Multirotor Drone Noise at Static Thrust

Charles E. Tinney∗

University of Texas at Austin, Austin, Texas 78713

and

Jayant Sirohi†

University of Texas at Austin, Austin, Texas 78712

DOI: 10.2514/1.J056827

A first principles understanding of the sound field produced by multirotor drones in hover is presented. Propeller

diameters ranging from 8 to 12 in. are examined and with configurations comprising an isolated rotor, quadcopter,

and hexacopter configuration. The drone pitch, defined as the ratio of drone diameter to rotor diameter, is the same

for all multirotor configurations and is valued at 2.25. A six-degree-of-freedom load cell is used to assess the

aerodynamic performance of each configuration,whereas an azimuthal array of 1∕2 in.microphones, placedbetween

two and three hub-center diameters from the drone center, is used to assess the acoustic near field. The analysis is

performed using standard statistical metrics such as sound pressure level and overall sound pressure level and is

presented to demonstrate the relationship between the number of rotors, the drone rotor size, and its aerodynamic

performance (thrust) relative to the near-field acoustics.

Nomenclature

Acs = airfoil cross-section areaA = propeller disk areaa = acoustic velocityCT = thrust coefficientCτ = torque coefficientc = propeller chordD = drone diameterd = propeller diameterE = wavelet energy densityFi = forceFM = figure of meritf = frequencyfs = sampling frequencyf� = f∕Ωb, nondimensional frequencyG = premultiplied spectral = wavelet time scaleMtip = propeller tip Mach numberMi = momentN = data partition sizen = number of propellersOASPL = overall sound pressure levelP, p = pressure~p = wavelet coefficient of pPSD = power spectral densityR = propeller radiusr = radial coordinate measured from propeller rootSPL = sound pressure levelT = temperaturet = propeller thickness, timeβ = propeller twist distribution, degγ = specific heat ratioδf = frequency incrementδθ = polar coordinate incrementϵb = bias error

ϵp = precision errorϵRSS = root sum of squares errorsθ = polar coordinateλ = drone pitchξ = propeller sweepρ = gas densityζ = time delayτ = torqueϕ = phaseφ = radial coordinate measured from drone centerψ = mother waveletΩ = motor rotation speedΩb = blade-pass frequency, passes per secondω = time per rotation, s

Subscripts

x, y, z = Cartesian coordinates∞ = ambient condition* = complex conjugate

I. Introduction

SMALL-SCALE unmanned air vehicles (UAVs) using multirotorpropulsion systems have become increasingly popular in recent

years due to their affordability and versatility. Commonly called“drones”, these UAVs provide a stable airborne platform on which avariety of equipment can bemounted, such as cameras and ultrasonicsensors. These multirotor vehicles are available in a wide range ofsizes, with the smallest drones for hobbyists measuring less than 2 in.in diameter, whereas the largest commercially available drones can bein excess of 5 ft. New and useful applications for drone vehiclesunfold daily, which in turn demands a range of propulsiverequirements, with configurations ranging fromquadcopters to largeroctocopter shapes.The performance of the propeller blade is undoubtedly important

to the design and efficiency of the vehicle because it affects theallowable size of its payload, its maneuverability, and ultimatelyloiter time. Some efforts to characterize propeller performance and toimprove propeller design optimization tools can be seen in the workof Deters and Selig [1] and Ol et al. [2]; the task of studying allavailable configurations is daunting. A secondary effect of thepropeller design, which has received considerably less attention, isthe acoustic signature that it produces. Given the growing demand fordrone related tasks and the proximity of these activities to populatedareas, the sound issue is becoming a topic of broad importance. It isfor this reason that the current study was performed.

Received 16October 2017; revision received22 January 2018; accepted forpublication 28 January 2018; published online 6 April 2018. Copyright© 2018 by the authors. Published by the American Institute of Aeronautics andAstronautics, Inc., with permission. All requests for copying and permission toreprint should be submitted to CCC at www.copyright.com; employ theISSN 0001-1452 (print) or 1533-385X (online) to initiate your request. See alsoAIAA Rights and Permissions www.aiaa.org/randp.

*Research Associate, Applied Research Laboratories; cetinney@utexas.edu. Associate Fellow AIAA (Corresponding Author).

†Associate Professor, Center for Mechanics of Solids, Structures andMaterials. Member AIAA.

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Here, we will show the results from a test campaign designed to

develop a basic understanding for the acoustic signatures produced

by multirotor (quadcopter and hexacopter) drone configurations

operating under static thrust conditions. Variables of primary interest

are the size and rotational speed of the propeller blades as well as the

number of propeller blades.

II. Experimental Hardware and Setup

Tominimize interference from background noise, the experiments

were performed in the anechoic chamber at the J. J. Pickle Research

Campus of the University of Texas at Austin (UT Austin).

Descriptions of this facility are provided byMula et al. [3] and Fiévet

et al. [4], with the current setup being configured in a quasi-hemi-

anechoic arrangement. That is, only the ceiling of the anechoic

chamber received full anechoic treatment (melamine foam wedges

with air cavity followed by 5.5 in. of recycled cotton-fiber insulation),

whereas the foam wedges on all four walls were removed to increase

air flow to the rotor; the floor was exposed concrete with one set of

wedges located beneath the microphone array. The resulting interior

dimensions (from wedge tips to walls) measured 18.5 ft (width)

×22.5 ft (length) ×14 ft (height).The three primary pieces of hardware used in this study were a

support structure with a six-degree-of-freedom load cell (for

measuring the aerodynamic performance of the drone), amicrophone

array (to capture the near-field acoustic signatures), and a multirotor

drone with relevant power and electrical systems. Unlike other

studies that use fully assembled off-the-shelf drone kits, a custom

fabricated multirotor drone test stand was built for this endeavor,

which resulted in a relatively more generic set of hardware that

provided additional degrees of freedom in the test matrix. An

illustration of the quadcopter configuration undergoing testing is

provided in Fig. 1 identifying some of these major hardware

components. A description of these three components follows.

A. Multirotor Drone and Electrical System

The multirotor drone was designed to mimic many of the off-the-shelf configurations that are available to hobbyists and enthusiastsalike. These commonly fall into three categories: quadcopter (fourpropellers), hexacopter (six propellers), and octocopter (eightpropellers) configurations; the former appear to bemore popular (andless expensive) but have a limited payload capacity. Therefore, theidea was to distribute an array of motors/propellers (four, six, andeventually eight) azimuthally with equidistant spacing so that thedrone pitch λ (the ratio of the drone diameterD to propeller diameterd) could be fixed for a range of propeller diameters of practicalinterest. Some design constraints must be considered of course. Forexample, if all rotor disks are at the same plane and are

nonoverlapping, then d ≤ D sin�π∕4� � D∕���2

pfor a quadcopter,

d ≤ D sin�π∕6� � D∕2 for a hexacopter, and d ≤ D sin�π∕8� �D

����������������2 −

���2

pp∕2 for an octocopter. With this in mind, a drone pitch of

λ � D∕d � 2.25 was chosen, which was not only within theconstraints of the D∕d limits for the quadcopter and hexacoptersetups but appeared to reflect many of the commercially availabledrone kits.The structural frame for the multirotor drone was fabricated in

house by combining aluminum plates with lightweight miniaturizedextruded aluminum rails. The aluminum plates were machined toaccommodate quadcopter, hexacopter, and octocopter configura-tions, whereas the extruded aluminum rails formed stiff adjustablesupport arms that were extended to increase D for larger diameterpropellers. An image of the fully assembled hexacopter is provided inFig. 1a alongside a close-up of one of the adjustable arms in Fig. 2b.Each propeller was driven directly (without gears) by its own

dedicated motor such that the angular position of each propeller wasdifferent for each test. The motors are a brushless outrunner type with13 circumferentially distributed magnets capable of handling up to229 W of power (∼11 V dc). As seen in Fig. 2b, each motor isconnected to a dedicated speed controller that can transmit up to 36 Aofdirect current from the power supply to themotor. Electrical power issupplied by a 10 kW (maximum) Lambda TKE ESS 50-200programmable dcpower supply that outputs up to50Vat 200A.Powerfrom the Lambda unit is transmitted to the drone test stand using 2American wire gauge (AWG) welders cable to reduce electricaltransmission losses; 6 AWG was used during earlier stages of the testprogram and proved to be problematic. The speed of each motor wasmonitored and controlled by a closed-loop controller via a 1∕revmagnetic sensor on each motor. This worked by changing the pulsewidth of themodulated signal that the speed controllers used to governpower to the motors. The 1∕rev sensor was also used for aligningacoustic data during the isolated propeller tests described later.There are numerous propeller blades to choose from for propelling

a drone, which will have a profound influence on both itsaerodynamic and aeroacoustic performance [5]. The propellerschosen here were models 8 × 4.5 MR�P�, 9 × 4.5 MR�P�,10 × 4.5 MR�P�, 11 × 4.5 MR�P�, and 12 × 4.5 MR�P�, manufac-tured by APC Propellers. These self-tightening propellers areintended for multirotor vehicle applications because they aremanufactured in both standard and reverse screw configurations.An image of the 8 and 12-in.-diam propellers is provided in Fig. 3.Fig. 1 Quadcopter during testing with 8-in.-diam propeller blades.

a) b)Fig. 2 Photographs of a) the hexacopter with 8-in.-diam propellers, and b) support arms and motor mounting configuration.

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Various geometrical properties are shown in Fig. 4 as provided by themanufacturer. Here, β is the twist distribution, ξ is the blade sweep,and Acs is the airfoil cross-section area.

B. Loads Measurement Apparatus

All loads were measured by a six-component load cell (ATIIndustrial AutomationMini40E), sampled at 10 kHz using aNationalInstruments PXI system. The electronics and data acquisition systemare similar to the setup used by Cameron et al. [6] to study coaxialcounter-rotating rotors during hover. This strain-gauge-based loadcell can measure three orthogonal forces (Fi � Fx,Fy,Fz) and threeorthogonal moments (Mi � Mx, My, Mz). The load cell wasmanufacturer calibrated to a full-scale Fz of 15 lbf and a full-scaletorqueMz of 10 lbf·in. The drone and load cell assemblywas elevatedto the center of the anechoic chamber using a stiff support structure.This positioned the rotor disk plane at 100 in. from the concrete floorbelow to suppress ground effects; see Mula et al. [7] for a descriptionof this rotor test stand. Two separate setups were tested. The firstcomprised isolated propellers in which a propeller and motorcombination was mounted on a long cylindrical support, which wasthen attached to the load cell. The cylindrical support was similar indiameter to themotor diameter tominimizewake interference effects.An illustration of this setup is shown in Fig. 5. The process wasrepeated for different diameter propellers and with propeller thrustand torque being taken as the Fz andMz force and moment acting onthe load cell, respectively.The second setup comprised themultirotor drone inwhich the long

cylindrical support was removed so that the entire vehicle could bemounted directly to the load cell. Like the isolated propeller study,vehicle thrust was measured as Fz and vehicle torque was measuredas Mz. Note that the propellers in the multirotor drone experimentswere configured to cancel torque (or was nearly zero in all cases), and

so half of the propellers were spinning clockwise, whereas the other

half were spinning counterclockwise.The total error in the measured thrust was determined by the root

sum of squares errors (ϵRSS) of the bias (ϵb) and precision (ϵp) errorsof the Fz measurements, as given by

ϵRSS �����������������ϵ2b � ϵ2p

q(1)

Bias errors were obtained from the manufacturer specified

calibration sheet for the load cell. Although the manufacturer

specifies a maximum, or worst-case bias error of 0.75% of full-scale

for theFz load, the calibration sheet indicates the actual bias error for

the range of loads encountered in these experiments to be less than

0.06% full scale. Therefore, a realistic estimate of the bias error is

taken to be 0.06% of the full-scale 15 lbf load, which is 0.009 lbf. The

mean and standard deviation of the loads at each test condition were

calculated from a set of 25,000 samples. Precision error is taken as the

standard deviation of these Fz samples. The largest standard

deviation is 0.05 lbf, which is taken as a conservative estimate of the

precision error in thrust. The resulting total estimated error in the

thrust Fz using Eq. (1) is 0.0508 lbf.Thrust coefficient CT , torque coefficient Cτ, and the rotor’s figure

of merit (FM) were then calculated for each test case using the

following well-known definitions:

CT � Fz

nρA�ΩR�2 (2)

Fig. 3 The 8 and 12-in.-diam propellers manufactured by APCPropellers.

a) b)

0

0.05

0.1

0.15

0.2

0.25

0

10

20

30

40

β

c) d)0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3

0

0.05

0.1

0.15

0.2

0.25

0.3

Fig. 4 Representations of a) propeller chord, b) twist distribution, c) thickness ratio and maximum thickness distributions, and d) sweep and cross-section area distributions.

Fig. 5 Isolated propeller with a 12-in.-diam propeller.

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Cτ �τ

nρA�ΩR�2R (3)

FM � C3∕2T ∕

���2

p

Cτ(4)

where τ is the measured torque, R � d∕2 is the propeller radius,A � πd2∕4 is the disk area, Ω is the motor rotation speed in rad∕s,and n is the number of propellers. For the isolated propeller case, n isvalued at 1.0.

C. Microphone Array

Given the dynamic range of the sound levels produced by thesekinds of vehicles, as well as the bandwidths of interest, four G.R.A.S.IEPE-powered 1∕2 in. free-field microphones were selected formeasuring the sound field. These microphones (model 46AE) withmatching preamplifiers (model 26CA) have a frequency responserange of 5 Hz to 10 kHz (�1 dB accuracy) or 3.15 Hz to 20 kHz(�2 dB accuracy) as well as a dynamic range of 17 dB(A) to 138 dBwith nominally 50 mV∕Pa sensitivity. To improve accuracy, both themicrophone capsules and preamplifiers were calibrated by themanufacturer as one unit. IEPE power was provided by a NationalInstruments PXI system (NI-PXI-4472 board), which also filtered(low pass Butterworth set to 84% of the Nyquist frequency) anddigitized their voltages using dedicated 24-bit accurate converters.The acquisition ratewas set to 40 kHz for an uninterrupted duration of20.48 s at each test condition. Digitized signals were converted toengineering units and partitioned into 100 data blocks comprising 213

data points per block.Both an arc array and a line array of microphone measurement

points were used in this study, with each array being in line with onerotor (not split between two). An illustration of this is provided inFig. 6with coordinate system. The arc array is such that 0 deg is at therotor disk plane, with positive angles θj being measured in thedirection of the thrust vector; a description of the line array isprovided in Sec. III.B.2. For the arc array, eight unique measurementpoints were selected, with microphones focused on the drone center.The first four points, further referred to as j � 1; : : : ; 4, covered thelocations at −45, −30, −15, and 0 deg, whereas the second, furtherreferred to as j � 5; : : : ; 8, covered locations at 7.5, 15, 22.5, and30 deg. Preliminarymeasurements revealed increased sound pressurelevels above the rotor disk plane, and so the positive angles weredesigned to capture a finer grid (δθ � 7.5 deg) relative to thenegative angles (δθ � 15 deg). Microphone diaphragms wereoriented so that they faced the multirotor drone at a distance ofφ � 43.5 in: from the drone center. Table 1 provides the placementof the arc array of microphones in dimensionless form. Given thebandwidths of interest and the close proximity of this microphonearray to the multirotor drone, corrections for atmospheric absorptionwere not implemented because they were found to be insignificant.The test matrix for this study is provided in Table 2 andwas chosen

to cover themaximum safe operating range, in revolutions per second(rev∕s), allowed by the motors for a given multirotor configuration

and propeller diameter. Only two propeller sizes were tested in thehexacopter configuration. However, the forthcoming analysis willshow how the trends from the quadcopter and hexacopterconfigurations can be extrapolated for different propeller diameters.

III. Results

A. Aerodynamic Performance

Measurements were acquired over a duration of severalconsecutive days with the drone operating in static hover conditionsonly. Though atmospheric propertieswere not recorded, it is assumedthat they are near standard sea-level conditions. Therefore, P∞ �14.696 psia (101,325 Pa), T∞ � 525.6 R (292 K), γ � 1.3991, andρ � 2.34 × 10−3 slug∕ft3 (1.2082 kg∕m3) so that the sound speed ofair is valued at a∞ � 1; 122 ft∕s (342 m∕s). An initial set ofmeasurements focused on gathering aerodynamic performance datafor the isolated propeller using the configuration shown in Fig. 5.Doing so provided a base set of measurements without the effect ofneighboring propellers. These measurements were conducted formotor speeds up to the maximum allowable power (within thethermal limits of the motor).Thrust and torque coefficients corresponding to all five propeller

diameters are shown in Figs. 7 and 8 for a range of rotor speeds (andpropeller tip Mach numbers, defined asΩR∕a∞). Overall, the trendsare as expected,with differences (between propeller diameters) beingattributed to Reynolds number effects; similar findings were reportedby Brandt and Selig [8] for the same propeller shapes. When plottedusing the propeller tip Mach number, a clear barrier forms for allpropeller diameters just beyond Mtip of 0.3. It is postulated that themotors’ maximum allowable safe amperage draw is limited by theelevated drag levels that accompany the onset of compressibilityeffects. Turning one’s attention to Fig. 8b, the figure ofmerit is shownto collapse reasonablywell using the propeller tipMach number,withmaximum values hovering between 0.65 and 0.70.A comparison of the thrust values measured using the isolated

propeller, quadcopter, and hexacopter configurations is shown inFig. 9a for the 8 and 10-in.-diam propellers. A second-order least-squares fit of the data (denoted by solid and dashed lines in Fig. 9) forthe individual cases is also displayed and reveals subtle differencesbetween the three configurations for a given propeller diameter. Thethrust values for the quadcopter and hexacopter have been divided bythe number of propellers in their respective setups to match theisolated propeller data. Because the drone pitch is the same for bothquadcopter and hexacopter configurations (λ � 2.25), the spacingbetween neighboring propeller tips is smaller for the hexacopterconfiguration than for the quadcopter, which has been found toelevate interactions between neighboring propeller disks andadversely affect thrust. For example, Intaratep et al. [9] measured thethrust and acoustics of a commercial quadcopter drone kit comprisinga drone pitch of approximately 1.45 and observed 5.8 and 7.3%reductions in thrust when going from the isolated propeller to abicopter configuration and then from a bicopter to quadcopterconfiguration, respectively. The current data exhibit this samephenomenon where the hexacopter configuration yields slightlysmaller thrust values relative to the quadcopter. Previously testedquadcopters at UTAustin (not shown) had the propellers thrusting upand with the support arms in close proximity to the propeller diskplane. Doing so placed the adjustable support arms directly in thepropeller downwash. This impedance not only reduced thrust(through some wake/pylon interaction effect) but also generated

Table 1 Multirotor drone testing configurations andposition relative to the arc array

D, in. d, in. D∕d φ∕D 2φ∕�D� d�18.00 8.0 2.25 2.42 3.3520.25 9.0 2.25 2.15 2.9722.50 10.0 2.25 1.93 2.6824.75 11.0 2.25 1.76 2.4327.00 12.0 2.25 1.61 2.23

Fig. 6 Arrangement of instrumentation relative to the quadcopterconfiguration with coordinate system.

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vortex interaction noise; these kinds of effects have been studied

recently by Zawodny and Boyd [10]. Therefore, the final multirotor

configuration entailed inverted propellers (thrusting down) that were

extended away from the drone body using motor extensions

(identified in Fig. 2), which ultimately provided a better comparison

to the isolated propeller case. The rotor offset distance, measured

from the top of the adjustable arms to the rotor disk plane, was

measured to be 4.25 in.In Fig. 9b, all thrust data are shown using log scales on both the

ordinate and abscissa axes. The agreement between the three

configurations (isolated, quadcopter, hexacopter) is quite good for all

propeller diameters and motor speeds. These trends exhibit a linear

second-order growth in thrust over the range of propeller speeds

tested. Offsets between different propeller diameters due to Reynoldsnumber effects are also uniform. In subsequent analysis, thepolynomial coefficients corresponding to the individual configura-tions are preserved, though the averages (corrected to the isolatedpropeller configuration values) are provided in Table 3 for theinterested reader.

B. Acoustic Performance

Given the overwhelming amount of data that were acquired duringthis test campaign, only a fraction of it will be presented here. Ouremphasis is on developing a general understanding of the acousticfootprint in terms of its spectral behavior, its decaywith distance fromthe source, and its directivity at angles surrounding the rotor disk

Table 2 Test matrix for quadcopter and hexacopter configurations

d, in. Configuration 30 rev∕s 45 rev∕s 60 rev∕s 75 rev∕s 90 rev∕s 105 rev∕s 120 rev∕s 135 rev∕s 150 rev∕s 165 rev∕s8.0 Quad

p p p p p p p p p p9.0 Quad

p p p p p p p p p p10.0 Quad

p p p p p p p p p— —

11.0 Quadp p p p p p p p

—— — —

12.0 Quadp p p p p p p

—— —— — —

8.0 Hexp p p p p p p p p p

10.0 Hexp p p p p p p p

—— — —

a) b)

20 40 60 80 100 120 140 160 180

6

8

10

12

14

16

0.05 0.1 0.15 0.2 0.25 0.3 0.35

6

8

10

12

14

16

Fig. 7 Thrust coefficient for an isolated propeller versus a) motor rotation speed, and b) propeller tip Mach number.

a) b)

0.05 0.1 0.15 0.2 0.25 0.3 0.35

1

1.5

2

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.3

0.4

0.5

0.6

0.7

Fig. 8 Representations of a) torque coefficient, and b) figure of merit for an isolated propeller.

a) b)

0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.5

1

1.5

2

2.5

3

40 60 80 100 120 140 160 180

0.1

1

Fig. 9 Representations of a) thrust of all configurations using 8 and 10-in.-diam propellers [comparison between raw data (symbols) and a second-orderleast-squares fit (lines)], and b) thrust for all propeller diameters and configurations.

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plane. For the isolated propeller configuration, the 1∕rev magneticsensor allowed acoustic pressure waveforms to be partitioned andthen aligned on a per revolution basis. This is demonstrated in Fig. 10where the average acoustic waveforms are displayed for twopropeller diameters (9 and 12 in.) and different rotor speeds. Eachaveragewaveform encompasses two rotor revolutions as recorded bythe 0 deg observer. As expected, increasing rotation speed isaccompanied by increasing pressure amplitude. At low rotationspeeds, the periods of the smaller-amplitude waveforms are difficultto identify because the total waveform shape is dominated by higher-frequency waveforms that are phase aligned with the propeller (theaveraging process removes only incoherent noise). The source ofthese high-frequency waveforms will become apparent in theupcoming discussion.To characterize the spectral makeup of these acoustic waveforms,

power spectral densities (PSDs) are computed. For a sensor setcomprising θj sensors, the two-sided autospectral density function isdefined as

PSD�θj; f� �1

2π

Z∞

−∞< p�θj; t�p�θj; t� ζ� > e−i2πfζ dζ (5)

where ζ signifies a time delay, hi denotes ensemble averaging, andlimits of integration are confined to the size of the partition. For theisolated propeller, the partition sizevaries and is basedon the number ofsamples required to cover two rotations of the propeller (N � 2fs∕Ω).Therefore, spectral resolutions range from δf � 14.88 Hz to

δf � 81.97 Hz for 30 and 165 rev∕s rotation speeds, respectively.

Doing so reduces spurious noise and low-frequency waveform

modulations from contaminating the spectral estimate. As for the

multirotor drone, a constant partition size of N� 213 data points is

used, thus yielding a narrow spectral resolution of δf � 4.88 Hz;propeller blades in the multirotor configuration are independently

operated with varying clock positions, and so the processingmethod is

less elaborate, relative to the isolated propeller case. Converting Eq. (5)

to the decibel scale yields the sound pressure level (SPL):

SPL�θj; f� � 10log10

�PSD�θj; f�

pref2

�(6)

and uses the standard reference pressure for air of

pref � 20 μPa∕������Hz

p. Corrections for human ear effects are achieved

using the A-weighting standard described by the International

Organization for Standardization (ISO226:2003). Published values for

the A-weighting function are first interpolated to match the resolution

of the narrowband spectra. The correction is then performed as follows:

SPLA�θj; f� � SPL�θj; f� � Ad�f�

� 10log10

�PSD�θj; f� ⋅ Ap�f�

pref2

�

� 10log10

�PSDA�θj; f�

pref2

�(7)

where PSDA�θj; f� � PSD�θj; f� ⋅ Ap�f�. Premultiplied spectra are

then computed for both the original,G�θj;f��PSD�θj;f� ⋅f∕σ2�θj�,and A-weighted, GA�θj; f� � PSDA�θj; f� ⋅ f∕σ2A�θj�, spectra

following the method described by Baars et al. [11]. Here, σ2�θj�and σ2A�θj� are the variances of the original and A-weighted signals,

respectively.Figures 11 and 12 illustrate these different processing methods

using the 0 deg microphone observer and the 9 and 12-in.-diam

isolated propellers operating at 105 rev∕s. Figure 11a shows how the

motor and speed controllers alone (without propeller blades installed)

produce a spectral peak around 1365Hz corresponding to clogging of

Table 3 Averaged coefficients (×103) from second-order fitof thrust with motor speed (revolutions per second)

d, in. Slope Quadratic coefficient

8.0 −1.1593 9.51119.0 −1.7459 10.574210.0 −2.0468 8.155611.0 −2.6858 8.078812.0 −3.5147 1.4668

aCoefficients normalized by the number of propellers in each configuration.

a) b)0 0.5 1.0 1.5 2.0

-0.1

-0.05

0

0.05

0.1

0 0.5 1.0 1.5 2.0

-0.1

0

0.1

Fig. 10 Average acousticwaveforms corresponding to two rotor revolutions of a) 9, andb) 12-in.-diam isolatedpropellers asmeasuredby theθ4 � 0 degobserver.

a) b)102 103 104

-20

-10

0

10

20

30

40

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1 10 100-20

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Fig. 11 Representations of a) SPL of the isolated propeller at 105 rev∕s for the θ4 � 0 deg observer, and b) effect of partition size on SPLA using the12-in.-diam isolated propeller at 105 rev∕s and the 0 deg observer.

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the motor magnets (13 magnets per revolution spinning at 105revolutions per second). The second equally significant peak at3.9 kHz is believed to be pulse noise produced by the speedcontroller, though this has not been verified. Nonetheless, the high-frequency waveforms displayed in Fig. 10 are shown here to berelated to nonrotor harmonic noise.As for the propeller noise in Fig. 11, the fundamental and its

harmonics appear crisp for both propeller sizes; the frequency scale inFig. 11b is defined by f� � f∕Ωb, which uses the blade-passfrequency Ωb to more easily identify peaks corresponding to thefundamental frequency, its harmonics (appearing as integermultiplesof f�), and even subharmonics. The noise floor from the facility andmicrophone data acquisition system is also included, though it hasbeen made nondimensional along the frequency axis in Fig. 11busing 60 Hz (common line noise). Comparing the unweighted(Fig. 11a) and A-weighted signals (Fig. 11b) reveals the significanceof the higher harmonics with respect to the human ear. Furthermore,the effect of partition size in Fig. 11b is seen to have little effect on theshape of the spectra, with the first few harmonics being displayed asthe dominant components of the signal. Overall, the spectral behavioris similar to themeasurements reported by Sinibaldi andMarino [12],Intaratep et al. [9], and Zawodny et al. [5], who studied single rotorsoperating at static thrust.A dimensionless display of these spectra using the premultiplied

spectra GA is provided in Fig. 12 for the same operating conditions.Relative to the SPL in Fig. 11, the higher harmonics are much moresignificant sources of audible noise. A-weighted premultipliedspectra are nearly void of energy in the fundamental with peakenergies residing in the 7th and 11th harmonics for the 9 and 12 in.propellers, respectively. Cross referencing the SPL in Fig. 11a withthe peaks in Fig. 12a reveals how the two peaks at f� � 7 and 19 arecaused by motor and speed controller noise, respectively, as opposedto propeller noise. From a human detection point of view, it is thehigher harmonic signatures, including the noise from the motor andspeed controller, that are the prominent sources of noise.

To now gauge the effect of rotor speed on the spectral footprint ofthis multirotor configuration, we turn our attention to Fig. 13, wherethe 9 and 12-in.-diam propellers are installed on the quadcopterconfiguration. This employs the same observer location as before andwith A-weighting applied. Because these spectra are rich withharmonic activity, the clutter that forms when overlaying the resultsfrommultiple test conditions conceals the details that are of interest tothis study. Therefore, a detailed understanding of the effect ofpropeller size and speed on the spectral footprint is not self-evidentwithout additional work; this kind of discussion is reserved forSec. III.B.3, where the amplitudes of the first few rotor harmonics aresegregated and compared for a range of operating conditions. Fornow, the discussion is confined to relatively general observations.The most conspicuous of these observations is the increased soundlevels that accompany increased rotor speeds. Additional propellersalso manifest increased sound amplitudes relative to the isolatedrotor. Once again, noise from the motor and speed controller persistsand is a significant source of sound at low rotation speeds when thenoise from the propeller (in the formof thickness noise) is quite small.It should be noted that any additional sources of noise caused byscattering of sound waves by electrical cables, extendable arms, orthe rotor test stand were not isolated in any of the configurationstested. Thus, although we believe these additional sources of noise tobe small, they are currently unknown, where comparison to theisolated propeller studies are concerned.

1. Time-Frequency Analysis

Because each propeller is driven by a motor that operatesindependently from all other motors and speed controllers, anydifferences in the individual rotation speeds will generate beatingphenomena due to quadratic interactions between their fundamentalblade-pass frequencies. Thus, quadratic interactions in the near fieldbetween frequenciesf1 andf2, andwith associated phasesϕ1 andϕ2,result in a spectral peak at frequency f and phase ϕ in the far fieldaccording to the selection rules f � f1 � f2 and ϕ � ϕ1 � ϕ2.

a) b)

0.1 1 10 1000

5

10

15

1 10 1000

0.5

1

1.5

2

Fig. 12 Acoustic filtering effects applied to a) 9, and b) 12-in.-diam isolated propellers at 105 rev∕s and the θ4 � 0 deg observer.

a) b)

1 10 100

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1 10 100

0

20

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60

Fig. 13 SPL�θ4; f� for a range of propeller speeds of the quadcopter with a) 9, and b) 12-in.-diam propellers.

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Quadratic interactions can be quantified using bispectral methods butare cumbersome to apply; see Baars and Tinney [13] and thereferences therein. Forward flight and dronemaneuvering exacerbatethe phenomena, which is of fundamental interest to the establishmentof a broader class of acoustic models for characterizing drone noise.For now, we reserve the application of higher-order spectral analysisof the sound produced by multirotor drones for future efforts andconsider an alternate route for determining whether quadraticcoupling may be present in this data set.An alternative way of identifying nonlinear coupling in these

acoustic signatures is to use time-frequency analysis to visualize thetemporal behavior of the signal’s spectral makeup. Any beatingphenomenon would be revealed by variations in the amplitude of thefundamental blade-pass frequencies over time. The process isthoroughly described elsewhere [14,15] and involves the convolutionof a mother wavelet ψ�t∕l� with a time-dependent signal to producewavelet coefficients as follows:

~p�θj; l; t� �Z

p�θj; t 0�ψ��t 0 − t

l

�dt (8)

The signal in this case is the unsteady acoustic pressure p�θj; t�with l being the time scale of the predefined wavelet. The Morletwavelet will be used here, given that it offers crisper resolutions infrequency at the expense of coarser resolutions in time, relative to theMexican hatwavelet; we are interested in the frequency content of the

signal, and so the Morlet wavelet is the suitable choice. This Morletwavelet is defined as

ψ�t∕l� � ejωψ t∕le−jt∕lj2∕2 (9)

with a central frequency ofωψ � 6. The analysis shown here mirrorsprevious efforts described by Baars and Tinney [16], Stephensonet al. [17], and Rojo et al. [18] and is performed in the Fourier domainusing 81 unique scales distributed logarithmically over the frequencyrange 100 Hz < f < fs∕2. Only regions inside the cone of influenceare shown and are constructed by overlapping signal partitionscomprising N� 217 samples. Like the Fourier transform, the energydensity can be computed and is known as thewavelet power spectrum(WPS):

E�θj; l; t� �j ~p�θj; l; t�j2

l(10)

which is then converted to Fourier frequency to obtain the double-sided WPS, denoted as E�x; f; t�. To simplify the analysis, we willfocus on the microphone signals located at θ1 � −45 deg and θ4 �0 deg relative to the rotor disk plane, which is in the general directionof where a far-field observer would reside.The findings from this analysis are shown in Figs. 14 and 15 for the

quadcopter and hexacopter configurations, respectively, and for aduration of 8 s. For the sake of simplicity, the results are confined to a

1 2 3 4 5 6 7 8

1

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60

a)

1 2 3 4 5 6 7 8

1

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60

b)Fig. 14 Morlet wavelet power spectra expressed as 10log10�E�θj; f;t�∕pref2� for a) θ1 � −45 deg, and b) θ4 � 0 deg observer with the quadcopterconfiguration using 10-in.-diam propellers at 135 rev∕s.

1 2 3 4 5 6 7 8

1

10

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40

60

a)

1 2 3 4 5 6 7 8

1

10

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60

b)Fig. 15 Morlet wavelet power spectra expressed as 10log10�E�θj; f;t�∕pref2� for a) θ1 � −45 deg, and b) θ4 � 0 deg observer with the hexacopterconfiguration using 10-in.-diam propellers at 135 rev∕s.

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motor rotation speed of 135 rev∕s (Ωb � 270 passes per second)using 10-in.-diam propeller blades. The y axis, again, has beennormalized by the blade-pass frequency and is confined to illustrateonly the first 10 harmonics. At first glance, three striking features areobserved. The first is the amplitude modulations at the fundamentalblade-pass frequency (f� � 1), which suggests quadratic interactionsbetween acoustic waves produced by neighboring propeller tips. Thesecond is the differences between the higher harmonics at the differentobserver stations. For a given multirotor configuration, the signalsfrom the two microphones were acquired simultaneously. Theobserver located below the rotor disk plane experiences a broaderspectrum of higher harmonic activity, relative to the observer alignedwith the disk plane, and is attributed to the directivity of dipole noisesources; wewill see evidence of this later on. A third observation is inthe hexacopter configuration where the amplitude modulation of thesecond harmonic (2Ωb) is much stronger than in the quadcopterconfiguration. This may be due to the closer proximity of the propellerblade tips in the hexacopter configuration that is amplifyinginteractions between neighboring blade tips.

2. Acoustic Pressure Decay

It is an essential part of any acoustic study to know what the decayrate and decay path are for the prominent sound source. This decaywas measured for two quadcopter configurations comprising the 9and 12-in.-diam propellers. Like the arc array, the line array wasalignedwith the rotor disk plane at θ � 0 deg andwithmeasurementpoints spanning the range φ � 18; : : : ; 72 in: for the 9 in. propellersand from φ � 24; : : : ; 72 in: for the 12 in. propellers usingincrements of δφ � 6 in: for both. The findings from this study areshown in Fig. 16 using a high-pass filter to removewaveforms below70Hz.Given that thickness noise is the prominent source of noise andis known to decay spherically from the source, themeasured pressureamplitude from thesemultirotor drones should decay like 1∕r. This isimportant for several reasons. Foremost, it is known that disturbancesclose to the propeller blade are dominated by evanescent pressurewaves (pseudosound waves) that decay within the first fewwavelengths from the source and do not propagate to the far field.Therefore, the radial position where these hydrodynamic pressurewaves are overtaken by acoustic pressure waves is needed to verifythat the microphone arc array is indeed located in a region whereacoustic pressure waves dominate the microphone signal. Second,

spherical decay laws are commonly used to propagate acoustic

pressure signals from the near field to the far field. To the authors’knowledge, the 1∕r decay law has not yet beenverified for multirotor

drones. Figure 16 supports the conjecture that the acoustic pressuresignal spreads spherically beyond 2φ∕�D� d� ≥ 2.5 and 2.0 for the9 and 12-in.-diam rotor configurations, respectively. This verifies thatthe arc array is placed within the acoustic near-field regions of the

multirotor drone for all configurations and blade sizes tested.However, these measurements only verify this decay along the rotor

disk plane, which may be different along other propagation pathsgiven the directivity pattern of the dipole sources.

3. Filtered Overall Sound Pressure Level and Directivity

Because the dominant features in these acoustic waveforms are

integer multiples of the fundamental blade-pass frequency, an effortis undertaken to track the effect of propeller diameter, rotor speed,

and configuration (quadcopter versus hexacopter) on the first fewharmonics associated with the blade-pass frequency. This is

performed following Parseval’s theorem as a guide so that

σ2i �θj� � 2

Zfi�2δf

fi−2δfPSD�θj; f� df (11)

where the subscript i is an integer identifier corresponding to thefundamental blade-pass frequency.A factor of 2 is inserted to account

for the energy neglected in the negative frequencies. The integrationwidth is 5δ, which corresponds to 24.41 Hz in the multirotor drone

setup. Thiswas needed to capture the energy in the tails of the spectral

peaks. Thus, σ2i quantifies the variance of the signal corresponding tothe blade-pass frequency and its harmonics. OASPLi is then

calculated in standard fashion as follows:

OASPLi�θj� � 10log10

�σ2i �θj�pref2

�(12)

so that OASPL1�θj� is the energy associated with the fundamental

blade-pass frequency of the jth sensor, OASPL2�θj� is associatedwith the second harmonic, and so on.The findings from this are displayed in Figs. 17–19 as a function of

the measured thrust and for a given drone configuration. Clear trends

a) b)

1 1.5 2 2.5 3 3.5 4 4.5

60

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80

90

100

1 1.5 2 2.5 3 3.5 460

70

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100

Fig. 16 Pressure decay along the line array compared with the spherical decay law (1∕r) for a quadcopter with a) 9, and b) 12-in.-diam propeller.

a) b)011

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Fig. 17 Fundamental blade-pass frequency noise at a) θ1 � −45 deg, and b) θ4 � 0 deg observer positions.

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are revealed that demonstrate the rate by which the sound pressure

amplitude of the fundamental frequency and its higher harmonicsincrease with increasing motor speed (thrust). In general, the change

in OASPL due to changes in thrust is similar for both the hexacopter

and quadcopter configurations and for different size propellers.Closer inspection reveals how the sound pressure, for a given thrust

value, decreases with increasing propeller diameter. The only

distinguishing factor is the blade-pass frequency. Energy in thefundamental blade-pass frequency is also very similar between

the shallow (−45 deg) and rotor disk (0 deg) observer stations. Onthe contrary, the second and third harmonics are similar in amplitude

to the fundamental frequency at shallow angles but nearly 10 dB

weaker along the rotor disk plane, which complements the findingsfrom the wavelet analysis in Figs. 14 and 15.Where the acoustic behaviors from all available measurement

stations are concerned, the same filtered data using Eq. (12) areshown in Fig. 20 for the quadcopter configuration only and for a rotor

speed of 105 rev∕s. Several points of interest are seen here.Foremost, the directivity patterns for the fundamental blade-pass

frequencies are found to be symmetric about a line located just below

the rotor disk plane for all propeller diameters. This suggests that

thickness noise is the predominant factor here, which is governedprincipally by blade thickness and tipMach number. On the contrary,the second and third harmonics are less symmetric and withsignificant drops in amplitude occurring at, or just above, the rotordisk plane; this was also observed in Figs. 17–19. These higherharmonics are thus attributed to loading noise, which is consistentwith large-scale rotorcraft studies. Furthermore, the shape of thedirectivity pattern appears to be unaffected by Reynolds numbereffects (due to changes in the propeller diameter). The onlydiscrepancies in the shape of the directivity pattern appear in thehigher harmonics and with the smaller-diameter propeller blades.

IV. Conclusions

This paper presents a study to understand the sound produced bymultirotor drones operating at static thrust. Loadmeasurements showthat, for a drone pitch of 2.25, defined as a ratio of the rotor diameterto hub diameter, thrust levels resort to integermultiples of the numberof propeller blades. The sound field is shown to encompass bothnonrotor harmonic noise (motor noise and noise from the speedcontroller) and main rotor harmonic noise (thickness noise and

a) b)011

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Fig. 18 Second harmonic noise at a) θ1 � −45 deg, and b) θj � 0 deg observer positions.

a) b)011

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01130

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Fig. 19 Third harmonic noise at a) θ1 � −45 deg, and b) θ4 � 0 deg observer positions.

20 40 60 80-50

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c)b)a)Fig. 20 OASPL directivity patterns for a) fundamental blade-pass frequency, b) second harmonic, and c) third harmonic for the quadcopterconfigurations at 105 rev∕s.

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loading noise). The former of these is as equally important as thelatter and is even more significant where human ear effects, onaccount of A-weighted filtering, are concerned. Time-frequencyanalysis of the sound field demonstrates modulations of the pressurelevels associated with the first few blade-pass frequencies that occurintermittently along the tip path plane caused by subtle variations inthe motor speeds among the multiple motors. Pressure levelsassociated with the higher harmonics are shown to be moresignificant at observer angles below the tip path plane but are stillsignificant at all observer angles studied.For a given thrust, the sound pressure of the first few harmonics is

shown to decrease with both increasing propeller diameter and thenumber of propellers. These changes are attributed to the lowerrotation speeds, and hence lower thickness and loading noise,required to maintain the same thrust levels. The spatial decay of theoverall sound pressure level along the tip path plane also revealed thedemarcation between evanescent and acoustic components of thepressure field; the latter is characterized by spherical spreading andwas found to occur at positions closer to the drone hub for smallerpropellers. Directivity patterns associated with the blade-passfrequency for different rotor diameters show it to be the result ofthickness noise produced by the rotor. The same study of the secondand third harmonics shows them to be loading-noise effects, similarto what is observed with full-scale helicopters.Although a basic understanding of the sound produced by

multirotor drones during static thrust conditions has been developed,there is still much to be learned about the effects of forward flight andmaneuvers of the vehicle. Such a topic should be the focus of futureefforts because theywill enhance impulsivelike noise effects not seenduring static operations of a drone.

Acknowledgment

The authors wish to thank Bryson Hill for assisting in the designand fabrication of the multirotor drone test stand as well as ChrisCameron and John Valdez for helping with the thrust and acousticmeasurements.

References

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[2] Ol,M.,Zeune,C., andLogan,M., “Analytical–ExperimentalComparisonfor Small Electric Unmanned Air Vehicles,” 26th AIAA Applied

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[8] Brandt, J. B., and Selig, M. S., “Propeller Performance Data at LowReynolds Numbers,” 49th AIAA Aerospace Sciences Meeting, AIAAPaper 2011-1255, Jan. 2011.

[9] Intaratep, N., Alexander, W. N., and Devenport, W. J., “ExperimentalStudy of Quadcopter Acoustics and Performance at Static ThrustConditions,” 22nd AIAA Aeroacoustics Conference, AIAA Paper 2016-2873, 2016.

[10] Zawodny, N. S., and Boyd, D. D., “Investigation of Rotor-AirframeInteractionNoiseAssociatedwith Small-ScaleRotary-WingUnmannedAircraft Systems,” Proceedings of the American Helicopter Society

73rd Annual Forum, Ft. Worth, TX, May 2017.[11] Baars, W. J., Tinney, C. E., and Hamilton, M. F., “Piecewise-Spreading

Regime Model for Calculating Effective Gol’dberg Numbers forSupersonic Jet Noise,” AIAA Journal, Vol. 54, No. 9, Sept. 2016,pp. 2833–2842.doi:10.2514/1.J054790

[12] Sinibaldi, G., and Marino, L., “Experimental Analysis on the Noise ofPropellers for Small UAV,” Journal of Applied Acoustics, Vol. 74, No. 1,2013, pp. 79–88.doi:10.1016/j.apacoust.2012.06.011

[13] Baars, W. J., and Tinney, C. E., “Proper Orthogonal Decomposition-Based Spectral Higher-Order Stochastic Estimation,” Physics of Fluids,Vol. 26, No. 5, 2014, Paper 055112.doi:10.1063/1.4879255

[14] Farge, M., “Wavelet Transforms and Their Application to Turbulence,”Annual Review of Fluid Mechanics, Vol. 24, Jan. 1992, pp. 395–458.doi:10.1146/annurev.fl.24.010192.002143

[15] Addison, P. S., The Illustrated Wavelet Transform Handbook, Taylorand Francis, New York, 2002, pp. 1–353.

[16] Baars, W. J., and Tinney, C. E., “Transient Wall Pressure in anOverexpanded and Large Area-Ratio Nozzle,” Experiments in Fluids,Vol. 54, No. 1468, Feb. 2013, pp. 1–17.doi:10.1007/s00348-013-1468-8

[17] Stephenson, J. H., Tinney, C. E., Green, E., and Watts, M. E., “TimeFrequency Analysis of Sound from a Maneuvering Rotorcraft,”Journal of Sound and Vibration, Vol. 333, No. 21, 2014, pp. 5324–5339.doi:10.1016/j.jsv.2014.05.018

[18] Rojo, R., Tinney, C. E., and Ruf, J. H., “Effect of Stagger on theVibroacoustic Loads from Clustered Rockets,” AIAA Journal, Vol. 54,No. 11, 2016, pp. 3588–3597.doi:10.2514/1.J055017

D. PapamoschouAssociate Editor

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