eVTOL Acoustic Intelligence Platform
SONONAI
OPEN ROTOR · CABIN ACOUSTICS · FAR-FIELD MAPPING

Physics-based noise prediction for eVTOL aircraft. BPF tonal analysis, cabin treatment design, far-field SPL mapping — all in your browser, in real time. Built on peer-reviewed aeroacoustics.

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18
AIRCRAFT TYPES
8
ACOUSTIC MODELS
5
ANALYSIS TOOLS
100%
BROWSER-BASED
ABOUT SONONAI

ACOUSTIC INTELLIGENCE FOR THE NEXT GENERATION OF AVIATION

SONONAI is an eVTOL acoustic prediction platform implementing the models used in real type-certification work — from rotor tonal noise to cabin treatment design to far-field community noise mapping.

The platform covers Lowson thickness noise, Ffowcs Williams-Hawkings loading noise, Brooks-Pope-Marcolini broadband model, JCA/Miki/Biot/Delany-Bazley porous media, Helmholtz and MPP resonators, and ISO 9613 far-field propagation.

All computations run entirely in your browser. No data leaves your device. Methodology follows ICAO Annex 16, EASA SC-VTOL-01, and SAE ARP1779.

ROTOR NOISE
BPF tonal analysis, thickness, loading, BVI and broadband. Polar directivity. EPNL estimation.
CABIN DESIGN
8 treatment models with live SPL reduction charts per treatment at any area fraction.
FAR-FIELD MAP
HD ground-level SPL heatmap. Multi-rotor sources with configurable positions. Contour rings at certification limits.
18 AIRCRAFT
Joby S4, Archer Midnight, Lilium Jet, Volocopter, EHang 216, DJI M300, Wingcopter and more.
PRODUCTS

ACOUSTIC ENGINEERING TOOLS

Browser-based · no installation · access anywhere

LIVE
SONONAI
eVTOL ACOUSTIC PREDICTION

Complete open-rotor noise prediction: aircraft selection, spectral analysis, cabin treatment design, far-field heatmap, and full acoustic glossary with 30+ cited references.

  • ✓  18 eVTOL & drone configurations
  • ✓  Real-time acoustic spectrum
  • ✓  8 cabin treatment models
  • ✓  HD far-field radiation map
  • ✓  EPNL & ICAO compliance
  • ✓  Complete glossary & references
CERTIQ
NOISE CERTIFICATION TOOLKIT

ICAO Annex 16 and EASA SC-VTOL data package generation. Measurement point analysis, flyover/approach/lateral noise limits, certification margin calculator.

COMING SOON
PROPAGIQ
URBAN PROPAGATION & MAPPING

Full ISO 9613-2 outdoor propagation with building reflections, barriers, and terrain. GIS-integrated community noise mapping for vertiport siting studies.

COMING SOON
THE SCIENCE

FOUNDED ON PEER-REVIEWED AEROACOUSTICS

Every model in SONONAI is traceable to a published, peer-reviewed source

THICKNESS NOISE
Lowson (1970)
J. Acoust. Soc. Am. 47(1B)
LOADING NOISE
Ffowcs Williams &
Hawkings (1969)
BROADBAND (BPM)
Brooks, Pope &
Marcolini (1989) NASA RP-1218
POROUS MEDIA (JCA)
Johnson-Champoux-
Allard (1987–1991)
MICRO-PERF (MPP)
Maa, D.Y. (1998)
J. Acoust. Soc. Am.
CERTIFICATION
ICAO Annex 16 Vol. I
EASA SC-VTOL-01 (2022)
CONTACT

GET IN TOUCH

For licensing enquiries, custom acoustic analysis, eVTOL certification support, or any technical questions — reach us directly.

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[email protected]
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WEBSITE
www.sononai.com
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eVTOL Acoustic Intelligence · sononai.com
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SONIQ
eVTOL Open Rotor Acoustics Noise Prediction & SPL Analysis Suite
SAE ARP1579
ICAO Annex 16
● LIVE
[email protected]

SELECT YOUR eVTOL PLATFORM

Choose an aircraft configuration to begin the open-rotor acoustic analysis. Each platform loads physics-appropriate default parameters.

QUAD
UAM · MULTIROTOR
QUADCOPTER
4-rotor X-frame. Most common UAM configuration. Alternating CW/CCW torque cancellation.
4 ROTORSVTOL3-BLADE
UAM · MULTIROTOR
HEXACOPTER
6-rotor hexagonal layout. Higher redundancy and lower disc loading per rotor than quad. Common in heavy-lift UAM.
6 ROTORSREDUNDANT3-BLADE
UAM · MULTIROTOR
OCTOCOPTER
8-rotor maximum redundancy platform. Used in heavy-lift cargo and professional cinematography drones.
8 ROTORSHIGH REDUND.2-BLADE
COAXIAL
UAM · COAXIAL
COAXIAL ROTOR
Two contra-rotating rotors on a single shaft. Compact footprint, high disc efficiency. Kamov helicopter tradition applied to eVTOL.
2 ROTORSCONTRA-ROT3-BLADE
TANDEM
UAM · TANDEM
TANDEM ROTOR
Front and rear rotor pairs. Long-body CG-range design like CH-47 Chinook applied to eVTOL. Wide acoustic footprint.
2 ROTORSLONGITUDINAL2-BLADE
LIFT+CRUISE
UAM · HYBRID
LIFT + CRUISE
Separate lift rotors + forward cruise propeller. Optimised for each phase. Higher cruise efficiency, complex acoustic signature.
3+ ROTORSHYBRIDCRUISE OPT
JOBY S4
PRODUCT · JOBY AVIATION
JOBY S4
6 tilting 5-blade props. 320 km/h cruise, 241 km range. FAA G-1 accepted. Quoted 45 dB(A) overhead at 500m — quietest certified eVTOL.
6 TILT-PROPS5-BLADEFAA CERT
MIDNIGHT
PRODUCT · ARCHER AVIATION
ARCHER MIDNIGHT
6 tilt-rotor 5-blade design. 4-passenger UAM. 240 km/h cruise, 100 km range. United Airlines launch customer.
6 TILT-PROPS5-BLADE4 PAX
36 DUCTED FANS
PRODUCT · LILIUM
LILIUM JET
36 ducted electric fans in canard/wing flaps. 280 km/h cruise, 300 km range. Unique distributed propulsion acoustic signature.
36 FANSDUCTEDJET-WING
18 ROTORS
PRODUCT · VOLOCOPTER
VOLOCOPTER 2X
18-rotor ring layout. Ultra-light 2-seat UAM. EASA type certification. Operating in Singapore, Dubai. 70 km/h, 27 km range.
18 ROTORSULTRA-LIGHTEASA CERT
EHANG 216
PRODUCT · EHANG
EHANG 216
8 coaxial props (4 arms, dual-stacked). First CAAC-type-certified AAV. Operational in China. 130 km/h, 21 km range.
8 COAX-PROPSCAAC CERTAUTONOMOUS
12 ROTORS
PRODUCT · WISK AERO
WISK CORA GEN2
12-rotor autonomous air taxi (Kitty Hawk + Boeing). Redundant multirotor + pusher prop. FAA G-1 accepted. Fully autonomous.
12 ROTORSAUTONOMOUSFAA G-1
M300 RTK
DRONE · DJI ENTERPRISE
DJI MATRICE 300
Industrial quadcopter. 55 min endurance, 9 kg payload. IP45, −20°C. Survey, inspection, search and rescue operations.
4 ROTORS9kg PAYLOADIP45
WINGCOPTER 198
DRONE · DELIVERY
WINGCOPTER 198
VTOL delivery drone with tilting wingtip rotors for efficient cruise. 110 km/h, 70 km range, 6 kg payload. Medical delivery.
4 TILT-ROTORSDELIVERY6kg
TILT-WING
CONCEPT · ADVANCED
TILT-WING
Full wing tilts with rotors for VTOL to cruise. Bell V-280 / NASA X-57 heritage. High cruise efficiency, complex transition acoustics.
4 ROTORSTILT-WINGHIGH SPEED
TILT-ROTOR
CONCEPT · V/STOL
TILTROTOR (V-22 TYPE)
Bell-Boeing V-22 / AW609 heritage. Large prop-rotors tilt 90°. High speed 400+ km/h, long range. Loudest in hover phase.
2 PROP-ROTORS400+ km/h3-BLADE
SONIQ › QUADCOPTER › ACOUSTIC ANALYSIS
AUTO-REFRESH
BLADE PASS FREQ.
—
Hz  (B × RPM/60)
TIP SPEED
—
m/s  Mach —
FAR-FIELD SPL
—
dB(A) @ 100m
CABIN INTERIOR
—
dB(A) interior
EPNL (ESTIMATE)
—
EPNdB flyover
ICAO COMPLIANCE
CALCULATING…
Limit: 65 dB(A)
NOISE
SOURCES
THICKNESS 35%
LOADING 28%
BVI 22%
BROADBAND 15%
– dB(A)
◈ FAR-FIELD SPL SPECTRUM
@ 100m · hover
ICAO OK
◈ CABIN INTERIOR NOISE
TL applied per band
COMFORT OK
◈ BPF HARMONIC TONES
BPF = – Hz
◈ NOISE POLAR DIRECTIVITY
0°=axis · 90°=in-plane
SONIQ LIVE
MODEL: Lowson + Farassat 1A + BPM
BPF: –
Vtip: –
SPL(ff): –
Cabin: –
Updated: –

GLOSSARY & FORMULAE

Complete reference of acoustic terms, symbols, physical models, equations and standards used in SONONAI. Follows ICAO Annex 16 Vol. I, SAE ARP1779, ISO 3744/3745 and IEC 61672 conventions.

FUNDAMENTAL ACOUSTIC QUANTITIES
SPL
Sound Pressure Level
Logarithmic ratio of RMS acoustic pressure to the standard reference pressure. Primary measurement metric for noise regulation.
SPL = 20·log₁₀(p_rms / p_ref)   p_ref = 20 µPa
Ref: IEC 61672-1:2013 · ISO 1683:2015
dB re 20 µPa
dB(A)
A-Weighted Sound Level
SPL corrected by the A-weighting curve approximating the human ear's frequency sensitivity. Mandatory for all community noise assessments.
L_A(f) = SPL(f) + W_A(f)
W_A(1kHz)=0, W_A(63Hz)=−26.2, W_A(125Hz)=−16.1 dB
Ref: IEC 61672-1:2013, Table B.1
dB(A)
OASPL
Overall Sound Pressure Level
Energy sum of SPL contributions from all frequency bands. Single-number broadband descriptor.
OASPL = 10·log₁₀(Σ 10^(SPLᵢ/10))
Sum over 1/3-octave or octave bands · ISO 3744:2010
dB or dB(A)
EPNL
Effective Perceived Noise Level
ICAO certification metric combining peak noise, duration, and tonality corrections for a flyover event. The primary type-certification standard.
EPNL = PNLTM + 10·log₁₀(∫₀^∞ 10^(PNLT(t)/10) dt) − 13
PNLT = PNL + C (tone correction)
Ref: ICAO Annex 16 Vol. I, Appendix 2
EPNdB
PNL
Perceived Noise Level
Frequency-weighted noise metric using noy scale that better matches perceived annoyance for aviation noise than dB(A). Basis for EPNL.
PNL = 40 + (10/log₁₀2)·log₁₀(N_total)
N = noy values from 1/3-oct SPL table
Ref: ICAO Annex 16, Appendix 2 §1.4
PNdB
SEL
Sound Exposure Level
Time-integrated noise metric normalised to 1-second duration. Used for cumulative noise assessment of multiple events.
SEL = 10·log₁₀(∫ p²(t)/p²_ref dt) − 10·log₁₀(T₀)
T₀ = 1 s
Ref: ISO 1996-1:2016
dB(A)·s
L_dn
Day-Night Average Level
24-hour average noise level with a 10 dB penalty applied to night-time events (22:00–07:00). US EPA and FAA standard for community impact.
L_dn = 10·log₁₀[(1/24)(15·10^(L_d/10) + 9·10^((L_n+10)/10))]
Ref: FAR Part 150 · EPA 550/9-74-004
dB(A)
L_den
Day-Evening-Night Level
European standard (ECAC, END Directive) equivalent to L_dn but with an additional 5 dB penalty for evening hours 19:00–23:00.
L_den = 10·log₁₀[(1/24)(12·10^(L_d/10) + 4·10^((L_e+5)/10) + 8·10^((L_n+10)/10))]
Ref: EC Directive 2002/49/EC · ECAC Doc 29
dB(A)
ROTOR GEOMETRY & OPERATING PARAMETERS
BPF
Blade Passage Frequency
Fundamental tonal frequency of a rotor. The dominant discrete tone in eVTOL noise spectra. Higher harmonics (2×BPF, 3×BPF…) are also significant.
BPF = B · RPM / 60   [Hz]
B = number of blades, RPM = rotational speed
Ref: Lowson (1970), J. Sound Vib. 9(4)
Hz
V_tip
Blade Tip Speed
Tangential velocity at the blade tip. Critical acoustic parameter — thickness noise scales as M⁴, making tip speed the dominant control lever.
V_tip = π · D · RPM / 60 = Ω · R   [m/s]
Ω = 2π·RPM/60, R = radius
Ref: SAE ARP1779 §4.2
m/s
M_tip
Blade Tip Mach Number
Tip speed relative to speed of sound. Nonlinear (transonic) noise mechanisms become significant above M≈0.70. For eVTOL: typically 0.55–0.70.
M_tip = V_tip / a₀ = V_tip / 340   (ISA SL)
a₀ = √(γRT) varies with altitude T
Target M_tip < 0.65 for quiet operation
—
DL
Disc Loading
Thrust per unit rotor disc area. Directly linked to induced velocity and hence to loading noise. Lower DL = quieter hover but larger rotors.
DL = T / A_disc = AUW·g / (N·πR²)   [N/m²]
v_i = √(DL / 2ρ) (induced velocity, actuator disc)
Ref: Leishman (2006), Principles of Helicopter Aero.
N/m²
μ
Advance Ratio
Ratio of forward flight speed to blade tip speed. Controls blade loading asymmetry and BVI occurrence in forward flight.
μ = V_∞ / (Ω · R) = V_cruise / V_tip
BVI typically significant for μ > 0.05
Ref: Johnson (1994), Helicopter Theory, §5.6
—
σ_r
Rotor Solidity
Ratio of total blade planform area to disc area. Higher solidity allows lower tip speed for the same thrust but increases profile drag noise.
σ_r = B · c · R / (π · R²) = B · c / (π · R)
c = chord, B = blades, R = radius
Ref: Stepniewski & Keys (1984), Rotary-Wing Aero.
—
ACOUSTIC NOISE MODELS
SPL_thick
Thickness Noise (Lowson 1970)
Noise from blade displacement of air as it rotates — proportional to blade volume rate of change. Dominant tonal source at high tip Mach.
SPL_thick = 20·log₁₀(ρ₀a₀BΩ²R²cτ / 4πR_obs) + 20·log₁₀(M)
τ = thickness ratio (≈0.12), c = chord
Ref: Lowson, M.V. (1970). Theoretical Analysis of Compressor Noise. J. Acoust. Soc. Am., 47(1B), 371–385.
dB
SPL_load
Loading Noise (FW-H)
Noise from unsteady aerodynamic forces (thrust and drag) on rotating blades. Dominant at low speeds and during manoeuvres.
SPL_load = 20·log₁₀(B·dT/dt / 4πa₀ρ₀R²_obs) + 94
dT/dt = B·Ω·T_single (time derivative of thrust)
Ref: Ffowcs Williams & Hawkings (1969). Phil. Trans. R. Soc. A, 264, 321–342.
dB
SPL_bb
Broadband Noise (BPM Model)
Trailing-edge turbulent boundary layer noise. Continuous spectrum peaking near frequency V_tip/c. Dominant at cruise for quiet eVTOL.
SPL_bb = 10·log₁₀(ρ²a₀³·c·δ*·M⁵ / R²_obs) + 128
δ* = 0.037·c·Re^(−0.2) (displacement thickness)
Ref: Brooks, Pope & Marcolini (1989). NASA RP-1218.
dB
SPL_BVI
Blade-Vortex Interaction Noise
Impulsive noise from blades striking tip vortices shed by preceding blades or rotors. Characteristic "blade slap" — most perceptually annoying eVTOL noise.
SPL_BVI ≈ SPL_load + 3·bvi_factor
bvi_factor = 8·μ (for μ > 0.05)
Ref: Leishman (2002). AIAA J. 40(7):1257–1272.
dB
Doppler
Doppler Frequency Shift
Frequency and amplitude change of tonal noise as a moving source approaches or recedes from an observer. Significant for certification flyover measurements.
f_obs = f_source / (1 ± M_flight·cos θ)
ΔL_Doppler = 20·log₁₀(1 / (1−M_flight)) [approaching]
Ref: Morse & Ingard (1968). Theoretical Acoustics, §11.2
dB / Hz
ΔL_gr
Ground Effect / Reflection
Constructive interference between direct and ground-reflected waves adds 0–6 dB depending on source height, receiver height, and ground impedance.
ΔL = 10·log₁₀(1 + |R_p|² + 2|R_p|·cos(kΔr))
Hard ground: R_p ≈ 1 → ΔL ≈ +6 dB near-field
Ref: Attenborough (1988). J. Acoust. Soc. Am. 83(6).
dB
ΔSPL_atm
Atmospheric Absorption
Frequency-dependent absorption of sound by air. ISO 9613-1 gives absorption coefficient α [dB/m] as function of T, RH, and frequency.
ΔSPL = −α · d   [dB]
α(1kHz, 20°C, 70%RH) ≈ 0.004 dB/m
α(8kHz) ≈ 0.09 dB/m
Ref: ISO 9613-1:1993
dB/m
ΔL_div
Geometric Divergence
Free-field point source loses 6 dB per doubling of distance (inverse square law). Actual propagation includes ground absorption corrections.
ΔL = −20·log₁₀(r₂/r₁)   [dB]
−6 dB per distance doubling
Ref: ISO 9613-2:2024
dB
STRUCTURAL ACOUSTICS & TRANSMISSION LOSS
TL
Transmission Loss
Reduction in sound power level when a wave passes through a partition. Key parameter for cabin noise design.
TL = L_wi − L_wt = 10·log₁₀(1/τ)
τ = transmission coefficient (power ratio)
Ref: ISO 717-1:2013 · ISO 10140:2021
dB
TL_mass
Mass Law Transmission Loss
Below the critical frequency, TL follows the mass law: 6 dB improvement per doubling of surface mass density or frequency. Foundation of panel design.
TL = 20·log₁₀(f · m) − 47.2   [dB]
m = surface mass density [kg/m²]
Ref: Fahy & Gardonio (2007). Sound and Structural Vibration, 2nd ed.
dB
f_c
Critical (Coincidence) Frequency
Frequency at which acoustic wavelength matches the bending wavelength in the panel. Severe TL dip occurs here due to trace-velocity matching.
f_c = (c₀²/2π)·√(m/B_p)
B_p = Eh³/12(1−ν²) (bending stiffness)
Ref: Cremer, Heckl & Ungar (1988). Structure-Borne Sound.
Hz
η
Structural Loss Factor
Fraction of stored elastic energy dissipated per radian. Controls TL at coincidence: TL_c ≈ TL_mass − 10·log₁₀(1/2η). Bare aluminium: η≈0.001; CLD: η≈0.1–0.3.
TL_at_fc = TL_mass + 10·log₁₀(2η/π) + 10·log₁₀(f/f_c)
CLD gain: ΔTL_c ≈ 10·log₁₀(η_CLD/η_bare)
Ref: Oberst (1945). Akust. Beih. 4:181–194.
—
R_w
Weighted Sound Reduction Index
Single-number rating of a partition's airborne sound insulation from laboratory measurements. Standardised European metric for comparing constructions.
R = L₁ − L₂ + 10·log₁₀(S/A)
R_w = R with ISO 717-1 reference curve fitting
Ref: ISO 717-1:2013 · EN ISO 140-3
dB
STC
Sound Transmission Class
North American single-number rating equivalent to R_w. Used in US building codes and aviation interior specification.
Determined by fitting standard contour to TL vs frequency curve
STC ≈ R_w (within ~2 dB for most constructions)
Ref: ASTM E413-22
—
POROUS MEDIA ACOUSTIC MODELS
φ
Open Porosity
Ratio of open pore volume to total material volume. Controls acoustic coupling: high φ → better coupling at high f. Melamine foam: φ≈0.99.
φ = V_pores / V_total
Measured per ISO 9053-1:2018 · ASTM C522
—
σ_f
Static Air Flow Resistivity
Resistance to steady airflow per unit thickness. Single most important parameter for porous absorber design. Melamine: ~8 kPa·s/m², mineral wool: ~20–80.
σ_f = ΔP / (u · d)   [Pa·s/m²]
ΔP = pressure drop, u = velocity, d = thickness
Ref: ISO 9053-1:2018
Pa·s/m²
α∞
Tortuosity (High-Freq Limit)
Ratio of actual to straight-line fluid path through pores. Increases effective density at high frequencies. Open-cell foam: α∞≈1.0–2.0; fibre: α∞≈1.0–1.5.
α∞ = (effective fluid path length / sample thickness)²
Ref: Johnson, Koplik & Dashen (1987). J. Fluid Mech. 176:379–402.
—
Λ, Λ'
Viscous & Thermal Characteristic Lengths
Pore geometry parameters controlling the transition from viscous- to inertia-dominated flow (Λ) and thermal losses (Λ'). Λ'≈2Λ for simple geometries.
JCA viscous: G₁(ω) = √(1 + 4α∞²μρ₀ω / σ²Λ²φ²)
JCA thermal: G₂(ω) = √(1 + 4α∞²μPrρ₀ω / σ²Λ'²φ²κ)
Ref: Champoux & Allard (1991). J. Appl. Phys. 70:1975–1979.
µm
JCA
Johnson-Champoux-Allard Model
5-parameter semi-phenomenological model for wave propagation in rigid-frame porous media. Standard for open-cell foam, mineral wool in aircraft interiors.
ρ_eff(ω) = (α∞ρ₀/φ)[1 + G₁·σφ/(iωα∞ρ₀)]
K_eff(ω) = κP₀/φ / [κ−(κ−1)/G₂]
α(f) via TMM on rigid backing: α = 1−|R|²
Ref: Johnson et al. (1987); Champoux & Allard (1991); Allard & Atalla (2009).
—
D-B
Delany-Bazley Empirical Model
Simple 1-parameter empirical model for fibrous media. Only flow resistivity σ needed. Valid for X = ρ₀f/σ ∈ [0.01, 1]. Widely used for mineral wool, glass fibre.
Z_c/ρ₀c₀ = 1 + 9.08X^0.75 − 11.9i·X^0.73
k_c/k₀ = 1 + 10.8X^0.70 − 10.3i·X^0.59
Ref: Delany & Bazley (1970). Appl. Acoust. 3:105–116.
—
Miki
Miki Revised Empirical Model (1990)
Improved Delany-Bazley coefficients with better accuracy at X < 0.01 and X > 1. Standard reference for fibrous absorbers in ISO 354 measurements.
Z_c/ρ₀c₀ = 1 + 5.50X^0.632 − 8.43i·X^0.632
k_c/k₀ = 1 + 7.81X^0.618 − 11.41i·X^0.618
Ref: Miki (1990). J. Acoust. Soc. Jpn. 11(1):19–24.
—
Biot
Biot Limp-Frame Model
Poroelastic model treating the solid skeleton as mechanically limp. Adds frame inertia ρ_s. Appropriate for heavy felt, mass-loaded vinyl, dense foam.
ρ_eff = ρ_s + φρ₀ + σ/iω (simplified limp approx.)
Combines fluid and skeleton inertia contributions
Ref: Biot (1956). J. Acoust. Soc. Am. 28:168–178; Zwikker & Kosten (1949).
—
TMM
Transfer Matrix Method
Layer-by-layer acoustic impedance cascade. Each layer (porous, solid, air gap) represented by a 2×2 transfer matrix. Numerically exact for planar multi-layer structures.
T_total = T₁ · T₂ · ··· · Tₙ
Surface impedance: Z_s = T_11/T_21 (rigid backing)
α = 1 − |((Z_s/Z_air)−1)/((Z_s/Z_air)+1)|²
Ref: Allard & Atalla (2009). Propagation of Sound in Porous Media.
—
RESONATOR & PANEL ABSORBER MODELS
f₀ (Helm)
Helmholtz Resonator Frequency
Resonance of perforated panel + cavity system. At f₀ the neck air mass oscillates against the cavity spring. Best for targeting discrete BPF tones.
f₀ = (c₀/2π)·√(φ_p / L_eff·L_cav)
L_eff = t + 2·0.85·r (Rayleigh end correction)
φ_p = πr²/B² (perforation ratio)
Ref: Ingard (1953). J. Acoust. Soc. Am. 25:1037–1061.
Hz
Q
Quality Factor (Resonator)
Ratio of peak frequency to −3dB bandwidth. High Q = sharp narrow absorption peak. Low Q (with foam backing) = broader but shallower response.
Q = f₀ / Δf₃dB ≈ ρ₀c₀φ_p / R_neck
R_neck = viscous resistance in the neck
Ref: Maa (1987). Acta Acust. Sinica.
—
MPP
Micro-Perforated Panel (Maa 1998)
Sub-mm holes at low perforation ratio. Viscous boundary layers fill the neck (k≈1), giving efficient broadband absorption without fibrous material. Standard in aircraft cabins.
α = 4r_m / [(1+r_m)² + x_total²]
r_m = 32μt/(φρ₀c₀d²)·√(1+k²/32), k = r√(ρ₀ω/μ)
x_m = ωt/(φc₀)[1+1/√(9+k²/2)] + 0.85ωd/(φc₀)
Ref: Maa (1998). J. Acoust. Soc. Am. 104(5):2861–2866.
—
CLD
Constrained Layer Damping
Viscoelastic layer constrained between host structure and face sheet. Shear deformation dissipates energy, raising η. Reduces coincidence dip by 10·log(η_CLD/η_bare).
ΔTL_c = 10·log₁₀(η_CLD/η_bare)
η_bare Al ≈ 0.001; η_CLD ≈ 0.05–0.3
Ref: Oberst (1945); Ross, Ungar & Kerwin (1959). ASME Publication.
—
CERTIFICATION STANDARDS & REGULATIONS
ICAO Ann.16
ICAO Annex 16 — Environmental Protection
International civil aviation noise certification standard. Volume I covers aircraft noise. Defines measurement procedures and noise limits for type certification at approach, flyover, and lateral measurement points.
Noise limits vary by MTOW:
MTOW < 600 kg (eVTOL class): 63–72 EPNdB
800+ kg: typically 75–89 EPNdB
Ref: ICAO Annex 16, Volume I, 8th ed. (2017) + Amendment 13
EPNdB
EASA SC-VTOL
EASA Special Condition VTOL
European type-certification framework for novel VTOL aircraft. Includes noise measurement procedures adapted from CS-27/29 and the ICAO eVTOL working paper (WP-595).
Noise reference point: 500 m lateral
Target: ≤ 65 dB(A) for urban operations
Ref: EASA SC-VTOL-01 Issue 2 (2022); ICAO WP-595
dB(A)
FAA AC 36-4
FAA Advisory Circular 36-4
FAA noise certification procedures for helicopters and powered-lift (which includes eVTOL under FAR Part 36, Subpart H). Specifies test conditions, data corrections, and acceptance criteria.
Helicopter limits (FAR 36 App. J): typically 73–82 EPNdB
eVTOL treated as powered-lift (Subpart K proposals)
Ref: 14 CFR Part 36, Subpart H; AC 36-4C
EPNdB
SAE ARP1779
SAE Rotorcraft Noise Measurement
Industry standard for helicopter and rotorcraft acoustic measurements. Defines microphone placement, data acquisition, background noise corrections, and reporting.
Far-field: ≥ 30 m, free-field conditions
S/N ≥ 10 dB for valid measurement
Ref: SAE ARP1779 Rev. B (2015)
—
ISO 3744
ISO 3744 — Sound Power Measurement
Measurement of sound power levels using a measurement surface of microphones surrounding the source. Engineering-grade method (Grade 2). Used for eVTOL ground-based characterisation.
L_W = L̄_p + 10·log₁₀(S/S₀)
S₀ = 1 m², S = measurement surface
Ref: ISO 3744:2010
dB re 1 pW
WHO 2018
WHO Environmental Noise Guidelines
World Health Organisation guidelines for community noise limits. Defines health-based limit values that urban air mobility operations must respect.
Outdoor L_den < 45 dB(A) (strong recommendation)
Night L_night < 40 dB(A)
Ref: WHO Environmental Noise Guidelines for the European Region (2018)
dB(A)
QUICK REFERENCE — ALL FORMULAE
QUANTITYFORMULAUNITSREFERENCE
BPFB · RPM / 60HzLowson (1970)
Tip Speedπ · D · RPM / 60 = Ω · Rm/sSAE ARP1779
Tip MachV_tip / a₀   a₀=340 m/s ISA SL—ISO 9613
Disc LoadingAUW·g / (N·πR²)N/m²Leishman (2006)
Induced velocityv_i = √(T/2ρ₀A) actuator discm/sGlauert (1935)
Advance ratioμ = V_∞ / (Ω·R)—Johnson (1994)
Rotor solidityσ = Bc / (πR)—Stepniewski (1984)
Thickness SPL20·log(ρ₀a₀BΩ²R²cτ/4πr) + 20·log(M)dBLowson (1970)
Loading SPL20·log(BdT/dt / 4πa₀ρ₀r²) + 94dBFW-H (1969)
BPM δ* (turbulent)0.037·c·Re^(−0.2)mBrooks et al. (1989)
Broadband SPL10·log(ρ²a₀³cδ*M⁵/r²) + 128dBBPM, NASA RP-1218
BVI factor8·μ (μ>0.05 forward flight)—Leishman (2002)
Doppler boost20·log(1/(1−M_flight)) approachingdBMorse & Ingard (1968)
Geometric spread−20·log(r₂/r₁) free-fielddBISO 9613-2
Atm. absorption−α·d   α from ISO 9613-1dBISO 9613-1:1993
Mass Law TL20·log(f·m) − 47.2dBFahy & Gardonio (2007)
Coincidence freq(c₀²/2π)·√(m/Eh³/12(1−ν²))HzCremer et al. (1988)
Helmholtz f₀(c₀/2π)·√(φ_p / L_eff·L_cav)HzIngard (1953)
Helm end correctionL_eff = t + 2·0.85·rmRayleigh (1945)
MPP absorptionα = 4r_m / [(1+r_m)² + x²]—Maa (1998)
JCA ρ_eff(α∞ρ₀/φ)[1 + G₁(ω)·σφ/iωα∞ρ₀]kg/m³Johnson et al. (1987)
JCA K_effκP₀/φ / [κ−(κ−1)/G₂(ω)]PaChampoux & Allard (1991)
Delany-Bazley Z_cρ₀c₀(1 + 9.08X^0.75 − 11.9i·X^0.73)Pa·s/mDelany & Bazley (1970)
Miki Z_cρ₀c₀(1 + 5.50X^0.632 − 8.43i·X^0.632)Pa·s/mMiki (1990)
A-weight 63 Hz−26.2 dBdBIEC 61672-1:2013
A-weight 125 Hz−16.1 dB (typical BPF range)dBIEC 61672-1:2013
EPNL estimateOASPL_A − 13 + 10·log(N·0.5)EPNdBICAO Ann.16 App.2
L_dn10·log[(15·10^(Ld/10) + 9·10^((Ln+10)/10))/24]dB(A)EPA 550/9-74-004
ISO 9613-2 propag.ΔL = A_div + A_atm + A_gr + A_bar + A_miscdBISO 9613-2:2024
KEY REFERENCES
FUNDAMENTAL ACOUSTICS
Morse & Ingard (1968). Theoretical Acoustics. McGraw-Hill.
Pierce (1989). Acoustics: An Introduction to its Physical Principles. ASA.
Fahy & Gardonio (2007). Sound and Structural Vibration, 2nd ed. Academic Press.
ROTOR AEROACOUSTICS
Ffowcs Williams & Hawkings (1969). Phil. Trans. R. Soc. A, 264, 321–342.
Lowson, M.V. (1970). J. Acoust. Soc. Am. 47(1B):371–385.
Brooks, Pope & Marcolini (1989). Airfoil Self-Noise. NASA RP-1218.
Leishman, J.G. (2002). AIAA J. 40(7):1257–1272. [BVI]
Schmitz, F.H. (1991). Aeroacoustics of Flight Vehicles. NASA RP-1258.
EVTOL ACOUSTICS
Rizzi et al. (2020). NASA/TM-2020-220630. UAM Noise Prediction.
Pascioni & Rizzi (2021). AIAA Paper 2021-2200. [eVTOL BVI]
Gur & Rosen (2009). J. Aircraft 46(5):1542–1555. [rotor acoustics]
POROUS MEDIA
Johnson, Koplik & Dashen (1987). J. Fluid Mech. 176:379–402.
Champoux & Allard (1991). J. Appl. Phys. 70:1975–1979.
Allard & Atalla (2009). Propagation of Sound in Porous Media, 2nd ed. Wiley.
Delany & Bazley (1970). Appl. Acoust. 3:105–116.
Miki, Y. (1990). J. Acoust. Soc. Jpn. 11(1):19–24.
Maa, D.Y. (1998). J. Acoust. Soc. Am. 104(5):2861–2866. [MPP]
Biot, M.A. (1956). J. Acoust. Soc. Am. 28:168–178.
STANDARDS
ICAO Annex 16 Volume I (2017), Amendment 13.
ISO 9613-1:1993 / ISO 9613-2:2024. Atm. absorption / outdoor propagation.
ISO 3744:2010. Sound power by pressure method.
ISO 717-1:2013. Airborne sound insulation rating.
IEC 61672-1:2013. Sound level meters, Part 1.
SAE ARP1779 Rev. B (2015). Rotorcraft noise measurement.
EASA SC-VTOL-01 Issue 2 (2022).
FAA AC 36-4C. Noise certification procedures.
CABIN NOISE
TREATMENT SOLUTIONS
⊕
OVERVIEW
All treatments compared
◫
POROUS FOAM
JCA · Delany-B · Miki · Biot
◎
HELMHOLTZ
Tuned cavity resonators
⊞
MICRO-PERF (MPP)
Maa 1998 · sub-mm holes
▣
CLD PANEL
Constrained layer damping
◻
GLAZING
Glass · lam · double pane
◈
COMBINED SYSTEM
Multi-layer result
SURFACE AREA FRACTIONS
FOAM (active model) 35%
HELMHOLTZ 15%
MPP PANEL 0%
CLD PANEL 10%
GLAZING 15%
TREATMENT SOLUTIONS OVERVIEW
LIVE BASELINE FROM CABIN INTERIOR · ACOUSTIC ANALYSIS PAGE · ALL 8 MODELS
Live baseline: Interior SPL is sourced directly from the Cabin Interior spectrum computed in the Acoustic Analysis page. Run the analysis first, then navigate here. Changes to rotor parameters, flight phase or TL setting on the analysis page are instantly reflected.
EXTERIOR vs INTERIOR SPL — BASELINE & TREATED
ALL TREATMENTS — INSERTION TL PER BAND
UNTREATED INTERIOR
–
dB(A)
TREATED INTERIOR
–
dB(A)
NOISE REDUCTION
–
STATUS
–
Target ≤ 70 dB(A)

PER-TREATMENT INTERIOR SPL (100% surface coverage)

MODEL
TYPE
PEAK FREQ
INT SPL dB(A)
JCA (Johnson-Champoux-Allard 1992)
5-param
250–2k Hz
–
Delany-Bazley fibrous (1970)
empirical
250–4k Hz
–
Miki revised fibrous (1990)
empirical
250–4k Hz
–
Biot Limp Frame (heavy felt/MLV)
poroelastic
125–1k Hz
–
Helmholtz resonator array
resonant
tuned BPF
–
Micro-Perforated Panel (Maa 1998)
MPP
500–2k Hz
–
Constrained Layer Damping
structural
broadband
–
Glazing (glass/lam/double pane)
mass law
500–8k Hz
–
Combined (current area mix)
area-wtd
all bands
–
POROUS FOAM ABSORBERS — 4 MODELS
SELECT MODEL · PARAMETERS · LIVE CABIN NOISE REDUCTION AT CURRENT AREA FRACTION
JCA (Johnson-Champoux-Allard 1992): Full 5-parameter semi-phenomenological model. Predicts complex ρ_eff(ω) via viscous correction G₁, and K_eff(ω) via thermal G₂. Transfer Matrix Method on rigid backing yields α(f) and insertion TL.

PARAMETERS

POROSITY φ 0.94
RESISTIVITY σ kPa·s/m² 10
TORTUOSITY α∞ 1.4
VISCOUS Λ µm 100
THERMAL Λ' µm 200
THICKNESS mm 50
α: –

ABSORPTION α(f)

CABIN NOISE REDUCTION (at set area %)

HELMHOLTZ RESONATOR ARRAY
PERFORATED PANEL + CAVITY · RAYLEIGH END-CORRECTION · TUNED TO BPF
f₀ = (c₀/2π)·√(φ / L_eff·L_cav) · L_eff = t + 2·0.85·r — At resonance, neck air mass oscillates against cavity spring. Best for discrete BPF harmonics. Fill cavity with foam to broaden Q.

GEOMETRY

HOLE DIAM d mm 8
PANEL THICK t mm 2
HOLE SPACING B cm 3
CAVITY DEPTH L mm 80
f₀
–
φ
–
Q
–
631252505001k2k4k8k
––––––––

ABSORPTION α(f)

CABIN NOISE REDUCTION (at set area %)

MICRO-PERFORATED PANEL — MAA (1998)
d < 1mm · NO FIBROUS FILL · AIRCRAFT INTERIOR GRADE · α = 4r_m/[(1+r_m)²+x²]
Maa (1998): At sub-mm hole diameters, viscous boundary layers fill the neck cross-section (k = r√(ρω/μ) ≈ 1), providing efficient resistive damping. No fibrous material — suitable for cleanrooms and pressurised aircraft cabins.
HOLE DIAM d mm 0.5
PANEL THICK t mm 1.0
PERFORATION % 1.0
CAVITY DEPTH mm 80
λ/4 TUNING FREQ
–

ABSORPTION α(f)

CABIN NOISE REDUCTION (at set area %)

CONSTRAINED LAYER DAMPING — STRUCTURAL PANELS
LOSS FACTOR η · COINCIDENCE DIP MITIGATION · TL GAIN ≈ 10·log(1/2η) dB
Principle: Viscoelastic layer constrained between host skin and face sheet. Raises structural loss factor η from 0.001 (bare alloy) to 0.1–0.3, cutting the coincidence dip. Critical when panel resonances coincide with BPF harmonics.
LOSS FACTOR η 0.10
STRUCTURE t_s mm 1.5
VEM LAYER t_v mm 1.5
f_c
–
m
–

TRANSMISSION LOSS [dB]

CABIN NOISE REDUCTION (at set area %)

GLAZING — WINDOW DESIGN
SINGLE · LAMINATED (PVB) · POLYCARBONATE · DOUBLE PANE · MASS LAW + COINCIDENCE
Mass Law: TL = 20·log(f·m) − 47.2 dB. Laminated PVB raises η from 0.01→0.25, reducing the coincidence dip by ~10 dB. Double pane adds +10–20 dB above 500 Hz but has a mass-air-mass resonance at low frequencies.
TYPE
PANE 1 mm 6
PANE 2 mm (dbl) 4
GAP mm (dbl) 12
W×H m 0.4×0.3
f_c
–
f_n
–
m
–

TRANSMISSION LOSS [dB]

CABIN NOISE REDUCTION (at set area %)

COMBINED SYSTEM RESULT
AREA-WEIGHTED · ADJUST FRACTIONS IN SIDEBAR · LIVE ACOUSTIC BASELINE
–
BASELINE dB(A)
→
–
TREATED dB(A)
– dB
REDUCTION
–
Target ≤ 70 dB(A)

SPL REDUCTION PER OCTAVE BAND

Recommended stack (inner → outer skin):
① Perforated inner liner (Helmholtz) + foam cavity fill — BPF tones 63–250 Hz
② JCA/Miki foam 25–50mm (melamine) — mid-frequency 250–2 kHz
③ CLD tape on structural skin panels — suppresses coincidence dip
④ MPP inner facing — clean broadband HF without fibrous contamination risk
⑤ Laminated glass windows (PVB ≥ 6mm) — avoids coincidence at BPF
Realistic total reduction: 15–25 dB(A)