic behaves similarly asthe baseline and has a comparable magnitude. The 1Pand 2P harmonics, which determine the peak-to-peakvariation, are 50-100% higher than baseline inboard of70% R at the highest advance ratio. The right hand sideplots indicate that this loading pattern is independentof thrust – remains the same regardless of CT /σ = 0.06or 0.02. The 3P harmonic in fact increases with a de-crease in thrust. Even though these comparisons arenot consistent parametric variations (the baseline hasa higher thrust and a lower shaft angle, and the µ = 1.0slowed rotor point has a different shaft angle from theother slowed rotor points) they illustrate the fact thatthe slowed rotor operating at a lower non-dimensionalthrust and negligible dimensional thrust carries bend-ing moments higher than the highest levels of the nom-

0 90 180 270 360−1800

−1200

−600

0

600

1200

18001800

Azimuth, deg

Pitc

h lin

k lo

ad, l

b

0 90 180 270 360−1800

−1200

−600

0

600

1200

1800

Azimuth, deg

Pitc

h lin

k lo

ad, l

b

(a) αS = 0°

(b) αS = 4°

θ75

=0°

CT / σ = 0.019

(9168)

θ75

=2°

CT / σ = 0.022

(9175)

θ75

=2°

CT / σ = 0.059

(9530)

θ75

=0°

CT / σ = 0.061

(9531)

Figure 35: Effect of collective on pitch link loadat µ = 1.0 for two different shaft angles; αS = 0

(θ75=0 and 2 produces CT /σ = 0.019 and 0.022)and αS = 4 (θ75=0 and 2 produces CT /σ = 0.061and 0.059 – reversal); 40% NR.

inal rotor under high speed conditions. The net thrustlevel is not even a remote indicator of these load levels.

A possible reason behind the high loads is a higherthan usual differential airloading between the inboardand outboard sections of the advancing side. If the re-verse flow produces little or no lift on the retreatingside, this differential airloading is required to trim therotor. If the reverse flow produces negative lift, thenthe differential airloading may even be greater, withthe outboard stations required to generate negative lift.These conjectures are tested in the next section on pres-sures and airloads, but the implication here is that theelastic twist on the blades must be significantly high toproduce this differential airloading. An examination ofthe torsion moments indicate that this may indeed betrue.

The torsion moment for the nominal rotor is shownin Fig. 28. The torsion moment for the slowed rotor atµ = 0.9 and at a comparable thrust level is shown inFig. 29. The peak-to-peak magnitudes are again simi-

15

0.2

0.4

0.6

0.8

1

090

180270

360

−4000

−2000

0

2000

4000

r/R

Azimuth, deg

Cho

rd b

endi

ng m

omen

t, ft−

lb

Figure 36: Chord bending moment at 100% NR;µ = 0.4, CT /σ = 0.07, αS = 0.

0.2

0.4

0.6

0.8

1

090

180270

360

−4000

−2000

0

2000

4000

r/R

Azimuth, deg

Cho

rd b

endi

ng m

omen

t, ft−

lb

Figure 37: Chord bending moment at 40% NR;µ = 0.9, CT /σ = 0.063, αS = 4.

lar. The spanwise distribution of harmonics, shown inFig. 30, indicates a large 1P gradient between the in-board and outboard stations (between 40% and 60% R)for the slowed rotor. The phase angle remains the same.The 2P harmonic also shows about a 20% increase atthe inboard stations. The vibratory harmonics are ingeneral lower than the nominal rotor, except for the 3Pharmonic, which has a comparable magnitude.

The azimuthal variation of torsion moment at 30%R are compared in Fig. 31. In the high advance ratiocase, the peak loading is more clearly determined by thewaveform in the retreating side. It is shown later, thatthe increase in loading around 240 azimuth is a directconsequence of the reverse flow negative lift shifting afttowards 3/4-c (1/4-c chord of reverse airfoil) and pro-ducing a nose up pitching moment impulse. Note thatthe nominal rotor also shows an impulsive behavior inthe fourth quadrant – around 300 – but this behavior

arises out of a 4/rev response and is phenomenologi-cally different. The increase in torsion loading on theretreating side due to reverse flow was first reportedin 1969 by Niebanck [37] (on a 9 ft dia model rotorat µ = 1.47, αS = 0, and θ75 = 2) and the loadingpattern observed here is similar.

The retreating side torsion loading is examined inmore detail in Fig. 32. The figure contains two pairs ofplots, one pair each for shaft angles of 0 and 4. Foreach shaft angle, two collective angles of 0 and 2 areconsidered. These correspond to the collective sweepsat µ = 1.0 in Table 4. The retreating side impulseincreases with collective angle due to increase in reverseflow angle of attack. It diminishes with shaft angle dueto decrease in reverse flow angle of attack. The reverseflow is clearly less severe for a positive shaft angle.

Note however, that it was the positive shaft anglethat produced a thrust reversal at µ = 1.0, between0 and 2 collectives (Table 4 and Fig. 10). A possibleexplanation of this apparent inconsistency is related toelastic twist at high advance ratios. The increasinglyhigher (negative) longitudinal cyclic needed to trim therotor, due to the little (or negative) lift on the retreat-ing side, drives the advancing side lower surface intosuper-critical flow and the resulting high pitching mo-ments generate large elastic twist. On the one hand,this twist drives the outboard sections deeper into neg-ative lift. On the other hand, it allows the inboardsections to produce more lift. The more severe the re-verse flow (i.e. more negative the reverse flow lift),the more severe the twist and greater the contributionsof inboard and outboard twists to positive and nega-tive lift. A harmonic break down of torsion moments(Fig. 33) suggests that the effect of increase in collectiveinfluences the inboard twist more. Thus, a lower shaftangle with more severe reverse flow can show a delayin thrust reversal compared to the higher shaft angle.However, because the reversals obtained in this test areweak with thrust differences of only ∆CT /σ ≈ 0.002,this conjecture cannot be tested conclusively. Some ofits implications, however, are tested in the next sectionwhere it is shown that the advancing side is indeed im-mersed deeply into negative lift and the lower surfaceindeed contains large regions of supersonic flow.

The pitch link loads behavior is similar to the in-board torsion moment, as expected. Figures 34 and35 summarize its behavior for an advance ratio sweep,and thrust and shaft angle sweeps at the highest ad-vance ratio, respectively. The pitch link loads areconsistent with the torsion moments shown earlier inFigs. 31 and 32. One difference is that the peak-to-peak torsion moment is determined by the retreatingside impulse µ = 0.9 onwards (see Fig. 31), whereasthe pitch link load peak is not (see Fig. 34), and beginsto be determined by the impulse only µ = 1.0 onwards(Fig. 35(a)). However, once it appears, the impulseis a key source of vibratory harmonics. As shown in

16

0 90 180 270 360−4000

−2000

0

2000

4000

Azimuth, deg

Dam

per

load

, lb

Effect of RPM

0 90 180 270 360−4000

−2000

0

2000

4000

Azimuth, deg

Effect of Advance Ratio

0 2 4 6 8

0

500

1000

1500

2000

2500

3000

Harmonics, P

Dam

per

load

, lb

0 2 4 6 8

0

500

1000

1500

2000

2500

3000

Harmonics, P

100%65%40%

µ=0.4

µ=0.5

µ=0.7

µ=0.9

µ=1.0

µ=0.4

µ=0.5

µ=0.7

µ=0.9

µ=1.0

100%65%40%

(a)

(b)

(c)

(d)

Figure 38: Effect of RPM and advance ratio variation on damper loads; (a) and (b): µ = 0.4,CT /σ = 0.07, αS = 0; (c) and (d): CT /σ ≈ 0.06, αS = 4; 40% NR.

0 90 180 270 360−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Azimuth, deg

Ver

tical

hub

she

ar a

nd p

itch

link

load

, lb

Blade 1Blade 2Blade 3Blade 4

Hub shear 3

Hub shear

Pitch link load Pitch link 3

Pitchlink 4

Figure 39: Vertical hub shear and pitch link loadson four blades; µ = 0.9, CT /σ = 0.063, αS = 4;40% NR.

Fig. 34(b), the sudden increase in 3-5P content beyondµ = 0.7 is a direct consequence of the impulse.

The chord bending moment for the nominal rotoris shown in Fig. 36. The chord bending moment forthe slowed rotor at µ = 0.9 at a comparable thrustlevel is shown in Fig. 37. The 50% and 60%R gageswere dysfunctional for the slowed rotor. The outboardmoments, at 70% and 80%R, are benign. The in-

0 90 180 270 360−3000

−2000

−1000

0

1000

2000

3000

4000

5000

6000

Azimuth, deg

Thr

ust (

lb)

and

hub

mom

ents

(ft−

lb)

Contribution fromhub shear

Contribution frompitch link

Pitch. mom.

Thrust

Thrust

Pitch. mom.

Figure 40: Contribution of hub shear and pitchlink loads on hub loads; µ = 0.9, CT /σ =0.063, αS = 4; 40% NR.

board moments, 20%–40%R, are primarily determinedby damper load similar to the nominal rotor. Thedamper load is studied in Fig. 38. With reduction inRPM, the load is reduced, Fig. 38(a). The 1P loadremains the same but the 2P and higher loads de-crease, Fig. 38(b). This implies there is little motion atthese frequencies to contribute to any substantial lossin damping available at the lag frequency. Thus, lag in-

17

40 60 80 100 120 140 160 1800

500

1000

1500

2000

4P V

ertic

al fo

rce,

lb

40 60 80 100 120 140 160 1800

1000

2000

3000

4000

4P R

oll m

omen

t, ft−

lb

40 60 80 100 120 140 160 1800

1000

2000

3000

4000

Speed, kt

4P P

itch

mom

ent,

ft−lb

(a)

(b)

(c)

αS = 0° α

S = 4°

100% NR

40% NR

40% NR

100% NR

αS = 4°α

S = 0°

Figure 41: Vibratory hub loads vs. speed fornominal and 40% NR slowed rotors; nominal:µ = 0.3, CT /σ = 0.082, αS = 0 (P6619) (symbol-); µ = 0.4, CT /σ = 0.071, αS = 0, (P6912)(symbol-); slowed: speed sweep at CT /σ =0.06, αS = 0 (symbol-) and at CT /σ = 0.06, αS =4 (symbol-).

stability was not a concern during the tests. Increasingadvance ratio increases the loads back up to nominallevels at µ = 1.0, Fig. 38(c). There is a curious 2Pspike around µ = 0.9 the reasons behind which are notunderstood, Fig. 38(d).

The effect of advance ratio on oscillatory hub loadsis evaluated using data from the rotating vertical hubshears and pitch link loads. These measurements arecombined to provide estimates for the vertical force andmoments at the hub. purpose. Gage failures are com-pensated for with phase shifted data from functionalgages. For example, Fig. 39 shows the hub shears andpitch link loads in one of the high advance ratio flights.Because the measurements are repeatable (within 2–5%), the faulty gages (on hub arm of blade 3 and pitchlinks of blades 3 and 4) are replaced with data fromblade 1. The contributions from hub shear and pitchlink loads are both important, particularly when thepitch link loads are high. For example, Fig. 40 showsthe the contributions separately for the same flight.Note that, ideally, the rotor balance would be used toprovide estimates for the oscillatory hub loads. How-ever, it is known that the transfer function betweenbalance readings and hub loads changes significantlybetween 4P frequency at 100% NR (17.2 Hz) and 4Pfrequency at 40% NR (6.9 Hz). A dynamic calibrationof the balance that accounts for this change is currentlyunder study.

The 4P hub loads are shown in Fig. 41 as a func-tion of RPM and tunnel speed. Unlike the blade loads,the hub loads appear to be relatively benign for theslowed rotor. The two nominal points correspond tothe µ = 0.3 and 0.4 points in Table. 2. These arecompared to the slowed rotor points for the two speedsweeps given in Table. 3 – the same conditions for whichblade loads were analyzed earlier. The 4P vertical forceis at least 50% lower for the slowed rotor. Even thoughthe flap bending moments showed a dramatic increasein 4P harmonic (Fig. 27), the increase mostly occurredoutboard of 40% R and did not affect the shear load-ing inboard. The rolling moment is already low, andremains comparable between the nominal and slowedrotors. The pitching moment is reduced by more than50%. The reason behind the pitching moment reduc-tion is the vanishing of the 5P harmonic from the flapbending moments (Fig. 27). The same trend was alsoobserved in the chord bending moments (not shown).The vanishing 5P is the result of the large frequencygap between the second flap and first torsion modes asshown earlier in Table 5.

In summary, the blade loads on the slowed rotorare comparable to or higher than the nominal rotor be-yond an advance ratio of µ = 0.8. Yet, the vibratoryhub loads remain benign with at least 50% reduction invertical force and pitching moments. The blade loadsappear to be driven by a high differential airloading be-tween the inboard and outboard sections of the blade

18

potentially caused by a large elastic twist deformation.The reduction in hub loads is due partly to the fre-quency gap between second flap and first torsion modesleading to the vanishing of 5P blade loads. At advanceratios beyond 0.9, the peak torsion loads were deter-mined (or significantly affected) by a nose up impulsiveloading on the retreating side.

BLADE PRESSURES AND AIRLOADS

This section analyses the azimuthal and chordwisevariations of blade surface pressures and sectional air-loads.

The radial stations where enough pressure tapsremained functional for sectional airloads calculationwere 22.5%, 86.5%, 92%R, and 99% R. Most of the in-board sections that are important for reverse flow, 40%to 77.5% R, all suffered losses. Nevertheless, many ofthe taps remained functional in these stations, and astudy of these functional taps provide significant in-sights into the flow phenomena in this regime. Thesephenomena can then be associated with the perfor-mance and structural load patterns observed in the pre-vious sections.

The azimuthal variation of pressures are studied asoffset plots of −M2Cp, where M is the local incidentMach number and Cp the pressure coefficient. In theseplots, only the leading-edge (or nearest working tap)values are correct, the rest are arbitrarily offset to re-veal chordwise and azimuthal trends. Because negativepressure is plotted, an increase implies flow accelera-tion, hence suction. For accelerated flow, the onset oflocal supersonic flow is estimated by the 1-D steadyisentropic relation:

Cp =2

γM2

(1 + γ−12 M2

l

1 + γ−12 M2

) γ1−γ

− 1

(8)

where Ml is the local surface Mach number. Substitut-ing Ml = 1 and M at any azimuth provides an estimateCP = C∗

P of the surface pressure for onset of supersonicflow.

Consider one of the severest reverse flow points(highest advance ratio, highest collective, zero shaft an-gle): µ = 1.0, θ75 = 1.9, and αS = 0 (P9175). Theupper and lower surface pressures at 22.5%R are shownin Figs. 42 and 43 respectively. The azimuthal extent ofreverse flow is demarcated in the plots by vertical lines.There is suction on both surfaces in the reverse flow re-gion but on the lower surface it appears to increase instrength from leading-edge (LE) towards trailing-edge(TE). If the TE were to behave as the effective LEof the reversed airfoil it is expected to operate undergreater suction. Unfortunately the three taps between0.395c to TE are dysfunctional and therefore whetherthe strength of these suction peaks indeed increase to-wards the TE cannot be ascertained.

0 90 180 270 360

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Azimuth, deg

−M

2 Cp

UPPER SURFACE22.5% R

x/c0.0490.1070.1640.2030.250.3950.6070.8190.963

Reverse flow

Leading−edge

Trailing−edge

Figure 42: Upper surface pressures at 22.5% R;µ = 1.0; CT /σ = 0.022 (θ75 = 2), αS = 0; 40%NR; (P9175).

0 90 180 270 360−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Azimuth, deg

−M

2 Cp

x/c0.010.0490.1070.1640.2030.250.395

LOWER SURFACE22.5% R

Reverse flow

Leading−edge

Trailing−edge

Figure 43: Lower surface pressures at 22.5% R;µ = 1.0; CT /σ = 0.022 (θ75 = 2), αS = 0; 40%NR; (P9175).

19

0 90 180 270 360

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Azimuth, deg

−M

2 Cp


x/c0.0490.1070.1640.2030.250.3950.6070.8190.963

Reverse flow


0 90 180 270 360−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Azimuth, deg

−M

2 Cp

x/c0.010.0490.1070.1640.2030.250.395


Reverse flow

Stall like perturbations


0 90 180 270 360−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Azimuth, deg

−M

2 Cp

x/c0.010.0490.1070.1640.2030.250.3950.6070.8190.963

LOWER SURFACE40% R

Perturbationsmove

from TE to LE

Figure 46: Lower surface pressures at 40% R; µ =0.8; CT /σ = 0.045 (θ75 = 8), αS = 0; 40% NR;(P9159).

0 90 180 270 360−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Azimuth, deg

−M

2 Cp

x/c0.0490.1070.250.3950.6070.819

Reverse flowLOWER SURFACE40% R

Figure 47: Lower surface pressures at 40% R; µ =0.9; CT /σ = 0.063 (θ75 = 6.2), αS = 4; 40% NR;(P9528).

20

For confirmation, consider the test point: µ = 0.8,αS = 0, and θ75 = 8 (P9159). The reason for select-ing this point is that the lower surface taps at 40%Rare functional and cover up to very near the TE. (Theupper surface taps are dysfunctional and prevent sec-tional integration). First, consider the upper and lowersurface pressures at 22.5%R, Figs. 44 and 45. Theadvance ratio is lower in this flight, but because thecollective angle is significantly higher, significant re-verse flow effects are expected. The figures show thatthere is suction on both surfaces as before, but suctionon the lower surface appears more marked. Comparedto the previous point, the lower surface impulses aresharper and have a greater azimuthal movement. Theimpulse at 0.25c occurs at a slightly delayed azimuthcompared to that at 0.395c, the impulse at 0.203c oc-curs at a slightly delayed azimuth compared to that at0.25c, and so on. This is a signature of a stall vortex– a reverse chord stall vortex – triggered at the TEand sweeping across the lower surface in reverse chorddirection towards the LE. The reason behind the dou-ble peak is not clear, but the the trailing edge beingsharp it is possible that two vortices are formed oneafter the other. The azimuthal motion is negligible asthe span location is very inboard. Next, consider thelower surface pressures at 40%R, Fig. 46. The reversechord stall vortex appears clearly at this station as welland displays a wider azimuthal movement. However,there appears to be no distinct suction peak near theTE in the retreating side. Thus, the precise mechanismthat triggers this vortex is not clear. It is clear how-ever, that these peaks are responsible for the retreatingside impulse in sectional pitching moments shown laterin Fig. 54 and the torsion loads shown earlier Figs. 32and 35.

Consider the test point: µ = 0.9, αS = 4, andθ75 = 6.2 (P9528). The shaft angle is higher here andconsequently the reverse flow is expected to be less se-vere. The reason for selecting this point is that thelower surface taps at 67.5%R are functional, and allowinsights into the flow field at a further outboard bladestation. First, the lower surface pressures at 40%R,Fig. 47, confirm that pattern is similar to that of theprevious point, although the reverse chord stall vor-tex is weaker as expected. The pressures at 67.5% Rare shown in Fig. 48. The reverse flow region appearstranquil – with no unsteady airloading – indicating thepossibility of a completely separated flow. This is ex-amined more closely in Fig. 49 where the chordwisevariation of lower surface pressures (Cp) are comparedat several azimuthal locations covering the advancingand retreating sides. The advancing side experiencesa high suction near the LE, Fig. 49(a). The retreat-ing side, Fig. 49(b), shows greater suction near the TE,but the pressure levels are negligible compared to theadvancing side. This again suggests a fully separatedflow. On the advancing side, high suction indicates sig-

0 90 180 270 360−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Azimuth, deg

−M

2 Cp

Reverseflow


x/c0.010.0490.1070.1640.2030.250.3950.6070.8190.963

−M2CP*

Ml = 1.0 line

Figure 48: Lower surface pressures at 67.5% R;µ = 0.9; CT /σ = 0.063 (θ75 = 6.2), αS = 4; 40%NR; (P9528).

nificant flow accelerations accompanied by the onset oflocal supersonic flow. The estimated azimuthal extentof the supersonic flow is demarcated in Fig. 48 by theintersection of the sonic line (Eq. 8 with Ml = 1.0) withthe pressure lines. (Henceforth only the intersectionsare shown indicating the onset and recovery). Only theLE (within 1% chord) experiences supersonic flow atthis station.

In order to examine stations further outboard, con-sider the highest advance ratio point again: µ = 1.0,θ75 = 1.9, and αS = 0 (P9175). The pressures at77.5% R are shown in Figs. 50 and 51. Similar to the67.5% R station of the previous point, the reverse flowregion in the retreating side at this point also appearstranquil, and like before, the lower surface of the ad-vancing side reveals significant supersonic flow. Thesame remains true further outboard at 86.5% R, seeFigs. 52 and 53. At this station more than 10% ofthe LE experiences supersonic flow. Note that, the ad-vancing tip Mach number MA is only 0.52 (even with-out the cosine sweep factor), the thrust CT /σ merely0.022, and the longitudinal cyclic a meagre −1.8. Lo-cal supersonic flow under such conditions appears tosupport the conjecture that the blades are carrying avery significant amount of elastic twist. This is fur-ther supported by the high negative loading seen in thesectional airloads at this station.

21

0 0.2 0.4 0.6 0.8 1−1

0

1

2

3

4

5

6

7

x/c

−C

P

0 0.2 0.4 0.6 0.8 1−0.1

0

0.1

0.2

0.3

0.4

0.5

x/c

−C

P

AZ=30°

AZ=60°

AZ=90°

AZ=120°

AZ=150°

AZ=210°

AZ=240°

AZ=270°

AZ=300°

AZ=330°

(a) Advancing side

(b) Retreating side

Figure 49: Chord-wise pressures along 67.5% Rlower surface on advancing and retreating sides;µ = 0.9; CT /σ = 0.063 (θ75 = 6.2), αS = 4; 40%NR; (P9528).

Figure 54 shows the inboard (22.5% R) and out-board (86.5% R) sectional airloads for the two highadvance ratio conditions at µ = 0.8 (characterized byreverse chord dynamic stall) and µ = 1.0 (character-ized by supersonic flow). The airloads are expressedin standard non-dimensional forms of forcing per unitspan: M2cn, M

2cc, and M2cm for normal force, chordforce, and pitching moment about local 1/4-th chord.The inboard station (22.5% R) shows the reverse chorddynamic stall vortex impulse in the retreating side.The normal force increment (∆M2cn) of about 0.05and the associated nose up pitching moment increment(∆M2cm) of about 0.0125 indicates that the reverseflow lift now acts roughly a further 1/4-c behind thelocal 1/4-c from the LE (i.e., at 1/2-c). Its contribu-tion to chord force is substantial – the amplitude ofthe spike is by itself greater than the peak amplitudeof chord force variation at the outboard station (86.5%

0 90 180 270 360−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

Azimuth, deg

−M

2 Cp

x/c0.010.0490.0800.1070.1640.2030.3950.6070.8190.963


Reverseflow


0 90 180 270 360−0.5

0

0.5

1

1.5

2

2.5

3

Azimuth, deg

−M

2 Cp


x/c0.010.030.0490.080.1070.164

−M2CP*

Reverseflow


22

0 90 180 270 360−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

Azimuth, deg

−M

2 Cp

x/c0.010.030.0490.080.1640.2030.320.3950.460.530.6070.8190.963


Reverseflow


R). The outboard station (86.5% R) is immersed deeplyinto negative loading. At µ = 1.0, almost the entire ad-vancing side at this station carries a negative loading.The transonic pitching moments on the advancing sidedrive this negative loading via elastic twist.

Unlike nominal rotors, supersonic flow poses nodanger of high speed impulsive noise in a slowed rotor.The sonic cylinder lies too far away from the tip for anylikelihood of shock delocalization. The primary dangeris that of excessive wave drag, and this is reflected inthe high performance penalty (high -CX) shown earlierin Fig. 21.

In summary, the retreating side lower surfaceshows evidence of reverse chord dynamic stall phenom-ena at the inboard stations (40% R and inboard) withthe stall vortex sweeping from TE to LE. The advanc-ing side lower surface shows evidence of supersonic flowat the outboard stations (67.5% R and outboard) evenat subsonic advancing tip Mach numbers. The reversechord dynamic stall inboard appears to be a key con-tributor to the retreating side impulse in torsion load-ing. The advancing side supersonic flow outboard ap-pears to be a key contributor to large elastic twist de-formations. The consequent high differential airloadingimmerses an outboard station (86.5% R) into negativelift on over the entire advancing side. The supersonicflow appears to be a significant contributor to the high

0 90 180 270 360−2

−1.5

−1

−0.5

0

0.5

1

1.5

Azimuth, degrees

−M

2 Cp

x/c0.010.030.0490.080.1070.2030.250.320.3950.6070.8190.963


−M2CP*

Reverseflow


drag penalty observed earlier in rotor performance.

SUMMARY AND CONCLUSIONS

A full-scale UH-60A rotor was tested at the NFAC40- by 80- ft wind tunnel under slowed RPM (65%and 40% of nominal) reaching a maximum advanceratio of 1.0. Comprehensive measurements of perfor-mance, blade loads, hub loads, pressures/airloads wereacquired. An initial examination of the measurementswere presented with emphasis on the fundamental un-derstanding of the aeromechanical phenomena uniqueto this regime. The intent was to gain useful knowledgefor the design of high speed, high efficiency, slowed ro-tors of the future and acquire a challenging databasefor advanced analyses validation. Based on this re-search, on this specific rotor, the following conclusionsare drawn:

1. The dynamic loads on the slowed rotor (bendingand torsion moments and pitch link loads) operat-ing at an advance ratio µ = 0.8 and beyond, arecomparable to or significantly greater than thoseencountered by the nominal rotor at its highestspeeds. The net thrust level is not even a remoteindicator of these load levels.

2. The primary reason behind the high dynamic loads

23

0 90 180 270 360−0.005

0

0.005

0.01

Azimuth, deg0 90 180 270 360

−0.01

−0.005

0

0.005

0.01

Azimuth, deg0 90 180 270 360

−0.1

−0.05

0

0.05

0.1

Azimuth, deg

86.5

% R

0 90 180 270 360−0.01

0

0.01

0.02

Chord force: M2 cc

0 90 180 270 360−0.01

−0.005

0

0.005

0.01

1/4−c pitch mom.: M2 cm

0 90 180 270 360−0.1

−0.05

0

0.05

0.122

.5%

R

Normal force: M2 cn

µ=1.0, CT / σ=0.022

µ=0.8, CT / σ=0.045

Reversechord

dynamicstall

µ=1.0

µ=0.8

∆ M2 cn

∆ M2 cm

Figure 54: Sectional airloads at 22.5% and 86.5% R for the 40% NR slowed rotor at two high advanceratio points: µ = 1.0, CT /σ = 0.022, θ = 2, αS = 0 (P9175); and µ = 0.8, CT /σ = 0.045, θ = 8, αS = 0

(P9159).

appears to be a high differential airloading betweenthe inboard and outboard sections of the advancingside. The requirement to achieve trim with largeregions of negative (or zero) lift on the retreat-ing side results in high longitudinal cyclic angleswhich, together with the high built-in twist, drivesthe lower surface of the advancing side to super-sonic flow – even as inboard as 67.5%R. The result-ing pitching moments generates very large elastictwist deformations that produces the differentialairloading.

3. The large elastic twist drives the advancing bladeoutboard sections deep into negative lift. At µ =1.0 (CT /σ = 0.022) the 86.5%R station is foundnegatively loaded over almost the entire first andsecond quadrants. These phenomena also appearto be an important driver behind thrust rever-sal. An increase in collective increases longitudi-nal cyclic which drives the elastic twist higher (seeabove) with little or no gain in net thrust.

4. The vibratory hub loads (dominantly 4P for thisrotor) remains benign. The 4P vertical force is re-duced by at least 50%. The 4P pitching momentis reduced by at least 50%–75% due to a dramaticreduction of 5P blade bending moments. This re-duction is in turn caused by the wide rotor fre-quency gap between the second flap (3.33P) and

first torsion (7.33P) modes.

5. The positively loaded (suction) lower surface of theretreating side reverse flow region shows evidenceof reverse chord dynamic stall: vortices sweepingacross the chord from trailing to leading edge. Theabsence of a distinct local suction acting as a trig-ger suggests a sharp trailing edge induced stall.Pressure spikes resembling multiple stall vorticesare also observed at 22.5%R.

6. Other than the reverse chord dynamic stall phe-nomena the reverse flow region appears tranquiland does not contribute to any significant unsteadyairloading.

7. At advance ratios beyond µ = 0.9, the peak torsionloads are significantly affected by a nose up reverseflow impulse on the retreating side. It generallyresults from the downward lift and an aft center ofpressure movement, but is significantly aggrevatedby the onset of reverse chord dynamic stall.

8. The performance measurements were consistentwith previous test data. The thrust reversal withcollective angle at high advance ratios is observedas expected. The rotor is more efficient at a posi-tive shaft angle, but at the expense of higher drag.It appears, that the large supersonic flow regionon the lower surface of the advancing side is a key

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contributor to the high drag even at low advancingtip Mach numbers.

ACKNOWLEDGEMENTS

The slowed rotor test was made possible by the col-laborative efforts of the project partners – NASA andU. S. Army – as well as the U. S. Air Force’s NFACteam. The authors acknowledge Sikorsky Aircraft’s re-view and recommendations of the special motions andloads allowables for the test. The authors thank WayneJohnson and Frank Harris for their involvement duringtest planning and preparation.

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