Dave Sree

Tuskegee University, Tuskegee, Alabama

Far-Field Acoustic Power Level and Performance 

Analyses of F31/A31 Open Rotor Model at

Simulated Scaled Takeoff, Nominal Takeoff,

and Approach Conditions

Technical Report I

NASA/CR—2015-218716

May 2015
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Dave Sree

Tuskegee University, Tuskegee, Alabama

Far-Field Acoustic Power Level and Performance 

Analyses of F31/A31 Open Rotor Model at

Simulated Scaled Takeoff, Nominal Takeoff,

and Approach Conditions

Technical Report I

NASA/CR—2015-218716

May 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNC13BA10B
Acknowledgments

The present work was sponsored by the NASA Environmentally Responsible Aviation Project Propulsion subtask, with

Ken Suder as Project Monitor. This work was performed under the Universities Space Research Association (USRA) Advanced 

Research and Technology Support Task Order, IDIQ Subcontract Number 04555-014 (Prime Contract Number NNC13BA10B) for 

NASA Glenn Research Center (NASA GRC). The support from USRA and Acoustics Branch at NASA GRC is greatly appreciated. 

The author would like to thank Dr. David B. Stephens of Acoustics Branch for all his help, suggestions, and fruitful discussions.

Available from

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either expressed or implied, by the National Aeronautics and 

Space Administration.

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This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
NASA/CR—2015-218716 iii 

Preface 

There are two parts to the technical aspects of the task under this Universities Space Research 

Association (USRA) subcontract number 04555-014. The first part involves performing and documenting 

the far-field acoustic (sound) power level and system performance analyses of open rotor model F31/A31 

at simulated scaled takeoff, nominal takeoff, and approach flight conditions based on data obtained from 

low-speed wind tunnel (LSWT) tests at NASA Glenn Research Center (NASA GRC). The second part 

involves performing and documenting the near-field acoustic power level analysis of the same model at 

simulated cruise conditions based on data obtained from high-speed wind tunnel (SWT) tests at NASA 

GRC. The nonproprietary portions of the test data were provided by NASA GRC to perform the analyses. 

This subcontractor’s report on the first part of the task is provided in the form of Technical Report I

which consists of model’s relevant sound power level and performance results from the analyses and their 

detailed discussions. The technical report is included as an attachment to this summary. The deliverables, 

namely, revised technical report, data analysis codes, spreadsheets of results, tables, figures, etc. will be 

shipped to the technical monitor at NASA GRC in electronic form at the end of the contract period. 

NASA/CR—2015-218716 1 

Far-Field Acoustic Power Level and Performance Analyses 

of F31/A31 Open Rotor Model at Simulated Scaled Takeoff, 

Nominal Takeoff, and Approach Conditions 

Technical Report I 

Dave Sree 

Tuskegee University 

Tuskegee, Alabama 36088 

Summary 

Far-field acoustic power level and performance analyses of open rotor model F31/A31 have been 

performed to determine its noise characteristics at simulated scaled takeoff, nominal takeoff, and 

approach flight conditions. The nonproprietary parts of the data obtained from experiments in 9- by 

15-Foot Low-Speed Wind Tunnel (915 LSWT) tests were provided by NASA Glenn Research Center to 

perform the analyses. The tone and broadband noise components have been separated from raw test data 

by using a new data analysis tool. Results in terms of sound pressure levels, acoustic power levels, and 

their variations with rotor speed, angle of attack, thrust, and input shaft power have been presented and 

discussed. The effect of an upstream pylon on the noise levels of the model has been addressed. Empirical 

equations relating model’s acoustic power level, thrust, and input shaft power have been developed. The 

far-field acoustic efficiency of the model is also determined for various simulated flight conditions. It is 

intended that the results presented in this work will serve as a database for comparison and improvement 

of other open rotor blade designs and also for validating open rotor noise prediction codes. 

Nomenclature 

Aa Reference rotor annular area Pac Measured acoustic power 

AOA Angle of attack Pref Reference acoustic power 

APP Approach Psp Input shaft power 

BSA Blade-pitch setting angles Pspb Input shaft power per blade 

c0 Speed of sound PWL Power watt level 

Cac Acoustic power coefficient R2

 Goodness-of-fit parameter 

Csp Input shaft power coefficient SPL Sound pressure level 

CT Net thrust coefficient STO Scaled takeoff 

d Sideline distance T Net thrust 

D Reference rotor diameter V0 Freestream velocity 

FFT Fast Fourier Transform ηp Propulsion efficiency 

J Advance ratio Π Acoustic power level 

M0 Freestream Mach number ρ0 Fluid density 

N Rotor speed (revolutions per unit time) 

NTO Nominal takeoff e Acoustic emission angle 

OAPWL Overall power watt level g Geometric angle 

OASPL Overall sound pressure level 

p′ തതതଶത(d,g) Time-averaged mean-squared pressure 
NASA/CR—2015-218716 2 

1.0 Introduction 

The term “open rotor” refers to unducted counter-rotating dual rotors (propellers) which are being 

considered as propulsion devices for future aircraft (Refs. 1 and 2). Open rotors are also known as 

“propfans.” Open-rotor propulsion technology is now being developed as a viable alternative to modern 

day turbofan engines mainly because of predicted fuel economy benefits and improved performance 

(Ref. 3). However, high noise levels associated with open rotors pose both environmental and 

technological challenges. These include community noise around airports, passenger discomfort, aircraft 

structural integrity, and meeting stringent federal noise regulations. 

NASA Glenn Research Center (NASA GRC), in collaboration with the U.S. aircraft industry, has 

been conducting both analytical and experimental research studies to address this noise issue and to 

develop improved open rotor systems (Ref. 4). Tests on scale-model systems have been conducted in lowand high-speed wind tunnels at NASA GRC to understand the noise mechanisms and evaluate the 

acoustic performance of open rotors. Large amounts of both far-field and near-field acoustic data have 

been collected during an extensive test campaign in 2011 to determine the noise levels under various 

simulated flight conditions (Refs. 5 to 7). The far-field measurements were acquired on a 2.4-diameter 

(about 5 ft) sideline in the 915 LSWT and are the subject of the present report. This measurement 

distance is considered adequate for the sound to propagate as spherical waves. The near-field 

measurements were made on a sideline as close as 0.18 diameters (about 4.4 in.) in the 8- by 6-Foot (high 

speed) Supersonic Wind Tunnel (SWT) and are the subject of a companion report. The open rotor model 

used for testing was a one-fifth scale model having a so-called “historical” baseline blade set made of 

carbon fiber composite with a metal spar. This blade set is designated as “F31/A31” and serves as a 

nonproprietary baseline design for comparison with other blade designs (Refs. 5 to 7). 

Far-field acoustic tests on the model were carried out in the 915 LSWT tunnel at NASA GRC to 

study its noise characteristics at simulated scaled takeoff (STO), nominal takeoff (NTO), and approach 

(APP) flight conditions. The expected takeoff speed for an aircraft equipped with open rotor was expected 

to be about Mach 0.25, while the 915 LSWT tunnel can only reliably reach about Mach 0.20 depending 

on ambient conditions. Thus “nominal takeoff” blade pitch settings correspond to producing 100 percent 

of takeoff thrust at 100 percent rotor speed with Mach 0.20 freestream. “Scaled takeoff” conditions are a 

lower tip speed blade pitch setting that would produce takeoff thrust at 100 percent rotor speed when 

extrapolated to a freestream speed of Mach 0.25. Then, at Mach 0.20, scaled takeoff will correspond to 

64 percent of takeoff thrust at 80 percent shaft speed. Tests were conducted at various rotor speeds, angles 

of attack (AOA), and freestream Mach numbers (M0) to conduct a parametric study on model noise 

levels. A pylon was also installed in some tests to determine its effect on the noise levels. The F31/A31 

blades are being used to validate open rotor noise prediction codes as well as to improve acoustic and 

aerodynamic performance of current and future blade designs. 

An initial investigation of the test data of F31/A31 model has been reported by Elliott (Ref. 5), and 

most recently by Stephens (Ref. 6), in terms of narrowband noise spectra, sound pressure levels (SPL) 

and power watt levels (PWL) at STO, NTO, and APP flight conditions. Some comparisons were also 

made to understand the noise effects of pylon installation and AOA changes. These investigations were 

based on the overall noise levels only. No attempts were made to separate the tone and broadband noise 

components from raw test data. They were estimated from the overall noise spectrum by chopping off the 

spectrum at the base of peaky “tones” and assuming the remaining part as the “broadband.” No proper 

data processing tools were available at the time to separate tone and broadband noise. 

It is known that the open rotor total (or overall) noise consists of both tonal and broadband components. 

(The terms “total” and “overall,” and “tonal” and “tone,” will be used interchangeably in this report.) The 

determination of tonal and broadband noise components from raw acoustic test data is very important for 

properly assessing the noise control parameters and also for validating the open rotor noise prediction codes 

(Refs. 8 to 11). A new data processing method developed by Sree (Ref. 12) is now available to separate the 

tonal and broadband noise (spectral) components from raw experimental data of open rotors. This method 

will be applied to examine the tone and broadband noise levels of F31/A31 model. 
NASA/CR—2015-218716 3 

The main purpose of the present work is to analyze the far-field experimental data available on 

F31/A31 and report separately the tone and broadband noise results together with total noise. The test 

data, portions of which are deemed nonproprietary, were provided by NASA GRC to perform the task. 

The noise levels will be expressed in terms of SPLs and PWLs at simulated STO, NTO, and APP 

conditions. Variations of the noise levels with rotor speed, AOA changes, and input shaft power will be 

studied. The results will also include the effects of pylon installation on model’s noise. The noise levels 

will be examined to obtain correlations with model performance variables, such as rotor speed, thrust, and 

input shaft power. Model performance evaluation will also be made in terms of nondimensional 

parameters and empirical equations will be developed. It is hoped that the results presented here will 

serve as a valuable database for comparing other open rotor blade designs with F31/A31 and also for 

validating open rotor noise simulation codes. 

2.0 F31/A31 Model and the Test Rig 

A detailed description of F31/A31 model and the test rig is given by Elliot (Ref. 5) and Stephens 

(Ref. 6). However, a few salient features of the model will be worth repeating here. The F31/A31 model 

has two counter-rotating rotors. The axial distance between their pitch axes is 19.9 cm (7.8 in.). The 

forward rotor is approximately 65.2 cm (25.7 in.) in diameter and has 12 blades whereas the aft rotor is 

approximately 63.0 cm (24.8 in.) in diameter and has 10 blades. The hub diameter of the forward rotor is 

approximately 26.6 cm (10.5 in.) and that of the aft rotor is 24.6 cm (9.7 in.). The pitch of the rotor blades 

could be adjusted to provide different simulated flight conditions. The blade-pitch setting angles (BSA) of 

forward and aft rotors for the three flight conditions considered are as shown in Table 1. These BSAs 

were chosen in order to obtain the best aerodynamic performance of the system at a given shaft speed and 

flight condition (Ref. 5). It should be noted here that a change in blade-pitch angles means a change in 

flight condition. 

For all the tests conducted in the 915 LSWT, the F31/A31 model was mounted on a test rig called 

the “Open Rotor Propulsion Rig (ORPR)” in a simulated pusher-type arrangement (Refs. 5 and 6). The 

turbines within the test rig were fed by high pressure air at about 20 atm (300 psi) to turn the rotor blades. 

The drive rig was mounted on a turntable to provide angle of attack (AOA) changes relative to 

longitudinal axis of the model. The test rig had the capability to install a pylon upstream of the forward 

rotor to study its effect on overall noise development. Photographs of the model and the test rig installed 

in the LSWT, with and without pylon, are shown in Figures 1(a) and (b), respectively. 

TABLE 1.—BLADE-PITCH SETTING ANGLES (BSA) FOR THE 

THREE SIMULATED FLIGHT CONDITIONS 

Simulated flight condition BSA (Forward/Aft) 

Scaled takeoff (STO) 43.0/43.5

Nominal takeoff (NTO) 40.1/40.8

Approach (APP) 33.7/35.7
NASA/CR—2015-218716 4 

(a) With pylon 

(b) Without pylon 

Figure 1.—Photographs of F31/A31 model and ORPR test rig installed in 915 LSWT; 

(a) with pylon; (b) without pylon; (Courtesy: Acoustics Branch, NASA GRC). 
NASA/CR—2015-218716 5 

3.0 Test Configurations 

The test configurations for the model are summarized as given in Table 2 where test runs were made 

at various rotor speeds and angles of attack, with and without pylon installation, using a freestream 

M0 = 0.20. The tests that were performed (indicated by “y” in Table 2) had both rotors running at 

approximately the same speed. The rotor speeds were taken as the percentage of corrected design speed 

which was 6530 rpm. A few limited tests were conducted with M0 = 0.22 but they are not considered in 

the present work. 

TABLE 2.—TEST CONFIGURATIONS FOR F31/A31 OPEN ROTOR MODEL IN LSWT 

[Cells showing “y” represent tests that were performed in the current study.] 
NASA/CR—2015-218716 6 

4.0 Far-Field Sideline Acoustic Measurements 

The far-field sideline acoustic measurements were made using a traversing microphone probe on a 

track parallel to and 1.524 m (5 ft) away from the model (centerline) longitudinal axis (Refs. 5 and 6). 

The track can be seen in Figure 1(b). Data were taken at 18 positions, or stops, as the traverse moved 

from rear side to front side of the model during each test. At each stop, 3 million samples were acquired at 

a sampling rate of 200 kHz. The 18 traversing microphone stops are depicted in Figure 2 and the 

corresponding calculated geometric angles, g, and acoustic emission angles (Ref. 6), e, relative to the aft 

rotor pitch-change axis at M0 = 0.20 and a sideline distance, d = 1.524 m are listed in Table 3. The angles 

are measured with respect to the longitudinal axis of the model from the front. 

Figure 2.—Sketch depicting microphone stops relative to aft rotor of F31/A31 model in 915 LSWT; 

(Courtesy: Acoustics Branch, NASA GRC). 

TABLE 3.—MICROPHONE STOPS AND CORRESPONDING 

STREAMWISE LOCATIONS, GEOMETRIC AND 

ACOUSTIC EMISSION ANGLES RELATIVE TO 

AFT ROTOR PITCH CHANGE AXIS AT M0 = 0.20 
NASA/CR—2015-218716 7 

5.0 Results and Discussions 

The results and discussions of computed far-field noise levels from the test data for the F31/A31 

model at different simulated flight conditions are presented in this section. As mentioned earlier, the new 

data processing technique was used to separate the tone and broadband noise components from raw test 

data. Noise levels of each component were computed in terms of SPLs and PWLs and as a function of 

rotor speed, thrust, and AOA changes. The results of the variations of noise levels at different simulated 

flight conditions and the effects of pylon installation are presented and discussed. Model performance 

characteristics are also studied. The necessary data required for performance evaluation were obtained 

from run logs of the model test in LSWT. Correlations of thrust and overall PWL (OAPWL) with input 

shaft power are also presented. 

5.1 Narrowband Noise Spectra 

As stated earlier, the total, tonal, and broadband narrowband noise spectra were first determined using 

the method developed by Sree (Ref. 12). The spectral analysis of the data was performed using a time 

history length of 15 sec (3 million samples) with a Fast Fourier Transform (FFT) block size of 

16,384 points, giving a frequency resolution of 12.2 Hz at 200 kHz sampling rate. In order to avoid the 

interference of wind tunnel background noise, particularly at low rotor speeds, the raw data was preprocessed using a 500 Hz to 50 kHz band-pass filter before the spectral analysis was carried out. The 

915 LSWT noise interference has already been reported earlier by Elliott (Ref. 5), Stephens (Ref. 6), 

and Woodward, et al. (Ref. 8). 

An example of the narrowband spectra of the total (blue) noise and its corresponding tonal (red) and 

broadband (green) components is shown in Figure 3. These spectra were computed from the far-field 

acoustic data measured at microphone stop no. 8 which is at 90 geometric (or 78.5 acoustic) directivity 

angle with respect to aft rotor pitch axis. The test case was 85 percent rotor design speed at simulated 

NTO condition without pylon and AOA = 0. The spectral values are given in SPL (dB) as a function of 

frequency, in Hz. 

Figure 3.—Narrowband noise spectra of total, tonal, and broadband components (stop no. 8) at simulated NTO 

condition without pylon; 85 percent rotor design speed, AOA = 0. 

 
NASA/CR—2015-218716 8 

It is seen from this example that the tone noise is dominant in the 1 to 10 kHz range. The tone and 

broadband noise components are reasonably well separated except for a few spikes in the broadband 

spectrum (green curve in Fig. 3). Notice that these spike levels are well below their corresponding (major) 

tonal levels. The spikes are attributed to random phase shifts and modulations in narrow tonal frequencies 

in the measured signal due to unsteadiness or jitter in rotor speeds, particularly at higher shaft speeds. 

Measured signals also get distorted by other extraneous effects. The new data processing technique by 

Sree (Ref. 12) is not able to eliminate the spikes completely. This is one of the limitations of the new 

technique, particularly at higher shaft speeds with jitter, as reported by Sree and Stephens (Ref. 13). 

5.2 Thrust Versus Speed Relation—Effect of AOA and Pylon 

Before considering the results of SPLs and PWLs, it is necessary to present the thrust versus speed 

relation for the model first. The net (or total) thrust was measured by running both forward and aft rotors 

at the same speed. The net thrust as a function of percent rotor design speed is shown in Figures 4 for 

AOA = 0, 3, and 8 at simulated STO, NTO, and APP conditions. Figure 4(a) shows the results when 

pylon was present and Figure 4(b) the results without it. It should be noted that all STO runs were made 

without pylon at AOA = 0 only (see Table 2). The results show that, at a given rotor speed and flight 

condition, there are very minor changes in the thrust value when AOA is changed. 

(a) With pylon 

(b) Without pylon 

Figure 4.—Net thrust as a function of rotor speed at 

AOA = 0, 3, and 8 for simulated STO, NTO, and 

APP conditions; (a) with pylon and (b) without pylon. 
NASA/CR—2015-218716 9 

Figure 5.—Comparison of net thrust versus rotor design 

speed for AOA = 0, 3, and 8 at STO, NTO, and APP 

conditions with and without pylon. 

The results shown in Figure 4 when combined together and replotted as shown in Figure 5, also 

reveal that the presence of pylon and/or the AOA change brings only minor differences in the thrust value 

for a given rotor speed and flight condition (or blade-pitch setting). It is also noticed that each blade-pitch 

setting has a different thrust value for a given rotor speed, or conversely, each flight (or BSA) case has a 

different rotor speed at a given thrust value. 

5.3 Integrated Sound Pressure Levels 

The integrated sound pressure levels of the total, tone, and broadband noise at simulated flight 

conditions are also computed and compared. The integration was carried out using their respective 

narrowband spectral values from 500 Hz to 50 kHz. The main purpose of comparison of integrated SPL 

results here is to determine the effects of AOA change and pylon presence. Only the NTO case is 

considered here. The STO case had no data with pylon or AOA change and hence is not included. Results 

for the simulated APP condition were found to be similar. 

5.3.1 Effect of AOA 

Figure 6 shows a comparison of the integrated SPLs of the overall and the corresponding tonal and 

broadband signals for the case of 85 percent rotor design speed at simulated NTO condition without 

pylon. Figure 6(a) shows the integrated SPLs of the overall signal (also referred to as the overall SPL or 

OASPL) as a function of acoustic emission angle relative to aft rotor pitch axis (see Table 3) for AOA = 

0, 3, and 8. The results show that the noise level increases as the AOA increases. Further investigation 

showed that, at higher speeds, the noise difference between 0 and 3 becomes smaller compared to that 

between 3 and 8. The results of the integrated SPLs of the corresponding tone and broadband noise 

components also had similar characteristics, as shown in Figures 6(b) and (c), respectively. 

5.3.2 Effect of Pylon 

A comparison of the noise levels to study the effect of pylon installation is made in Figure 7. It shows 

the variation of integrated SPLs of the total and the corresponding tone and broadband noise components 

as a function of acoustic emission angle for the case with and without pylon. These results are again from 

data taken at 85 percent rotor design speed for the simulated NTO condition with AOA = 0. The results 

show that the presence of pylon causes a 1 to 3 dB increase in each noise component. A separate study 

showed that the difference in broadband noise levels with and without pylon was becoming smaller at 

higher speeds. Similar results were found at other AOAs and rotor speeds also. 
NASA/CR—2015-218716 10 

(a) Overall 

(b) Tone 

(c) Broadband 

Figure 6.—Comparison of integrated SPLs of (a) overall 

and the corresponding (b) tone, and (c) broadband noise 

components as a function of acoustic emission angle at 

simulated NTO condition without pylon; 85 percent rotor 

design speed. 
NASA/CR—2015-218716 11 

Figure 7.—Comparison of integrated SPLs of total and the 

corresponding tonal and broadband noise components as 

a function of acoustic emission angle at simulated NTO 

condition with and without pylon; 85 percent rotor design 

speed, AOA = 0. 

5.3.3 Effect of Flight Condition 

The integrated SPLs of the noise levels for a given rotor speed and thrust are also compared to 

understand the relative differences among the three simulated flight conditions. Since the data obtained 

for the simulated STO condition were only for AOA = 0 without pylon, the comparison made here will 

be with similar data at NTO and APP conditions also. 

5.3.3.1 Comparison at a Given Rotor Speed 

Figure 8 shows a comparison of the integrated SPLs of the overall and the corresponding tonal and 

broadband signals for the three simulated flight conditions at a given rotor design speed of 85 percent, 

without pylon and AOA = 0, in each case. Figure 8(a) shows the integrated SPLs of the overall noise as a 

function of acoustic emission angle. The results show that the SPLs of the total noise at STO are higher 

than the SPLs at NTO which, in turn, are higher than those at APP. This is the same order in which the 

thrust increases for a given rotor speed (Fig. 5). Similar results are obtained for the tone and broadband 

noise components also as shown in Figures 8(b) and (c), respectively. 

5.3.3.2 Comparison at a Given Thrust 

Figure 9 shows a comparison of the integrated SPLs of the overall and the corresponding tonal and 

broadband signals for the three simulated flight conditions at a given net thrust of 2224 N (500 lb), 

without pylon and AOA = 0, in each case. Figure 9(a) shows the integrated SPLs of the overall noise as a 

function of acoustic emission angle. The results show that the overall noise levels for the three cases are 

generally between 105 and 116 dB with larger values occurring around higher emission angles. The tonal 

results, given in Figure 9(b), shows generally higher SPLs for APP than for NTO and STO. The STO 

values are lower than NTO values for the large part. However, a separate study showed that at lower 

thrust values the tonal SPLs were fluctuating (1 to 5 dB) with APP being generally higher. The broadband 

noise results are shown in Figure 9(c) where the STO levels are higher than those for NTO or APP, but 

NTO values are higher than APP values. At lower thrust values, the broadband SPL differences between 

NTO and APP cases were found to be less than 2 dB. 
NASA/CR—2015-218716 12 

(a) Overall 

(b) Tone 

(c) Broadband 

Figure 8.—Comparison of integrated SPLs of (a) overall 

and the corresponding (b) tone, and (c) broadband noise 

components as a function of acoustic emission angle at 

simulated STO, NTO, and APP conditions without pylon; 

85 percent rotor design speed, AOA = 0. 
NASA/CR—2015-218716 13 

(a) Overall 

(b) Tone 

(c) Broadband 

Figure 9.—Comparison of integrated SPLs of (a) overall 

and the corresponding (b) tone, and (c) broadband noise 

components as a function of acoustic emission angle at 

simulated STO, NTO, and APP conditions without pylon; 

2224 N (500 lb) thrust, AOA = 0. 
NASA/CR—2015-218716 14 

5.4 Acoustic Power Levels 

Sound or acoustic power is sonic energy per unit time and is measured in Watts (W). The sound 

power level, sometimes, is expressed as Power Watt Level (PWL) in dB unit. PWL is a logarithmic 

measure of the sound power level in comparison to a reference level of 10–12 W, i.e., PWLdB = 10 log10

(Pac/Pref) where Pac = measured acoustic power in W and Pref = 10–12 W. 

In this work, the acoustic power level, Π (or PWL), was calculated using the following equation 

which takes into account the tunnel or freestream Mach number effect (Ref. 14): 

Π ൌ

2πdଶ

ρ଴c଴

න ሺ1െM଴ cos θୣሻଶ p′ തതതଶത൫d, θ୥൯

sin θୣ

dθୣ

஠

଴

where 

d sideline distance from model centerline 

0 ambient air density 

c0 speed of sound 

M0 tunnel or freestream Mach number 

e acoustic or sound emission angle 

g geometric (measurement) angle 

p′ തതതଶത(d,g) time-averaged sideline mean-squared pressure at measurement angle, g

[Note: e = g – sin–1(M0 sin g)] 

by assuming the measured sideline pressures were in the acoustic far-field. Spherical spreading was used 

to map the sideline measurement on to a constant radius arc. The acoustic intensity (Ref. 14) at each 

speed was calculated using the information from corresponding narrowband spectra and was integrated 

over frequencies between 500 Hz and 50 kHz. The intensity was assumed to be symmetric about the axis 

of the model and integrated over the portion of the spherical surface spanned by the sideline measurement 

angles. The upstream and downstream portion beyond the measurement angle was excluded from the 

calculation. 

5.4.1 Overall PWL Versus Rotor Speed; Effect of AOA 

Overall PWLs of the total noise were computed as a function of rotor speed for the three angles of 

attack considered both with and without pylon. Results are given in Figure 10. Figure 10(a) shows the 

results computed at AOA = 0, 3, and 8 for the STO, NTO, and APP conditions with pylon. (Note that 

the STO case had no data with pylon.) Similar results are shown in Figure 10(b) for the case without 

pylon. The results show that, in each flight case, there is very little difference in the overall PWL (less 

than 1 dB) for AOA = 0 and 3, but that difference becomes 1 to 3 dB when AOA is increased to 8. In 

general, for a given rotor speed, the overall PWL values for STO are higher than the values for NTO 

which, in turn, are higher than those for APP. Tone and broadband noise were found to have similar 

characteristics. 
NASA/CR—2015-218716 15 

(a) With pylon 

(b) Without pylon 

Figure 10.—Overall PWL as a function of rotor speed at 

AOA = 0, 3, and 8 for simulated STO, NTO, and 

APP conditions; (a) with pylon and (b) without pylon. 

5.4.2 PWLs of Noise Components; Effect of Pylon 

The results in Figure 10, after careful examination, also show that there are differences in the overall 

PWL value when the pylon is present. These differences are shown in Figure 11(a) by replotting the 

results exclusively for the AOA = 0 case. These overall PWL results show that, in general, the PWL is 

higher when pylon is present. (STO case had no data with pylon.) The PWL difference starts at about 

4 dB at lower rotor speeds and gradually decreases to about 1 dB or less at higher speeds for each 

simulated flight condition. A similar analysis was performed for the tonal and broadband noise 

components also and the results are shown in Figures 11(b) and (c), respectively. In the tonal case, the 

PWL difference when pylon is present starts at about 5 dB and gradually decreases to about 1 dB or less 

at higher speeds for a given simulated flight condition. In the broadband case, these differences are less 

than about 2 dB. 
NASA/CR—2015-218716 16 

(a) Overall 

(b) Tonal 

(c) Broadband 

Figure 11.—Comparison of (a) overall and the corresponding 

(b) tonal and (c) broadband PWLs as a function of rotor 

design speed at simulated STO, NTO, and APP conditions 

with and without pylon; AOA = 0. 
NASA/CR—2015-218716 17 

5.4.3 Comparison of PWLs of Noise Components at a Given Flight Condition 

The overall and the corresponding tonal and broadband PWLs together are once again presented 

separately for each simulated flight condition as shown in Figures 12. This helps to understand and 

visualize the relative contribution from tone and broadband noise to make up the total noise. 

(a) STO 

(b) NTO 

(c) APP 

Figure 12.—Overall and the corresponding tonal and 

broadband PWLs as a function of rotor design speed at 

(a) STO, (b) NTO, and (c) APP; AOA = 0, without pylon. 
NASA/CR—2015-218716 18 

The results are given as a function of rotor design speed for AOA = 0, without pylon, only. It is 

interesting to see that, in the STO case (Fig. 12(a)), the broadband levels become higher than the tonal 

levels for rotor speeds beyond about 82 percent. This could be due to thicker and more turbulent blade 

wakes or possibly flow separation occurring at higher blade-pitch setting at STO. This is not so in the 

NTO (Fig. 12(b)) or APP (Fig. 12(c)) case where the tonal levels are always higher than the broadband 

levels for any given rotor speed. Also it is seen that, in general, the noise levels (of each component) in 

STO case are higher than the levels in NTO which, in turn, are higher than those in APP case for a given 

rotor speed. 

5.5 Acoustic Performance of F31/A31 

The acoustic performance of open rotors is also of great concern in the open rotor research and design 

community. It is usually evaluated based on correlation between emitted acoustic power and a system 

performance variable, such as thrust or input shaft power. Here an attempt will be made to develop a 

correlation between overall PWL and input shaft power for F31/A31 model. Before considering this 

correlation, it is also important to study the variations of input shaft power with rotor speed, as well as 

thrust, for the model at all the simulated flight conditions. The study is given below. 

5.5.1 Input Shaft Power Versus Rotor Speed 

The variations input shaft power with rotor speed for the F31/A31 model at all the test conditions are 

shown in Figure 13. It is seen that the shaft power, for a given rotor speed and flight condition, is almost 

independent of AOA change and pylon presence. These results have similar characteristics to that of 

thrust versus rotor speed (Fig. 5). Also noticed is that each simulated flight condition has a different input 

shaft power value for a given rotor speed. 

Figure 13.—Comparison of input shaft power versus rotor design 

speed at simulated STO, NTO, and APP conditions with and without 

pylon for AOA = 0, 3, and 8. 
NASA/CR—2015-218716 19 

Figure 14.—Variation of net thrust with input shaft power at STO, NTO, 

and APP conditions with and without pylon for AOA = 0, 3, and 8. 

5.5.2 Thrust Versus Input Shaft Power 

It is also important to know how thrust varies with shaft power for the model. The variations of net 

thrust with input shaft power from all the test cases are shown in Figure 14. The results exhibit a very 

good correlation between thrust and input shaft power for the F31/A31 model. From regression analysis, a 

polynomial curve-fit of the form: 

 T = - 0.0058 Psp

2

 + 9.7138 Psp + 104.7926 (1) 

with a goodness-of-fit parameter R2 = 0.9995, has been determined. In the equation above, T stands for 

net or total thrust, in N, and Psp for total input shaft power, in kW. 

5.5.3 Overall PWL Versus Input Shaft Power 

As mentioned before, STO, NTO, and APP comparison means comparison of different BSAs for the 

open rotor model. Several parameters can be used to establish correlation between acoustic power levels 

and model performance variables. Janardan and Gliebe (Ref. 15) found a good correlation between 

overall PWL (OAPWL) and input shaft power for one of the earlier open rotor models they tested. They 

suggested to use a plot of overall PWL as a function of shaft power per blade, or log10 (shaft power per 

blade), to obtain a good indication of blade loading for a given input shaft power. Both types of plots are 

presented in Figure 15 for the F31/A31 model. The results shown in the plots are for the case where 

AOA = 0, without pylon, at simulated STO, NTO, and APP conditions. As seen from these results, a 

good correlation between OAPWL and input shaft power is observed. Using regression analysis, a power 

curve-fit of the form: 

 OAPWL = 104.2 Pspb

0.09 (2) 

with R2 = 0.99 is found for the results in Figure 15(a), whereas a linear curve-fit of the form: 

 OAPWL = 24.8 log10 (Pspb) + 102.2 (3) 

with R2 = 0.99 is found for the results in Figure 15(b). In both of these equations, Pspb stands for input 

shaft power per blade, in kW, and OAPWL is in dB. Based on the actual results obtained in this work, the 

maximum error associated with these empirical equations is found to be less than 1.5 dB. Similar 

correlations can be obtained for tonal and broadband PWLs also. 
NASA/CR—2015-218716 20 

(a) OAPWL versus Shaft Power per Blade 

(b) OAPWL versus log10 (Shaft Power per Blade) 

Figure 15.—Variation of OAPWL with input shaft power at STO, 

NTO, and APP conditions for AOA = 0 without pylon. 

5.6 Acoustic Efficiency 

The acoustic efficiency is defined as the ratio of the radiated acoustic power to the input shaft power 

where the radiated acoustic power is taken as the OAPWL (Refs. 15 and 16). Both powers are taken in 

kilowatt units in this work. Janardan and Gliebe (Ref. 15) came up with an acoustic efficiency of less than 

0.1 percent for the F7A7 (8/8) open rotor blade design they tested. Hanson (Ref. 16) quotes typical 

acoustic efficiency values in the range of 0.02 to 0.05 percent for modern turbofan engines. [Huff 

(Ref. 17) reports that there has been considerable reduction (about 20 dB) in average noise levels for 

commercial aircraft since the 1960s.] Hanson also states that the significantly higher values for open 

rotors are attributed to the open tips and smaller number of blades. 

Based on computed values in the present study, the acoustic efficiency for the F31/A31 model is 

found to be less than 0.007 percent for the BSAs at STO, NTO, and APP conditions, as shown in 

Figure 16. This order of magnitude reduction is presumably attributed to significant improvements in 

open rotor design compared to those since the mid 1980s. The results shown in this plot are for the case of 

AOA = 0, without pylon, only. 
NASA/CR—2015-218716 21 

Figure 16.—Acoustic efficiency of F31/A31 model based on results from 

simulated STO, NTO, and APP conditions at AOA = 0 without pylon. 

5.7 Nondimensional Plots of Model Performance 

The F31/A31 open rotor model performance characteristics can also be visualized through some 

traditionally-used nondimensional parameters. Generalized empirical equations of model performance can 

be obtained by plotting these parameters in certain ways. The parameters used in this work are defined as 

follows: 

Advance ratio (J): J = V0 / N D 

Thrust coefficient (CT): CT = T /0N2

D2Aa

Propulsion efficiency (ηp): ηp = T V0 / Psp

Input shaft power coefficient (Csp): Csp = Psp /0N3

D3Aa

Acoustic power coefficient (Cac): Cac = Pac /0N3

D3Aa

where 

V0 Freestream velocity T Net thrust 

0 Fluid density Psp Net input shaft power 

N Rotor speed (revs per unit time) Pac Measured acoustic power 

D Reference rotor diameter Aa Reference rotor annular area 

Note that the forward rotor was referenced for all the above calculations in this work. 

Advance ratio (J) of a propeller (or rotor) is the ratio between the distance the propeller moves 

forward through the fluid medium during one revolution and the diameter of the propeller (Ref. 18). High 

advance ratio means high speed of that propeller-driven vehicle relative to the fluid through which it 

moves; and low advance ratio means low speed of the vehicle. The advance ratio is a means of describing 

the incoming angle of the fluid relative to the propeller blade. It is analogous to the angle of attack of an 

airfoil (Ref. 18). 
NASA/CR—2015-218716 22 

5.7.1 Thrust Coefficient Versus Advance Ratio 

Figures 17 shows a plot of thrust coefficient, CT, as a function of advance ratio, J, for the F31/A31 

open rotor model tested at the three simulated flight conditions considered in this work. It is seen that CT

decreases as J is increased. The change in angle of attack and/or presence of pylon seems to have no 

significant effect on the results. 

5.7.2 Input Shaft Power Coefficient Versus Advance Ratio 

Figures 18 shows a plot of input shaft power coefficient, Csp, as a function of advance ratio, J, for the 

F31/A31 model tested at the three simulated flight conditions mentioned before. Just like CT, Csp also

decreases as J is increased. There is little effect on the results with angle of attack change and/or pylon 

presence. 

Figure 17.—Plot of CT versus J for F31/A31 open rotor model. 

Figure 18.—Plot of Csp versus J for F31/A31 model. 

 
NASA/CR—2015-218716 23 

5.7.3 Thrust Coefficient Versus Input Shaft Power Coefficient 

Figure 19 shows a plot of CT versus Csp at the three flight conditions considered for F31/A31 model. 

As expected, CT increases with Csp. These results, as noticed, do not fall on a line. 

However, by normalizing CT with J2

, and Csp with J3, the results can be combined together to get a 

single curve, as shown in Figure 20, and a correlation between CT/J2 and Csp/J3 can be obtained as: 

 CT/J2 = - 0.0460 (Csp/J3)

2

 + 0.6759 (Csp/J3) + 0.0722 (4) 

with R2 = 0.9993. This could be a generalized equation for CT as a function of Csp and J for future open 

rotor designs similar to F31/A31. The maximum error using this CT prediction equation is estimated to be 

less than 2.5 percent. 

Figure 19.—Plot of CT versus Csp for F31/A31 model. 

Figure 20.—Plot of CT/J2 versus Csp/J3 for F31/A31 model. 
NASA/CR—2015-218716 24 

5.7.4 Acoustic Power Coefficient Versus Input Shaft Power Coefficient 

A plot of acoustic power coefficient, Cac, versus the input shaft power coefficient, Csp, for the three 

flight cases of F31/A31 model is shown in Figure 21. Small variations due to the presence of pylon and 

changes in AOA can be observed in NTO and APP cases. (Recall that the STO case did not have AOA 

changes or pylon installed.) No reasonable correlation was found for this case. 

5.7.5 Propulsion Efficiency Versus Advance Ratio 

Figure 22 shows a plot of propulsion efficiency (ηp) as a function of advance ratio, J, for the F31/A31 

model tested at all three simulated flight conditions. As noticed, ηp increases as J is increased in each 

case. Also seen is that, for a given J, ηp decreases as the blade setting angles are increased, i.e., from APP 

to NTO to STO. Small variations in ηp due to AOA changes and pylon presence can also be observed. 

Figure 21.—Plot of Cac versus Csp for F31/A31 model. 

Figure 22.—Plot of ηp versus J for F31/A31 model. 

 
NASA/CR—2015-218716 25 

Figure 23.—Plot of ηp/J7 versus J for F31/A31 model. 

The results in Figure 22 can be combined to yield a single curve by plotting ηp/J7

 versus J, as shown 

in Figure 23. Based on regression analysis, an empirical equation for propulsion efficiency of the 

F31/A31 model can be obtained as: 

ηp /J 7 = 0.6063 J - 6.5363 or ηp = 0.6063 J 0.4637 (5) 

with R2 = 0.9917. Using this prediction and based on current results, the maximum error in ηp is estimated 

to be less than 16.5 percent, but it seems rather high. 

6.0 Conclusions 

Analyses of far-field SPLs, PWLs, and performance characteristics of open rotor model F31/A31 at 

three simulated flight conditions (STO, NTO, and APP) have been presented in this work. The analyses 

were performed based on the nonproprietary portion of the test data provided by NASA GRC. Tests cases 

consisted of variations in rotor speed and angle of attack. An upstream pylon was installed in some cases. 

All tests were carried out at a freestream Mach number of 0.20 and with both rotors running at the same 

speed. 

A new data analysis technique has been successfully applied to separate the tone and broadband noise 

components from the measured raw data to understand their level of contribution to total noise. Computed 

overall, tonal, and broadband SPLs, PWLs, and their variations with rotor speed, angle of attack, thrust, 

and input shaft power at each simulated flight condition have been presented and discussed. The effect of 

pylon on the noise levels of the model has been addressed. 

The results show that, depending upon rotor design speed and angle of attack, the presence of pylon 

causes 1 to 5 dB increase in noise level. At any given rotor speed, the STO condition, because of higher 

thrust involved, shows higher noise level than those at NTO or APP condition. At any given thrust, the 

APP condition, because of higher speeds involved, shows slightly higher tone noise than those at STO or 

NTO condition, but, in the case of broadband noise, the opposite happens. 

Based on regression analysis, correlations have been developed for relations between thrust and input 

shaft power, acoustic power and input shaft power, and, propulsion efficiency and advance ratio. The 

acoustic efficiency of the model is found to be less than 0.007 percent at the three simulated flight 

conditions. 
NASA/CR—2015-218716 26 

Finally, it is hoped that the results presented in this work will serve as a good database for comparison and 

improvement of other open rotor blade designs, as well as for validating open rotor noise prediction codes. 

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