Initial Development of a Quadcopter SimulationEnvironment for Auralization

Andrew Chr istianResearch Engineer (Psychoacoustics)

Structural AcousticsBranchNASA Langley Research Center

Hampton, VA, U.S.A.

Joseph LawrenceUndergraduate (Physics)

College of Physical and Mathematical SciencesBrigham Young University

Provo, UT, U.S.A.

ABSTRACTThis paper describes a recently created computer simulation of quadcopter flight dynamics for the NASA DELIVERproject. Thegoal of thiseffort is to produceasimulation that includesanumber of physical effects that arenot usuallyfound in other dynamics simulations (e.g., those used for flight controller development). These effects will be shownto have a significant impact on the fidelity of auralizations — entirely synthetic time-domain predictions of sound— based on this simulation when compared to a recording. High-fidelity auralizations are an important precursor tohuman subject tests that seek to understand the impact of vehicle configurationson noise and annoyance.

INTRODUCTION

Given the continuing proliferation of small unmanned aerialsystems (sUAS) of all sizes and flight capabilities, as well asthe innumerableconcepts that entrepreneursaround theworldhave thought of for their use, it is only a matter of time be-fore communities will be faced with large swarms of thesemachines in close proximity to humans. This situation willlikely create many problems: safety, privacy, etc. One of theprincipal issues may become noise and annoyance.

At NASA, theDELIVER project seeksto get ahead of thisproblem by working to create a design environment for thesenovel vertical-lift vehicles. Oneof thecomponentsof thisen-vironment will seek to predict the acoustic impact of sUASsystems, evaluated in terms of human annoyance. In orderto create such a design tool, researches at NASA will have tocreatewaysto predict not only theacoustic output of theseve-hicles, but also how that output (which may vary significantlyin overall level as well as qualitatively between vehicles) iscorrelated with human annoyance.

In pursuit of this goal, a computer simulation of a quad-copter was developed that takes into account several aerome-chanical effects that are not typically implemented in sUASsimulations. This simulation can be combined with an ex-isting capability to generate auralizations — completely syn-thetic sounds based on the simulation outputs (this process isdetailed in many previouspublications, themost pertinent be-ing by Christian (Ref. 1), and Rizzi (Ref. 2)). These auraliza-tions can then be evaluated by human subjects in a controlledenvironment such astheExterior EffectsRoom at NASA Lan-gley Research Center (Refs. 3,4), in order to explore the rela-tionship between the input parameters of the simulation (e.g.,

quadcopter design parameters, control parameters, etc.) andthe human annoyance generated by the resulting sounds.

Throughout this paper, spectrograms based on auraliza-tions and a recording of quadcopters will be presented. Thereader is encouraged to access the openly available wave-fileversions of these sounds and “ listen along” as they are dis-cussed in this paper. The sounds can be found on the NASAStructural Acousticswebsite:

http://stabserv.larc.nasa.gov/flyover/

Operational Concepts

For smaller quadcopters, like the DJI Phantom II that willbe used in this study, the speeds of the four rotors (mea-sured in revolutions-per-minute (rpm)) are controlled di-rectly through variable speed motors. A simple propor-tional/integral/derivative (PID) closed-loop feedback controlsystem on the vehicle modulates the speed of the individualrotors in order to maintain thevehicle’sattitude. For instance,in thecaseof forward flight, thespeed of the two stern motorsare increased, while the the bow motors are kept near hoverspeed. This causes thevehicle to pitch forward. ThePID sys-tem maintains the overall lift of the vehicle in order to resistgravity, and thecomponent of the total forcegenerated by therotors that is not pointed directly skyward causes a net thrustforce to act on thevehiclegenerating motion in that direction.Thisapproach leads to constantly-changing and unequal rotorspeeds that in turn leads to perceptually significant frequencymodulation of the rotor noise.

The Phantom II was among an array of vehicles includedin a recent series of outdoor vehicle flight tests conductedby NASA (Ref. 5). The purpose of these flight tests wasto acquire acoustic and flight telemetry data for the vehiclewhile operating under realistic flight conditions. Some sam-

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https://ntrs.nasa.gov/search.jsp?R=20160009104 2020-06-27T04:24:03+00:00Z

Fig. 1. Spectrogram of recorded quadcopter flyover.

ple acoustic data from a nominally straight and level over-head flight of the Phantom 2 is provided in Figure 1. Thepairs of lines running relatively horizontally through the fig-urerepresent bladepassagefrequency (BPF) harmonicsof thefront and rear pairs of rotors. Momentary variation withinpairs indicates roll compensation, and momentary variationbetween the pairs indicates pitch compensation. These sortsof variations are clearly audible as the vehicle control sys-tem constantly makes adjustments in order maintain forwardflight in the presence of wind, turbulence, and mass loadingby the payload. It is likely that the annoyance caused bysUAS will have some component that is correlated with theattributes of these variations (for example, see recent workby Palumbo (Ref. 6)). The ability to accurately simulate andauralize these features of the noise would allow for the con-trolled human subject testing needed to evaluate how thesemodulations, aswell asother factors, contribute to theannoy-ance generated by these machines.

Extant Simulators

Most contemporary quadcopter simulations only include thebasic mechanics of quadcopter flight. For most applications,these simulations are run in order to test and develop controlschemes for sUAS. The concept behind taking such a sim-ple approach to modeling is that if a control system can beshown to be robust enough to control a vehicle under thesebasic conditions, the addition of smaller effects such as slightatmospheric turbulenceshould not affect thecontrollersover-all ability to keep the vehicle aloft. Further, many of theseeffects can be computationally expensive so that it is easy todeem their inclusion in simulationsunnecessary if they arenotlikely to greatly impact theoutcome.

As an example, consider the spectrogram of Figure 2.1

This shows an auralization that was based on the output of

1For all of the spectrograms shown here, the processingsettings (the frequency and time steps) have been matchedclosely between the various source materials. The simula-

Fig. 2. Spectrogram of auralization of basic simulationoutput.

a quadcopter dynamics model named Quad-Sim (see Hart-man (Ref. 7), discussed further below). In this case, thereisno drag or turbulence. Thismeans that once thequadcoptergetsup to speed (an event that takesplacebefore time= 0 s inFig. 2), thevehiclecan right itself and cut horizontally thoughthe air — effectively hovering while sliding in the intendeddirection. This is patently unrealistic and there are multiplephysical effects that, in the real world, perturb and resist thisflight operation. Some of these effects have been pointed outin thepast by sUASresearches(e.g., seeMahony (Ref. 8) andBangura (Ref. 9)).

There are many clear audible differences between thesoundsrepresented in Figs. 1 and 2. Perhapstheprimary defi-ciency isthat theBPFsof all four rotorsareperfectly thesamefor theentire timeshown. Thisshortcoming, aswell asothersare addressed implicitly by the addition of the aeromechani-cal effects discussed below that are left out of the Quad-Simmodel.

The rest of this document is divided into two main parts.Thefirst two following sectionsdetail the source of the simu-lator created for thiseffort. First, thebasisof thesimulation isdescribed asaport of acommonly availableprogram. Second,theadded aeromechanical effectsaredescribed along with thevarious assumptions and approximations needed to interfacethose effects with the existing simulation.

TheAuralization Resultssection showsaseriesof spectro-grams (similar to that shown in Fig. 2) which incrementallyadd the aeromechanical effects. The impact of these addi-

tions shown are all based on the attributes of theflyover fromFig. 1. Also, the color scale of each is normalized to the peakof that figure, although thedynamic rangeof thecolor scale isthe same between all spectrograms (e.g., the ‘background’ ofFig. 1 is not as dark of a blue as that of Fig. 2 as there is am-bient noiseon therecording whereastheauralization containsonly the BPFs and their harmonics). Color figures availableonline.

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tions on the resulting auralizations are discussed along withthe likely importance of the inclusion of these effect on theperception of the sound of the quadcopter.

THE DYNAMICSMODEL

This section introduces the sources of the core dynamicsmodel used for the simulation. For the sake of brevity, noequations are given in this section, as the references uponwhich this work is based are freely available and extensivelydocumented.

Quad-Sim

The core dynamics of this simulation are derived from Quad-Sim, an open sourcequadcopter model implemented in MAT-LAB Simulink (see Hartman (Ref. 7)). Earlier work by Ma-hony (Ref. 8) is the basis for many of the equations used inQuad-Sim.

The starting point for this effort was to use the dynam-ics model of a quadcopter in the ‘x’ configuration — the casewherethedirection of flight isbetween two rotorsso that thereare two front rotors and two rear rotors as discussed above2.This model provides the formulations for the mass momentof inertia matrix based on the physical properties (i.e., massdistribution) of the vehicle under study, the gyroscopic mo-ments that affect the vehicle, and the state equation formu-lation for the vehicle. Although Quad-Sim does not includeaerodynamic effects, places to add them are available. Quad-Sim was also used as the basis for the model of the on-boardPID controller.

Procedural Por t

The freely available version of Quad-Sim is programmed inMATLAB Simulink, which is a graphical environment. Oneof the first steps in this effort was to port Quad-Sim to com-pletely procedural MATLAB without the use of functions be-longing to ‘ toolboxes.’ This was done both to gain more con-trol over the simulation and to facilitate possible future trans-lations to other procedural languages, such as C, that can in-terfacemoreeasily with theauralization toolscurrently in useat NASA (i.e., the NASA Auralization Framework, see Au-mann (Ref. 10)).

In order to create thisport, an order-4 Runge-Kutta (an ex-plicit forward-time stepping) ODE solver was created to op-erate on the state equations of the Quad-Sim model (see, forexample, Atkinson and Han (Ref. 11)). A time step of .001s was found to give results that were convergent in all testedcases and generated rpm time histories with an error of lessthan 1 rpm — suitably accurate for thiseffort.

2The Quad-Sim model also has provisions for a ‘+’ con-figuration in which there isone front rotor, one rear rotor, andtwo rotorswhich flank thecenter of mass. Thiscapability wasdisregarded for this effort as the DJI Phantom II runs only inan ‘x’ configuration.

The original Quad-Sim implementation was then used tobenchmark the port. It was found that not only was the portmore accurate than the original (in terms of error in rpm), butalso, for thenon-extended model, that it ran morequickly thanQuad-Sim.

MODEL EXTENSIONS

Thissection discussesextensions that wereadded to thebasicdynamics model. The only equations and methods that willbegiven hereare those that do not appear comprehensively inany single source. For instance, equations are given when in-termediatestepsand approximationsarenecessary in order tointerface the core model with either the model extensions orthe input data available. Otherwise readers are encouraged tolook to the references for the complete background and tech-nical detailsof thedifferent extensions.

Rotorcraft Aeromechanics

The first and most fundamental change that was made to themodel was to upgrade the aeromechanics that were includedin the original Quad-Sim program. The new model followsthe development of work by Hoffman (Ref. 12), and usesfundamentals from textbooks by Prouty (Ref. 13) and Leish-man (Ref. 14). The results used here come from actuator disctheory.

Rotor Coefficients:

The original Quad-Sim model requires separate specifica-tion of 3 lumped parameter coefficients that define theperfor-mance of the rotor/motor combination. These are the thrust,torque, and power coefficients, the standard non-dimensionalversionsof which are:

CT =T

r AW2R2 (1)

CQ =Q

r AW2R3 (2)

CP =P

r AW3R3 (3)

In Equations 1-3, r is thedensity of theair, A is thecross-sectional area of the rotor’s rotation, Wis theangular velocityof the rotor, and R is the radius of the rotor. Using SI units,thisgives thrust T in unitsof Newtons, torqueQ in N�m, andpower P in N�m

s (Watts).

One of the other activities of the DELIVER project is tomeasuretheacousticoutput of rotorsand motorsisolated fromsUAS vehicles while at the same time analyzing their perfor-mance characteristics (see Zawodny (Ref. 15)). These mea-surementsproduceestimates for the thrust coefficient, but notfor the other two. In order to use this information in the sim-ulation, an approximation ismadewhich allowsCP andCQ tobecalculated from themeasured CT.

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First, a basic relationship between power and thrust is es-tablished using the induced velocity through the rotor whilehovering (vh).

P = Tvh (4)

vh =

sT

2r A(5)

Theseequationssimplify to arelationship betweenCT andCP:

CP =C3=2

Tp2

(6)

This is only strictly valid in the hover condition, though itis used as a constant in this simulation. Another assumptionis that power is directly related to torque as P = WQ. Thisimplies that simply:

CQ = CP (7)

Thus, the3 coefficientscan befully determined from avail-ableexperimental data.

Upgraded Aeromechanics:

In the Quad-Sim program, thrust is simply proportional torotor speed squared. However, more accurately, the quad-copter speed and angle of attack relative to the airflow willchange the induced velocity of air through the rotor disk, thuschanging the thrust. Thrust can be expressed as the ratio ofpower to the airflow through the rotor disk:

T =P

v• sina + vi(8)

where vi is the induced velocity, v• is the magnitude ofthe air-stream velocity relative to the rotor, and a is the angleof attack (where a positive angle corresponds with pitchingforward)3. Note that this equation supersedes Eq. 1. In orderto calculate the thrust, both vi and P need to be calculated.Using an expression from Leishman (pp. 64), the inducedvelocity can be written as:

vi =v2

hq(v• cosa )2 + (v• sina + vi)

2(9)

At hover or during a climb, the rotor is in the ‘normalworking state,’ where there is a defined flow of air downwardthrough the rotor and the resultant thrust pushes the rotor up-wards. At fast descent velocities, the rotor is in the ‘wind-mill brake state,’ where there is a defined flow of air upwardthrough therotor creating athrust that pushestherotor further

3Both v• and a can be calculated from the apparent windvelocity vector va discussed in the next section.

downwards. Both of thesestateshavesimplesolutions for theinduced velocity given the aboveequation.

At slow descent velocities, the rotor is in the ‘vortex ringstate.’ This means that air flows downward through the rotor,and then circlesback in a toroidal ring around the rotor to be-fore being ingested by the rotor again. In some cases this cancause a turbulent descent condition and even a loss of thrust.However, it is not straightforward to account for the vortexring stateusing Equation 9. In most cases, assuming anormalworking state for thevortex ring state results in an acceptableapproximation that works for all directionsof motion, not justclimb and descent.4

Equation 9 is a transcendental function as vi appears onboth sides. Therefore an indirect method must be used to cal-culate the current value of vi . Newton’s method is used hereto find thesolution, though an appropriate initial guess isnec-essary to make the method converge to the desired solution.In the normal working and vortex ring states, defined as theregime in which the ratio of the apparent vertical velocity Wto the induced hover velocity vh is greater than �2, the guessis:

vi;0 = �W2

+

rV•

2+ v2

h (10)

In thecaseof thewindmill brakestate (when Wvh

< �2) theguess is:

vi;0 = �W2

�

rV•

2� v2

h (11)

The Ground Effect:

Finally, thereisamodification for theground effect. Whena rotor is close to the ground, the induced air stream is re-flected by the ground creating an increase in thrust. The cal-culation for the ratio of thrust with ground effect compared tothethrust expected in freespacecomesfrom Bangura(Ref. 9).

TGround

T=

1

1��

r4z

�2�

1+ V2•

v2i

��1 (12)

where z is the height above the ground surface and r isthe radius of the whole rotor area. For the quadcopter con-figuration here this radius is defined as the distance from thequadcopter (hub) center to the rotor center plus the radius ofa rotor. This has a negligible effect unless the quadcopter isonly a few feet above theground.

Wind Effects

Before adding effects such as drag, it is necessary to definethe air through which the model quadcopter will be moving.

4For further exposition on the differences between theseoperating states, see e.g., Prouty (pp. 94).

4

The velocity of the air is defined as a single vector called the“apparent wind velocity” denoted as va. This is the wind ve-locity relative to the quadcopter at any instant in time. In thissimulation, this vector is the sum of 3 sources:

1. Themotion of thequadcopter itself. In acompletely stillatmosphere, the quadcopter will see an apparent windequal to the negative of its own velocity.

2. A “ laminar” wind component. This component is thesameat all points in the simulation domain.

3. A turbulent wind component. This is a small spatiallyvarying perturbation, thesourceand simulation of whichis discussed below.

The ambient temperature, relative humidity, and ambi-ent pressure are constant throughout the simulation domain.These constants are used to calculate the ambient air densityused, for example, in Equations 1-3. These parameters arealso inputs to the auralization process (i.e., to calculate thespeed of sound and atmospheric absorption).

Body Drag

The next effect comes in the form of a simple resistive dragterm. This drag arises from any body moving through a gas,and always opposes the apparent wind velocity. In aircraft, itis known as ‘parasitic’ or ‘body’ drag, as it does not take intoaccount drag generated by the components of the aircraft thatcreate lift (in this case, the rotor surfaces).

The simplest implementation of this force comes in theform of the common drag equation (see, e.g., Bangura):

Fd;Body =12

r v2aCDA (13)

wherer isthedensity of theair that thequadcopter ismov-ing through, va is themagnitudeof theapparent wind velocityfrom the previous section (va = kvak2), CD is the drag coeffi-cient, and A is the projected surface area of the quadcopter.

For this basic model, the quadcopter is treated as the rect-angular volume that enclosesall of the components of theve-hicle except for the rotors (that is, the motors are includedat theextremity of thevolume, but not the rotors themselves).Computing theprojection of thequadcopter volume(modifiedby the quadcopter’s current attitude) onto the 2-dimensionalplaneorthogonal to thedirection of va will producetheareaAin Equation 13.

Thevalueof CD isset to be.9, which isatypical valueusedfor the drag coefficient of a cube with arbitrary orientationrelative to the wind. This selection of CD corroborates withwork by Cano (Ref. 16).

The force generated by this drag acts at the center of the‘hub’ of thequadcopter (see theQuad-Sim documentation fortheexplanation of themassdistribution). In theevent that this

‘aerodynamic center’ is different from the center of mass, atorquing moment may be generated by this force.

Although thismodel is quite rudimentary, it is likely suffi-cient since drag created by the lifting surfaces (rotors) are themoresignificant factor, asdiscussed below.

Rotor Drag

There are at least 3 sources of drag forces that can act on therotors of a quadcopter. The sum of these forces is known asthe “H-force” in rotorcraft literature. Much of the develop-ment of this section comes from a synthesis of expressionsthat can be found throughout Prouty (Ref. 13). These resultscome from simplifications of blade element momentum the-ory.

Flapping Drag:

In forward flight, aspinning rotor will generatemorethrustover theadvancing sideof the rotor disk than over the retreat-ing side. This imbalance can lead to vehicle instabilities. Tocompensate for this effect, rotor blades are made to be some-what flexible so that they bend as they spin, evening out thethrust. This flapping makes the entire rotor disk rotate back-wards, creating adrag-like forceopposite thedirection of mo-tion. Thebackwardsforceisproportional to both velocity andto rotor thrust.5

To calculate flapping drag, the collective pitch must firstbedetermined as:

q0 =

4CTas

�1+ 3

2m2�

� q12

�1� 3

2m2 + 32m4

�� l 0

�1� m2

2

�

23 � 2

3m2 + 32m4

(14)

Thisequation has several components:

� a is the slope of the lift curve per radian. A value of 6.0can be used for most rotors (Prouty, pp. 12).

� CT is the nondimensional thrust coefficient defined ear-lier (Eq. 1).

� s is the rotor solidity, which is the ratio of blade area torotor disk area.

� q1 isthebladetwist from center to end, which istypicallyaround -10 degrees (Prouty, pp. 13).

� m is the tip speed ratio, which is the magnitude of thecomponent of theapparent wind velocity va that is in thetip path plane divided by the tip speed vt .

� l 0 is the inflow ratio: the ratio of airflow through therotor disk divided by tip speed (Prouty, pp. 166). It canbecalculated as:

5Quadcopter blades are relatively stiff, so this effect isproportionally smaller — however still significant — than itwould be for full-scale helicopters.

5

l 0=� (v• sina + vi)

vt(15)

Here v• , vi , and a are defined as they were in Equation 8.The tip speed, given rpm w and rotor radius r, can be calcu-lated simply as:

vt = wr2p60

(16)

Using theseelements, the angleat which the rotor disk ro-tatesagainst thedirection of motion is(from Prouty, pp. 169):

a1;s =m

1� m2

2

�83

q0 + 2q1 + 2

�

mtana �vi

vt

��

(17)

Theforcedueto flapping drag (for asinglerotor producingthrust T) isgiven as:

FF = T sina1;s (18)

Theseforcesact on the location of thecenter of each rotor.Aswith thebody drag, sincetheseforcesarenot acting on thecenter of mass, they will produce torquing moments on thequadcopter that must be taken into account.

Induced and Profile Drag:

In addition to drag from blade flapping, there are othercomponentsof rotor drag dueto induced dragand profiledrag.The coefficients for these remaining components of the H-force are given in Equation 19 (on page 7). In that equationcd is the drag coefficient of the rotor, which can be assumedto be 0.01 for the entire operating envelope of the quadcopter(see the figure in Prouty, pp. 23). CH can be used as a dragcoefficient in order to find the force opposing the direction ofmotion:

FI;P = CHr Arv2t (20)

where Ar is the projection of the rotor area and not theprojected areaof thequadcopter volumefrom theearlier bodydrag equation.

Turbulence

Oneof thestarkest differencesbetween Figures1 and 2 is thelack of rapid fluctuation of the BPFs in the latter. In the realworld, the free atmosphere is filled with small-scale turbu-lent eddies (including those that are about the size of a quad-copter). Theseeddiesarelikely theprimary sourceof thefluc-tuations present in the recording. Accordingly, an effort wasmade to add asimplemodel for near-ground turbulence to thequadcopter model.

For this effect, the starting point is a model used for flightqualification for theUSMilitary (Handbook #1797 (Ref. 17)).

Thismodel specifieshow to generatea“velocity distancehis-tory,” which is a data set that specifies the turbulent compo-nent of the apparent wind velocity at a given distance alonga flight path6. This component is realized as velocities in thex, y, and zdirections(positive-zbeing thedirection away fromthe surface of the Earth). An example output for a 20 ft flightpath is shown in Figure 3.

Fig. 3. An example velocity distance history.

There are a number of details needed to make this modelcompatiblewith the quadcopter simulation:

� The original specification gives different expressions fortheeddy sizedistribution in thex and y directions(thedi-rections of motion of the aircraft and that orthogonal tothedirection of motion and thezdirection, respectively).In quadcopter operations, the x and y directions are in-terchangeable, as a quadcopter is just as likely to fly in acircle as it is to go straight (whereas fixed-wing aircraftmust fly primarily in astraight line in order to stay aloft).Accordingly, the expression for the x distribution of tur-bulent eddy length scales ismadethesameasthat for they distribution for this simulation.

� The specification also provides methods for computingthe pitching, yawing, and rolling moments generated bythe turbulent field on the aircraft. These expressions uti-lize the geometry of a fixed-wing aircraft (i.e., fuselagelength and wingspan). For this application, these valuesare taken to be the distance between adjacent rotor cen-ters.

� In the original specification, the eddy size distribution isgiven asaDryden spectrum, whereas it iscommonly un-derstood that atmospheric turbulenceismoreclosely rep-

6This nomenclature can be related to the term “pressuretime history,” which is common in acoustics, indicating astream of data that is meant to describe how a measurementof pressure at a singlepoint changes as time evolves.

6

CH

s=

cdm4

�a4

ml 0

1+ 32m2

! �

q0

�

�13

+32

m2�

+q1

2

�

�1+32

m2�

� l 0�

+a4

m

1+ 12m2

! �a2

0

2

�19

+m2

2

�

+13

ma0vi

vt+

18

�v2

i

v2t

��

(19)

resented by avon Karman spectrum. Theuseof theDry-den spectrum in legacy applicationsallowed for thegen-eration of an IIR filter that could produce the needed ve-locity distance histories. This effort is not constrained tousesuchfiltersand can thereforeemploy thevon Karmanspectrum directly.

For completeness, the equations specifying the turbulenteddy length scales that wereused are:

Lx = Ly =h

2(0:177+ 0:000823h)6=5(21)

Lz =h2

(22)

where h is the height of the quadcopter above the groundin feet. The turbulence ‘ intensities’ are:

sx = sy =sz

(0:177+ 0:000823h)2=5(23)

sz = 0:1Wh (24)

whereWh is the wind speed at the specified height in ft/s.Lastly, the formula to generate a von Karman power densityfunction for any direction (x;y;z) and spatial frequency w is:

F i(w) = s 2i

2Li

p

1+ 83(2:678Liw)2

(1+ (2:678Liw)2)11=6(25)

These equations are valid (for this model) between 10 and1000 ft. An IFFT can be used to produce the desired dis-tancevelocity historiesas in Fig. 3 from the resultsof Eq. 25.Expressions for computing the pitching, yawing, and rollingmoments from the above results are available in the originalreference.

Deficiencies:

There are a number of immediate deficiencies that comewith using this turbulence model in this application. Mostarise from the fact that this model makes the assumption thatthe aircraft under study is traveling at a speed much greaterthan the speed of the turbulent eddies – both the speed atwhich the gas is moving within the eddy and the speed atwhich an eddy is evolving or translating through the atmo-sphere. This allows the use of a “ frozen atmosphere” condi-tion and the generation of the single distance time history asshown above.

In the case of sUAS vehicles, the speed of the aircraft islow enough that it may be commensurate to the advectionvelocities present in the a real turbulent field. Additionally,one of the main operational modes of many sUAS vehicles ishover — where the aircraft is (nominally) not moving at all.In this condition, the lack of motion of the vehicle would im-ply that the turbulence history is not advancing so that, in theextreme case, the vehicle equilibrates with a particular mo-ment in the turbulence history (e.g., a zero-velocity crossing)and the effect of turbulence completely disappears.

There are several naıve methods of addressing this prob-lem including forcing thedistancevelocity history to advancewith thelaminar wind speed or with thespeed indicated by thecurrent position in theturbulent velocity timehistory. Asbothof these ideas do not necessarily arise from the physics be-hind the model, and given that the model is an accepted stan-dardized formulation, no attempt was made to include suchmodifications.

Manufactur ing Error

In the recording shown in Figure1, aswell as in other record-ings, it has been observed that the four rotor BPFs of quad-copters do not vary around the same nominal values. This isan expected effect, as one of the tasks during the setup of aquadcopter is to ‘calibrate’ a zero-point between the four ro-tors— where the forcesbeing exerted arerelatively balanced.This gives the PID control scheme a solid starting point andallows for important components of flight such as a smoothinitial take-off.

These offsets in rpm translate to differences in mean fre-quencies for the blade passage harmonics in the sound gener-ated by the quadcopter. When two sinusoids are sufficientlyclose to one another in frequency, human listeners will hear a“beating” effect instead of two distinct tones. In the record-ing, the mean frequencies are far enough apart that this effectis not heard. If these frequencies were closer or overlapping,one would hear an additional layer of interference effects be-tween rotorsthat isabsent in therecording of Fig. 1. This lackof beating is clearly a salient subjective feature of the record-ings — as will be demonstrated below when observing thedifferences between auralizations that are generated with andwithout these “error” offsets.

In order to simulatethisbehavior, an optional random errorterm was built into the simulation. This error term applies arandom (normally distributed) component to thetorquecoeffi-cient CT (from Equation 1 above) of the four individual rotors

7

of thequadcopter. ThisforcesthePID control schemeto com-pensate for differences between rotors by changing their ex-pected nominal operating BPFs. (For the simulator describedhere, unlike the real vehicle, the PID controller does this au-tomatically and there isno need to pre-calibrate thesystem.)

AURALIZATION RESULTS

This section discusses the effects that arise from incremen-tally adding thesimulation extensionsdiscussed above. With-out any of the extensions, the auralization spectrogram fromtheintroduction isproduced (Figure2). That figure, aswell asthoseshown below areall based on asimulation that attemptsto recreatetheflyover from therecording shown in Fig. 1. Thebaseline details of the simulations are mostly nominal valuesmeant to reflect thoseeither recorded during theflyover or in-tended by the operator. Also, the atmospheric parameters arechosen to approximatetheconditionspresent on therecordingday. These parameters are summarized in Table 1.

Table 1. Simulation/auralization parameters.Parameter Value UnitAltitude 18 ftSpeed 20 ft/sMassDistribution DJI Phantom IIRotor Spec. DJI Phantom II (OEM)Payloada 1 kg

Atmospheric PropertiesTemperature 20 oCPressure 101,325 PaRelative Humidity 50 %Wind Speedb 12 ft/s

Auralization PropertiesListener Location h0;0;4i ftGround Impedance Rigid

aPayload is symmetrically under-hung. The real payloadwas likely non-symmetric and closer to .6 kg.

bWind direction is in opposition to the quadcopter direc-tion of motion. Wind does not affect auralization processing.

Body Drag

The first introduced effect is the drag created by the body ofthe quadcopter passing through the air.7 This drag is depen-dent on theapparent wind velocity — thevelocity of the lam-inar wind component as well as the negative of the instanta-neousvelocity of thevehicle.

The addition of this effect serves to separate the BPFs ofthe front and rear motor pairs slightly, though not as much asis observed in the recording. In this simulation, the split iscaused by two sources of torque balancing each other: One isthe torqueneeded for thequadcopter to pitch forward in order

7N.B. The upgrades discussed in the “Rotorcraft Aerome-chanics” section aboveare included for all simulations.

Fig. 4. Spectrogram of auralization: Only body drag in-cluded in the simulation. (All auralizations shown hereuse thebasic model with theupgraded aeromechanics.)

to overcomethe forward momentum that is lost to thedrag onthe body. The other is the moment created by gravity on theunder-hung payload and components of the quadcopter (forthe Phantom II, the center of mass, even without a payload,is below the rotor plane). If the total center of mass of thequadcopter and its payload was in plane with the rotors, thisBPF-splitting effect would disappear.

Rotor Drag

Figure 5 shows the result of adding the sources of drag onthe rotors to the simulation. This drag is added in accordancewith the rotor geometry used and the assumptions noted inthe development of this effect (above). In this case, the splitbetween the front and rear motor BPFs is similar to that ob-served in the recording. There are two primary reasons whytherotor drag ismuch moreeffectiveat creating thissplit thanthe body drag:

1. The rotor drag creates a force on the vehicle that is di-rectly related to theapparent windvelocity (Fd;rotor µ va),whereas the drag caused by the body is proportional tothe square of the apparent wind (Fd;body µ v2

a). The sim-ulated vehicle is operating in the regime in which va islow enough that the rotor drag is dominant. If the vehi-cle were to be able to travel faster, it could get into theregime in which body drag became the dominant sourceof drag — where full-size rotorcraft and fixed-wing air-craft operate.

2. Theaddition of rotor drag createsadeleterious feedbackeffect on the operation of the vehicle. In order to main-tain forward speed, the vehicle must tip forward so thatsomeof the thrust of the rotorsgoes to replacing the for-ward momentum that is lost to drag effects (aswith bodydrag). However, unlike body drag, the drag on an indi-vidual rotor is also proportional to the speed at which

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Fig. 5. Spectrogram of auralization: Body and rotor drageffects included in simulation.

that rotor isspinning (Fd;rotor µ r pm). Therefore, tippingforward creates a further differential drag between thefront and rear rotor pairs — a force that acts to tip thevehicle back down (toward a neutral, 0-pitch, position).This feedback situation causes the large split in rpm thatis observed.

For both of the reasons noted, but especially for the latter,rotor drag appears to be a critically important element to in-clude in a quadcopter model meant for auralization. Also, aswill be discussed next, it is an important effect to include inconcert with simulations of turbulence.

Turbulence

Figure6 showstheresult of theaddition of aturbulent compo-nent to theapparent wind field. It is important to note that themagnitudeof thisfield isnot an arbitrary choiceand, in accor-dancewith the turbulencemodel discussed above, isbased onother parameters of the simulation including the height of thequadcopter above the ground and the laminar wind velocity.8

Comparing Figures 1 and 6, the depth of frequency mod-ulation can be seen to be commensurate between the twosounds. That is, the BPF modulations induced by turbulencepresent at the site of the recording is on the order of those in-duced by the addition of the turbulence model to the simula-tion. Thereare longer variationsthat arepresent in therecord-ing (e.g, thenoticeabledip in BPF between 1 and 3 secondsinFig. 1) that are not found in the simulation. This difference islikely dueto thefact that theflyover that generated therecord-ing was not a programmed ‘way point’ operation as is flownin the simulation, but was executed by a human pilot makingadjustments in real time.

8The random seed that is used to generate the turbulentfield is a controllable parameter of the simulation. BothFig.s6 and 7 (below) usethesamerandom seed and thereforeare impacted by the same turbulent velocity distance history.

Fig. 6. Spectrogram of auralization: Drag effects and tur-bulencemodel included in simulation.

Onevery important observation that isnot evident from thefigures is the fact that the turbulent field is affecting the vehi-cle primarily through rotor drag. Although not shown here, iftheeffect of rotor drag is turned off in thesimulation, and tur-bulence is left on, theresulting auralization significantly lacksthe BPF variation seen in the recording. This is again due tothe fact that the turbulent componentsof va arequitesmall —on the order of 1 ft/s (see Fig. 3). Therefore, the componentof drag that is proportional to va will have a much greater ef-fect on thedynamicsof thevehicle than thecomponent that isrelated to v2

a.

Manufactur ing Error

The last effect to be added is the error term described above.The result of this simulation is shown in the spectrogram ofFigure7. Here, anormally distributed error of 10% — atypi-cal manufacturing tolerance level for massproduced electron-ics — has been added to the nominal values of CT for the4 rotors. With this addition, the four traces of the BPFs donot overlap. This causes the interference effect present in theauralization of Fig. 6 to disappear. (Again, this effect is notobservable in thespectrogram of Fig. 1, nor is it present whenlistening to the recording thereof.)

Another observed effect of this final case is the fact thattherear two motorsaresplit in frequency by asmaller amountthan the two front motors. This effect is not due to just therandom draw of the errors added to CT in this particular run,in fact this effect is seen in the vast majority of draws. Thesourceof thiseffect comes from the fact that the thrust gener-ated by an individual rotor isproportional to thesquareof therpm of the rotor. Therefore, for rotors spinning more quickly(as therear two arerelative to the front two), asmaller adjust-ment needs to bemade to their respectivespeeds to overcomethe same magnitude of difference in CT that may be presentbetween the two due to this error term. It is interesting tonote that not only was this effect not programmed into the

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Fig. 7. Spectrogram of auralization: Drags, turbulence,and “ er ror ” included in simulation.

simulation explicitly, it was also not directly observed fromthe recording until after it was consistently observed in aural-izations. In this way the developed tool chain of simulationand auralization wound up offering insights into the physicsbehind quadcopter flight that wereemergent from the interac-tionsof the programmed effects.

It is important to notethat whiletheimplementation of thiserror term has focused on direct manipulation of the value ofCT, there are some simple physical effects that could havecaused thissplit in the recording:

� The presence of a non-centered payload. In the case ofthe recording, the payload was known to not have a cen-ter of massdirectly underneath thephysical center of thevehicle (although thisoffset wasnot measured).

� The presence of a laminar wind component that is notdirectly opposing thedirection of movement of thevehi-cle. In general this will be the case in real-world condi-tions. Although the recording of Fig. 1 was taken whenthe quadcopter was flying into a stiff wind, it was notlikely to have been perfectly aligned in opposition to thevehicle. The auralizations shown here are all based onsimulations with a laminar wind that does perfectly op-pose the (nominal) direction of motion of the vehicle.

CONCLUSIONS

This paper has outlined the current state of a quadcopter sim-ulation capability that has been developed for the NASA DE-LIVER project. The development of the model from a num-ber of sources was described. Incrementally adding effects tothesimulation revealshow important each effect can beon anauralization based upon the model. Further, the ability to se-lectively turn on and off effects can provide insight into thesourceof aurally-significant details found in real-world data.

Theprincipal result of thiswork so far (aside from thecre-ation of thetool itself), is to point out thenecessity of many of

theeffectsincluded hereif asimulation isto beused for aural-ization. For many other applicationsof quadcopter simulation(e.g., control scheme development), these effects are unnec-essary and computationally expensive. However, the compli-cated and nuanced natureof thedesired sound leads to aneedfor an equally complicated simulation capability.

Andrew Christian is thecorresponding author. eMail:andrew.christian@nasa.gov

ACKNOWLEDGMENTS

Support for this work comes from the NASA DELIVER sub-project. This is contained within the CAS project of theTAC program within the Aeronautics Research Mission Di-rectorate.

Much of the technical work described here was producedduring Joseph Lawrence’sinternship at NASA Langley duringthe summer of 2015. Accordingly, the facilitatorsand coordi-nators of the NIFS internship program deserve acknowledg-ment for providing the environment within which extraordi-nary stepsareconsistently taken by undergraduates in only 10weeks. Eric Greenwood, Nik Zawodny, and other researchersin theAeroacousticsBranch also deservecredit for their guid-ance on the rotorcraft aeromechanics section.

Lastly, agreat deal of thanks isowed to Andrew’scowork-ers including: Kevin Shepherd, Stephen Rizzi, Ran Cabell,Menachem Rafaelof, Brian Tuttle, Aric Aumann and JamesStephenson who have been infinitely helpful in accommodat-ing his reduced capacity for work during a protracted (andongoing) period of immoderatehealth.

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