NASA/TM—2016–219070

Assessment of JVX Proprotor Performance 

Data in Hover and Airplane-Mode Flight 

Conditions

C. W. Acree, Jr.

Ames Research Center

Moffett Field, California

February 2016
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NASA/TM—2016–219070

Assessment of JVX Proprotor Performance 

Data in Hover and Airplane-Mode Flight 

Conditions

C. W. Acree, Jr.

Ames Research Center

Moffett Field, California

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, CA 94035-1000

February 2016
Acknowledgments

The author wishes to thank Randy Peterson of Ames Research Center for maintaining several 

priceless rotor test datasets extending back over three decades. Such efforts are too often 

undervalued. Further thanks are owed to Wayne Johnson, also of Ames, for his long-standing 

support and encouragement for this research.

Available from:

NASA STI Support Services National Technical Information Service

Mail Stop 148 5301 Shawnee Road

NASA Langley Research Center Alexandria, VA 22312

Hampton, VA 23681-2199 webmail@ntis.gov

757-864-9658 703-605-6000

This report is also available in electronic form at

http://ntrs.nasa.gov
iii 

Table of Contents 

List of Figures ................................................................................................................................. v

List of Tables ................................................................................................................................. ix

Notations ........................................................................................................................................ xi

Summary ......................................................................................................................................... 1

Introduction ................................................................................................................................. 1

A Note on Statistics Terminology............................................................................................... 2

The JVX Test Rotor ........................................................................................................................ 3

Test Summary ................................................................................................................................. 5

Hover Data and Analyses ................................................................................................................ 5

Regression Analysis of Hover Data .............................................................................................. 11

Effects of Wind Corrections ..................................................................................................... 17

Effects of Coefficient Conversions ........................................................................................... 19

Considerations for Off-Trend Data ........................................................................................... 20

Uncertainty Comparisons for Hover ......................................................................................... 20

Uncertainties in Airfoil Drag .................................................................................................... 23

Hover Data for Mtip = 0.73 ........................................................................................................ 26

CAMRAD II and U2NCLE Predictions for Hover ....................................................................... 29

Inflow Models ........................................................................................................................... 29

Stall-Delay Models ................................................................................................................... 32

Reynolds Number Corrections .................................................................................................. 33

Wind Tunnel Data ......................................................................................................................... 34

Summary Rotor Performance Data ........................................................................................... 35

JVX Spinner Tares .................................................................................................................... 37

Torque/Thrust Interactions........................................................................................................ 40

Data Consistency ...................................................................................................................... 45

Regression Analysis .................................................................................................................. 46

Additional CAMRAD II Predictions ........................................................................................ 53

Conclusions ................................................................................................................................... 56

OARF Hover Data .................................................................................................................... 57

40x80 Airplane-Mode Data ...................................................................................................... 57

CAMRAD II and U2NCLE Predictions .................................................................................... 58

Recommendations ..................................................................................................................... 58
iv 

Table of Contents (continued) 

Appendix A: JVX Wind Tunnel Hover Data ................................................................................ 61

Appendix B: Analysis of Spinner Drag Tares .............................................................................. 63

Appendix C: Glauert Blockage Correction ................................................................................... 69

Appendix D: JVX Test Data ......................................................................................................... 71

References ..................................................................................................................................... 87
v 

List of Figures 

Figure 1. The JVX rotor mounted on the PTR for hover tests at the OARF. ......................... 3

Figure 2. The JVX rotor mounted on the PTR for airplane-mode tests in the NFAC. .......... 4

Figure 3. Hover power (corrected for wind) versus thrust, Mtip = 0.68. ................................. 7

Figure 4. Figure of merit (corrected for wind) versus thrust, Mtip = 0.68. .............................. 7

Figure 5. Figure of merit (without wind corrections) versus thrust, Mtip = 0.68. ................... 8

Figure 6. Figure of merit (corrected for wind) versus thrust, Mtip = 0.68 and wind <1 knot. . 8

Figure 7(a). Distribution of Mtip values. ...................................................................................... 9

Figure 7(b). Distribution of q.75R values. ..................................................................................... 9

Figure 7(c). Distribution of Vtip values. ....................................................................................... 9

Figure 8. Non-ideal power versus ideal power (corrected for wind), Mtip = 0.68. ............... 10

Figure 9. Thrust sweeps by run (corrected for wind), Mtip = 0.68. ....................................... 11

Figure 10. Swirl- and tip-loss factors versus thrust for N = 3. ............................................... 13

Figure 11. Quadratic curve fit of hover power (corrected for wind) versus ideal power, 

for Mtip = 0.68 with ±2se bands. ............................................................................ 15

Figure 12(a). Quadratic curve fit of hover power (corrected for wind) versus thrust, 

converted to figure of merit, for Mtip = 0.68 with ±2se bands. .............................. 16

Figure 12(b). Quadratic curve fit of hover power versus thrust (expanded scales). ................... 16

Figure 13. Quadratic curve fit of hover power (corrected for wind) versus ideal power, 

converted to non-ideal power, for Mtip = 0.68 with ±2se bands. ........................... 17

Figure 14. Alternative curve fit of hover power (corrected for wind) versus ideal power, 

converted to non-ideal power, for Mtip = 0.68. ...................................................... 18

Figure 15. Quadratic curve fit of hover power (without wind corrections) versus thrust, 

converted to figure of merit, for Mtip = 0.68 with ±2se bands. .............................. 18

Figure 16. Quadratic curve fit of hover power (corrected for wind) versus thrust, 

converted to figure of merit, for Mtip = 0.68 with ±2σFM bands. ........................... 22

Figure 17. Quadratic curve fit of hover power (corrected for wind), converted to figure 

of merit versus thrust, with confidence and prediction intervals, Mtip = 0.68. ...... 23

Figure 18. Quadratic curve fits of hover power, converted to figure of merit versus 

thrust, with ±2se bands and ±2sd (cd0) bands. ........................................................ 25

Figure 19. Figure of merit (corrected for wind) versus thrust, Mtip = 0.73. ........................... 26

Figure 20. Figure of merit (corrected for wind) versus thrust for Mtip = 0.73 and 

Mtip = 0.68, with ±2se bands for Mtip = 0.68. ......................................................... 27

Figure 21. Quadratic curve fit of hover power (corrected for wind) versus thrust, 

converted to figure of merit, for Mtip = 0.73 with ±2se bands. .............................. 28
vi 

List of Figures (continued) 

Figure 22. Quadratic curve fit of hover power (corrected for wind) versus ideal power, 

converted to non-ideal power, for Mtip = 0.73 with ±2se bands. ........................... 28

Figure 23. CAMRAD II predictions of JVX figure of merit with five aerodynamic 

models, compared with OARF test data. .............................................................. 30

Figure 24. CAMRAD II predictions of JVX figure of merit with four aerodynamic 

models, compared with test data uncertainty. The ±2se bands are for the 

quadratic curve fit (Eq. 5). .................................................................................... 30

Figure 25. CAMRAD II predictions of JVX figure of merit with nominal and reduced 

section cd, compared with OARF test data. .......................................................... 31

Figure 26. CAMRAD II predictions of JVX figure of merit with three stall-delay 

models. The ±2se bands are for the quadratic curve fit to data (Eq. 5). ................ 33

Figure 27. CAMRAD II predictions of JVX figure of merit with three Reynolds 

number correction models. The ±2se bands are for the quadratic curve fit 

to data (Eq. 5). ....................................................................................................... 34

Figure 28. Measured JVX rotor propulsive efficiency from the NFAC Phase II test. ........... 36

Figure 29. Measured JVX rotor power from the NFAC Phase II test. ................................... 37

Figure 30. Close-up of the JVX rotor on the PTR in the OARF test configuration. .............. 37

Figure 31. The JVX rotor on the PTR with the wing in airplane mode. ................................ 38

Figure 32. Phase I spinner tare data, plotted as raw drag versus q0. ...................................... 39

Figure 33. Difference between predicted and measured thrust versus torque. ....................... 41

Figure 34. Rotor propulsive efficiency from the Phase I and Phase II tests at Mtip = 0.58. ... 43

Figure 35. Rotor power from the Phase I and Phase II tests at Mtip = 0.58. ........................... 43

Figure 36. Measured JVX shaft torque versus rotor drag sorted by run. ............................... 45

Figure 37. Curve fit to measured rotor power from the NFAC Phase II test. ........................ 46

Figure 38. Curve fit to measured rotor power, converted to propulsive efficiency. .............. 47

Figure 39. Curve fits to measured rotor power, with propulsive power subtracted. .............. 47

Figure 40. Curve fits to measured rotor power, with ideal power subtracted. ....................... 48

Figure 41. Uncertainty bands (±2se) for propulsive efficiency at μ = 0.263 with 

±2sd (cd0) bands. ..................................................................................................... 50

Figure 42. Uncertainty bands (±2se) for propulsive efficiency at μ = 0.523 with 

±2sd (cd0) bands. ..................................................................................................... 51

Figure 43. Curve fit of power at μ = 0.263, converted to propulsive efficiency, with 

confidence and prediction intervals. ..................................................................... 51
vii 

List of Figures (concluded) 

Figure 44. Curve fit of power at μ = 0.523, converted to propulsive efficiency, with 

confidence and prediction intervals. ..................................................................... 52

Figure 45. CAMRAD II predictions of JVX propulsive efficiency at μ = 0.263 with 

data uncertainty bands........................................................................................... 54

Figure 46. CAMRAD II predictions of JVX propulsive efficiency at μ = 0.523 with 

data uncertainty bands........................................................................................... 54

Figure 47. CAMRAD II predictions of JVX propulsive efficiency with three 

Reynolds number correction models. ................................................................... 55

Figure 48. CAMRAD and U2NCLE predictions of JVX propulsive efficiency in 

axial flow. ............................................................................................................. 56 

Figure A-1. JVX 40x80 hover data at Mtip = 0.709, downstream orientation, superimposed 

on OARF data at Mtip = 0.728. ................................................................................62 

Figure B-1. Phase I spinner tare data at 495 rpm, plotted as flat-plate area versus dynamic 

pressure. .................................................................................................................63 

Figure B-2. PTR balance thrust-measurement error (Ref. 11, Fig. 6.3). ...................................65 

Figure B-3. Phase I spinner tare internal pressure data. ............................................................67 

Figure C-1. Measured JVX propulsive efficiency with and without Glauert blockage 

corrections. The nominal data are the same as in Figure 28. .................................70 

 
viii 
ix 

List of Tables 

Table 1. JVX and TRAM Rotor Characteristics. ................................................................... 4

Table 2. Proprotor Test Datasets. ........................................................................................... 5

Table 3. JVX Summary Test Conditions. ............................................................................... 5

Table 4. Polynomial regressions for hover data. .................................................................. 12

Table 5. Mean test conditions for JVX wind tunnel data, with standard deviations. 

Vtip and Mtip are nominal hover values. .................................................................. 35

Table 6. Data runs for each value of advance ratio. ............................................................. 41

Table 7. Mean test conditions for JVX Phase I wind tunnel data, with standard 

deviations. Vtip and Mtip are nominal hover values. ................................................ 42 

Table D-1. JVX OARF hover data (ref. 1), rotor only, Mtip = 0.67–0.68. ................................72 

Table D-2. JVX OARF hover data (ref. 1), rotor only, Mtip = 0.73. .........................................73 

Table D-3. JVX hover data, isolated rotor in the 40x80 test section, downstream 

orientation, Mtip = 0.71. Tunnel velocity V is induced by the rotor. .......................74 

Table D-4. JVX summary cruise operating conditions and thrust ranges. ................................75 

Table D-5. JVX data labels, definitions, and units. ...................................................................76 

Table D-6a. JVX 1988 Phase I airplane-mode operating conditions. .........................................79 

Table D-6b. JVX 1988 Phase I rotor performance data, as given in the database. .....................79 

Table D-6c. JVX 1988 Phase I rotor performance data, original (text labels) and as 

recalculated (italic symbols). ...................................................................................79 

Table D-7a. JVX 1991 Phase II airplane-mode operating conditions (Test 579). ......................80 

Table D-7b. JVX 1991 Phase II rotor performance data, as given in the database. ....................81 

Table D-7c. JVX 1991 Phase II rotor performance data, original (text labels) and as 

recalculated (italic symbols). ...................................................................................82 

Table D-8. JVX 1988 Phase I spinner pressures, blades on. .....................................................83 

Table D-9. JVX 1991 Phase II spinner pressure data. SPBSF is recalculated. .........................84 

Table D-10a. JVX 1998 Phase I spinner tare test conditions, blades off. .....................................85 

Table D-10b. JVX 1998 Phase I spinner tare data, blades off. ......................................................85 

 
x 

 
xi 

Notations 

ATB Advanced Technology Blade 

BEMT Blade Element/Momentum Theory 

CAMRAD Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics 

CFD Computational Fluid Dynamics 

DES Detached Eddy Simulation 

DNW Deutsch-Niederlandischer Windkanal 

JVX Joint Vertical Experimental 

NFAC National Full-Scale Aerodynamics Complex 

OARF Outdoor Aerodynamic Research Facility 

PTR Propeller Test Rig 

RDRS Rotor Data Reduction System 

TRAM Tilt Rotor Aeroacoustic Model 

TTR Tiltrotor Test Rig 

U2

NCLE Unstructured UNsteady Computation of fieLd Equations 

2D Two-dimensional 

3D Three-dimensional 

40x80 40- by 80-ft NFAC test section 

A rotor disk area 

ASP effective spinner drag area, ft2

B Prandtl tip-loss factor

cd airfoil section drag coefficient 

cdmean mean blade section drag coefficient 

cd0 section drag coefficient at zero lift 

cl airfoil section lift coefficient 

clmax maximum section lift coefficient 

cd 2D drag coefficient from 2D airfoil table 

cl2D lift coefficient from 2D airfoil table 

C wind tunnel cross-section area 

CP rotor power coefficient, P /(ρAVtip

3 )

CPi induced power coefficient, P

i /(ρAVtip

3 )

CPideal ideal power coefficient (hover), CT

3 / 2 / 2

CPm ideal power coefficient, P

m

/(ρAVtip

3 )

CPo profile power coefficient, P

o

/(ρAVtip

3 )

CQ rotor torque coefficient, Q /(ρAVtip

2 )R

CT rotor thrust coefficient, T /(ρAVtip

2 )
xii 

Notations (continued) 

FM rotor hover figure of merit, ( ) T T / 2ρA /P

FP profile power factor 

k number of data points

KL Reynolds number factor for lift 

KD Reynolds number factor for drag 

KQT torque/thrust correction coefficient 

KTQ thrust/torque correction coefficient 

m order of curve fit 

Mtip rotor tip Mach number 

n exponent in Reynolds no. correction 

N number of blades

P rotor power, hp 

Pi rotor induced power, hp 

Po rotor profile power, hp 

Pm ideal (minimum) rotor power, hp 

q0 tunnel dynamic pressure, lb/ft2

.75R q dynamic pressure at 0.75 R

Q rotor torque, ft-lb 

Qs measured shaft torque 

r regression coefficient

R rotor radius, ft 

Re Reynolds number (actual) 

Ret Reynolds number of airfoil table

sd standard deviation 

se standard error of estimate 

T rotor thrust, lb 

v induced velocity, ft/sec 

V tunnel wind speed, knots 

V′ Glauert equivalent velocity, knots 

Vtip rotor tip speed, ft/sec 

Xb X-force measured at the balance 

Xc corrected X-force 

Xs measured residual shaft thrust 

y measured value

yˆ predicted value 

α angle of attack 

α1 area ratio A/C 
xiii 

Notations (concluded) 

∆x change in x

η propulsive efficiency TV/P 

λ induced velocity ratio, v/Vtip

κ induced power ratio, CPi ⁄CPideal

κσ power factor for swirl losses

κτ power factor for tip losses (=1/B) 

Ω rotor rotational speed 

μ advance ratio V/Vtip 

ρ atmospheric density, slug/ft3

σ rotor solidity (thrust weighted) 

σx measurement uncertainty of x

τ Glauert thrust coefficient, T /(ρAV 2

) 

ψs rotor shaft yaw angle, deg 

 
xiv 
1 

Summary 

A 0.656-scale V-22 proprotor, the Joint Vertical Experimental (JVX) rotor, was tested at the 

NASA Ames Research Center in both hover and airplane-mode (high-speed axial flow) flight 

conditions, up to an advance ratio of 0.562 (231 knots). This paper examines the two principal 

data sets generated by those tests, and includes investigations of hub spinner tares, torque/thrust 

measurement interactions, tunnel blockage effects, and other phenomena suspected of causing 

erroneous measurements or predictions. Uncertainties in hover and high-speed data are 

characterized. The results are reported here to provide guidance for future wind tunnel tests, data 

processing, and data analysis. 

Introduction

The JVX rotor was an experimental precursor to the V-22 rotor, hence the name “Joint Vertical 

Experimental.” Several tests of the JVX rotor were performed at NASA Ames Research Center, 

including hover testing at the NASA Outdoor Aerodynamic Research Facility (OARF) and highspeed, axial-flow tests in the 40- by 80-ft test section (the “40x80”) of the National Full-Scale 

Aerodynamics Complex (NFAC). The hover data were originally reported in reference 1 and the 

high-speed data in reference 2. Data are also available for the 1/4-scale Tilt Rotor Aeroacoustic 

Model (TRAM) rotor (ref. 3). This report is a major expansion of references 4 and 5. 

Several motivations underlie this work: 

• NASA, with the support of the U.S. Army and Air Force, is developing the Tiltrotor Test Rig 

(TTR) for testing large (26-ft-diameter) proprotors in the NFAC. A re-examination of 

previous tests and test data was undertaken to assist with equipment design, test planning, 

and improved data analysis. 

• Anomalies in the JVX rotor test data prompted a close look at data and data processing 

requirements. The uncertainty analyses reported here started out as an effort to detect and 

understand any errors in the existing database. The methods described here may lead to 

improved test data collection, processing, and interpretation of the data expected from the 

TTR. In some cases, the value of the work lies in determining what cannot be definitively 

analyzed, with the hope that future tests can be planned to generate more useful data sets. 

• There was a difference between predictions and high-speed performance data for the JVX 

isolated rotor (refs. 4 and 5); the problem persists with newly available, independent analyses 

(ref. 6). A possible cause is suggested here. 

This report begins with a description of the JVX rotor and test history, plus a brief summary of 

the TRAM rotor and test data. Uncertainty analyses of JVX hover and high-speed axial-flow test 

data are given in separate sections, each with comparisons with CAMRAD II and U2

NCLE 

predictions. This report also includes Appendix A that summarizes an attempt to measure hover 

performance in the 40x80, plus Appendices B and C that discuss spinner tares and wind tunnel 
2 

blockage effects, respectively. Numerical data are tabulated in Appendix D (a major revision to 

the data published in reference 5). 

Hover thrust of a proprotor is greater than airplane-mode thrust by approximately the lift-to-drag 

ratio of the aircraft. For a modern tiltrotor or tilt-wing aircraft, the ratio is at least a factor of 10. 

The relative effect of any measurement error, nonlinearity, or uncertainty on airplane-mode data 

is therefore an order of magnitude greater than on hover data. This effect is compounded by large 

spinner drag tares. These considerations raise major challenges for analysis of wind tunnel data 

for high-speed proprotors, as reflected by the different approaches taken to analyze the hover and 

airplane-mode data described in this report. 

A Note on Statistics Terminology 

While no claims of statistical or terminological rigor are made here, this paper generally 

observes the difference between error and uncertainty. Strictly speaking, it is not possible to 

determine errors in the test data presented here, because there are no independent measurements. 

(There is a minor exception for calibration data, where the reference values have much lower 

uncertainties than the test data.) In contrast, uncertainty can be characterized by statistical means. 

This paper uses the traditional term standard deviation to refer to variations about a point value, 

and standard error of estimate (or simply standard error), confidence interval, and prediction 

interval to refer to variations about a regression line, with the implication that they refer to 

uncertainties in the measurements. 

Statistical significance is a measure of the reliability of a test or measurement. The traditional 

definition of statistical significance is the probability that an observed effect is due purely to 

chance. Tests of statistical significance were always made at the 5-percent level. 

Too little data from the JVX tests survive to perform a proper uncertainty analysis to the 

standards of reference 7. While this paper freely applies curve fits and makes statistical tests of 

the data, the purpose is to gain insight into the physical properties of the rotor, not to generate 

definitive statistical analyses. 

The primary reference used for statistics was the classic “Statistics Manual” by Crow, Davis, and 

Maxfield (ref. 8). A useful and readily available introduction to the newer methods and 

terminology is NIST Technical Note 1297 (ref. 9). Reference 7 is also recommended. 
3 

The JVX Test Rotor 

Sometimes referred to as a “2/3-scale V-22,” and more rarely “M901 rotor,” the JVX rotor in 

fact differed from the V-22 in several respects, as described below. The following description 

includes information from references 1 and 2. See also reference 10 for JVX airfoil data. 

The JVX rotor was 25 feet in diameter, which is 0.656-scale relative to the production V-22. The 

JVX rotor used an XV-15 hub with fixed, 2.5-deg precone, whereas the V-22 hub has a coning 

flexure with slightly different at-rest precone. An XV-15 spinner was used for the JVX rotor, 

instead of the proportionately much shorter V-22 spinner. Hover testing was done with the 

original JVX blade planform and airfoil distribution, which had linear taper and an XN-28 airfoil 

at the root. JVX wind tunnel testing was done with a thicker root section to model the V-22 

production blade, which must accommodate a folding hinge; the resulting inboard planform did 

not match that used for the hover tests. The JVX rotor was always tested when mounted to the 

Propeller Test Rig (PTR), which had a fairing over the rotor balance just behind the hub (Figs. 1 

and 2). The trailing edges at the blade roots were slightly clipped to clear the rotor balance 

fairing. See reference 11 for additional details of the PTR and its installation at the OARF. 

All JVX rotor tests were done at the OARF or in the 40x80 test section of the NFAC. No wing 

was installed for any data reported here. The test article no longer survives. 

Another scale V-22 test rotor is the Tilt Rotor Aeroacoustics Model (TRAM); its data are useful 

for comparison with JVX (and of course V-22). TRAM is a 1/4-scale V-22, designed for 

acoustics and blade loads measurements; a detailed description is given in reference 3. 

Figure 1. The JVX rotor mounted on the PTR for hover tests at the OARF. 
4 

Figure 2. The JVX rotor mounted on the PTR for airplane-mode tests in the NFAC. 

JVX and TRAM rotor characteristics are summarized in Table 1, with V-22 data for reference. 

The V-22 data apply to the production version. The test conditions for data presented in this 

report are summarized in Table 2. Additional details are given in reference 12, from which 

Table 1 was adapted. Reference 13 presents the most important TRAM test data. 

At least five different variations of the blade cuff have been built and tested. For consistent 

comparisons, the linear portion of each blade, running from about 25 percent radius to the tip, 

was extrapolated to the root to define a nominal root chord. The values of taper in Table 1 are 

based on the nominal chord value. 

Existing publications of JVX, TRAM, and V-22 typically use nominal, thrust-weighted values of 

solidity and not necessarily literal values derived from as-built geometry. Table 1 conforms to 

that convention. 

Table 1. JVX and TRAM Rotor Characteristics. 

 JVX TRAM V-22 

Scale, referenced to V-22 0.656 0.25 1 

Rotor radius (in.) 150 57 228.5 

Solidity (thrust weighted) 0.1138 0.105 0.105 

Tip chord (in.) 15.79 5.5 22.0 

Taper (tip/root chord) 0.646 0.641 0.641 
5 

Test Summary

Complete JVX hover test data were published in reference 1, and very limited airplane-mode 

data from a subsequent 40x80 test were published in reference 2. A more extensive set of 

airplane-mode wind tunnel data acquired in 1991 were published in reference 5. A limited 

amount of hover data were taken during the 1988 40x80 entry (ref. 14). 

This paper incorporates data from five separate tests, primarily the 1984 JVX OARF hover test 

and the 1991 JVX 40x80 test (refs. 1 and 5). Supplementary data include JVX spinner drag data 

from the 1988 40x80 wind tunnel test (ref. 2) and a very limited amount of balance check-loads 

data from the 1984 Advanced Technology Blade (ATB) OARF tests (ref. 11). The 1970 XV-15 

40x80 wind tunnel test (ref. 15) provides useful data for cross reference, but no actual data from 

that test are included here. Table 2 summarizes the major tests and datasets. 

Table 3 summarizes the JVX test conditions analyzed in depth here. Limited hover data at other 

tip speeds are reported in reference 1; a subset is briefly examined here. Limited comparisons 

between OARF and 40x80 hover test data are given in Appendix A. 

Table 2. Proprotor Test Datasets. 

Test Article Facility Date Dataset No. Reference No. 

XV-15 40x80 1970 Test 374 15 

ATB OARF 1984 Test 910 11 

JVX OARF 1984 Test 911 1 

JVX Phase I 40x80 1988 Test 568 14 

JVX Phase II 40x80 1991 Test 579 5 

TRAM DNW 1998 Test 20 3 

Table 3. JVX Summary Test Conditions. 

 Hover Airplane Mode 

Tip Mach no. 0.676 0.575 0.625 

Tip speed (ft/sec) 754 640 695 

Airspeed (knots) 0 99–200 231 

Density (slug/ft3

) 0.00239 0.00224–0.00234 0.00220 

Hover Data and Analyses 

JVX hover data were taken outdoors at near-zero wind conditions. The bulk of the hover data 

were for a nominal tip Mach number (Mtip) of 0.68 (754 ft/sec), with a small amount of data at 

Mtip = 0.73. The following discussion is focused on the lower tip speed, which is the design 

operating condition for the JVX rotor. 

 
6 

Reference 1 provides corrections for wind and plots data at a variety of cut-off wind speeds. 

Previous publications of JVX hover data (e.g., refs. 4, 5, and 16) typically exclude data above 

1 knot. Criteria are developed here for including more data from the dataset. See reference 17 for 

a completely different approach to wind corrections. 

Figures 3 and 4 plot all data at nominal Mtip = 0.68 and CT/σ > 0. Different plot symbols denote 

different data runs. Each run included one or more thrust sweeps from low to high thrust. The 

PTR was shut down between each run, and the data system reset with new zeros and resistance 

calibration checks (R-cals). There were 6 runs at Mtip = 0.68 for a total of 100 data points. 

The maximum attained thrust was CT/σ = 0.1600, whereas typical V-22 design hover conditions 

are CT/σ = 0.16 to 0.17 (ref. 18). The V-22 rotor also has lower solidity than the JVX rotor 

(Table 1). Comparison of JVX OARF data to flight data should therefore be treated with due 

caution. 

The CP/σ data (Fig. 3) appear to be tightly clustered, but the expanded scale of Figure 4 reveals 

considerable scatter in figure of merit (FM). All data in Figures 3 and 4 are corrected for the 

effects of wind; the corrections are given in reference 1. Figure 5 shows figure of merit without 

wind corrections. With wind corrections, the data are generally more consistent run-to-run, most 

obviously between Run 5 and Run 6. However, there is little apparent effect on the scatter within 

each run; the scatter in Run 3 is possibly even worse near CT/σ = 0.11 for the corrected data 

(compare Figure 4 to Figure 5). 

Figure 6 plots the data of Figure 4, but only for wind <1 knot. The data from Run 5 have been 

completely eliminated, as have the high-thrust data from Run 6 and most of the data from Run 2. 

However, the anomalous data point from Run 3 at the highest measured figure of merit 

(CT/σ = 0.11 and FM = 0.83) has not been eliminated. A different method of selecting data is 

clearly desirable. 

Figure 7 shows histograms of selected parameters for all runs at Mtip = 0.68 and CT/σ > 0 (the 

same data points as Figures 3–5). Included are counts of Mtip, .75R q , and Vtip, where .75R q is the 

dynamic pressure at 3/4 blade radius and Vtip is the rotor tip speed. Vtip is the most accurately 

measured parameter because it requires only a measurement of rotation speed, whereas Mtip

requires a measurement of temperature and .75R q requires a measurement of atmospheric density. 

Mtip shows little variation (Fig. 7a), as does .75R q (Fig. 7b), and both have an approximately 

Gaussian distribution as expected. However, Vtip has a much more erratic distribution (Fig. 7c). 

Furthermore, all of the points below Vtip = 750 ft/sec are from Run 3, but Vtip ≥750 ft/sec for all 

other data. Also, no points from Run 1 exceed 753 ft/sec. The spread in the Mtip data—the 

difference between maximum and minimum values, divided by the mean—is ±0.33 percent; but 

for Vtip, the spread is ±1.03 percent (over three times as much). The spread in the .75R q data is 

±0.62 percent. 
7 

Figure 3. Hover power (corrected for wind) versus thrust, Mtip = 0.68. 

Figure 4. Figure of merit (corrected for wind) versus thrust, Mtip = 0.68. 
8 

Figure 5. Figure of merit (without wind corrections) versus thrust, Mtip = 0.68. 

Figure 6. Figure of merit (corrected for wind) versus thrust, Mtip = 0.68 and wind <1 knot. 
9 

Figure 7(a). Distribution of Mtip values. 

Figure 7(b). Distribution of q.75R values. 

Figure 7(c). Distribution of Vtip values. 
10 

Some additional insight may be gained by examining the non-ideal power C C P P − ideal , based on 

the classic momentum-theory relation 

CPideal = CT

3/2 2 [1] 

Figure 8 plots the wind-corrected data as non-ideal versus ideal power. It is evident that the 

Run 3 data (solid markers) have an anomalous trend between CPideal = 0.00044 and 0.00095 

(CT/σ from 0.064 to 0.107). These five data points have the lowest tip speeds of any hover data, 

and tip speed drops monotonically as thrust increases. Trimming the rotor to constant Mtip

instead of Vtip should give more consistent results, but Figures 4 and 8 suggest otherwise, at least 

for Run 3. The data from Run 3 are questionable and were therefore excluded from all further 

analyses reported here. 

All of the data were taken by progressively increasing collective to sweep from low to high 

thrust. Figure 9 shows the data organized by thrust sweep. Runs 2 and 5 had two such sweeps 

each, with the thrust returned to near-zero at the beginning of the second sweep. These repeated 

sweeps are here labeled 2A and 2B, and 5A and 5B. Each sweep is plotted as a continuous line, 

instead of point-by-point, to emphasize the trend within each sweep. Runs 1 and 2B are not 

shown because they did not extend above CT/σ = 0.10. The purpose is to select data for further 

analysis, so it is desirable to include only data runs that span the full range of thrust. 

It is evident that Run 4 has consistently higher figure of merit at high thrust, and Runs 2A and 5B 

have arguably less consistent trends than the other data. There are no obvious parameters in the 

database that explain these differences, although only a few of the many possible correlations 

were closely examined. Efforts were instead spent on curve-fitting the data to get the best 

possible estimate of the rotor performance trend, as described in the next section. 

Figure 8. Non-ideal power versus ideal power (corrected for wind), Mtip = 0.68. 
11 

Figure 9. Thrust sweeps by run (corrected for wind), Mtip = 0.68. 

Regression Analysis of Hover Data 

The goal is to estimate the rotor performance trend from several collective sweeps, which have 

variations in performance trends and scatter between runs. The data were not taken at exactly 

repeated values of collective or thrust, so point-by-point averaging is not possible. Curve fits 

across a range of thrust are therefore necessary. Multiple-linear regression is needed to properly 

capture the trends in the data and to provide reliable estimates of uncertainty in measured 

performance. 

Data at medium and high thrust are generally of more interest that at low thrust, so data for 

CT/σ < 0.04 were excluded. Figure 3 shows that CT/σ > 0.04 includes nearly all of the data but 

excludes the low-thrust data with reversed power trend. Run 3 data were also excluded, for 

reasons discussed above. The data so filtered comprised 75 data points. Power corrections for 

wind were included in all curve fits described here, except where noted. 

Although some authors have fit figure of merit directly to thrust, this requires a highly nonlinear 

regression analysis, typically with high-order polynomials in thrust. Fitting power to thrust (or 

equivalently, CP to CT) permits an equally good, if not better, fit with fewer high-order terms 

(thanks to M. A. McVeigh for pointing this out). The curve fit is then readily transformed to 

figure of merit. The problem is simplified here because the JVX test never achieved stall, so the 

data do not show any major change in trend at the high-thrust limit. 
12 

Physical reasoning can reduce the choice of functions of the independent variable CT to a few 

likely possibilities. Power should approximately follow the momentum theory trend 

3/2

ideal = 2 C C P T . Below stall, airfoil section drag varies quadratically with lift. For constant tip 

speed, profile power should therefore vary with 2 CT . There is also the option of including higherorder terms in CPideal . The scales of Figure 8 were chosen so that a linear fit in CPideal would yield 

a straight line. It is evident that a linear fit will not give a good fit, unless the data are restricted 

to a narrow range of thrust values (e.g., CT/σ > 0.10). 

Momentum theory can be extended to include swirl losses, and actuator vortex theory provides 

an approximation of tip losses (the Prandtl tip-loss correction). From reference 19, a power factor 

κs for swirl losses can be expressed as 

κ s = 1+ 2 CT

2

ln CT

2





 





−1/2

 [2] 

and a factor κt for tip losses can be expressed as 1/B, where B is the Prandtl tip-loss function 

B = 1− 2ln2 CT

N [3] 

Combining factors, C C P st P = κ κ ideal . 

The two loss factors are plotted against / CT σ in Figure 10 for a three-bladed rotor. Except at 

very low thrust, the variation of swirl losses with thrust is approximately linear. At medium-tohigh thrust, the variation of the tip-loss factor is approximately quadratic, with a negative 

second-order coefficient. The curve fit for CP could, therefore, reasonably contain terms in both 

CT and 2 CT . Profile power and tip losses should both vary with 2 CT and therefore cannot be 

readily distinguished by regression analysis. 

Several polynomial curve fits were computed, with different terms as listed in Table 4. Each 

polynomial also included a constant term (not listed separately in the table). 

Table 4. Polynomial regressions for hover data. 

Fit No. Polynomial Terms 

1 CPideal and 2 CPideal

2 CPideal and 2 CT

3 CPideal and CT

4 CT and 2 CT

5 CPideal , 2 CT , and CT

6 CPideal , 2 CPideal , 2 CT , and CT
13 

Figure 10. Swirl- and tip-loss factors versus thrust for N = 3. 

Not listed in Table 4 are three special cases: a linear fit to CPideal , and linear and quadratic fits to 

CPideal with swirl- and tip-loss corrections from Eqs. 2 and 3. 

The uncertainty of any given curve fit can be expressed as the standard error of estimate se. From 

reference 7, the standard error of estimate is calculated as 

se = (y − yˆ)

k − (m +1) [4] 

where y is the measured value, yˆ is the predicted value, k is the number of data points, and m is 

the order of the curve fit. For fits 1–4, y = CP, k = 75, and m = 2. For fits 5 and 6, m = 3 and 

m = 4, respectively. For each curve fit, the individual coefficients were tested for statistical 

significance, but their uncertainties are not otherwise critical and are not explored here. 

The linear fits to CPideal , both with and without swirl- and tip-loss factors, all had significantly 

higher standard error se than the quadratic fit (no. 1 in Table 4). Including swirl and tip losses 

gave a significant improvement to se when compared to the linear fit without. Thus there was a 

hierarchy of curve fits: the linear fit to CPideal had the largest uncertainty, followed by the linear 

fit to CPideal with swirl and tip losses, then by the quadratic fit to CPideal ; each reduction in se was 

statistically significant. Adding swirl- and tip-loss factors to the quadratic fit made only a trivial 

improvement. For this reason, swirl and tip losses were not further analyzed nor applied to any 

other curve fits. 
14 

The last three combinations in Table 4 yielded the lowest standard errors, but the trends were 

unrealistic at the extremes of the range of fitted data, with non-physical inflections at low thrust 

and sometimes at high thrust. For the last two combinations, not all coefficients were statistically 

significant, meaning that they were over-fitted. The last three combinations were therefore 

rejected. Of the remaining three, the second combination had the lowest standard error, and the 

first had the second lowest, but the difference was only in the fourth decimal place. The third 

combination fit the low-thrust, out-of-range data surprisingly well, but at the cost of a higher 

standard error. Of all the fits, the first combination yielded a coefficient to the CPideal term closest 

to unity. 

The difference between the standard errors of a linear curve fit to CPideal (no term in 2 CPideal) and a 

quadratic fit (no. 1 in Table 4) was statistically significant. However, the differences between the 

standard errors of any two curve fits in Table 4 were never significant. For these reasons, no 

further combinations were analyzed. 

Swirl and tip losses should be captured by curve fits no. 3 and 2, respectively, and the secondorder effects of profile power should be captured by curve fit no. 2. The least uncertainty was 

seen with the fit to CPideal and 2 CT (fit no. 2). However, the reduction in se was too small to be 

statistically significant, so the effects of profile power and tip losses cannot be proven here. 

These results do not prove that tip and swirl losses are unimportant for this rotor, or are less 

important than second-order effects of profile power—they all surely apply—but instead that 

some other source of nonlinearity is dominant. 

If the requirement is to compare predictions or another data set to the data analyzed here, then 

the best curve fit option depends on the range of data of greatest interest. For the JVX data 

filtered as CT/σ > 0.04, the fit to CPideal and 2 CPideal is recommended because the coefficient of the 

CPideal term should be close to one and is therefore a useful check of the validity of the fit. (A 

different approach was required for high-speed data, as described in the section “Wind Tunnel 

Data.”) 

The resulting equation is 

3 3/2 =+ + 103.5 2 0.9535 2 0.0001956 CC C PT T [5] 

The associated se = 0.00001309, about 0.61 percent of the maximum measured value of CP. 

The constant term can be expressed in terms of profile power, 

o = ( / 8) P d o C c σ [6] 

Hence, 

3 3/2 =+ + 103.5 2 0.9535 2 0.01375 / 8 CC C PT T σ . 
15 

However, the constant term includes induced-power effects in addition to profile power. 

Figures 11–13 plot the data and curve fit of Eq. 5, including uncertainty bands of ±2se. Figure 11 

plots power versus ideal power ( 3/2

ideal = 2 C C P T ); bands based on the standard error with the 

traditional multiplier of ±2 yield the smallest metric of uncertainty that can be discerned at the 

scale of the plot. The uncertainty bands are a little easier to see when plotted as figure of merit 

versus CT/σ (Fig. 12). The fitted curve and uncertainty bands are limited to the range of data 

fitted; the lighter gray line extends the fit to the limits of the plot. Although not included in the 

curve fit, data for CT/σ < 0.04 ideal ( 2 < 0.000 17) CP are included for reference. 

Figure 13 plots the data as non-ideal versus ideal power. Here, it is obvious that the curve fit 

does not match the trend in the data at very low thrust, even though figure of merit (Fig. 12) 

superficially appears to be well matched. The plotted curve fit is that of Eq. 5, converted to nonideal units (not a fit to non-ideal power). 

Figure 11. Quadratic curve fit of hover power (corrected for wind) versus ideal power, for Mtip = 0.68 

with ±2se bands. 
16 

Figure 12(a). Quadratic curve fit of hover power (corrected for wind) versus thrust, converted to 

figure of merit, for Mtip = 0.68 with ±2se bands. 

Figure 12(b). Quadratic curve fit of hover power versus thrust (expanded scales). 
17 

Figure 13. Quadratic curve fit of hover power (corrected for wind) versus ideal power, converted to 

non-ideal power, for Mtip = 0.68 with ±2se bands. 

It may be of interest to show the curve fit with terms of CPideal and CT (combination no. 3 

discussed previously). The resulting equation is 

3 =− + + 0.05493 2 1.636 0.02195 8 C CC P TT σ [7] 

The associated se = 0.00001333. 

The curve fit is plotted in Figure 14 as non-ideal versus ideal power. The trend at very low thrust 

is much better than in Figure 13, even though no data below CT/σ = 0.04 are included in the fit. 

The choice of Eq. 5 or 7 depends on the intended use of the curve fit, although inclusion of a 

different range of data would doubtless be of benefit if extremely low thrust is of interest. 

Because the uncertainty bands are easier to see when plotted as figure of merit or non-ideal 

power, all of the following comparisons of uncertainty in the hover data are made in terms of one 

of these two performance metrics. 

Effects of Wind Corrections 

An additional check on the value of wind corrections was made by applying the regression with 

terms in CPideal and 2 CPideal to the same data as Figures 11–14, but without wind corrections. The 

results are shown in Figure 15 (compare with Figure 5 for the data set, and with Figure 12 for the 

curve fit). It is obvious that the wind corrections are successful in generating more consistent 
18 

performance trends. Without wind corrections, the scatter, in terms of standard error, is nearly 

doubled: se = 0.0000237 versus 0.0000131. The difference between the standard errors is 

statistically significant. 

Figure 14. Alternative curve fit of hover power (corrected for wind) versus ideal power, converted to 

non-ideal power, for Mtip = 0.68. 

Figure 15. Quadratic curve fit of hover power (without wind corrections) versus thrust, converted to 

figure of merit, for Mtip = 0.68 with ±2se bands. 
19 

Because the power corrections of reference 1 are based on known physical phenomena, wind 

corrections are included in all hover data plotted and analyzed here except where explicitly 

noted. 

Effects of Coefficient Conversions 

In principle, the cleanest curve fits would be of torque Q versus thrust T, or against T 3/2. The 

classic performance coefficients CT and CP (or CQ) include terms in atmospheric density and 

rotor speed (ρ and Ω), both of which are subject to measurement uncertainty. Although 

measurements of Ω, or equivalently Vtip, can be expected to be very accurate, any error will 

occur in the second power for CT and CQ, and in the third power for CP. Power was measured as 

Q×Ω, hence compared with torque, power contains an additional uncertainty contributed by the 

measurement of Ω. 

The ideal power is a fundamental characteristic of the rotor not subject to statistical error: given 

measured T and ρ, ideal power = / 2 P TT A m ρ can be directly computed without introducing 

any additional uncertainty. The following analyses used curve fits to Pm and 2 Pm , equivalent to 

curve fit no. 1 in Table 4. 

The difference in standard errors between quadratic fits of P versus Pm and Q versus Pm is not 

statistically significant (all uncorrected for wind). While the fit to Q yields a lower standard 

error, the difference is in the third decimal place (0.0000235 versus 0.0000239, in units of CP ). 

A reasonable conclusion is that the uncertainty in the measurement of Ω is insignificant. The 

conversion of standard errors to units of CP requires averaged values of Ω and ρ, and therefore

introduces additional uncertainty, but the averaged values are the same for both conversions and 

do not affect the validity of the comparison. The differences are extremely small in any case. 

The difference between the standard errors of quadratic fits of CP versus CPideal and of Q versus 

T 3/2, both uncorrected for wind and the latter scaled to CP , differ only in the third significant 

figure (0.0000237 versus 0.0000242, respectively). It is obvious that conversions from physical 

units to rotor coefficients introduce no meaningful increase in uncertainty. These results imply 

that ρ and Ω were measured more accurately than T and Q, or at least that ρ and Ω had too little 

uncertainty to affect the curve fits. 

For the purposes of this paper, the curve fits to hover data as converted to performance 

coefficients CP and CT give completely acceptable results and are perhaps easier to interpret in 

the context of traditional rotor performance analysis. Therefore, the remainder of this paper 

reports fits and comparisons in terms of CP and CT (or CP/σ and CT/σ) except where explicitly 

noted. 
20 

Considerations for Off-Trend Data 

There are several physical reasons why CP σ would not exactly follow the 3/2 2 CT trend line 

including, but not limited to, profile power, stall at high collective settings, and variations in the 

lift distribution, which will rarely if ever approach the ideal. The JVX hover tests never achieved 

full stall. A few other possibilities are briefly explored here. 

The JVX rotor has very high total twist (–47.5 deg nominal). As the total thrust approaches zero, 

the tip experiences negative lift to cancel out residual positive lift at the root. Induced power may 

then increase as thrust further decreases, even without stall. Under such conditions, the rotor no 

longer behaves like an actuator disk of radius R, and Eq. 1 is not appropriate. Figure 3 shows a 

trend reversal at about CT /ߪ = 0.02. 

The design lift distribution is necessarily a compromise, but for a well-designed rotor, the lift 

distribution will yield minimum non-ideal induced power near the design CT, with higher nonideal power at lower and higher CT. However, the JVX twist distribution must work in highspeed axial flow, and therefore varies greatly from the ideal for hover. The effect of non-ideal lift 

distribution can be significant, and minimum induced power may not occur exactly at design CT. 

The JVX design CT is well above the mid-thrust data, where non-ideal power is increasing 

rapidly (Fig. 13). 

In hover, profile power is dominated by rotational velocity, not thrust, and the JVX twist is large 

enough (–47.5 deg) that the root and tip cannot simultaneously operate in the unstalled regions of 

their respective airfoils. Three-dimensional (3D) stall delay may mitigate this effect but cannot 

achieve an ideal lift distribution. Given a large enough data set, with large variations in thrust, tip 

speed, and axial velocity, it might be possible to separate the effects of profile power from those 

of twist distribution, but not with the existing JVX data. 

The close quadratic fit to ideal power (Eq. 5 and Figs. 11–13) does not prove that the variations 

from the ideal power trend are caused by variations in lift distribution, or indeed by any other 

particular physical mechanism, but it is plausible and consistent with the data. The larger point is 

that a quadratic curve fit to ideal power gives a very close fit to the data, and the resulting 

estimate of uncertainty is unlikely to be usefully reduced by any reasonable set of physical or 

mathematical assumptions. 

Uncertainty Comparisons for Hover 

The PTR measures thrust and torque with a combination of a rotor balance and an instrumented 

flex coupling on the rotor shaft (refs. 1 and 11). The documentation for the JVX OARF test has 

incomplete data for measurement uncertainty. The balance was bench-calibrated prior to 

installation, and check loads were applied afterwards to determine the as-installed accuracy, 

including corrections for known interactions. Torque/thrust interactions proved problematical for 

the Phase II wind tunnel data and are discussed in context later in this report. There was no 

evidence of problems with interactions during the OARF test. 

 
21 

Reference 11 states that thrust is measured within ±50 lb up to the maximum range of 16,000 lb, 

and torque is measured within ±10 ft-lb with a maximum range of 21,000 ft-lb. Reference 1 

states that check loads applied during the JVX tests revealed thrust and torque accuracies of 

±200 N and ±70 Nm, respectively. The ±200 N accuracy is consistent with ±50 lb, but ±70 Nm is 

decidedly greater than ±10 ft-lb. 

There is scant documentation of how uncertainties for balance and shaft instrumentation were 

determined and combined to generate the stated measurement accuracies. The given values of 

accuracy—the terminology used in the references—appear to be the greatest excursions from the 

nominal values, not the standard deviations from the mean, root mean square, or other metric. 

The accuracies are given to one significant figure, with likely but unknown round-off errors from 

conversion between English and S.I. units. 

Data plots in reference 11 imply that much of the uncertainty in both thrust and torque is 

hysteresis, which possibly would be physically averaged out by vibration during a data point, but 

there is no way to prove that assumption. See Appendix B for further discussion of balance 

uncertainties. 

For the following analysis, the accuracies given in reference 1 are taken at face value, but 

converted to English units of ±50 lb thrust and ±50 ft-lb torque (hence a slight rounding up in 

thrust, consistent with reference 11). It is further assumed that the given values of accuracy are 

twice the standard deviations, giving measurement uncertainties of 25 lb thrust (σT) and 25 ft-lb 

torque (σQ ). 

Figure of merit can be written in terms of the directly measured quantities T and Q as 

FM T T A Q = Ω ( ) / 2ρ . 

Assuming that ρ and Ω do not contribute significantly to the total uncertainty, the uncertainty in 

figure of merit, expressed as σ FM , can be estimated as 

σ FM

2 = T

Q2

Ω22ρA

9

4

σ T

2 +

T 2

Q2 σ Q

2 



 



 [8a] 

or 

2 2

2 2

2 2

9

4

 

= +  

 

T Q

FM FM

T Q

σ σ

σ [8b]

 
22 

Figure 16 plots the curve fit of Figure 12 but with ±2σ FM uncertainty bands, here at expanded 

scales to match Figure 12 (b). At CT/σ = 0.10, the thrust term in Eq. 7 contributes about three 

times to the uncertainty 2 σ FM as the torque term. The estimates of balance measurement 

uncertainties used here are very rough. The check loads data in reference 11 suggest that the 

error in thrust measurement is much reduced over the range of data analyzed here; further 

reductions in measurement error may be assumed if hysteresis is averaged out over each data 

point. On the other hand, thermal effects and uncorrected interactions could increase the 

measurement errors. Nevertheless, it is clear that the uncertainty bands in Figure 12 (b) are larger 

than those contributed by the balance and shaft instrumentation. See also the discussion of airfoil 

drag in the next section of this report. 

Other measures of uncertainty are available, such as the confidence interval, which characterizes 

the dispersion of the regression line, and the prediction interval, which is the uncertainty in the 

prediction of a given data point; both of these metrics account for the increase in uncertainty with 

distance from the mean value of the independent variable (ref. 8). Figure 17 plots these metrics 

in the same format as Figure 12. The prediction interval (P.I.) is comparable to the ±2se

uncertainty bands, while the confidence interval (C.I.) is much smaller. The data transformation 

from power to figure of merit inverts the usual spread of the prediction interval about the mean 

regression line, in that the spread is greatest at mid-thrust and decreases at the ends of the range 

of thrust. The spread in the confidence interval increases slightly at maximum thrust, as can just 

barely be discerned in Figure 17. 

Figure 16. Quadratic curve fit of hover power (corrected for wind) versus thrust, converted to 

figure of merit, for Mtip = 0.68 with ±2σFM bands. 
23 

Figure 17. Quadratic curve fit of hover power (corrected for wind), converted to figure of merit versus 

thrust, with confidence and prediction intervals, Mtip = 0.68. 

Uncertainties in Airfoil Drag 

The focus of this report is the JVX OARF and wind tunnel data, which are used to validate 

predictive methods such as CAMRAD II (ref. 20). Other sources of measurement uncertainty, 

namely experimentally determined airfoil data, are also relevant and are briefly explored here to 

illustrate their importance relative to the JVX test data. 

CAMRAD II relies on external airfoil tables for aerodynamic analysis. An inflow model—here a 

free-wake model—computes the local aerodynamic environment of each blade section, and 

values of lift, drag, and pitching moment read are from the tables to determine the section loads. 

It was conjectured that uncertainties in airfoil drag data might explain the mismatch between 

CAMRAD II predictions of high-speed performance (refs. 4 and 5), so estimates of airfoil drag 

uncertainty were generated and converted to equivalent performance uncertainty. Although 

airfoil drag has less effect on rotor performance in hover than at high speed, the statistical 

comparisons for hover are nevertheless revealing. Furthermore, the XN-series airfoil data were 

determined experimentally, so comparing the two types of uncertainty—two-dimensional (2D) 

airfoil section data versus rotor performance data—provides useful insight into the relative 

importance of different sources of uncertainty. An important caveat is that the uncertainties in 

airfoil data were estimated by indirect means, as described next. 

 
24 

The statistical comparison was derived from the results reported by Bousman (ref. 21). 

Extending the work of McCroskey (ref. 22), Bousman calculated variations in airfoil 

performance as measured in several different wind tunnel tests. The SC1095 and SC1094 R8 

airfoils were chosen, largely because of the availability of data from 10 different tests. Although 

no equivalent variety of test data exists for the XN-series airfoils used on the JVX rotor, the 

SC-series airfoils and test data are of similar vintage to those of the JVX airfoils. Therefore, the 

uncertainty in the airfoil characteristics analyzed by Bousman should be similar to what would 

be expected if an equivalent series of wind tunnel tests were carried out for the JVX airfoils. 

For a well-designed rotor operating below stall, the airfoil characteristic critical for hover is cd0

, 

the section drag coefficient at zero lift. Its effect on figure of merit may be estimated by adjusting 

total power by the estimated profile power, Eq. 6: 

= ( 8) P d o o C c σ . 

The uncertainty in measured cd0

 may then be compared to the uncertainty in measured figure of 

merit by substituting the standard deviation of cd0 into Eq. 6 to get ∆CPo, then plotting 

ΔFM = CT

3/2 2

CP ± 2ΔCPo

, where ±2∆CPo is used for comparison to ±2se of the curve fit to the data 

(Eq. 5). 

The SC1095 airfoil was taken as an appropriate surrogate for the JVX airfoils (the SC1094 R8 

has nose droop not present in the JVX airfoils). To avoid contaminating the uncertainty measure 

with drag-divergence effects, only data below Mach 0.7 were used. Furthermore, the 

“Experiment 4” data were deleted because they have a clearly different trend (Figure 31 of 

reference 21). The uncertainty in cd0

, computed as the standard deviation, was thereby 

determined to be 0.000872; the equivalent variation in figure of merit is plotted in Figure 18 with 

the usual multiplier of ±2. 

Whereas the cd0

 uncertainty band in Figure 18 was derived from airfoil data, the JVX rotor has a 

fixed but unknown value of cd0 at any given test condition. The fact that cd0 is unknown does not 

contribute to uncertainty in measurements of rotor performance. The sd (cd0

) uncertainty band is, 

therefore, an indicator of prediction uncertainty arising from imperfect knowledge of isolated 

airfoil performance. In contrast, the se uncertainty band characterizes the experimental 

measurement of JVX rotor performance. It is almost certainly a coincidence that both uncertainty 

bands are nearly the same magnitude. 

 
25 

Figure 18. Quadratic curve fits of hover power, converted to figure of merit versus thrust, with ±2se bands 

and ±2sd (cd0

) bands. 

The value of uncertainty in cd0

 given here is much larger than that reported in reference 23 for 

low-drag conditions. Reference 23 gives uncertainties for a single wind tunnel (at Penn State 

University), whereas reference 21 gives pooled uncertainties for 10 wind tunnels, none the same 

as that of reference 23. The JVX airfoil tables were generated from data taken in a yet another 

wind tunnel (the Boeing Supersonic Wind Tunnel, ref. 10). 

The uncertainty of cd0

 determined as described for the SC1095 airfoil is only an approximation. 

A logarithmic curve fit to the data, as suggested in reference 21 to account for Reynolds number, 

would have yielded a standard error of fit slightly less than the standard deviation about the 

mean. On the other hand, including “Experiment 4” data would have increased the standard 

deviation. The exact value of the standard deviation would also have been affected by choosing a 

different maximum Mach number. Finally, multiple tests of the JVX airfoils would doubtlessly 

have yielded further differences. The larger point, however, is that airfoil drag alone can 

contribute uncertainty to predicted rotor performance of similar magnitude as the uncertainty in 

measured performance. 

Were the JVX rotor to have been driven into stall, maximum section lift clmax would have also 

provided a useful statistical comparison. Because of the highly nonlinear behavior that is 

characteristic of stall, there is no simple estimate of the effect of clmax on power corresponding to 

Eq. 6. An indirect estimate may be made with a rotor performance code by modifying the airfoil 

 
26 

tables, or perhaps by repurposing a stall-delay model to adjust the section lift by the uncertainty 

in clmax. The latter approach was carried out with CAMRAD II, using the SC1095 statistics of 

reference 21, but the effect was negligible within the range of test CT/σ (hence not shown here). 

Hover Data for Mtip = 0.73 

A limited amount of hover data were taken at Mtip = 0.728. Run 7 included two separate thrust 

sweeps, labeled Run 7A and 7B in Figure 19. Three additional data points were taken in Run 8, 

but at Mtip = 0.724. All data in Figure 19 have been corrected for wind. The maximum wind 

speed for Run 7 was 3.0 knots, but the wind speed for Run 8 was 3.6 to 4.5 knots. Because of the 

higher wind speed and slightly lower tip speed, the Run 8 data were not used in any further plots 

or analyses. 

Figure 20 plots the Mtip = 0.73 data (Run 7) against the data for Mtip = 0.68 (the same data as in 

Figure 12). Here, all data at a given Mtip have the same symbol. Also shown are ±2se uncertainty 

bands for the Mtip = 0.68 data (also the same as Figure 12). The data taken at the higher tip speed 

rarely fall outside of the uncertainty bands and then only at high thrust. 

Figure 19. Figure of merit (corrected for wind) versus thrust, Mtip = 0.73. 

 
27 

Figure 20. Figure of merit (corrected for wind) versus thrust for Mtip = 0.73 and Mtip = 0.68, with ±2se bands 

for Mtip = 0.68. 

Figure 21 shows a quadratic curve fit to ideal power, with ±2se uncertainty bands. The fit is 

directly equivalent to that of Figure 12 and Eq. 5 for Mtip = 0.68. The fitted equation for 

Mtip = 0.73 is 

3 3/2 =+ + 144.8 2 0.9037 2 0.01493 8 CC C PT T σ [9] 

The associated se = 0.00000533, about 0.28 percent of the maximum measured value of CP. The 

uncertainty is less than half that for Mtip = 0.68 (Eq. 5); the difference in standard errors is 

statistically significant. However, the range of thrust is narrower and there are fewer repeated 

runs. A run-by-run comparison would likely yield different results, but without an explicit 

understanding of the reasons for the higher scatter at the lower tip speed, definitive conclusions 

would be elusive. The results presented here accordingly do not prove that the data at Mtip = 0.73 

are somehow better than the data at Mtip = 0.68, although the former may be more pleasing to 

look at. Figure 22 replots the data as non-ideal versus ideal power (compare to Figure 13). 

Reference 1 includes an even smaller data set at Mtip = 0.60. There was only one thrust sweep, 

hence limited scope for examining repeatability and uncertainty. Accordingly, the data at 

Mtip = 0.60 are not examined here. 
28 

Figure 21. Quadratic curve fit of hover power (corrected for wind) versus thrust, converted to 

figure of merit, for Mtip = 0.73 with ±2se bands. 

Figure 22. Quadratic curve fit of hover power (corrected for wind) versus ideal power, converted to 

non-ideal power, for Mtip = 0.73 with ±2se bands. 
29 

CAMRAD II and U2NCLE Predictions for Hover 

With analyses of hover performance data in hand, meaningful evaluations of the accuracy of 

performance predictions can be made. References 4 and 5 presented CAMRAD II predictions of 

hover performance compared with selected JVX test data (wind <1 knot). The predictions were 

updated and plotted here against the expanded hover data set described previously. Plots of 

figure of merit versus thrust are preferred here because they emphasize the magnitude of any 

mismatch to the data, thus highlighting any differences. 

Inflow Models 

Figure 23 plots CAMRAD II predictions made using four different aerodynamic models: 

uniform inflow, blade element/momentum theory (BEMT), rolled-up free wake (single-tip 

vortex), and multiple-trailer wake (two outboard vortex trailers). Figure 23 also includes 

U2NCLE computational fluid dynamics (CFD) predictions (kindly provided by Dr. Chunhua 

Sheng). The CAMRAD predictions are essentially the same predictions as reported in 

reference 5, but plotted here against an expanded data set; the models are described in detail in 

reference 20. The uniform-inflow model used an induced velocity factor κ = 1.10, and the 

BEMT model used κ = 1.04. (In this context, the induced velocity factor is equivalent to the 

induced power factor C C Pi Pideal .) BEMT is implemented in CAMRAD as a differentialmomentum model and includes the Prandtl tip-loss correction (Eq. 3). The wake models used 

second-order lifting-line theory for the aerodynamic collocation points. CAMRAD used a 3D 

stall-delay model, discussed in the next section. The U2

NCLE predictions used the SpalartAllmaras detached eddy simulation (DES) model (ref. 6). 

To better reveal detail, Figure 24 is a simplified and rescaled version of Figure 23, but with ±2se

uncertainty bands from Eq. 5 instead of individual data points (the same as Figures 11–13). The 

uncertainty bands terminate at = 0.16 CT σ , the limit of measured thrust, beyond which the 

validity of the curve fit becomes questionable. 

The multiple-trailer predictions match the data very well and always fall within the ±2se bands, at 

least within the limit of measured thrust. The BEMT predictions are almost as good, and exceed 

the uncertainty bands only at very high and low thrust where there are relatively few data points 

to define the local trends. The uniform-inflow model is nearly as good as the BEMT model 

above = 0.06 CT σ , but falls below the measured data shortly below that thrust value. The 

uniform-inflow and BEMT models each required a different empirical induced velocity factor 

κ to match the data, so the good results do not indicate robust models. The BEMT predictions, 

for example, can be better matched to the data at high thrust by slightly increasing κ , but will 

then have a worse match at medium thrust. There is ample reason to believe that a wake model 

or CFD is required for a good fit to the data. 

 
30 

Figure 23. CAMRAD II predictions of JVX figure of merit with five aerodynamic models, compared with 

OARF test data. 

Figure 24. CAMRAD II predictions of JVX figure of merit with five aerodynamic models, compared with 

test data uncertainty. The ±2se bands are for the quadratic curve fit (Eq. 5). 

 
31 

The most surprising result is the relatively poor accuracy of the conventional rolled-up wake 

model. It exceeded the ±2se uncertainty bands more than any other model, although the trend of 

figure of merit at high thrust is better than either of the simpler models and matches the trend of 

the multiple-trailer model. The rolled-up model plotted here used a second-order lifting-line 

model for the blade aerodynamics (inner solution, see reference 20). The second-order model 

improved the match to data at high thrust, compared to the first-order model used in references 4 

and 5. However, figure of merit is still underpredicted at low-to-medium thrust. 

Considerable effort was put into refining the rolled-up wake model, but with little useful 

improvement to the predictions. Adjusting the radial location of the tip vortex, fraction of peak 

circulation entrained in the tip vortex, extent of initial wake convection, and other measures 

resulted in either small or inconsistent improvements. The only measure that made for a general 

improvement over a large range of thrust conditions was to reduce section cd by 0.002, which is 

a lower value of drag than expected. However, the JVX rotor was cleaned every day and 

operated only in low wind, so it is possible that some degree of laminar flow was achieved. The 

airfoil tables used by CAMRAD did not include this effect (assuming it did indeed exist). 

Figure 25 shows CAMRAD predictions with nominal drag and with all values of section cd

reduced by 0.002. The results are consistent with laminar flow at low thrust, changing to 

turbulent flow at high thrust. However, the multiple-trailer wake also gave good results at low 

thrust with nominal drag. The existence of laminar flow remains speculative. A constant 

reduction in cd, independent of both radius and thrust, is too crude an adjustment to constitute a 

reliable model. 

Figure 25. CAMRAD II predictions of JVX figure of merit with nominal and reduced section cd, 

compared with OARF test data. 
32 

Wake models need semi-empirical inputs such as core size, tip vortex radial location, etc., but 

once such parameters are established, wake models typically give good results over a wide range 

of operating conditions. The simpler models, notably BEMT, are much more computationally 

efficient than the wake models, and in this implementation proved more computationally robust. 

The multiple-trailer model in particular had major problems with convergence at very low thrust. 

Although more accurate than the rolled-up wake model, the multiple-trailer model requires an 

additional parameter: the radial location of the additional trailer. The model used here had a 

trailer at 0.8R, which Figures 23 and 24 show to be completely adequate. The predictions were 

little affected by variations in trailer location from 0.7 to 0.9R. The multiple-trailer model 

received much further tuning of various convergence parameters, but with little net effect on 

computational efficiency or accuracy. The multiple-trailer model has not proven robust for other 

rotors and is no longer being developed. 

Finally, the U2NCLE CFD predictions match the data nearly as well as the multiple-trailer 

model, except at high thrust where U2NCLE prematurely predicts stall. Given that the CFD 

predictions required far fewer empirical parameters, the achievement is quite impressive. 

Stall-Delay Models 

Reference 5 presents results for three different, 3D stall-delay models: the “Bell” model 

(ref. 24), the “Selig” model (ref. 25), and no stall delay. Those analyses were repeated, always 

using the multiple-trailer wake model, and are plotted in Figure 26 against the uncertainty bands 

from Eq. 5. It is evident that a stall-delay model is necessary at high thrust; it is also evident that 

the difference between the Bell and Selig models is much less than the uncertainty in the test 

data, except at low thrust where numerical problems begin to appear (off-scale in Figure 26). The 

near-coincidence of results of using the different stall-delay models is not surprising because 

they both incorporate empirical adjustments. Aside from Fig. 26, all CAMRAD predictions 

shown here used the Selig stall-delay model. 
33 

Figure 26. CAMRAD II predictions of JVX figure of merit with three stall-delay models. The ±2se bands 

are for the quadratic curve fit to data (Eq. 5). 

Reynolds Number Corrections 

The CAMRAD II aerodynamic model relies on externally supplied airfoil tables and optionally 

provides for corrections for Reynolds number effects. The airfoil tables used here were derived 

from 2D wind tunnel tests of full-scale V-22 airfoils (ref. 10). At 0.656 scale to the V-22, the 

JVX rotor should experience minor Reynolds number effects. Nevertheless, the CAMRAD II 

multiple-trailer model was run separately with corrections for turbulent flow, laminar flow, and 

no correction. 

From references 20 and 26, the corrections are implemented as 

cd = 1

KD

cd 2D [10a] 

cl = KLcl 2D (α /KL ) [10b] 

where K = (Re/Ret)

n

 . 

The 2D coefficients are those given in the airfoil tables. Here, KD = KL, and n = 0.2 (turbulent), 

0.5 (laminar); or 0 (no correction). The results are plotted in Figure 27, which shows that while 

the differences are detectable, they are less than the uncertainty in the test data, except at very 

low thrust where convergence problems begin to dominate (off-scale in Figure 27). Corrections 

for turbulent flow (n = 0.2) were used for all CAMRAD analyses unless explicitly noted 

otherwise. 
34 

Figure 27. CAMRAD II predictions of JVX figure of merit with three Reynolds number correction models. 

The ±2se bands are for the quadratic curve fit to data (Eq. 5). 

Wind Tunnel Data 

The wind tunnel tests used the same rotor and test stand as the hover tests, but with a revised cuff 

on the inboard section of the blade, nearest the spinner (Fig. 2). The same rotor balance was used 

for the wind tunnel tests as for the hover tests. There is no reason to suspect that conversion from 

physical units to rotor coefficients would introduce any changes to the statistics worse than those 

in the hover data. Therefore, the analyses of wind tunnel data were usually done in terms of rotor 

coefficients. 

Crosswind corrections do not apply to the wind tunnel data. The nonlinearities seen at very low 

hover thrust data are not evident in the wind tunnel data and would not be expected for such test 

conditions (minimum speed, 99 knots). Therefore, the process for deleting non-representative 

data was not needed for the wind tunnel data. 

The Phase II data presented here differ from those reported in references 4 and 5 in two ways: 

different spinner drag tare corrections are used, and the thrust is recomputed without any 

adjustment for torque/thrust interaction. An effective spinner drag area of 0.901 ft2 was applied 

to the balance data to generate net rotor thrust. Deleting the torque/thrust interaction gave results 

that matched the Phase I data. 

 
35 

A summary of the Phase II rotor performance data is presented first, including CAMRAD II 

predictions. Discussions of spinner tares and torque/thrust interaction follow, including selected 

Phase I performance data. Next is a deeper look at rotor performance, including data consistency 

and regression analyses. The discussion of wind tunnel data closes with a comparison of 

CAMRAD II predictions to those of U2

NCLE, an independent CFD analysis. 

More detailed discussions of spinner tares, including the (unsuccessful) use of internal pressure 

data, are included in Appendix B. Justification for rejecting the recommendations of reference 2 

are also included. 

A simple analysis of wind tunnel blockage effects is given in Appendix C. The effects are small 

for the range of operating conditions reported here. No corrections for blockage are used 

elsewhere in this report. 

Numerical tables of the data presented in this report are included in Appendix D. 

Summary Rotor Performance Data 

The 40x80 wind tunnel airplane-mode data were taken at several different tunnel wind speeds 

but only two tip speeds. The JVX rotor tests typically varied thrust at a fixed tunnel speed and 

rotor tip speed. The resulting data group into five speeds, from μ = 0.263 to μ = 0.562, listed in 

Table 5. All data at μ = 0.523 and below were taken at about 487 rpm, but the data at μ = 0.562 

were taken at 531 rpm. There were no data points at the same tunnel speed but different tip 

speeds. 

The JVX airplane-mode data are plotted as propulsive efficiency η versus thrust CT/σ in 

Figure 28. No single advance ratio μ has data that span the full range of thrust. In Figure 28, the 

data points are offset in CT/σ by multiples of 0.01 to make the trends easier to see. CAMRAD II 

predictions of rotor performance are also plotted. The same data are plotted in Figure 29 as 

power CP/σ versus CT/σ, here without any plotting offsets. The data use a spinner drag tare of 

0.901 ft2

 and do not include any torque/thrust interaction corrections. The justifications for using 

the stated spinner tare and for omitting the torque/thrust interactions are discussed at length 

following the summary data plots. 

Table 5. Mean test conditions for JVX wind tunnel data, with standard deviations. 

Vtip and Mtip are nominal hover values. 

μ Ω Vtip Mtip V sd (μ) sd (Vtip) sd (V)

(rpm) (ft/sec) (knots) (ft/sec) (knots)

0.210 487 638 0.57 99 0.0009 1.9 0.4 

0.349 489 640 0.58 132 0.0009 1.7 0.5 

0.438 489 641 0.58 166 0.0015 2.0 0.4 

0.523 491 642 0.58 199 0.0018 1.9 0.3 

0.562 531 695 0.63 231 0.0007 1.1 0.2 
36 

The CAMRAD predictions in Figures 28 and 29 used a free-wake model equivalent to the rolledup model used for hover (Figs. 23–27). Three-dimensional stall delay is not important at the low 

blade-lift coefficients typical of airplane mode at high speed, so no stall-delay model was used. 

The multiple-trailer model was not considered here, because blade-vortex interaction does not 

occur in high-speed axial flow, even at low thrust. There is, therefore, no advantage to be gained 

from higher-order wake models. The CAMRAD analysis used airfoil section drag coefficients 

adjusted by −0.002. The drag adjustment is discussed in a later section, Additional CAMRAD II 

Predictions. That section also compares CAMRAD with U2

NCLE predictions. 

Reference 15 reported higher values of propulsive efficiency for the XV-15 rotor. However, the 

XV-15 had 22 percent lower solidity than the JVX rotor and was operated at tip speeds as low as 

400 ft/sec (compare Table 5). Both of these differences should substantially improve propulsive 

efficiency. 

Figure 28. Measured JVX rotor propulsive efficiency from the NFAC Phase II test. 
37 

Figure 29. Measured JVX rotor power from the NFAC Phase II test. 

JVX Spinner Tares 

This section documents the selection of a recommended value of JVX spinner drag tare. See 

Appendix B for discussion of alternative analyses of spinner drag. For this report, “spinner” 

refers to the entire fairing around the hub, including an ogival cone upstream of the hub and a 

skirt fairing immediately behind the cone (Fig. 30). The seam between the cone and skirt is 

barely visible in the photo. The cone and skirt rotated with the hub but did not gimbal. The skirt 

had oblong holes to accommodate the pitch and flap motions of the blade shanks and spindles. 

Figure 30. Close-up of the JVX rotor on the PTR in the OARF test configuration. 
38 

Figure 31. The JVX rotor on the PTR with the wing in airplane mode. 

A limited amount of spinner tare data were taken during the Phase I wind tunnel test. Data were 

taken with the rotor blades removed over a range of airspeeds from 131 to 238 knots. With one 

exception, the spinner was always rotating at 495 rpm. Data were taken at three different yaw 

(ψs) angles: 0, −3, and −6 deg (rotor shaft yaw, set by the tunnel turntable). No equivalent tare 

data were taken during the Phase II test database. All spinner tare data were taken with a wing 

installed in airplane mode (Fig. 31), but the wing was sufficiently far behind the spinner that 

interference effects can be assumed to be negligible. 

The Phase I spinner tare data are plotted in Figure 32, in units of drag versus tunnel dynamic 

pressure q0. The data fall into three distinct, narrow bands, one for each yaw angle. The data 

point at 52 rpm, ψs = −6 (marked with a solid symbol in the plot), is slightly off the trend for the 

495-rpm data, but a solo data point is insufficient for judging sensitivity to rpm. 

The trends are highly linear and apparently closely similar. Linear curve fits to the 495-rpm data 

yield the following equations: 

ψs = 0 deg: 2 Drag 0.901 ft 6.25 lb = +0 q r

2

 = 0.99222 

ψs = −3 deg: 2 Drag 0.876 ft 14.83 lb = +0 q r

2

 = 0.99734 

ψs = −6 deg: 2 Drag 0.912 ft 16.77 lb = +0 q r

2

 = 0.99836 

where r

2

 is the correlation coefficient. For clarity, only the fit to ψs = 0 deg is shown in 

Figure 32. The intercepts differ from zero by less than the claimed accuracy of the balance 

(refs. 1 and 11). 
39 

Figure 32. Phase I spinner tare data, plotted as raw drag versus q0. 

The drag values are lower than those of references 4, 5, and 15. For the data presented in this 

report, the spinner drag tare is taken from the curve fit to the data at zero yaw angle, but without 

any zero offset. Hence the equivalent flat-plate drag tare ASP = 0.901 ft2, which is less than the 

plotted values in reference 15. That report is for a full-scale test of the XV-15 rotor, which used a 

hub and spinner identical to those used for the JVX test. For the data presented in this report, 

ASP = 0.901 ft2 resulted in calculated spinner drag as high as 23 percent of the measured axial 

load. 

The spinner was instrumented with internal pressure transducers, but the pressure data were 

questionable and were not used here. The spinner tares used here are accordingly different from 

those of reference 2. See Appendix B for further discussion of spinner pressures. 

A complication is the somewhat imprecise definition of “spinner drag.” Reference 15 (Fig. IV-6) 

gives limited data for three different XV-15 blades-off configurations: with spindles; without 

spindles, spinner openings covered; and without spindles, openings uncovered. The spinner 

radius is 13.63 in. at the base, and slightly less at the spindle holes. The spindles project about 

5 in. beyond the spinner surface; each spindle diameter is about 4 in. at the outboard end. 

Dimensions are approximate because of the compound curve of the spinner and the nonuniform 

taper of the spindles. The spindles add about 0.3 ft2

 to the spinner drag area, relative to the drag 

with spindle holes closed (ref. 15). 

The data presented in Figure 32 with spindles exposed roughly match the data in reference 15 

with the spindles removed. The reason for the discrepancy is unknown. However, the data in 

Figure 32 were taken from the onboard rotor balance, whereas the data in reference 15 were 

taken from the tunnel scales. Reference 15 does not describe how XV-15 spinner tares were 

distinguished from total installation tares. The rotor balance used for the JVX tests directly 
40 

measured the spinner loads transferred to the rotor shaft, so its data should be more reliable at the 

low drag levels characteristic of spinner tares. 

When the blades are installed, the spindles are almost entirely enclosed within the blade shanks. 

A spindle is just barely visible for the lower JVX blade in Figure 30. The effect on spinner tares 

of the different root shapes for the JVX and XV-15 blades is unknown. 

The assumptions underlying the use of spinner drag ASP = 0.901 ft2

 can be summarized as 

follows: (1) the data from the JVX Phase I test are more accurate than the XV-15 data at the 

measured levels of spinner drag; (2) the wing had a negligible effect on spinner drag; and (3) 

installation of the rotor blades had negligible effect on spinner drag. The last statement has three 

supporting assumptions: the shorter but thicker blade shanks contributed the same net drag as the 

spindles, aerodynamic interference from the blade root section was small, and the blades did not 

change the internal spinner pressures. 

Torque/Thrust Interactions 

In the original JVX database, the rotor balance data were corrected for residual rotor shaft axial 

thrust with an equation of the following form: 

 [11] 

where Xc is the corrected X-force (thrust), Xb is the X-force measured at the balance, Xs is the 

residual shaft thrust, KTQ is the thrust/torque correction coefficient, and Qs is the raw shaft 

torque. Spinner drag corrections are accounted for separately. The accuracy of the X-force 

corrections, as applied to the Phase II database, is thrown into question by the following analysis. 

In order to check for the possibility of incorrect values of thrust, CAMRAD II predictions of 

JVX performance were trimmed to the values of torque measured at each wind tunnel data point, 

with airfoil section drag cd adjusted by −0.002. The difference between measured and predicted 

thrust is plotted at each data point in Figure 33. The CAMRAD free-wake model was used here, 

but the results are barely distinguishable from those obtained with a BEMT analysis. BEMT is 

too well-proven for those predictions to be easily discarded as erroneous. The good consistency 

between aerodynamic models is an important justification for the assumptions made here. See 

also the discussion of U2

NCLE predictions in the section “Additional CAMRAD II Predictions.” 

Figure 33 shows a clear trend of thrust difference versus torque. Without the cd adjustment, the 

data are shifted downwards but with little change in slope. A linear curve fit yields a slope of 

−0.0080 lb/ft-lb. The value of KTQ used to generate the database was −0.0086 lb/ft-lb; the slope 

of the plotted data is not significantly different from KTQ (per a t-test at the 5-percent level). 

Xc = Xb + Xs − KTQQs
41 

Figure 33. Difference between predicted and measured thrust versus torque. 

There is a discernible variation in slope with advance ratio, but the variation is consistent only 

for the data taken at 489 rpm (μ < 0.562). The slope at the highest μ is similar to that at the 

lowest μ. For all but the μ = 0.532 data, the slopes vary linearly with both tunnel velocity and air 

temperature (not shown here). Unfortunately, there are no data for balance or rotor shaft 

temperature, so it is not possible to separate residual aerodynamic effects from thermal effects on 

instrumentation. 

The data at different advance ratios were not all taken during the same test run. Table 6 lists the 

data runs for each advance ratio. The only subset that includes data from Run 8 is μ = 0.263, and 

μ = 0.523 is the only subset with data from Run 9. Figure 33 shows that these are the two 

advance ratios with the largest difference in slope. This raises further suspicion of an 

instrumentation problem or thermal effect, but it falls far short of proof. 

There is no evident aerodynamic mechanism that can explain these results. An error in 

computation of induced power could result in an error that varies linearly with torque, but such a 

close match to KTQ would be a remarkable coincidence. An error in predicted rotor drag, hence 

profile power, such as might be caused by an error in the airfoil tables, would vary with both 

airspeed and tip speed. An error in spinner drag would vary strongly with airspeed. 

Table 6. Data runs for each value of advance ratio. 

μ Data Run 

0.263 4, 8 

0.349 4 

0.438 4 

0.523 5, 9 

0.562 5 
42 

A more likely explanation is that the thrust/torque correction was improperly applied to the data, 

or possibly that the measurements of residual shaft thrust were inaccurate. The numerical 

equivalence of the slope in Figure 33 and the database value of KTQ is telling. 

Not all intermediate values of balance data and corrections were recorded in the OARF hover 

database, so the thrust for the OARF tests cannot be corrected in exactly the same manner. The 

shaft torque Qs is itself subject to corrections for thrust/torque interaction and bearing friction, 

which should not be applied to KTQ. The torque data have these corrections. An approximate 

correction would simply add KTQ times torque (as corrected) to thrust, which for a negative value 

of KTQ will reduce figure of merit. The result would be a worse match to the CAMRAD II 

predictions for high-speed data, but a better match to the wind tunnel hover data (see Fig. A-1). 

The wind tunnel hover data should be less accurate than the OARF data, so a better match would 

not necessarily be an improvement. Accordingly, all OARF data presented here use rotor thrust 

exactly as in the database. The possibility remains that the OARF data are less accurate than 

thought, and the wind tunnel hover data more accurate, but this is highly unlikely. 

The flex coupling had multiple strain gages. A different set was used for Phase II, compared to 

the Phase I wind tunnel test and the OARF hover test. This could explain why the problem—

assuming it is real—was seen only in the Phase II data. The counterpart to KTQ, the thrust/torque 

interaction KQT, was nearly the same for Phase I and Phase II: 0.2089 versus 0.2143 ft-lb/lb, 

respectively, a difference of less than 3 percent. In contrast, the Phase I and Phase II values of 

KTQ differed by nearly a factor of 4: −0.0023 versus −0.0086 lb/ft-lb, respectively. 

There are too little data in the Phase I wind tunnel test to check the KTQ adjustment in the manner 

of Figure 33. No correction to KTQ was applied to the spinner tare data. However, the spinner 

drag data were taken at extremely low torque, therefore terms in KTQ should have negligible 

effect on spinner tares. 

Further justification for doubting the database value of KTQ is given by Figures 34 and 35, which 

compare the Phase I results with KTQ with those of Phase II without KTQ. During Phase I, few 

data points were taken at the same values of tip speed as during Phase II, and fewer still where 

thrust was varied systematically at constant values of tip speed and tunnel speed. There were 

only two advance ratios at which the Phase I and Phase II data had the same tip speed, and even 

here, neither μ nor Mtip quite match for the two data sets. Table 5 gives the values for the Phase II 

data, and Table 7 gives the equivalent data for the Phase I data plotted in Figures 34 and 35. For 

ease of comparison, the figures show only the data at Mtip = 0.58. 

Table 7. Mean test conditions for JVX Phase I wind tunnel data, with standard deviations. 

Vtip and Mtip are nominal hover values. 

μ Ω Vtip Mtip V sd (μ) sd (Vtip) sd (V)

(rpm) (ft/sec) (knots) (ft/sec) (knots)

0.210 494 646 0.57 80 0.0005 2.7 0.2 

0.259 497 650 0.57 100 0.0011 0.7 0.3 

0.344 497 650 0.57 132 0.0002 1.4 0.3 

 
43 

Figure 34. Rotor propulsive efficiency from the Phase I and Phase II tests at Mtip = 0.58. 

Figure 35. Rotor power from the Phase I and Phase II tests at Mtip = 0.58. 

Figure 34 plots propulsive efficiency versus thrust, here without any plotting offsets (compare 

Figure 28). Collapsing the data emphasizes that the Phase II trends of μ versus thrust are similar 

for all advance ratios at the given tip speed (Mtip = 0.58). The trends for the Phase I data are not 

as consistent, but at least some of the variation may be caused by disparities in operating 

condition. The Phase II data lie roughly within the bounds of the Phase I data, but this is hardly a 

rigorous comparison, again considering the imperfectly matched operating conditions. 

Nevertheless, the two data sets, generated with the same assumptions of spinner drag but 

different assumptions of torque/thrust interaction, give very similar results. 
44 

Figure 35 plots power versus thrust, including the two advance ratios from Phase I that match 

test conditions in Phase II. A difference in slope is discernible at both advance ratios where the 

data overlap. The data at μ = 0.349 were analyzed in more detail by curve fits to ideal power. 

The analysis was limited to μ = 0.349 because that is the only advance ratio at which both tests 

had more than two data points. Given fixed Mtip and μ, power should vary as P = T(V+v), which 

at the low levels of thrust seen here is close to CP = μCT, plus a constant term for profile power. 

(This analysis is developed more fully in the section “Regression Analysis,” later in this report.) 

Comparing the Phase I and Phase II curve fits, the ratio of the slopes was less than the ratio of μ, 

and both ratios were less than the standard error of the slopes. Therefore, the difference in slope 

can be fully explained by the difference in μ. 

Furthermore, there is one data point, at μ = 0.349 and CT/σ = 0.022, at which tunnel velocity 

matches within 0.02 percent, and Phase II thrust and torque are both less than 

1 percent lower than the Phase I data. At that operating condition, Phase II tip speed is lower 

than Phase I by 1.4 percent, hence μ and η are slightly higher, as shown in Figure 34. Even 

though the match is imperfect, the variations are all small and consistent, so there is no evident 

bias in either thrust or power. 

The preceding argument rests on a handful of data points at a single combination of Mtip and μ, 

and at the extreme compares one data point from each of the two tests. This is hardly a rigorous 

analysis, but unfortunately the two data sets are not sufficiently well-matched to allow much 

improvement. Nevertheless, inspection of Figures 34 and 35 shows that the data are closely 

similar if the Phase I data use the nominal value of KTQ and the Phase II data use KTQ = 0. 

There are physical reasons to expect that the flex coupling will exhibit torque/thrust interactions 

under high strain. If the strain gages were perfect, then KTQ would be an exact measure of 

material strain effects, and the same coefficient could be used for both Phase I and Phase II data. 

However, KTQ necessarily includes the imperfections of the strain gages, and the same coefficient 

should not be applied to data from different strain gages. 

If the nominal value of KTQ = −0.0086 is applied to the Phase II data, the result is much higher 

propulsive efficiency, as high as η = 0.93. This value is almost as high as the maximum value 

for the XV-15 data (ref. 15), but taken at a higher tip speed and with a higher solidity rotor. Such 

an improvement strains credibility, and the Phase I and Phase II data cannot possibly match if the 

nominal values of KTQ are applied to both data sets. Accordingly, the torque/thrust interaction 

term was not applied to the Phase II data reported here. Enough data are given in Appendix D to 

recompute thrust with the nominal interaction, or any other value of KTQ, should the reader so 

choose. 

While these results do not prove the existence of a misapplied thrust/torque interaction for 

Phase II, the excellent match between predictions and wind tunnel data (as corrected), and 

between the two different tests, cannot be lightly dismissed. It would be of questionable 

legitimacy to derive a new value of KTQ using CAMRAD II predictions. Nevertheless, 

CAMRAD proved useful for revealing the torque/thrust correction as the likely source of the 

discrepancy between Phase I and Phase II. The results shown here may point the way towards 
45 

more extensive data-consistency checks that could be applied during future rotor tests, in hopes 

of early detection and correction of errors in data acquisition and processing. 

Data Consistency 

Data consistency was examined for the two advance ratios with the most data points. For 

μ = 0.263 and μ = 0.523, there were two separate runs with repeated data at most thrust 

conditions, as shown in Figure 36. Shaft torque and measured drag are plotted without any 

adjustments for spinner tares: the data include only balance and torque calibration corrections, 

without the torque/thrust interaction term. Nor were the data converted to rotor coefficients, so 

the plotted points are as close as practical to raw balance data. Total drag, as measured by the 

balance, includes spinner drag, so measured drag is zero when rotor thrust equals spinner drag. 

At a given tunnel speed, spinner drag is constant and does not affect the run-to-run comparisons 

discussed next. 

The data in Figure 36 match closely at each advance ratio and are highly linear. At a fixed tunnel 

speed and rotor tip speed, power, hence shaft torque, should include a constant contribution of 

profile power and a linearly varying contribution of induced power. Linear curve fits determined 

the slopes and intercepts separately for the two runs at each advance ratio. None of the 

differences between runs at a given advance ratio were statistically significant. For all four curve 

fits, the worst-case correlation coefficient was 0.9995. 

Strictly speaking, neither shaft torque nor rotor drag is an independent variable: both are 

functions of collective. Hence the simple regression analysis summarized here is not as rigorous 

as might be desired. Nevertheless, the measurements showed excellent linearity and consistency. 

The intercepts, in terms of thrust, varied less than the claimed accuracy in thrust measurement 

(refs. 1 and 11). Similar results were obtained if the torque/thrust interaction was included. 

Summarizing, the measurements were acceptably repeatable from run to run and from point to 

point. 

Figure 36. Measured JVX shaft torque versus rotor drag sorted by run. 
46 

Regression Analysis 

Following the same general procedure as applied to the hover data, a regression analysis was 

used to estimate the uncertainty in the wind tunnel data. Measured JVX rotor power is plotted 

against thrust in Figure 37. A linear curve fit to ideal power and profile power factor is also 

shown (equations are given later in this section). Figures 38 and 39 show the curve fit converted 

to propulsive efficiency and non-propulsive power, respectively (conversions provided later). 

The scales are expanded to more clearly show the data points. For Figure 38, the data points are 

offset in CT/σ by multiples of 0.01 to make the trends easier to see. The plot of non-propulsive 

power (Fig. 39) better reveals the nonlinear trends in the data. 

In high-speed axial flight, the induced power is low but not zero. The total rotor power comprises 

the propulsive power TV, induced power Tv, profile power P0, and possibly parasite power from 

hub drag, depending on how drag tares are accounted for in the data processing. Following 

reference 19, the ideal or minimum possible power Pm can be defined as 

 [12a] 

or 

 [12b] 

Equation 12 is based on the same physical considerations as those of Eq. 1, but adds the effects 

of axial flow. 

Figure 37. Curve fit to measured rotor power from the NFAC Phase II test. 

 

Pm = T(V + v) = T V

2

+

V

2





 





2

+

T

2ρA

















CPm = CT

2 μ + μ2 + 2CT



 
47 

Figure 38. Curve fit to measured rotor power, converted to propulsive efficiency. 

Figure 39. Curve fits to measured rotor power, with propulsive power subtracted. 

If v<<V, Pm is nearly linear in T. However, the induced power term is physically important and 

statistically significant. A linear fit to CT at one airspeed can give good results only for that 

airspeed. The curve fit shown here includes all terms in Eq. 12. Non-ideal power (Fig. 40) is 

simply measured CP/σ–CPm/σ; note that propulsive power μCT/σ has also been subtracted 

(compare with Figure 39). 

To account for the effects of airspeed, a profile power term must be added. Using the notation of 

reference 19, the equation can be written as 
48 

, [13] 

where cdmean is the mean blade section drag coefficient and the function FP accounts for the 

increase in blade section velocity as V increases: 

 [14] 

(compare Eq. 6; see also reference 2). For the data plotted here, FP ranges from 1.225 to 2.259. 

Equation 14 is physically exact for a constant cdmean. The twist distribution of the JVX rotor is a 

compromise between hover and airplane-mode performance. There is no guarantee that all blade 

sections will always operate near cd0, hence cdmean is not necessarily constant with airspeed. 

Nevertheless, Eq. 14 gives good results, as shown in Figures 37–40, with the exception of the 

highest advance ratio. 

Figure 37 shows a multiple-linear curve fit to measured CP/σ with CPm/σ and FP as the 

independent variables; Figure 38 shows the same fit, converted to propulsive efficiency

= = / / η μ TV P C C T P . Figures 39 and 40 respectively plot the fit as non-propulsive power 

CP/σ–μCT/σ and non-ideal power CP/σ–CPm/σ. The latter figure shows the effects of profile 

power plus non-ideal induced power. 

The regression analysis used exact values of μ and Fp, but the plotted curve used averaged values 

of μ and Fp for smoothing. Except where noted, there is only one curve fit, derived from the 

entire data set. It plots as multiple lines because it includes terms in μ (Eq. 14). 

Figure 40. Curve fits to measured rotor power, with ideal power subtracted. 

CPo = (σ /8)cd meanFP

FP = 1+ μ2 1+ 5

2 μ2

( ) + 3

2 μ4 ln 1+ μ2 +1

μ
















49 

The curve fit plotted in Figures 37–40 is 

CC F P Pm P / 1.049 / 0.001632 0.001136 σ σ = +− [15] 

with a standard error se(CP/σ) = 0.000125. This is 0.46 percent of the maximum measured value 

of CP/σ. The intercept is not significantly different from zero. For comparison to hover, the 

uncertainty can be expressed in terms of CP: se(CP) = 0.0000143. The standard error is slightly 

greater than that for the quadratic fit to hover data (Eq. 5). The coefficient of FP is equivalent to 

mean = 0.01306 d c . 

Figure 40 reveals the non-ideal power trends versus thrust; that is, the power not explainable by 

momentum theory. Comparing Figure 37 with Figure 40, non-ideal power is an order of 

magnitude less than measured power. Subtracting both propulsive power and ideal induced 

power results in a series of linear trends with airspeed (compare with the nonlinear trends in 

Figure 39). The vertical offsets of the trend lines represent profile power that is essentially 

constant at any given airspeed, and the linear trends represent non-ideal induced power, or thrust 

multiplied by non-ideal induced velocity. 

A slightly nonlinear trend can be seen in the data at μ = 0.263, notably above CT/σ = 0.06. There 

is no physical requirement for the losses to be perfectly linear with thrust (a linear variation 

would imply constant induced velocity). Only one other advance ratio, μ = 0.349, has any data at 

CT/σ >0.06, and only two data points at that. Unfortunately, the limitations of the data do not 

encourage further refinement of the analysis in the manner done for hover data. 

Figure 40 also reveals that the data at μ = 0.438 have high scatter, and the data at μ = 0.562 

appear to follow a different trend than predicted by Eq. 15. The JVX data at μ = 0.562 are 

problematic, simply because the average tip speed is different from that at all other data points 

(695 ft/sec versus 641 ft/sec), and because there are so few data points at that speed. Any curve 

fit will best fit the test conditions with the most data points, so the regression lines should not be 

expected to closely follow the data at μ = 0.562. 

Re-running the regression analysis of Eq. 15, but without the data at μ = 0.562, resulted in a 

standard error se(CP/σ) = 0.0000920. The difference with respect to the fit with the high-speed 

data is statistically significant, despite the reduced degrees of freedom. This result implies that 

the data at maximum speed contribute a disproportionate amount of uncertainty. 

Two advance ratios, μ = 0.263 and μ = 0.523, each contain considerably more data points than 

the others, making these data subsets useful for more detailed comparisons. Curve fits to these 

data subsets were performed separately at each advance ratio, using only CPm/σ as the 

independent variable. There was a slight improvement in standard error for each fit, compared to 

the fits shown in Figures 37–40 and Eq. 12, but the differences were not statistically significant. 

While the scatter in the data at each advance ratio may possibly be less than the aggregate for all 

data points, the reduction in degrees of freedom for separate fits will adversely affect the 

uncertainty. For this reason, all following comparisons are based on the global curve fit to the 

entire data set, as given in Eq. 12, unless otherwise noted. 
50 

In order to better reveal the data, Figures 41 and 42 re-plot the curve fit of Figure 37 for the two 

values of μ with the greatest number of points. Also plotted are ±2se uncertainty bands. 

Uncertainty bands are potentially misleading for values of thrust outside the range of the data, 

and are therefore extended only slightly beyond the data in the figures. The thrust scale of 

Figure 41 is twice that of Figure 42. All but one data point fall within ±2se of the global fit. 

For these two figures, the uncertainty bands are the standard errors of CP/σ converted to 

= / η μC C T P . The advance ratio in Figure 42 is almost exactly twice that of Figure 41, but the 

efficiency is similar. At the same value of CT/σ, the μ = 0.523 data has about twice the value of 

CP/σ. Therefore, a constant value of se plots as uncertainty bands with about half the vertical 

spread as those for μ = 0.263. 

Figures 43 and 44 show the prediction interval (P.I.) and the confidence interval (C.I.) for the 

same curve fit as in Figures 41 and 42, converted to η. The thrust scale of Figure 43 is twice that 

of Figure 44. The prediction interval is the uncertainty in the prediction of a given data point, 

whereas the confidence interval is a measure of uncertainty in the regression line. The prediction 

interval is similar to the standard error, but takes into account the increase in uncertainty with 

distance from the mean value of the independent variable. For the data in Figures 43 and 44, the 

prediction interval is comparable to the standard error. 

Figure 41. Uncertainty bands (±2se) for propulsive efficiency at μ = 0.263 with ±2sd (cd0) bands. 

 
51 

Figure 42. Uncertainty bands (±2se) for propulsive efficiency at μ = 0.523 with ±2sd (cd0) bands. 

Figure 43. Curve fit of power at μ = 0.263, converted to propulsive efficiency, with confidence and 

prediction intervals. 

 
52 

Figure 44. Curve fit of power at μ = 0.523, converted to propulsive efficiency, with confidence and 

prediction intervals. 

The relative importance of uncertainty in the airfoil performance may be evaluated by following 

the same procedure used for hover. Substituting sd (cd0) into Eq. 13 gives an estimated ∆CPo, 

which can be readily converted to an equivalent ∆η. In Figures 41 and 42, the estimated 

uncertainty in η due to airfoil properties, ±2sd (cd0), is plotted with the ±2se bands due to 

uncertainty in measured power (from Eq. 15). 

Any uncertainty in drag will have a larger effect on power at high speed than at lower speed. At 

μ = 0.263 (Fig. 41), the uncertainty in airfoil drag sd(cd0) is nearly the same magnitude as the 

uncertainty of the curve fit se(CP). This result is similar to that for hover (Fig. 18). At twice the 

airspeed, μ = 0.523 (Fig. 42), the uncertainty in drag is about twice the uncertainty of the curve 

fit. 

For the JVX Phase II data, the maximum helical Mach number at 0.75 R was 0.59, which is 

comfortably below drag divergence for the XN-12 airfoil at that radial station (ref. 27). Had the 

maximum airspeed been higher, drag-divergence effects might have become important, at least at 

high rotor tip speeds. Reference 21 presents statistics for drag divergence, which could usefully 

be compared to future high-speed test data. 
53 

Additional CAMRAD II Predictions 

CAMRAD II predictions of rotor performance are plotted in Figures 28–29, all made with the 

rolled-up free-wake model and cd adjusted by −0.002. Figures 45 and 46 expand the scale and 

add the uncertainty bands of the curve fits to the wind tunnel data (Eq. 15). These plots include 

the advance ratios with the most data points (μ = 0.263 and μ = 0.523). The uncertainty is 

expressed as ±95 percent prediction intervals. 

The uncertainty bands shown in Figures 45 and 46 are those for the multiple-linear curve fit to 

the entire data set (Eq. 15) and do not perfectly capture the trend for any given advance ratio. 

The discrepancy is most obvious at high CT/σ and low μ (Fig. 45). 

Also shown are CAMRAD predictions with a uniform-inflow model. Predictions were made 

with a blade element/momentum theory (BEMT); they are not shown because they vary from the 

free-wake predictions by barely more than one line width at most. At μ = 0.523, the CAMRAD 

predictions closely follow the data and always fall within the uncertainty bands. At μ = 0.263, 

the CAMRAD predictions exceed the uncertainty bands at high thrust, although CAMRAD 

follows the nonlinear trend in the data. 

The uniform-inflow and BEMT models require empirical adjustments to the inflow velocity, 

expressed as the induced power ratio κ. To match the free-wake predictions, BEMT required 

κ = 1.25 at μ = 0.263 and κ = 1.60 at μ = 0.263. In contrast, the free-wake model requires no 

empiricism in the calculation of induced velocity and was therefore used for all airplane-mode 

predictions in this report, except as noted in Figures 45 and 46. The free-wake model does allow 

for empirical adjustments to the tip vortex model, particularly the core size and radial location. 

The analyses done for this report used the CAMRAD II default values of core size (20 percent 

mean chord) and recommended values of radial location (98 percent radius), although the 

predictions showed little sensitivity to these two parameters. The low sensitivity to the wake 

model is expected at high axial velocity. See references 20 and 28 for details of the CAMRAD II 

wake model. 

The uniform-inflow model appears to follow the data better than the free-wake model, but that 

was achieved only by adjusting κ. In Figures 45 and 46, the uniform-inflow model required 

κ = 1.7 at μ = 0.263 and κ = 5.5 at μ = 0.263. The very large value of κ required at low μ

suggests that the uniform-inflow model has reached the limits of its validity. Further 

optimization of κ should yield a better match of BEMT to the data, or uniform inflow to the free 

wake, but no further effort was made here to improve what are, after all, purely empirical 

adjustments. 

 
54 

Figure 45. CAMRAD II predictions of JVX propulsive efficiency at μ = 0.263 with data 

uncertainty bands. 

Figure 46. CAMRAD II predictions of JVX propulsive efficiency at μ = 0.523 with data 

uncertainty bands. 

With the data and uncertainty bands plotted on the expanded scales of Figures 45 and 46, it is 

evident that the curve fit of Eq. 15 does not fully capture the trends in the data, particularly at 

low μ and high CT/σ. While extending the regression analysis to higher orders of the independent 

variables is possible, it is not recommended here because of the limited data set. Figure 40 shows 

that the scatter at μ = 0.438 is large, and the range of thrust at μ = 0.438 and μ = 0.562 is small. 

Furthermore, there are very few data points at Mtip = 0.63 (μ = 0.562). For these reasons, it is 
55 

highly unlikely that a more elaborate regression model could better capture the trends with thrust 

or tip speed. 

CAMRAD allows for different Reynolds number corrections to be applied to the input airfoil 

coefficients; details of the correction method are given at the end of the discussions of hover 

data. Unless otherwise noted, the turbulent correction (Eq. 10, n = 0.2) was used for all 

CAMRAD predictions. Figure 47 shows predictions made with the same three models as were 

applied for hover, but here applied at μ = 0.263 and μ = 0.523. No adjustments were made to 

section cd, in contrast to all previous plots of CAMRAD predictions for axial-flow conditions. 

Data and predictions at μ = 0.523 are offset vertically by –0.01. It is clear that the predictions 

fall short of measured rotor performance, and that Reynolds number corrections can only 

partially account for the shortfall. 

CAMRAD and U2

NCLE predictions for axial flow are compared in Figure 48. No adjustments 

were made to section cd for either code. As in Figure 47, the CAMRAD predictions in Figure 48 

used a free-wake model with a turbulent Reynolds number correction. The U2

NCLE predictions 

used the Steady DES turbulence model (ref. 6). 

The CAMRAD and U2NCLE predictions match each other very well, especially at high speed. 

However, neither code predicts performance as well as the CAMRAD predictions with 

∆cd = −0.002; this holds true for free-wake, BEMT, and uniform-inflow models. The two codes, 

CAMRAD and U2

NCLE, were independently developed and their rotor models independently 

constructed. Furthermore, CAMRAD relies on external airfoil tables for blade section 

aerodynamics, here based on 2D wind tunnel test data, in contrast to U2NCLE, which is a CFD 

code. The likelihood of both sets of predictions having identical errors is small. 

Figure 47. CAMRAD II predictions of JVX propulsive efficiency with three Reynolds number 

correction models. 
56 

Figure 48. CAMRAD and U2NCLE predictions of JVX propulsive efficiency in axial flow. 

There remains the possibility that the rotor experienced some degree of laminar flow during the 

test that would explain the mismatch for both codes. The rotor blades were cleaned every day, 

and were operated inside a closed-circuit wind tunnel and thereby protected from the elements. 

Laminar flow over some portion of the rotor is entirely possible, and would not be properly 

represented in the airfoil tables, and conceivably not by the aerodynamic representation within 

U2NCLE. Furthermore, the results for hover are also consistent with partial laminar flow and 

section cd reduced by 0.002 at low thrust (Fig. 25). It is unreasonable to expect the extent of 

laminar flow, both chordwise and spanwise, to be constant at all flight conditions. Therefore, a 

uniform adjustment in cd is unlikely to be an accurate model; it is merely the simplest adjustment 

that gives good results. 

Conclusions 

Test data for the Joint Vertical Experimental (JVX) rotor were extensively reviewed. The data 

were taken on the OARF and in the NFAC at NASA Ames Research Center and included hover 

and high-speed cruise conditions (all axial flow). The great majority of the hover data were taken 

on the OARF; a much smaller data set was taken in the 40x80 wind tunnel test section. The highspeed data reported here were largely taken during the Phase II wind tunnel entry, with a limited 

amount of data from the Phase I entry. For these tests, cruise data were equivalent to tiltrotor 

airplane-mode operations. 

Multiple-linear regression was used to estimate hover and airplane-mode performance from the 

data, with uncertainty bands about measured power in terms of classic ±2se limits, plus 

confidence intervals and prediction intervals. The nonlinearities inherent in rotor performance 

were accommodated by curve fitting to ideal power from momentum theory. The results were 

compared to CAMRAD II and U2NCLE performance predictions. 
57 

A new method of data selection was devised that greatly expanded the range of useable hover 

data. The wind tunnel data were significantly revised. Revisions included an improved method of 

estimating spinner drag tares and deletion of questionable thrust/torque interaction corrections. 

These revisions resulted in much greater consistency between Phase I and Phase II wind tunnel 

data. Expanded tables of hover data and revised tables of airplane-mode data are included in 

Appendix D. 

OARF Hover Data 

A quadratic curve fit to ideal hover power gave a statistically significant improvement over a 

linear fit. Several combinations of terms in thrust and ideal power were examined, but none 

showed a statistically significant improvement over the quadratic fit to ideal power (terms 

in 3/2 / 2 CT and 3 / 2 CT ). The uncertainty, computed as the standard error of fit, was about 

0.61 percent of maximum measured power CP. 

Corrections for swirl- and tip-loss effects gave statistically significant improvements to a linear 

fit, but not to the quadratic fit. Conversion from physical units to rotor performance coefficients 

had no statistically significant effect on uncertainty.

The previous practice of rejecting hover data with wind >1 knot was determined to be overly 

restrictive. Run-to-run consistency checks revealed questionable data, but also showed that 

additional data could be admitted. The number of useable data points was thereby more than 

doubled. 

40x80 Airplane-Mode Data 

Multiple-linear curve fits were needed to match the airplane-mode data. The fits required terms 

in ideal power CPm (from momentum theory, ref. 19) and profile power factor Fp (ref. 19). Nearly 

all of the high-speed data were taken at Mtip = 0.58, and there were no data points at the same 

tunnel speed but different tip speeds. The limited range of tip speeds, combined with other 

limitations of the data set, would render inconclusive many otherwise desirable statistical 

analyses. 

The JVX Phase II database values of spinner drag were recalculated with a linear fit of drag 

versus dynamic pressure. Incorporating spinner internal pressure data into the drag calculations 

did not yield realistic values of net spinner drag. 

The Phase II airplane-mode data matched the Phase I data only if a thrust/torque interaction term 

was deleted from the data conversions. Including the nominal interaction resulted in unrealistic 

values of propulsive efficiency. 

 
58 

CAMRAD II and U2

NCLE Predictions 

The CAMRAD II predictions of references 4 and 5 were updated and combined with U2NCLE 

predictions (ref. 6) for comparison with the expanded hover data and revised airplane-mode data. 

The results are summarized here. 

A free-wake model with a single tip vortex matched the hover data well at high thrust, but a 

multiple-trailer model was needed for accuracy at low thrust. The multiple-trailer model showed 

little sensitivity to the radial location of the additional trailer over a reasonable range of values. 

However, the multiple-trailer model was computationally much less efficient than the 

conventional model. Differential-momentum (BEMT) and uniform-inflow models could be 

adjusted for a good fit to hover performance data, but required empirical corrections to do so. 

Both the Corrigan and Selig stall-delay models (refs. 24 and 25) provided equally good fits to 

hover data. Reynolds number corrections had only a small effect on predicted hover 

performance, as was expected given the small difference in scale between the JVX rotor chord 

and the airfoils tested to develop the airfoil tables. 

The U2NCLE predictions matched the hover data as well as any of the CAMRAD models, except 

at maximum thrust where U2NCLE appeared to prematurely predict stall. U2NCLE predicted 

slightly lower airplane-mode performance than did CAMRAD, but the number of data points 

was too limited to permit in-depth comparisons. Both CAMRAD and U2NCLE underpredicted 

airplane-mode performance with the default aerodynamic models. The CAMRAD predictions 

closely matched the wind tunnel data only after reducing blade section cd by −0.002. These 

results suggest that at least partial laminar flow was achieved during the test. 

Recommendations 

The present work relies on fairly simple statistical analyses of curve fits to rotor performance 

data, namely comparisons of the standard error of estimate. Other statistics could usefully be 

derived from the data set. Unfortunately, too little data survive to perform a proper Pareto 

analysis to the standards of reference 7, which is an important motivation for many of the 

following recommendations. 

Calibration data should be considered an integral part of the experimental database, including 

data for all transducers. The database should also contain as many intermediate calculations as 

possible, including unit and axis conversions, computation of nondimensional coefficients, and 

calibration corrections. It is equally important to document all data reduction equations, from 

individual measurements through to final calculated values. There are two distinct but related 

purposes: to provide better physical insight into the meaning of the results, the subtleties of 

which may be elusive; and to generate more detailed statistical tests, which can reveal 

shortcomings in the data that may bias interpretation of the results. 

 
59 

The intent of these recommendations is not only to facilitate troubleshooting: test planners 

should keep in mind that future researchers may wish to use the data for purposes not envisioned 

until long after the test is completed, and may therefore require different methods of analysis 

than normally applied to the raw data. 

Similarly, provisions for uncertainty analysis should be a part of test planning. This is another 

motivation for retaining all calibration data. A simple example is the sensitivity of spinner drag 

to tunnel velocity. Spinner drag scales as V 2

, and the propulsive power lost to spinner drag scales 

as V 3

. Tests of proprotors to speeds even higher than the JVX test may find that even very small 

uncertainties in tunnel velocity or spinner drag measurements will have non-trivial effects on net 

measured rotor thrust and propulsive power. 

Pretest predictions are an essential part of any test. The obvious example for the JVX data is 

airplane-mode performance, where the existence of CAMRAD or other predictions might have 

alerted the test team to potential problems with the data while the PTR and rotor were still in 

their as-tested condition. The discovery of an unrealistic torque/thrust interaction coefficient 

derived from a peculiar consistency in the mismatch of CAMRAD predictions to data. As it 

stands, there is no way to rigorously determine whether the failure to match predictions with the 

nominal database values is due to transducer failure, data processing error, corruption of the 

database, or modeling error. 

 
60 

 
61 

Appendix A: JVX Wind Tunnel Hover Data 

A limited amount of hover data were taken during the 1998 Phase I entry in the 40x80 test 

section. The overhead doors, high-bay doors, 40x80 exhaust louvers, and main air exchange 

were all open to minimize recirculation; see references 2 and 14 for details. The rotor shaft was 

tilted 2.5 deg nose up, which represented the V-22 nacelle outboard cant. Most of the hover data 

were taken with the rotor facing downstream, the reverse of that used for high-speed data, and 

with the image plane installed but the wing removed; average Mtip = 0.709. 

 

A few data points were taken with the rotor facing upstream without the image plane or wing. 

The upstream test condition gave poor results, which are not shown here. An extremely limited 

amount of hover data were taken during the 1991 Phase II 40x80 test. The results were very 

poor, with excessive scatter, and are accordingly not shown here. 

Figure A-1 shows the wind tunnel data from the Phase I test (downstream orientation, 

Mtip = 0.709) superimposed on the OARF data at Mtip = 0.728 (Run 7). For the wind tunnel data, 

there was residual wind in the test section, measured to be 8–16 knots. The wind tunnel data in 

Figure A-1 have not been corrected for wind. Attempts to correct for wind using the methods of 

reference 1 yielded unrealistically low values of figure of merit. 

The reason for the unsatisfactory wind corrections is unknown. Attempts to fit the data with 

terms in CPm and Fp (Eqs. 12 and 14) also failed to give usable results. All of the these 

corrections require accurate measurements of free-stream velocity, which is problematic for a 

large rotor in the 40x80 test section. The data set contains measurements of tunnel speed from 

only one set of transducers, so there is no way to retroactively determine velocity variations 

along the length of the test section, nor to determine recirculation velocity independent of test 

section velocity. For this reason, there was no further attempt to statistically analyze the wind 

tunnel data. 

The reason for the shortfall in figure of merit at high thrust in the wind tunnel is also unknown. 

One would expect to see a slight reduction in performance because of the larger cuff, but the 

magnitude of the cuff effect should be very small for the JVX rotor. The slight reduction in tip 

speed and the small residual wind should result in an increase in performance, not a decrease. 

These caveats aside, the OARF and 40x80 data are encouragingly close. Neither 40x80 entry had 

measurement of isolated-rotor hover performance as a primary objective. There appears to have 

been little or no previous attempt to closely compare 40x80 data to OARF data. The results 

presented here suggest that the 40x80 test section—or more realistically, the 80x120 test 

section—with careful attention to rotor installation, flow control and low-speed velocity 

measurement, may yet become a viable facility for measuring proprotor hover performance. 

 
62 

Figure A-1. JVX 40x80 hover data at Mtip = 0.709, downstream orientation, superimposed on 

OARF data at Mtip = 0.728. 

 
63 

Appendix B: Analysis of Spinner Drag Tares 

Alternative Interpretations of Spinner Tare Data 

A few of the pitfalls in statistical analysis can be illustrated with the spinner tare data from the 

Phase I wind tunnel test. Data were taken with the rotor blades removed over a range of 

airspeeds from 131 to 238 knots. For the data discussed here, the spinner was rotating at 

495 rpm. Data were taken at three different yaw (ψs) angles: 0, 3, and 6 deg. No spinner tare 

measurements were taken for the JVX Phase II entry. 

The Phase I spinner tare data in Figure 32 are replotted in Figure B-1, in units of equivalent flatplate area (drag/q0) versus tunnel dynamic pressure (q0). Most of the data fall into three distinct, 

narrow bands, one for each yaw angle. The trends are highly linear, except for the data point at 

zero yaw, 131 knots, or q0 = 56 lb/ft2

 (marked with a solid symbol in the plot). 

Reference 2 shows an additional, off-trend data point for ψs = 0 at just over 200 knots (roughly 

130 lb/ft2 in Figure B-1). No comparable data could be recovered from the data set for the 

analyses described here. The data in Figure A2 of reference 2 are adjusted for internal spinner 

pressure, and therefore are of lower magnitude than shown here. For the present report, pressure 

corrections were rejected for reasons discussed later in this appendix. 

Figure B-1. Phase I spinner tare data at 495 rpm, plotted as flat-plate area versus dynamic pressure. 

 
64 

Linear curve fits are shown for each yaw angle. The anomalous data point at zero yaw, 56 lb/ft2

, 

is not included in any curve fit. The fits are consistent, in that no two slopes are statistically 

different from each other. That is, even though slight differences are visible, the scatter in the 

data is too large to reliably calculate those differences. However, the dependent variable is 

divided by the independent variable. The data transformation more clearly reveals the anomaly at 

q0 = 56 lb/ft2 but violates the assumptions underlying the classic curve fitting method used here. 

A curve fit to drag versus q0, as in Figure 32, should give more reliable results. 

It is unlikely that the spinner would have highly nonlinear drag behavior only at zero yaw near 

130 knots (50 lb/ft2

 in Figure B-1) and linear behavior elsewhere. A deeper look at the database 

reveals that this is the first data point taken during that run, which hints at a measurement 

problem. Two possibilities are explored in the following sections. 

The total force on the exposed spindles should vary with q0, but that force projected in the 

longitudinal and circumferential directions should result in drag and torque trends that vary with 

slightly different functions of airspeed. In principle, it should be possible to separate spindle drag 

from total drag by comparing the different trends. However, the torque measured during the tare 

runs was 0.1 percent of full scale at best, and sometimes much less, which is far too low for 

reliable analysis. Again, the curve fit of Figure 32 is the more reliable method. 

Balance Hysteresis 

Reference 11 plots PTR balance check-loads data in terms of measurement error versus applied 

thrust. The balance data were collected during tests of the Advanced Technology Blade (ATB) 

(ref. 11), but the test rig, balance, and rotor hub were identical to those used for all JVX tests 

reported herein. Figure B-2, reconstructed from reference 11, clearly shows hysteresis at low 

thrust, separate nonlinear trends for “up” and “down” data, plus a large anomaly at about 1000 lb 

applied thrust. The anomalous data, plus the nonlinearities, make curve-fitting problematic. 

Nevertheless, it is instructive to estimate the hysteresis by averaging the “up” and “down” values 

separately for data at 2000 lb applied thrust and above. The result is a nominal hysteresis of 

5.5 lb (±2.75 lb). 

If the curve fit in Figure B-1 to spinner drag at 0-deg yaw is extrapolated to q0 = 56 lb/ft2

, the 

predicted value of spinner drag is 1.05 ft2, and the difference between the predicted and 

measured values is 0.10 ft2, equivalent to 5.6 lb—almost exactly the estimated value of 

hysteresis. While the near-perfect match is most likely a coincidence, the evidence is strongly 

suggestive that the first data point for spinner drag (the solid symbol in Figure B-1) does not 

represent the correct trend line and should not be used for curve fitting. Moreover, the balance 

hysteresis appears to be much worse at the low-thrust levels corresponding to spinner drag. 

Unfortunately, there are no balance check-loads data at negative thrust to directly compare the 

spinner drag data against. 

A different possible explanation of the anomalous data point is presented in the following 

section, in the discussion of Figure B-3. 
65 

Figure B-2. PTR balance thrust-measurement error (Ref. 11, Fig. 6.3). 

Spinner Pressures 

Reference 2 discusses spinner pressure measurements, reconsidered here. In traditional propeller 

tests with an external balance, aerodynamic loads on the spinner and nacelle must be measured 

and subtracted from the measured axial force to get net propeller thrust. The spinner may 

experience both external drag forces and internal pressure forces, both of which must be taken 

into account. In contrast, the JVX tests used an internal balance that was shielded from 

aerodynamic loads. A tacit assumption is that the PTR cowling did indeed shield the balance 

from aerodynamic effects, and that internal pressures on the upstream and downstream sides of 

the balance were equal. The internal balance was added to the PTR after the XV-15 tests, so one 

must be careful when comparing XV-15 and later data. 

To determine the effects of spinner pressures, the difference between the measured internal 

pressure and free-stream static pressure is required. The JVX spinner was open at the rear, so the 

net load caused by internal pressure was calculated by multiplying the pressure by the projected 

spinner area (the area of the base of the spinner). The presence of the spinner openings makes 

this an imprecise calculation. 

Measured spinner pressures were always lower than free-stream static pressure, hence the net 

spinner pressure force was always negative in the thrust direction. 

Internal spinner pressures were measured during both the Phase I and Phase II tests, but the 

transducer configuration was changed so no direct comparison is possible. Two indirect methods 

of correcting the data were tried, as discussed next. 

 
66 

Reference 2 estimated spinner tares for the Phase I tests by subtracting the internal spinner 

pressures, times the projected area, from the total force measured by the rotor balance. However, 

the resulting net spinner drag, with blade spindles exposed, was less than that measured during 

the XV-15 tests with spindles removed (ref. 15). While not physically impossible, this result is 

not very credible. It cannot be determined whether the XV-15 data or the JVX data, or both, are 

incorrect. 

The procedure described above was repeated with the Phase I tare data and the Phase II pressure 

data, which as noted had a different transducer installation. However, this gave unrealistic results 

for the Phase II data: the resulting spinner drag was much too large (equivalent to about 4 ft2

frontal area). The Phase II pressure data were much greater in magnitude than the Phase I data, 

which is again unrealistic. It has been conjectured that the static pressures were misrecorded or 

improperly applied to the data, but this has not been proven. The discrepancy may merely be an 

artifact of mislabeled data, but no alternative interpretation of the database has yielded 

reasonable results, so this matter has not been further pursued. Selected Phase II pressure data 

are included in Appendix D, in the event that someone wishes to try their hand with a different 

approach to the problem. 

An alternative method is to use the Phase I pressure data to correct the spinner tares for the 

presence of the rotor blades, then use the same trend for Phase II, thereby avoiding the need to 

use any Phase II pressure data. The Phase I test acquired both blades-on and blades-off pressure 

data. An equivalent blades-on tare can be calculated as: 

blades-on tare = blades-off drag – blades-off pressure + blades-on pressure 

where drag is the total force measured by the rotor balance, and the spinner pressures have been 

converted to net drag forces. Alternatively, drag and pressure forces may be converted to 

equivalent flat-plate areas. 

Both sets of Phase I pressure data, blades-on and blades-off, showed approximately linear trends 

with tunnel dynamic pressure q0 (but see Figure B-3). The trends were converted to flat-plate 

areas and combined with the raw drag data (Fig. B-1) to get a corrected spinner tare. However, 

the resulting effective spinner drag was unrealistically high: about 1.7 ft2

, which is much higher 

than that reported for the XV-15 tests (ref. 15). 

A closer look at the spinner pressure data is revealing. The pressure data taken during the Phase I 

spinner tares are plotted versus q0 in Figure B-3, transformed into force/q0 to emphasize the 

nonlinearities. The previous caveat concerning the interpretation of data so transformed applies. 

Perfect spinner pressures would presumably fall on a straight, horizontal line. It is evident that 

the trends with q0 are not only nonlinear, but vary inconsistently with yaw angle. Curve-fitting is 

unlikely to give reliable results. 

 
67 

Figure B-3. Phase I spinner tare internal pressure data. 

The spinner tare data in Figure B-1 include the effects of spinner pressure. In Figure B-3, the 

trend in the data for ψs = 0 is very different if the first data point is excluded. If the trend without

the first data point is correct, then the first data point is off-trend in the same direction as the 

presumed hysteresis effect, and of similar magnitude. The anomalous data point in Figure B-1 

can possibly be explained as an effect either of hysteresis in the balance data or of scatter in the 

pressure data, but there is no way to determine which, if either, actually applies. 

There are several ways to approach the problem of erratic pressure data. A partial list includes 

(1) delete the first data point and fit to the remaining data at ψs = 0; (2) fit to all of the data, with 

or without the first point; (3) apply curve fits to the pressure data separately from the balance 

data; or (4) fit to all of the data at ψs = 0. The last of these methods was chosen for this paper, 

using a linear curve fit, on the grounds that it makes the fewest assumptions about the nature and 

quality of the data. The results are shown in Figure 32 in the main body of this paper. No attempt 

was made to correct for presumed hysteresis in the balance or nonlinear trends of spinner 

pressure versus q0. 

 
68 

 
69 

Appendix C: Glauert Blockage Correction 

The shortfall in CAMRAD II predicted propulsive efficiency can, perhaps, be partially explained 

by wind tunnel flow blockage effects. The method used here was originally developed by 

Glauert (ref. 29); the equations below are taken from reference 30, here rewritten in terms of 

helicopter thrust coefficient. 

In the wind tunnel, the influence of the test section walls changes the flow conditions at the rotor 

disk relative to what would exist in free-stream flow (that is, with an infinitely large wind 

tunnel). The Glauert correction derives an equivalent free-stream velocity V′ at which the rotor 

will experience the same axial velocity as in the wind tunnel, and for which “this condition will 

maintain the same working conditions for the airscrew blades” (ref. 29). 

Let τ = T /ρAV 2 = CT /μ2

, and α1 = A/C, where C = wind tunnel cross-section area. The Glauert 

correction is then 

V ′

V =1− τα1

2 1+ 2τ

. 

For any combination of μ and CT/σ, the nominal value of η is first calculated, along with V′/V. 

CT/σ and CQ/σ are the same at V and V′, but η′, the propulsive efficiency in free air, is 

recalculated as η′ = ηV V′ . 

Figure C-1 shows the data with and without the Glauert correction. The open symbols are the 

nominal data with spinner tare corrections and thrust bias adjustment applied (the same data as in 

Figure 28). The dots are the data with the Glauert correction. 

The figure shows that the Glauert correction has little effect except at the highest values of CT/σ. 

At the maximum value of CT/σ, the Glauert correction is 1.01 percent, which is slightly less than 

the ±2se uncertainty band in the data (Eq. 15). However, the trend is consistent and suggests that 

the correction may be significant at higher values of CT/σ, at least at low μ; the effect is 

negligible at low CT/σ and high μ. Furthermore, V′/V was calculated using a literal interpretation 

of the Glauert formula, with no allowance made for the wind tunnel’s non-circular cross section 

(visible in Figure 2), nor with any other blockage correction, such as for the PTR’s long 

afterbody. The blockage effect could easily be larger than shown here. The trend in the reduction 

in η is consistent with the CAMRAD II predictions at high CT/σ (Fig. 45). However, the 

adjustment, even if significant, cannot by itself explain the discrepancy between the predictions 

and the data. 

A more subtle consideration is that the Glauert correction assumes a uniform change in velocity 

across the rotor disk, even for large α1. The JVX rotor would have in fact experienced a nonuniform radial inflow perturbation, which could combine with non-ideal circulation distribution 

to further change the effective η. Although frankly speculative, this assumed effect could be 

important for rotors operating at combined high thrust and off-design V or Vtip. 
70 

Figure C-1. Measured JVX propulsive efficiency with and without Glauert blockage corrections. 

The nominal data are the same as in Figure 28. 

Far more sophisticated blockage corrections have been developed; reference 31 includes 

comparative data for three methods and provides a list of further references. A deeper study of 

blockage corrections appropriate for proprotors is recommended, but is beyond the scope of the 

present inquiry. 

 
71 

Appendix D: JVX Test Data 

The JVX 1984 hover (ref. 1) and 1991 airplane-mode data used for this report are tabulated here, 

as extracted from the Rotor Data Reduction System (RDRS) database. They generally include 

the highest quality data that could be extracted from archives, but do not constitute the complete 

test data set. The data presented in this appendix include corrections for hub drag, as detailed in 

Appendix B. Limited data from the JVX 1988 airplane-mode test (ref. 2) are also included. 

JVX Hover Data 

The JVX hover data presented in the main body of this report are a subset of the data in 

reference 1 (Test 911). These test conditions are rotor only (no wing or ground plane) for 

Mtip = 0.67–0.68. Table D-1 lists the data meeting these criteria. CP and FM are corrected for 

ambient wind using the methodology described in reference 1. 

A more limited set of hover data was taken at Mtip = 0.73 and is listed in Table D-2. These data 

were used for comparison with 40x80 hover data in Appendix A. 

A few hover data points were taken in the wind tunnel during the 1988 Phase I entry. See 

Appendix A for discussion. The “downstream” data are listed in Table D-3. 

 

For all comparisons between data and theory (CAMRAD II predictions) in the main body of this 

report, the values of Vtip, Mtip, and ρ were averaged at each test condition, and ambient wind was 

assumed to be zero for the predictions. 
72 

 Table D-1. JVX OARF hover data (ref. 1), rotor only, Mtip = 0.67–0.68. 

Run Point Vtip 

(ft/sec)

Mtip Wind 

(knots)

ρ 

(slug/ft3)

CT/σ CP/σ FM

1 10 752.8 0.6768 0.81 0.002406 0.02311 0.002632 0.3183

1 11 752.8 0.6765 0.75 0.002404 0.03479 0.003107 0.4981

1 12 752.7 0.6765 1.79 0.002404 0.04504 0.003853 0.5916

1 13 752.5 0.6762 0.64 0.002403 0.06134 0.005232 0.6926

1 16 752.4 0.6760 1.44 0.002403 0.08027 0.007163 0.7572

1 17 752.3 0.6759 1.45 0.002403 0.07977 0.007211 0.7451

2 9 759.3 0.6765 1.78 0.002359 0.04352 0.003721 0.5819

2 11 759.2 0.6761 0.87 0.002357 0.06159 0.005384 0.6771

2 12 759.1 0.6760 1.07 0.002357 0.06894 0.006095 0.7084

2 13 759.0 0.6755 1.61 0.002354 0.07559 0.006839 0.7248

2 14 758.9 0.6755 0.83 0.002354 0.08395 0.007577 0.7657

2 15 758.7 0.6753 -0.09 0.002354 0.09729 0.009185 0.7879

2 16 758.6 0.6752 0.13 0.002354 0.10291 0.009947 0.7916

2 17 760.6 0.6766 0.85 0.002351 0.11551 0.011682 0.8015

2 20 760.2 0.6769 1.97 0.002356 0.13034 0.014238 0.7883

2 21 759.8 0.6769 1.47 0.002359 0.14504 0.016467 0.8000

2 22 759.6 0.6760 -0.14 0.002354 0.16001 0.018856 0.8095

3 4 746.8 0.6758 2.10 0.002436 0.05091 0.004433 0.6180

3 5 746.7 0.6757 1.98 0.002436 0.05791 0.005080 0.6542

3 6 746.6 0.6753 1.59 0.002433 0.06374 0.005692 0.6742

3 7 746.5 0.6749 1.56 0.002431 0.07119 0.006339 0.7146

3 8 746.4 0.6747 0.62 0.002430 0.08109 0.007315 0.7529

3 9 746.3 0.6745 0.62 0.002430 0.09365 0.008545 0.7999

3 10 746.1 0.6743 0.98 0.002429 0.10685 0.010008 0.8324

3 11 749.5 0.6772 0.94 0.002428 0.11303 0.011202 0.8090

3 12 749.3 0.6769 0.90 0.002427 0.12562 0.012886 0.8240

3 13 749.2 0.6767 0.98 0.002426 0.13269 0.013941 0.8269

4 5 754.4 0.6773 0.64 0.002396 0.02382 0.002728 0.3213

4 6 754.3 0.6772 0.76 0.002396 0.03422 0.003209 0.4704

4 7 754.2 0.6771 0.92 0.002396 0.04635 0.004036 0.5896

4 8 754.1 0.6770 0.89 0.002396 0.06152 0.005300 0.6867

4 9 754.0 0.6768 0.95 0.002395 0.06986 0.006087 0.7234

4 10 753.9 0.6765 1.23 0.002394 0.07886 0.006938 0.7612

4 11 753.8 0.6765 0.98 0.002394 0.08727 0.007819 0.7863

4 12 753.7 0.6763 1.57 0.002394 0.09578 0.008948 0.7901

4 13 753.5 0.6762 1.37 0.002394 0.10754 0.010346 0.8130

4 14 753.3 0.6758 1.20 0.002393 0.11753 0.011826 0.8126

4 15 753.1 0.6756 0.54 0.002393 0.12731 0.013204 0.8205

4 16 752.9 0.6755 0.90 0.002393 0.13770 0.014849 0.8208

4 17 752.7 0.6751 0.99 0.002392 0.14523 0.016247 0.8124

5 3 756.7 0.6766 2.02 0.002375 0.04246 0.003730 0.5594

5 5 756.5 0.6765 2.09 0.002376 0.05729 0.005007 0.6532

5 9 756.0 0.6760 2.10 0.002375 0.09367 0.008809 0.7762

5 13 755.4 0.6756 1.77 0.002377 0.13272 0.014366 0.8027

5 16 756.6 0.6767 1.80 0.002377 0.04777 0.004208 0.5918
73 

Table D-1. JVX OARF hover data (ref. 1), rotor only, Mtip = 0.67–0.68 (continued). 

Run Point Vtip 

(ft/sec)

Mtip Wind 

(knots)

ρ 

(slug/ft3)

CT/σ CP/σ FM

 

5 22 755.9 0.6760 1.79 0.002376 0.09807 0.009469 0.7736

5 24 755.6 0.6755 1.21 0.002375 0.11672 0.012109 0.7854

5 27 754.9 0.6748 1.60 0.002374 0.14760 0.016999 0.7956

6 6 755.6 0.6761 -0.05 0.002383 0.04507 0.004000 0.5704

6 7 755.5 0.6756 0.48 0.002380 0.05198 0.004569 0.6187

6 8 755.4 0.6753 0.47 0.002378 0.06558 0.005836 0.6863

6 9 755.4 0.6751 0.55 0.002377 0.06955 0.006163 0.7098

6 10 755.3 0.6749 0.42 0.002376 0.07684 0.006899 0.7364

6 11 755.2 0.6746 0.41 0.002375 0.08674 0.007949 0.7665

6 12 755.0 0.6745 0.13 0.002375 0.09636 0.009116 0.7825

6 13 754.9 0.6742 0.42 0.002373 0.10636 0.010391 0.7961

6 14 758.1 0.6768 1.73 0.002371 0.11727 0.011879 0.8063

6 15 757.9 0.6766 2.11 0.002371 0.12788 0.013520 0.8067

 

Table D-2. JVX OARF hover data (ref. 1), rotor only, Mtip = 0.73. 

Run Point Vtip 

(ft/sec)

Mtip Wind 

(knots)

ρ 

(slug/ft3)

CT/σ CP/σ FM

7 4 818.1 0.7289 1.23 0.002361 0.05151 0.004507 0.6186

7 5 818.0 0.7288 1.46 0.002361 0.05911 0.005158 0.6645

7 6 817.9 0.7285 1.42 0.002359 0.06726 0.005966 0.6973

7 7 817.8 0.7283 1.14 0.002358 0.07575 0.006780 0.7334

7 8 817.7 0.7280 1.61 0.002357 0.08467 0.007675 0.7657

7 9 817.5 0.7279 1.83 0.002357 0.09361 0.008788 0.7773

7 10 817.4 0.7276 1.55 0.002356 0.10584 0.010401 0.7896

7 11 817.2 0.7274 1.86 0.002356 0.11405 0.011557 0.7948

7 12 818.4 0.7286 1.13 0.002357 0.12394 0.013069 0.7962

7 13 818.0 0.7284 1.05 0.002358 0.13605 0.015008 0.7975

7 14 817.8 0.7279 1.41 0.002356 0.14416 0.016413 0.7954

7 15 819.1 0.7289 1.83 0.002354 0.08346 0.007619 0.7547

7 18 818.5 0.7285 2.02 0.002355 0.11293 0.011431 0.7918

 

 
74 

Table D-3. JVX hover data, isolated rotor in the 40x80 test section, downstream orientation, 

Mtip = 0.71. Tunnel velocity V is induced by the rotor. 

Run Point Vtip 

(ft/sec)

Mtip V 

(knots)

ρ 

(slug/ft3)

CT/σ CP/σ FM

4 10 799.8 0.7084 8.39 0.002303 0.03747 0.009603 0.5277

4 11 799.8 0.7084 10.67 0.002303 0.05627 0.003291 0.6624

4 12 795.9 0.7054 14.98 0.002306 0.09990 0.004859 0.7788

4 13 797.2 0.7071 13.18 0.002310 0.11414 0.009628 0.7865

4 14 803.7 0.7130 15.94 0.002311 0.11860 0.011502 0.7895

4 15 802.4 0.7120 13.80 0.002313 0.11975 0.012373 0.7944

4 16 797.2 0.7078 10.80 0.002317 0.05764 0.012589 0.6796

4 17 799.8 0.7104 11.83 0.002319 0.07548 0.004823 0.7400

4 18 801.1 0.7116 10.16 0.002320 0.09055 0.006664 0.7602

4 19 798.5 0.7094 13.16 0.002320 0.10573 0.008606 0.7785

4 20 799.8 0.7108 16.32 0.002322 0.11616 0.010494 0.7807

4 21 798.5 0.7099 14.36 0.002323 0.12241 0.012128 0.7821

4 22 794.6 0.7065 14.92 0.002324 0.12745 0.013185 0.7878

4 23 797.2 0.7089 15.14 0.002325 0.12461 0.013684 0.7837

4 24 795.9 0.7077 13.14 0.002325 0.12620 0.013431 0.7839

4 25 797.2 0.7090 13.14 0.002326 0.12929 0.013592 0.7916

4 26 793.3 0.7057 16.30 0.002327 0.13539 0.014138 0.7780

4 27 790.6 0.7035 12.88 0.002328 0.13769 0.015364 0.7789

 

JVX Airplane-Mode Data 

The JVX airplane-mode data tabulated here are a subset of the 1991 Phase II database (Test 

579). A limited amount of data from Phase I (1988, Test 568) are also included. Because of 

uncertainty in the measurement of rotor performance at very low wind tunnel speed, data below 

30 knots are not included in this report. The Phase II rotor performance data presented here are 

limited to five advance ratios. The objective is to prove a wide range of advance ratios with the 

constraint that each advance ratio must include data covering a reasonable range of thrust 

coefficients. There was a further requirement that rotational speed be constant at a given tunnel 

speed, but this eliminated only one data point. 

Mean operating conditions and the CT/σ range for each chosen advance ratio are listed in 

Table D-4. See also Tables 5 and 7 in the main body of this report. 

RDRS database label definitions and units are listed in Table D-5. The data are listed in 

Tables D-6 and D-7 using the data labels in the database; data that were rederived have column 

labels in italics. The data are sorted by advance ratio, then run and point number. Derivative data 

that can be readily recalculated, such as helical tip Mach number, are generally not included in 

the tables. In addition, spinner pressure data are listed in Tables D-8 and D-9, and spinner drag 

tare data from the Phase I test are listed in Table D-10. 

 
75 

 Table D-4. JVX summary cruise operating conditions and thrust ranges. 

 (a) 1988 Phase I entry (Test 568) 

μ Vtip 

(ft/sec)

V

(knots)

CT/σ

.210 646 80 .040–.061

.259 650 100 .050–.089

.344 650 132 .022–.038

(b) 1991 Phase II entry (Test 579) 

μ Vtip 

(ft/sec)

V

(knots)

CT/σ

.263 638 100 .029–.085

.349 640 132 .022–.068

.438 641 166 .031–.057

.523 642 199 .011–.045

.562 695 231 .016–.034

Power coefficient calculations

The power coefficient CP/σ (CPS) is calculated by the following equations in the database 

specifications: 

 CPS = CP / SIGMA 

 CP = TORQC / (DENOM * R) 

 DENOM = RHO × AREA × VTIP**2 

where RHO is the air density and AREA is the total disk area. VTIP data are sometimes labeled 

OMEGA*R in the database. 

For all wind tunnel data plots in this report, CP/σ and CQ/σ were recalculated from the rotor 

torque data using the above formulas. The data stored in the Phase II database as CPS (for CP/σ) 

plot with severe scatter and are not presented here (the Phase I data appear to be correct). The 

cause of the anomalies in the stored data was not determined. 
76 

Table D-5. JVX data labels, definitions, and units. 

Label Symbol(s) Definition and units 

AFFLEX Xs instrumented shaft axial force, lb 

AFRB Xc rotor balance axial force with shaft corrections, lb 

AFRBC Xb rotor balance axial force, lb 

COLL rotor blade collective pitch, deg 

CTISS CT/σ rotor thrust coefficient, divided by solidity 

ETAIS,F η rotor propulsive efficiency 

DSP spinner drag, lb 

KAFXTQ KQT shaft torque/thrust interaction constant, ft-lb/lb 

KTQAFX KTQ shaft thrust/torque interaction constant, lb/ft-lb 

MTUN tunnel Mach number 

PSI ψs yaw angle, deg 

QPSF q0 corrected tunnel dynamic pressure, lb/ft2

RHO100 ρ tunnel air density, slug/ft2

 (inconsistent scales in database) 

RPM Ω rotor rotational speed, rpm 

RTRDFS rotor drag force, including spinner loads, lb 

SPBP spinner base pressure (Phase I test), lb/in2

SPBPR spinner base pressure (Phase II test), lb/in2

SPBPI1 " " " " " " " 

SPBPI2 " " " " " " " 

SPBSF spinner base force, positive in thrust direction, lb 

TEMP total tunnel temperature, deg F 

TIPM Mtip rotor tip Mach number 

TORQ Qs instrumented rotor shaft torque, ft-lb 

TORQC corrected rotor shaft torque, ft-lb 

VKTS V tunnel air velocity, knots 

VTIP Vtip = ΩR rotor tip speed, ft/sec (also OMEGA*R) 

V/OR μ =Vtip/V rotor advance ratio 

Several different types of corrections were applied to the data in the database. Tunnel dynamic 

pressure QPSF is corrected for compressibility. Rotor shaft torque TORQC is corrected for shaft 

force interaction. Rotor balance axial force AFRBC is corrected for balance interactions. Rotor 

drag force RTRDFS is the rotor balance axial force corrected for rotor shaft axial force and 

torque interactions (positive in drag direction). Not all interactions were applied to the Phase II 

data given in this report, as described next. 

 
77 

Interactions

The values given in the Phase II database for rotor shaft torque/thrust interaction are suspect, as 

detailed in the section Torque/Thrust Interactions in the main body of this report. The defining 

equation is Eq. 11, here rewritten with database labels from Table D-5: 

AFRB = AFRBC + AFFLEX – KTQAFX × TORQ 

The counterpart equation for torque is 

TORQC = TORQ – KAFXTQ × [ AFFLEX – (KTQAFX × TORQ) ] 

TORQ does not include corrections for shaft torque/thrust interaction or bearing friction, 

whereas TORQC includes these corrections. The raw values of AFRBC, AFFLEX, and TORQ 

are included in the tables for reference. (AFRBC data are not available for Phase I.) The nominal 

interaction coefficients are different for Phase I and Phase II: 

Test KTQAFX 

lb/ft-lb 

KAFXTQ 

ft-lb/lb 

Phase I −0.0023 0.2089 

Phase II −0.0086 0.2143 

For the Phase II data, axial force and torque were recalculated with KTQAFX set to zero, then 

spinner tares added, and finally the coefficients CP/σ, CQ/σ, and η computed. The nominal 

corrections were retained for Phase I. 

Drag corrections

In the database, rotor drag force (negative thrust) is defined as 

RTRDF = RTRDFS – DSP + SPBSF 

Here DSP is the spinner drag tare (stored as equivalent drag area), and SPBSF is the spinner base 

force calculated from internal spinner pressure. However, DSP data were not stored for Phase II, 

and spinner base force gives unreasonable results. Furthermore, if DSP is the spinner drag tare, 

then SPBSF should reflect the difference between the blades-on and blades-off pressures, not the 

literal pressure. 

For this report, net rotor thrust is recalculated as 

T = –RTRDFS + QPSF × Asp

where Asp = 0.901 ft2

, as detailed under JVX Spinner Tares in the main body of this report. The 

values of rotor thrust, torque, and related coefficients plotted in the main body of this report were 

recalculated using the equations immediately above. 

 
78 

Allowing for the possibility that some of the data were simply mislabeled or misinterpreted, or 

that better means of correcting the data may be devised, the original values of RTRDFS, CTISS, 

SPBSF, and ETAIS,F are included in the tables of this appendix, along with the values corrected 

as explained previously. 

Not all data were stored for all tests. In particular, the uncorrected values of shaft torque (TORQ) 

were stored only for the wind tunnel tests, making it impossible to recalculate rotor axial force 

for hover data in the same manner as was done here for the Phase II data. As already mentioned, 

rotor balance axial force (AFRBC), uncorrected for shaft interactions, was not stored for Phase I. 

Accordingly, all hover data in Tables D-1, D-2, and D-3 use rotor thrust exactly as in the 

database. 

Caution is advised when comparing these data with RDRS data from other tests. RHO100 

usually means 100 times density, as in Table D-6a, but the multiplication was evidently not 

applied to the JVX Phase II test data (Table D-7a). 

 
79 

Table D-6a. JVX 1988 Phase I airplane-mode operating conditions. 

Run Point TEMP RHO100 VTIP VKTS V/OR TIPM MTUN RPM QPSF

35 6 78.81 0.2264 642.7 80.2 0.2106 0.5658 0.1191 491 20.7

35 7 79.60 0.2261 646.6 80.3 0.2097 0.5688 0.1193 494 20.8

35 8 80.38 0.2257 649.3 80.6 0.2095 0.5707 0.1195 496 20.9

37 3 73.68 0.2276 650.6 99.3 0.2576 0.5759 0.1483 497 32.0

37 4 75.10 0.2269 649.3 99.9 0.2598 0.5740 0.1491 496 32.3

37 5 78.06 0.2243 648.0 131.8 0.3433 0.5722 0.1964 495 55.5

37 6 78.65 0.2240 650.6 132.4 0.3434 0.5742 0.1972 497 55.9

37 7 79.22 0.2237 650.6 132.5 0.3438 0.5739 0.1973 497 56.0

37 8 79.99 0.2234 651.9 132.7 0.3436 0.5746 0.1974 498 56.0

Table D-6b. JVX 1988 Phase I rotor performance data, as given in the database.

Run Point RTRDFS AFFLEX COLL TORQ TORQC SPBP 

35 6 -2087.9 -30.4 20.21 6471 6450 -0.0624 

35 7 -2395.8 -19.4 20.68 7357 7334 -0.0642 

35 8 -3212.6 -2.0 21.90 9864 9833 -0.0668 

37 3 -2657.2 -31.0 24.97 9945 9914 -0.0827 

37 4 -4727.4 5.7 28.35 17791 17764 -0.0920 

37 5 -1100.5 -605.2 29.90 5991 6098 -0.1440 

37 6 -1960.4 -373.8 30.83 9871 9926 -0.1451 

37 7 -2785.4 -95.4 31.96 13795 13790 -0.1478 

37 8 -3516.7 -63.6 32.76 17175 17162 -0.1500 

Table D-6c. JVX 1988 Phase I rotor performance data, original (text labels) 

and as recalculated (italic symbols). 

Run Point ETAIS,F CTISS T CT/σ CP/σ η 

35 6 0.8520 0.03996 2106.5 0.04032 0.00988 0.8596

35 7 0.8563 0.04537 2414.5 0.04572 0.01111 0.8630

35 8 0.8554 0.06044 3231.4 0.06079 0.01480 0.8604

37 3 0.8631 0.04939 2686.0 0.04992 0.01474 0.8724

37 4 0.8642 0.08846 4756.5 0.08900 0.02659 0.8695

37 5 0.7746 0.02093 1150.5 0.02188 0.00928 0.8097

37 6 0.8477 0.03702 2010.7 0.03797 0.01500 0.8694

37 7 0.8681 0.02922 1423.3 0.02679 0.00904 0.7765

37 8 0.8801 0.04088 2050.9 0.03847 0.01228 0.8227
80 

Table D-7a. JVX 1991 Phase II airplane-mode operating conditions (Test 579). 

Run Point TEMP RHO100 VTIP VKTS V/OR TIPM MTUN RPM QPSF

4 6 56.60 0.002332 637.8 99.5 0.2633 0.5739 0.1511 487.2 32.9

4 7 56.72 0.002331 638.7 99.6 0.2631 0.5746 0.1512 487.9 32.9

4 8 56.97 0.002330 635.8 99.7 0.2646 0.5719 0.1513 485.7 33.0

4 9 57.20 0.002329 639.8 99.5 0.2625 0.5754 0.1510 488.8 32.8

4 10 57.25 0.002329 641.8 99.6 0.2618 0.5771 0.1511 490.3 32.9

4 11 57.52 0.002327 638.5 100.2 0.2648 0.5740 0.1520 487.8 33.3

4 12 57.55 0.002327 640.9 100.2 0.2638 0.5762 0.1520 489.6 33.3

8 5 52.74 0.002355 635.5 98.7 0.2621 0.5739 0.1504 485.5 32.7

8 6 53.00 0.002354 636.8 99.1 0.2627 0.5750 0.1510 486.4 32.9

8 7 53.14 0.002353 638.0 99.1 0.2620 0.5760 0.1509 487.4 32.9

8 8 53.20 0.002352 635.9 99.2 0.2634 0.5740 0.1512 485.8 33.0

8 9 53.60 0.002350 638.3 99.5 0.2632 0.5760 0.1516 487.6 33.2

8 10 53.66 0.002350 636.7 99.5 0.2638 0.5745 0.1516 486.4 33.2

4 14 58.90 0.002304 639.1 131.8 0.3481 0.5747 0.2000 488.2 57.0

4 15 59.00 0.002303 636.6 132.2 0.3504 0.5725 0.2006 486.3 57.3

4 16 59.20 0.002302 640.9 132.3 0.3483 0.5762 0.2007 489.6 57.4

4 17 59.38 0.002301 638.9 132.2 0.3493 0.5743 0.2006 488.1 57.3

4 18 59.73 0.002299 640.9 133.0 0.3503 0.5759 0.2018 489.6 57.9

4 19 59.80 0.002298 641.8 133.0 0.3499 0.5767 0.2018 490.3 57.9

4 23 62.09 0.002265 642.5 165.8 0.4354 0.5774 0.2514 490.9 88.7

4 24 62.06 0.002266 639.8 165.6 0.4370 0.5749 0.2513 488.7 88.6

4 25 62.52 0.002263 637.9 166.2 0.4399 0.5730 0.2520 487.3 89.1

4 26 62.60 0.002263 639.4 166.2 0.4388 0.5744 0.2520 488.5 89.1

4 27 62.73 0.002264 643.1 166.7 0.4374 0.5776 0.2526 491.3 89.6

5 25 65.43 0.002234 642.5 199.2 0.5233 0.5771 0.3020 490.8 126.3

5 26 64.94 0.002237 643.1 199.1 0.5227 0.5779 0.3021 491.3 126.3

5 27 65.18 0.002235 639.0 199.3 0.5263 0.5741 0.3022 488.2 126.4

5 28 64.88 0.002236 642.8 199.8 0.5245 0.5777 0.3030 491.1 127.1

5 29 62.80 0.002246 638.5 198.9 0.5259 0.5750 0.3024 487.8 126.6

5 30 63.32 0.002244 640.2 198.7 0.5238 0.5762 0.3018 489.1 126.2

5 31 63.50 0.002243 641.6 199.1 0.5238 0.5773 0.3024 490.1 126.7

9 5 68.79 0.002237 641.4 198.8 0.5233 0.5742 0.3005 490.0 126.0

9 6 70.64 0.002229 643.6 198.8 0.5215 0.5751 0.2999 491.6 125.5

9 7 70.43 0.002230 643.9 198.9 0.5215 0.5755 0.3001 491.9 125.7

9 8 70.60 0.002230 644.7 198.4 0.5194 0.5761 0.2993 492.5 125.0

9 9 70.82 0.002229 644.3 199.5 0.5225 0.5758 0.3008 492.2 126.3

9 10 70.65 0.002230 642.3 199.4 0.5240 0.5741 0.3008 490.7 126.3

5 19 67.02 0.002197 695.5 231.3 0.5613 0.6257 0.3512 531.3 167.4

5 20 67.40 0.002195 695.7 231.1 0.5608 0.6257 0.3509 531.5 167.1

5 21 67.40 0.002196 693.0 231.0 0.5626 0.6233 0.3507 529.4 166.9

5 22 67.50 0.002195 694.5 231.4 0.5624 0.6246 0.3513 530.6 167.4

5 23 67.78 0.002193 696.2 231.7 0.5616 0.6260 0.3515 531.9 167.7

 
81 

Table D-7b. JVX 1991 Phase II rotor performance data, as given in the database. 

Run Point RTRDFS AFRBC AFFLEX COLL TORQ TORQC SPBSF

4 6 -1602.9 1818.4 -268.2 23.51 6126 6173 134.5

4 7 -2158.6 2326.3 -237.3 24.30 8090 8126 131.8

4 8 -2724.5 2861.3 -223.7 25.22 10118 10148 126.2

4 9 -3328.9 3433.8 -209.4 25.89 12154 12176 124.3

4 10 -3868.1 3945.3 -199.2 26.58 14191 14208 127.7

4 11 -4268.0 4327.1 -195.9 27.49 15903 15916 128.5

4 12 -4542.5 4588.6 -191.8 27.84 16935 16945 133.6

8 5 -1551.8 1761.3 -260.7 23.58 5960 6005 125.2

8 6 -2179.2 2276.4 -167.4 24.37 8165 8186 123.3

8 7 -2729.7 2823.0 -179.9 25.31 10061 10081 124.0

8 8 -3283.6 3363.9 -184.3 26.29 12093 12110 122.3

8 9 -3871.2 3931.1 -182.5 27.18 14251 14264 130.0

8 10 -4320.8 4364.5 -181.4 27.96 16000 16010 122.6

4 14 -1139.6 1633.1 -544.5 29.64 5933 6039 214.7

4 15 -1620.0 1965.4 -415.4 30.33 8135 8209 241.8

4 16 -2153.7 2351.7 -289.1 30.77 10584 10627 227.6

4 17 -2496.2 2670.5 -279.0 31.34 12164 12202 228.7

4 18 -3301.1 3417.4 -253.6 32.40 15962 15986 229.6

4 19 -3593.9 3700.8 -255.3 32.78 17250 17273 228.9

4 23 -1632.1 2081.5 -538.0 36.23 10296 10393 356.8

4 24 -1966.5 2313.1 -452.4 36.72 12304 12378 356.1

4 25 -2208.0 2484.6 -394.2 37.00 13680 13739 353.9

4 26 -2531.0 2749.3 -351.8 37.42 15529 15575 360.3

4 27 -2956.1 3097.4 -295.0 37.61 17870 17900 364.0

5 25 -630.3 1375.3 -796.5 40.87 5992 6151 510.7

5 26 -899.7 1610.8 -777.8 41.27 7762 7915 508.7

5 27 -1283.1 1923.7 -728.6 41.73 10228 10365 516.8

5 28 -1617.7 2144.0 -634.2 42.04 12538 12651 511.5

5 29 -1846.8 2279.5 -554.1 42.15 14116 14209 510.6

5 30 -2031.6 2368.6 -468.9 42.26 15335 15407 499.7

5 31 -2297.8 2641.2 -490.0 42.57 17049 17123 500.9

9 5 -550.7 1272.2 -768.2 40.62 5431 5585 500.6

9 6 -820.6 1486.8 -728.1 40.79 7192 7334 499.8

9 7 -1254.5 1830.5 -661.1 41.15 9897 10021 508.5

9 8 -1614.3 2068.1 -560.2 41.46 12382 12479 495.8

9 9 -1972.3 2286.9 -442.4 41.88 14860 14928 501.6

9 10 -2253.4 2677.9 -567.9 42.58 16670 16761 518.7

5 19 -834.4 1556.2 -796.9 44.04 8725 8879 676.2

5 20 -962.8 1677.9 -796.4 44.13 9464 9618 677.5

5 21 -1287.1 1968.5 -782.6 44.46 11761 11907 677.1

5 22 -1747.7 2369.9 -749.2 44.72 14772 14905 677.6

5 23 -1995.6 2572.8 -719.0 44.94 16490 16614 672.1

 
82 

Table D-7c. JVX 1991 Phase II rotor performance data, original (text labels) and 

as recalculated (italic symbols). 

Run Point ETAIS,F CTISS T CT/σ CP/σ η 

4 6 0.8546 0.03026 1474.6 0.02783 0.00932 0.7862 

4 7 0.8736 0.04063 2030.3 0.03822 0.01224 0.8216 

4 8 0.8881 0.05179 2596.3 0.04935 0.01543 0.8463 

4 9 0.8970 0.06250 3200.6 0.06009 0.01829 0.8624 

4 10 0.8910 0.07218 3739.8 0.06978 0.02121 0.8615 

4 11 0.8876 0.08054 4140.0 0.07813 0.02403 0.8609 

4 12 0.8840 0.08506 4414.6 0.08267 0.02539 0.8591 

8 5 0.8467 0.02922 1423.3 0.02679 0.00904 0.7765 

8 6 0.8742 0.04088 2050.9 0.03847 0.01228 0.8227 

8 7 0.8869 0.05102 2601.3 0.04862 0.01507 0.8452 

8 8 0.8927 0.06181 3155.4 0.05940 0.01824 0.8578 

8 9 0.8930 0.07238 3743.1 0.06998 0.02133 0.8634 

8 10 0.8900 0.08120 4192.7 0.07879 0.02407 0.8636 

4 14 0.8210 0.02168 1034.5 0.01968 0.00919 0.7453 

4 15 0.8644 0.03107 1515.2 0.02906 0.01260 0.8085 

4 16 0.8824 0.04078 2048.9 0.03879 0.01610 0.8395 

4 17 0.8932 0.04757 2391.4 0.04557 0.01860 0.8557 

4 18 0.9042 0.06259 3196.9 0.06061 0.02425 0.8756 

4 19 0.9100 0.06797 3489.7 0.06600 0.02614 0.8836 

4 23 0.8547 0.03124 1557.5 0.02982 0.01592 0.8157 

4 24 0.8679 0.03797 1891.8 0.03652 0.01911 0.8349 

4 25 0.8836 0.04293 2133.8 0.04148 0.02137 0.8539 

4 26 0.8914 0.04897 2456.8 0.04753 0.02411 0.8652 

4 27 0.9029 0.05652 2882.3 0.05511 0.02738 0.8804 

5 25 0.6702 0.01224 591.8 0.01149 0.00955 0.6293 

5 26 0.7427 0.01741 861.4 0.01667 0.01225 0.7110 

5 27 0.8144 0.02516 1244.8 0.02442 0.01627 0.7901 

5 28 0.8384 0.03134 1580.1 0.03062 0.01961 0.8190 

5 29 0.8544 0.03610 1808.8 0.03536 0.02222 0.8368 

5 30 0.8634 0.03954 1993.1 0.03879 0.02399 0.8470 

5 31 0.8787 0.04455 2259.8 0.04382 0.02656 0.8642 

9 5 0.6449 0.01072 512.0 0.00996 0.00869 0.5996 

9 6 0.7293 0.01591 781.5 0.01515 0.01138 0.6945 

9 7 0.8160 0.02429 1215.6 0.02354 0.01552 0.7907 

9 8 0.8399 0.03118 1574.8 0.03042 0.01928 0.8193 

9 9 0.8630 0.03816 1934.0 0.03741 0.02310 0.8462 

9 10 0.8805 0.04385 2215.0 0.04310 0.02609 0.8655 

5 19 0.6593 0.01406 835.6 0.01408 0.01197 0.6602 

5 20 0.7017 0.01622 963.7 0.01624 0.01297 0.7024 

5 21 0.7602 0.02185 1287.8 0.02186 0.01617 0.7606 

5 22 0.8243 0.02955 1748.9 0.02957 0.02016 0.8249 

5 23 0.8432 0.03360 1997.1 0.03363 0.02238 0.8439 

 
83 

Spinner Pressure Data 

Phase I spinner pressure data were taken from a single transducer (SPBP), in units of lb/in2, 

referenced to the static pressure ring. Table D-8 lists the spinner pressures for three tip speeds 

not in Table D-6. Here, RHO100 evidently means that the density was multiplied by a factor of 

100, and SPBP has the opposite sign as SPBPR etc. in Phase II. For Phase I, the nominal spinner 

base force is computed as 

SPBSF = SPBP × 577.7in2

Phase II spinner pressure data were taken from three transducers, listed in the database as 

SPBPR, SPBPI1, and SPBI2, all in lb/in2

 and referenced to the static pressure ring. The values 

are listed in Table D-9. The spinner base force is computed as 

SPBSF = SPBPR × 96.1in2

 + SPBPI1 × 190.0in2 + SPBP2 × 237.3in2

The Phase II pressure data are questionable: the values are an order of magnitude higher than the 

Phase I pressures and are of the wrong expected sign. They are included here only for reference. 

Table D-8. JVX 1988 Phase I spinner pressures, blades on. 

Run Point RHO100 VTIP VKTS MTUN QPSF SPBP

38 4 0.2305 435.9 98.5 0.1480 31.85 -0.0752 

38 5 0.2302 433.3 98.9 0.1486 32.08 -0.0784 

38 6 0.2277 429.4 130.8 0.1963 55.46 -0.1325 

38 7 0.2273 432.0 131.2 0.1968 55.72 -0.1318 

38 8 0.2239 429.4 165.4 0.2478 87.21 -0.2028 

38 9 0.2233 437.2 165.7 0.2479 87.28 -0.2049 

38 10 0.2192 430.7 199.6 0.2983 124.36 -0.2937 

38 11 0.2188 411.0 199.7 0.2982 124.25 -0.2938 

43 3 0.2283 651.9 131.2 0.1965 55.97 -0.1426 

43 5 0.2268 658.4 143.0 0.2138 66.02 -0.1730 

43 6 0.2267 655.8 143.0 0.2139 66.08 -0.1747 

43 8 0.2249 653.2 143.3 0.2134 65.79 -0.1746 

46 3 0.2147 654.5 220.0 0.3284 149.54 -0.3560 

50 3 0.2179 646.6 217.5 0.3273 148.37 -0.3520 

51 3 0.2132 547.2 217.9 0.3225 144.18 -0.3257 

52 3 0.2150 548.5 216.8 0.3245 145.47 -0.3250 

 
84 

Table D-9. JVX 1991 Phase II spinner pressure data. SPBSF is recalculated. 

Run Point SPBPR SPBPI1 SPBPI2 SPBSF 

4 6 0.2103 0.2649 0.2694 134.5 

4 7 0.2050 0.2593 0.2647 131.8 

4 8 0.1922 0.2503 0.2537 126.2 

4 9 0.1868 0.2476 0.2497 124.3 

4 10 0.1947 0.2538 0.2561 127.7 

4 11 0.1943 0.2562 0.2576 128.5 

4 12 0.2038 0.2659 0.2677 133.6 

8 5 0.1933 0.2500 0.2493 125.2 

8 6 0.1899 0.2467 0.2453 123.3 

8 7 0.1880 0.2498 0.2465 124.0 

8 8 0.1844 0.2473 0.2429 122.3 

8 9 0.2009 0.2588 0.2591 130.0 

8 10 0.1869 0.2456 0.2445 122.6 

4 14 0.3278 0.4249 0.4319 214.7 

4 15 0.3789 0.4769 0.4837 241.8 

4 16 0.3514 0.4500 0.4566 227.6 

4 17 0.3528 0.4527 0.4585 228.7 

4 18 0.3534 0.4557 0.4598 229.6 

4 19 0.3503 0.4540 0.4592 228.9 

4 23 0.5585 0.7050 0.7130 356.8 

4 24 0.5567 0.7032 0.7120 356.1 

4 25 0.5520 0.7004 0.7072 353.9 

4 26 0.5648 0.7117 0.7198 360.3 

4 27 0.5721 0.7197 0.7259 364.0 

5 25 0.8147 1.0104 1.0133 510.7 

5 26 0.8084 1.0067 1.0101 508.7 

5 27 0.8256 1.0201 1.0268 516.8 

5 28 0.8126 1.0107 1.0171 511.5 

5 29 0.8110 1.0078 1.0162 510.6 

5 30 0.7898 0.9879 0.9949 499.7 

5 31 0.7911 0.9873 0.9999 500.9 

9 5 0.8002 0.9945 0.9892 500.6 

9 6 0.8044 0.9912 0.9868 499.8 

9 7 0.8165 1.0090 1.0042 508.5 

9 8 0.7970 0.9832 0.9795 495.8 

9 9 0.8055 0.9948 0.9909 501.6 

9 10 0.8397 1.0259 1.0243 518.7 

5 19 1.0825 1.3340 1.3429 676.2 

5 20 1.0842 1.3370 1.3456 677.5 

5 21 1.0821 1.3390 1.3430 677.1 

5 22 1.0831 1.3390 1.3447 677.6 

5 23 1.0765 1.3260 1.3347 672.1 

 
85 

Phase I Tares 

In the absence of reliable spinner drag measurements from the Phase II test, the best spinner tare 

data are those from the Phase I test. Test conditions and tare data are tabulated in Table D-10, all 

at 495–496 rpm, blades off. 

Table D-10a. JVX 1998 Phase I spinner tare test conditions, blades off. 

Run Point TEMP RHO100 VKTS MTUN RPM QPSF

57 3 69.99 0.2271 131.2 0.1971 496 55.7

57 4 73.93 0.2253 131.4 0.1966 495 55.4

57 5 74.85 0.2250 131.2 0.1961 495 55.1

57 6 77.33 0.2220 165.3 0.2471 495 86.4

57 7 78.99 0.2213 165.2 0.2466 495 86.1

57 8 79.75 0.2210 165.1 0.2462 495 85.8

57 9 81.46 0.2177 203.0 0.3031 495 127.7

57 10 83.56 0.2169 203.0 0.3025 495 127.3

57 11 84.81 0.2165 202.9 0.3020 495 126.9

57 13 87.44 0.2140 220.7 0.3283 495 148.5

57 14 88.85 0.2135 220.5 0.3276 495 147.9

57 15 89.79 0.2132 220.4 0.3272 495 147.5

57 16 91.62 0.2109 238.4 0.3539 496 170.8

57 17 93.22 0.2105 238.2 0.3530 495 170.0

57 18 93.76 0.2102 238.1 0.3527 496 169.6

57 19 95.08 0.2098 237.9 0.3520 52 169.1 

Table D-10b. JVX 1998 Phase I spinner tare data, blades off. 

Run Point PSI RTRDFS DSP/QPSF SPBP 

57 3 0 52.6 0.945 -0.0324 

57 4 -3 61.2 1.104 -0.0351 

57 5 -6 65.7 1.192 -0.0375 

57 6 0 87.2 1.009 -0.0590 

57 7 -3 92.2 1.071 -0.0587 

57 8 -6 95.5 1.113 -0.0624 

57 9 0 124.6 0.976 -0.0855 

57 10 -3 127.6 1.003 -0.0902 

57 11 -6 134.4 1.059 -0.0935 

57 13 0 141.7 0.954 -0.1063 

57 14 -3 145.6 0.985 -0.1114 

57 15 -6 152.4 1.033 -0.1142 

57 16 0 155.9 0.913 -0.1246 

57 17 -3 161.4 0.949 -0.1327 

57 18 -6 169.2 0.997 -0.1400 

57 19 -6 165.8 0.980 -0.1403 

 
86 

 
87 

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