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Correlation of aircraft certification noise levels EPNL
with controlling physical parameters
Ulf Michel ∗
CFD Software GmbH, Berlin, Germany
It is demonstrated that the EPNL values obtained during the certification of turbofan powered aircraft can
be correlated fairly well (within ±2EPNdB) with the controlling physical parameters. The noise levels for
the three certification measuring points lateral,flyover, and approach are correlated with respect to the known
values for static thrust, fan diameter, maximum take-off mass, maximum landing mass, wing span, and wing
area. In addition estimates for the lift coefficients and the lift-to-drag ratios during take-off (including the one
engine out case) and final approach and for some engine parameters are needed. The analysis of the approach
EPNL values led to a new scaling relation for airframe noise with high-lift devices in the approach configura-
tion, which depends on wing loading and wing span and is independent of airspeed. The resulting formulas can
be used to estimate the noise levels and noise margins relative to the certification limits for arbitrary aircraft.
Nomenclature
Ajjet cross section
Annozzle cross section
Afan fan cross section
asound speed
bwing span
Bconstant in calculation of jet density
cwing chord
cllift coefficient
cddrag coefficient
Cconstant in take-off field length calculation
Ddiameter
EPNL equivalent perceived noise level
Ftthrust
ggravity acceleration
˙minlet mass flow of fan stream
Hflyover altitude
Ltake-off field length
maircraft mass
mrel relative velocity exponent jet noise
MMach number
MTOM maximimum take-off mass
MLM maximum landing mass
nvelocity exponent jet noise
Nnumber engines on aircraft
pstatic pressure, sound pressure
pwwing loading
Ppower of jet stream
rdistance of microphone from nozzle
Rgas constant
SLS sea level standard
TOC top of climb
Tstatic temperature, duration
Vspeed
V2 minimum safe airspeed
βclimb rate over flight speed
γisentropic exponent
∆Lpnoise level adjustment
ΓCirculation around wing profile
µbypass ratio
ξfan hub-to-tip ratio
πfan fan pressure ratio
ρdensity
Indices
0in ambience
1core stream
2bypass stream
app approach
cclimb
cb cutback
eeffective
fflight
fan fan
jjet
lat lateral
ldg loading adjusted
meas measured values
norm normalized value
ref reference value
sstatic
span span adjusted
∗Member AIAA, Member DGLR, CFD Software GmbH, Berlin, 10623 Berlin, Germany, ulf.michel@cfd-berlin.com
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I. Introduction
DURING the certification process of an aircraft its manufacturer has to demonstrate that the aircraft meets the noise
certification limits, currently defined in chapter 4 of Annex 161of ICAO. New Standards (cumulatively 7 EPNdB
more stringent) are defined in a new chapter 14,2which will likely become effective from 31 December 2017 (MTOM
≥55 tonnes) or 31 December 2020 (MTOM <55 tonnes). There are three certification noise levels, which have to be
determined for the lateral, flyover, and approach measuring points (see figure 1). The certifications in the lateral and
flyover measuring points have to be performed for the maximum take-off mass (MTOM) while the maximum landing
mass (MLM) has to be used for approach noise. The certification for the lateral measuring point has to be performed
for full take-off thrust. The thrust may be reduced for the flyover certification point. The approach certification is
carried out for the thrust necessary to maintain a constant glide slope of 3◦. The origin of the glide path is located
300 m behind the runway threshold.
Figure 1. Positions of measuring points for aircraft noise certification. The lateral measuring points are located symmetrically on both
sides of the runway, and the position with the highest average (left and right) equivalent perceived noise level EPNL has to be selected for
the certification.
The detailed procedures for the evaluation of the equivalent perceived noise levels EPNL are described in the
Environmental Technical Manual.3The noise levels are determined from flyovers with different engine powers and
altitudes with flight trajectories that are calculated based on the aerodynamic performance data of the aircraft. These
data are proprietary but have to be submitted to the certification authorities. Since these data are not available in the
open literature, an attempt is made in this paper to correlate existing noise certification data at each certification point
with an appropriate selection of known or estimated controlling physical parameters. If this attempt were successful
these correlations could be used to predict the noise margins of turbofan powered aircraft over a large range of aircraft
sizes and operating performances. This would be especially valuable for future aircraft designs using engines with
very large bypass ratios.
II. Required data
A. Published data
The certification noise levels can be found in the noise type certificates, which can be downloaded for each aircraft
type, e.g., from the European Aviation Safety Agency.4In general, the manufacturer certifies each aircraft type
for various maximum take-off masses MTOM and maximum landing masses MLM. Each entry in the noise type
certificate is valid for a specific engine type, often for a specific sub version of the engine, which may differ from other
sub versions only in the settings inside the full authority digital engine control FADEC. The certification level for the
lateral measuring point has to be determined for the largest thrust of the used engine version. The value Fts,max of
the maximum static thrust at sea level standard (SLS) for each engine version can be obtained from the corresponding
engine type certificate.5The fan diameter is not reported in the engine type certificate but is generally available from
other sources, often from the manufacturer’s website. The bypass ratios µ(ratio of mass flow in the bypass duct over
the core mass flow) are also reported, e.g. in the ICAO Aircraft Engine Emissions Databank.6The wing span and
wing area of all aircraft are published, usually by the aircraft manufacturers.
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B. Data to be estimated
The publicly available data are not sufficient for noise estimations. Jet noise, e.g., depends primarily on jet speed Vj,
airspeed Vf, and jet diameter Djor jet cross section Aj. The aerodynamic performance of the aircraft needs also to
be estimated. The lift-to-drag ratio for the take-off run up to the flyover measuring point determines the length of the
take-off run and the climb rate. The lift-to-drag value in the case of asymmetric thrust with one engine inoperative
determines the cut-back thrust setting for the flyover measuring point. The lift-to-drag ratio on approach determines
the amount of approach thrust.
1. Thrust, mass flow, and jet cross section
An equivalent single stream jet is used for the correlations. Its thrust is defined by
Ft= ˙m(Vj−Vf)(1)
The mass flow is defined by
˙m=ρjVjAj,(2)
where ρjis the jet density and Ajthe jet cross section. In case of slightly supersonic jets, equation 1 is approximately
valid for the fully expanded jet. Only the thrust for Vf= 0 is known from the engine type certificate. The thrust for
Vf>0and all other quantities in these two equations have to be estimated. The fan diameter Dfan and the bypass
ratio µare used for this purpose.
Turbofans have dual-stream jets, where we have (index 1 for core jet, 2 for bypass jet)
Ft1= ˙m1(Vj1−Vf),(3)
Ft2= ˙m2(Vj2−Vf),(4)
˙m1=ρj1Vj1Aj1,(5)
˙m2=ρj2Vj2Aj2.(6)
The bypass ratio is defined by
µ=˙m2
˙m1
=ρj2
ρj1
Vj2
Vj1
Aj2
Aj1
.(7)
and is known for the static condition, also for derated engines. The density ratio is given by
ρj2
ρj1
=R1
R2
T1
T2
,(8)
where the ratio R1/R2= 1 of the gas constants of air and the exhaust gases is assumed. The jet area ratio is then
Aj2
Aj1
=µM1
M2rT2
T1
(9)
It can be concluded that in the case of separate streams (short-cowl nozzle) with a constant ratio Aj2/Aj1a lower
temperature T1of the core stream for derated engines is accompanied with a lower Mach number of the core stream.
In the case of a common nozzle for both streams (long-cowl nozzles) it is assumed that the Mach numbers M1and
M2in the two streams are identical because the nozzle pressure ratios are equal for both streams. This yields
V1
V2
=rT1
T2
.(10)
Further relations describe the total thrust, mass flow, and the density.
Ft=Ft1+Ft2(11)
˙m= ˙m1+ ˙m2(12)
ρj=µρj2+ρj1
µ+ 1 (13)
These three equations are inserted in equations 1 and 2 to compute the specific thrust Vj−Vfand the equivalent jet
cross section Aj, which is by the way generally smaller than the sums of the two jet cross sections Aj1and Aj2.
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The density ρj2of the bypass jet is only slightly smaller than the ambient density. The density ρj1of the core jet
depends on unknown data of the turbofan engine cycle. A rough estimate based on the bypass ratio and the kinetic
energy of the jet is used. The jet power per unit mass flow of the core stream is given by
Pm=P
˙m1
=V2
j1+µV 2
j2
2.(14)
The density ratio is assumed to depend linearly on Pm.
ρj2
ρj1
= 1 + BPm(15)
If the engine mass flow ˙msfor the static jet were known, the jet speed Vjs of the static jet could be calculated
with equation 1 for Vf= 0, since the static thrust Fts is known. Engine mass flows are reported on the websites of
some manufacturers, e.g., Roll-Royce, CFM, and MTU. However, these mass flows appear to be rather high for the
take-off condition and are more likely the reduced mass flows at top of climb (TOC) where the reduced mass flow
reaches a maximum value to support a minimum climb rate in addition to compensating the cruise drag of the aircraft.
Therefore, these published mass flows can only be used as a guideline to check the correlations. The actual mass flows
during take-off and initial climb are smaller.
A further check for the mass flow is a comparison with the nozzle exit cross section An=Aj1+Aj2which is
similarly not disclosed by the manufacturers but is directly measurable for all engines with long-cowl nozzles. An
has been measured by the German Aerospace Center DLR for the IAE V2527-A5 engine on its A320 that is equipped
with this engine. DLR currently assesses the cycle of this engine and the aerodynamics of the fan stage.7The cross
sections of the primary and secondary nozzles of a short-cowl nozzle could also be measured but none were available
for this paper. As mentioned above, the cross section Ajof the fully mixed jet is smaller than An. The measured areas
can only be used as upper limits.
To get an estimate for the jet diameter Dj, it can be compared with the fan diameter Dfan. The ratios Dj/Dfan
of various engines with short-cowl nozzles are plotted in figure 2 as function of the static specific thrust (static mean
jet speed). The results for the long-cowl nozzle are shown in figure 3. It can be seen that the ratio is in the range of
0.77 . . . 0.81 for short-cowl nozzles, slightly rising for smaller specific thrust values, and in the range of 0.75 . . . 0.77
for long-cowl nozzles with one exception with a value 0.72. Smaller values for Dj/Dfan mean that the fan diameter is
relatively large for the mass flow through the fan. This could be the consequence of a larger hub-to-tip ratio of the fan
or of a smaller fan face Mach number to increase fan efficiency.
Figure 2. Ratio of equivalent jet diameter and fan diameter as function of static specific thrust for short-cowl nozzles. The line indicates a
possible correlation for the data points.
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Figure 3. Ratio of jet diameter and fan diameter as function of static specific thrust for long-cowl nozzles. It can be seen that the data
points are below the correlation line for short-cowl nozzles.
In order to compare engines of different sizes the quantities have to be discussed in a normalized form. The jet area
Ajcould be made non-dimensional for this purpose with the known static thrust Fts of the engine and the ambient
pressure p0.
A∗
j=Ajp0
Fts
(16)
However, a thrust-normalized jet cross section is used instead, which is defined by
Aj,norm =Aj
Fts,ref
Fts
(17)
with the reference thrust Fts,ref = 100 kN. Alternatively, a normalized jet diameter can be used.
Dj,norm =DjrFts,ref
Fts
(18)
The normalized fan diameters are plotted in figure 4 as function of static specific thrust for engines with short-cowl
nozzles. The figure includes some values derived from the NASA UHB turbofan study8on a short-medium range
aircraft with ultra-high bypass ratio engines. A correlation line proportional to V−0.8
j,s is also shown, where Vj,s is the
specific thrust of the static engine. It may be noted that the correlation is even valid for derated engines. Exceptions
are the CFM56 engines and the CF34-8E of the Embraer E-170, which feature slightly larger normalized diameters.
Figure 5 shows the results for engines with long-cowl nozzles. It can be seen that the normalized fan diame-
ters (usually with forced mixers inside) are slightly larger than those for short-cowl nozzles. The trendline here is
proportional to V−0.9
j,s .
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Figure 4. Normalized jet diameter as function of static specific thrust for short-cowl nozzles. Nozzle diameter is normalized for a thrust of
100 kN. The green circles show the results of a NASA study8for very large bypass ratio turbofans.
Figure 5. Normalized jet diameter as function of static specific thrust for long-cowl nozzles. Nozzle diameter is normalized for a thrust of
100 kN. It can be seen that the fan diameters for a given jet speed are larger for long-cowl nozzles than for the short-cowl nozzles shown in
figure 4. The trendline is different from the trendline in figure 4.
Finally the bypass ratio µas function of jet speed is shown in figure 6. The dashed line indicates a correlation for
the highest thrust rating for modern engines with high overall pressure ratios. Derated engines are located to the left
of this line, because the bypass ratio increases only slightly when the thrust is decreased with an unchanged nozzle.
Figure 7 includes the results of the NASA study8mentioned above and excludes the derated engines to demonstrate
that the correlation is valid up to very large bypass ratios.
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Figure 6. Bypass ratio µas function of static specific thrust. Derated engines are located on the left of the correlation line.
Figure 7. Bypass ratio µas function of static specific thrust. Derated engines are excluded. The NASA study8was included to demonstrate
that the correlation is valid up to very large bypass ratios.
2. Iterative procedure for determination of inlet mass flow of static engine
The following procedure is chosen to find the mass flow ˙mfor the calculation of the specific thrust Vjfor the static jet
with equation 1.
1. Estimate static mass flow ˙ms.
2. Compute static jet speed Vjs with equation 1 for Vf= 0 and known static thrust Fts .
3. Check if location of (Vjs , µ) in figure 6 is reasonable.
4. Compute mass flows ˙m1and ˙m2of the core and bypass streams based on the known bypass ratio µwith
equations 7 and 12.
5. Estimate densities ρ1and ρ2of core jet and bypass jet. While ρ2is only slightly smaller than the ambient
density, ρ1depends on the temperature of the core flow and is estimated with equation 15.
6. Compute mean density ρjfrom the two streams with equation 13.
7. Compute Ajfrom equation 2 and determine Dj.
8. Compute Dj,norm with equation 18.
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9. Check location of point (Vjs , Dj,norm) in figure 4. Point should be close to correlation line in figure for Dj,norm <
2.
10. Check location of point (Vjs , Dj/Dfan) in figure 2 for short-cowl nozzles and figure 3 for long-cowl nozzles.
11. Repeat all items until result acceptable. This procedure has not yet been automated.
An error of 1% of the mass flow in step 1 will yield an error of 1% of the jet speed and approximately an error
of 0.2 EPNdB in the later prediction of the noise level. An error of 1% of the core density in step 4 will yield much
smaller errors since only a small part of the jet flow is affected.
3. Influence of flight Mach number
The mass flow ˙m, thrust Ft, and jet speed Vjdepend on the flight Mach number. Since the fan performance map is
not available it is assumed that the fan pressure ratio remains constant during take-off with maximum engine thrust in
the speed range up to an airspeed of Vf=V2 + 20 kts. V2 is the minimum airspeed at which the aircraft can safely
be operated and depends on the aircraft’s weight. The noise certifications in the lateral and flyover measuring points
can be performed with airspeeds of up to V2+20 kts.
The investigation of the influence of flight Mach number on the engine performance needs the introduction of the
jet Mach number Mj.
˙m=ρjajMjAj,(19)
where ajis the sound speed inside the jet.
The ratio of the jet Mach number Mj2of the fan stream for a flight Mach number Mfto the jet Mach number
Mjs2for the static jet is defined by
Mj2
Mjs2
=v
u
u
u
t1 + γ−1
2M2
fπ
γ−1
γ
fan −1
π
γ−1
γ
fan −1
.(20)
The fan pressure ratio of the fan stream of the static jet is defined by
πfan =1 + γ−1
2M2
js2γ
γ−1
.(21)
For simplicity it is assumed that equations 20 and 21 can be applied for the jet velocity ratio Vj/Vjs and the pressure
ratio of the whole jet.
Assuming that ρjand ajare not changed in the speed range up to V2+20 kts, we obtain
˙m
˙ms
=Vj
Vjs
=Mj
Mjs
(22)
and Ft
Fts
=˙m
˙ms
Vj−Vf
Vjs
=Vj(Vj−Vf)
V2
js
.(23)
4. Lift and drag coefficients
The take-off field length and the climb gradient are influenced by the lift coefficient and the lift-to-drag ratio. The
cut-back thrust in the flyover certification point is determined by either the lift-to-drag ratio with all engines operating
or with the lower lift-to-drag ratio due to the asymmetric thrust with one inoperative engine. The thrust required in
the final approach is determined by the drag coefficient in the landing configuration. Assumptions of these values are
highly speculative. The lift-to-drag ratios of the most modern long-range aircraft in cruise are about cl/cd= 21.9
They are of course smaller at lower cruising altitudes and much smaller when high-lift devices and the landing gear
are extended. Values close to reality can be extracted with the software Piano-X a, for which aircraft data for the A380,
787-8, and the A340-600 are freely available. The lift coefficient depends on flight speed because the aircraft weight
is constant. The influence of flight speed on the lift coefficient is described by
cl=cl,ref Vf,ref
Vf2
,(24)
ahttp://www.lissys.demon.co.uk/PianoX.html
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where the reference speed is V2, which is defined by
V2 =rmg
cl,refρ0Aw
.(25)
Awis the wing area, mthe aircraft mass and gthe gravity acceleration. The reference lift coefficient cl,ref has to be
estimated.
5. Take-off field length, climb rate, and flyover altitude
The take-off field length Lis needed for the estimation of the flyover altitude in the flyover certification point.
L=mg
ρ0AwclFt,lat
C , (26)
where C= 1.3is an experimentally derived free constant. The aircraft mass mon take-off is equal to the maximum
take-off mass MTOM
The flyover altitude at the flyover measuring point 6500 m from the start of roll is determined by the initial climb
gradient with full thrust and the climb gradient with cut-back thrust.
H=(6500 m−L)(Vc1/Vf)
1 + b(Vc1/Vf−Vc2/Vf)(27)
It is assumed that the thrust cutback occurs abruptly in a distance 6500 m−bH from the start of roll with b= 2.Vc1/Vf
and Vc2/Vfare the climb rates for full thrust and cutback thrust, respectively. The mean-square sound pressure p2is
inversely proportional to H2.
The noise levels depend on the duration Tof the noise signal, which is inversely proportional to the flight speed
Vfand proportional to the flyover altitude H.
T=Tref
H
Href
Vf,ref
Vf
(28)
6. Cutback thrust and approach thrust
The required cutback thrust per engine Ft,cb is defined by the condition that the take-off thrust may be reduced to a
setting not less than the greater of that which will maintain a climb gradient of 4% (with all engines operating) or level
flight with one engine inoperative.
The corresponding two equations are
Ft,cb =MTOM
N1
cl/cd
+ 0.04(29)
and
Ft,cb =MTOM
N−1
1
cl/cd
.(30)
where Nis the number of engines. The lift-to-drag ratios for the all-engines-operating and one-engine-inoperative
cases have to be estimated.
The required approach thrust per engine is defined by
Ft,app =MLM
N1
cl/cd
−0.0524.(31)
The lift-to-drag ratio at approach has to be estimated.
C. Mean-square sound pressure and overall sound pressure level
The noise in the lateral and flyover certification points is dominated by engine noise, which consists of jet mixing
noise and various internal engine noise sources. Engine noise also plays a significant role in the approach certification
point. The descent with engines in the flight idle condition is dominated by airframe noise, but this happens far before
the approach certification point.
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For a given nozzle, jet mixing noise depends primarily on the jet speed Vjand the flight speed Vf. The mean
square ˜p2of the sound pressure of jet mixing noise for an emission angle of θ= 90◦and a distance rfrom the nozzle
is approximately defined by
˜p2∝p2
0
Aj
r2Vj
a0nVj−Vf
Vjmrel
,(32)
where the exponent nand the relative velocity exponent mrel depend on the emission angle θ. The power n= 8 is valid
for θ= 90◦for unheated jets.10 If the radiated sound power of the jet is considered, n > 8for unheated and heated
jets.11 mrel = 5 . . . 6may be assumed for the emission angle θ= 90◦according to Tanna and Morris12 Szewczyk13 or
Stevens and Bryce.14 Viswanathan and Czech15 propose smaller values in the range mrel = 3.2. . . 3.6. The velocity
exponent nand the relative velocity exponent mrel increase for angles in the rear arc. The mean-square sound-pressure
of jet mixing noise is proportional to the jet exit area Ajfor all emission angles, which is a basic assumption in many
jet noise prediction codes such as the SAE method.16
If we normalize the mean square sound pressure of equation 32 with the thrust of equation 1 and mass flow of
equation 2, we obtain
˜p2
Ft
∝p0
r2
ρo
ρjVj
a0n−2Vj−Vf
Vjmrel−1
(33)
Note that Ftis the actual thrust of the jet in flight. With
arel =mrel −1
n−2(34)
we may define an effective jet speed
Ve=VjVj−Vf
Vjarel
,(35)
which simplifies the relation 33 for the mean square sound pressure level to
˜p2
Ft
∝p0
r2
ρo
ρjVe
a0n−2
.(36)
Neglecting the influence of a possibly changing ρj, the overall sound pressure level is defined by
Lp=Lp,ref + 10 lg Ft
Ft,ref
−20 lg r
rref
+ 10(n−2) lg Ve
Ve,ref
.(37)
Ftis the actual thrust, Vethe actual effective jet speed after equation 35 and Lp,ref,Ft,ref,Ve,ref , and rref are free
constants.
The certification noise levels are determined in terms of equivalent perceived noise levels EPNL. The one-third
octave noise spectra are frequency weighted and it is likely that the EPNL values behave slightly differently than the
OASPL values. But this uncertainty has to be accepted to enable a scaling.
The calculation of the EPNL includes the duration of the noise signal, which is in principle proportional to the
flyover altitude Hand inversely proportional to the flight speed Vf. Starting from equation 37 we get
EPNL =EPNLref + 10 lg Ft
Ft,ref
−10 lg H
Href
−10 lg Vf
Vf,ref
+ 10(n−2) lg Ve
Ve,ref
.(38)
Href is a reference flyover altitude and Vf,ref a reference flight speed.
The second important engine noise source is the fan. A bold assumption is made for it: the noise of the fan is
proportional to jet noise. This means that it is assumed that the engine manufacturers were successful in reducing fan
noise of their newer engines with higher bypass ratios proportionally to jet noise. This is not unreasonable, because
smaller jet speeds require smaller fan pressure ratios, which allow smaller fan tip speeds. This assumption is not true
for engines with severe rotor-alone noise (Buzz), which changes rapidly with fan speed for supersonic fan tip speeds.
III. Lateral measuring point
The noise in the lateral measuring point is dominated by the engine. The engine has to be operated at full take-off
power throughout. The distance between the aircraft and the microphone does not change very much between different
aircraft models and different aircraft weights. Therefore, the flying altitudes are assumed to vary only little between
the various certification cases and this influence on the EPNL-values has been neglected. The measured EPNL values
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American Institute of Aeronautics and Astronautics
in this certification point are first adjusted for the influences of thrust Ft,lat, duration (airspeed Vf), and climb ratio
β=Vc/Vfwith climb speed Vcto yield a normalized EPNL value.
EPNLnorm =EPNLmeas,lat −10 lg(Ft,lat/Ft,ref ) + 10 lg(Vf/Vf,ref)−Aclg(β/βref)(39)
Ft,ref = 100 kN, Vf,ref = 100 m/s, and βref = 0.15.Ac= 2 has been obtained empirically.
These EPNLnorm values are plotted in figure 8 as function of the effective jet speed Ve(see equation 35) for several
aircraft with wing mounted engines and short-cowl nozzle. The wing mounting increases the noise due to jet-wing
interaction effects which are absent on tail mounted engines.
The figure includes a correlation line
EPNLnorm =EPNLref,lat +Allg(Ve/Ve,ref).(40)
The slope Alis a free constant which is based on equation 36.
Al= 10(n−2) .(41)
Actually a value of Al= 65 with n= 8.5is used in the correlations of this paper. The reference EPNL is defined as
EPNLref,lat = 69 EPNdB for Ve,ref = 150 m/s. Veis computed with equation 35 using the actual thrust at the lateral
point with airspeed of Vf=V2+ 20 kts and from the actual inlet mass flow ˙m.
The scatter between the normalized noise levels of existing newer aircraft and the correlation is about ±2EPNdB.
The data points for some CFM56 powered A320 and A321 aircraft and GE90 powered 777 are up to 4 EPNdB above
the correlation line. These higher values might be caused by the strong buzz-saw noise of these engines.
Note that the correlation is valid for all aircraft categories, independent of mass and number of engines, or range.
The three red diamonds for the Boeing 747-8 and the three turquoise diamonds for the Boeing 777-300ER relate to
different maximum take-off masses, all flown with the same thrust setting. Due to the different weights, the airspeeds
(and effective jet speeds) and climb angles are different, yet the normalized noise levels are very close.
Figure 8. Correlation of normalized lateral certification noise levels with effective jet speed. The power in equation 36 was chosen n= 8.5.
Quad engine aircraft only are shown in figure 9. It can be seen that the scatter is only ±1.5EPNdB, except for the
747-400, which is at +2 EPNdB.
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Figure 9. Correlation of normalized lateral certification noise levels with effective jet speed of quad-engine aircraft.
The EPNL in the lateral measuring point for an arbitrary aircraft is then defined by
EPNL =EPNLref,lat + 10 lg(Ft/Ft,ref ) + Allg(Ve/Ve,ref)−10 lg(Vf/Vf,ref) + Aclg(β/βref ),(42)
where the Ft,Ve,Vfand βhave to be determined for the flight conditions in the lateral measuring point with the
equations developed in section IIB.
IV. Flyover measuring point
The certification noise levels in the flyover measuring point are much more difficult to correlate because many
aerodynamic data have to be estimated. The thrust may be reduced from take-off thrust to a setting not less than the
greater of that which will maintain a climb gradient of 4% (with all engines operating) or level flight with one engine
inoperative. This thrust setting depends a lot on the aerodynamic performance of the aircraft with the selected take-off
flap setting.
The EPNL at the flyover measuring point depends on the effective jet speed at cutback for an airspeed of V2+20 kts
and the flyover altitude. The latter depends on the take-off field length, the initial climb ratio and the climb ratio at the
flyover point and the cutback distance from start-of roll. The climb ratios depend on the thrust-to-weight ratio and the
lift-to-drag ratio. The field length depends on thrust-to-weight ratio and the V2 speed of the aircraft. The measured
certification noise levels EPNLmeas,fo are normalized with
EPNLnorm,fo =EPNLmeas,fo −10 lg(Ft,cb/Ft,ref ) + 10 lg(Vf/Vf,ref) + 10 lg(H/Href ),(43)
where the reference values were chosen as Ft,ref = 100 kN, Vf,ref = 100 m/s, and Href = 500 m.
The scatter between the normalized noise levels EPNL of existing newer twin engine aircraft and the correlation is
less than ±1.5EPNdB, as shown in figure 10 with the exception of the buzz-saw noise dominated engines of the A320
and A321. The Boeing 777-300ER and 787-8 are certificated with the same engine for different maximum take-off
masses MTOM. The cutback thrust settings and airspeeds are smaller for the lighter variants, yielding smaller effective
jet speeds.
It is surprising to note that the noise levels of the 787 continue to follow the correlation even down to effective jet
speeds of 180 m/s. One would expect that the slope would start to flatten for smaller jet speeds to take into account that
the relative contribution of jet mixing noise might decrease and the noise reduction of fan noise may be less dependent
on jet speed. Also combustion noise should start to have a noticeable influence for small jet speeds.
The results for quad-engine turbofans are shown in figure 11. It can be seen that the quad engine aircraft data are
substantially above the correlation line for the twins. As long as the reason is not found, different correlations have to
be used for twins and quads.
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Figure 10. Normalized flyover certification noise levels of twin engine aircraft as function of effective cutback jet speed
Figure 11. Normalized flyover certification noise levels of quad engine aircraft as function of effective cutback jet speed. It can be seen that
the noise levels are roughly 4 dB higher than the levels of twin-engine aircraft. The reason for this has not yet been found.
The EPNL in the flyover measuring point for an arbitrary aircraft is then defined by
EPNL =EPNLref,fo + 10 lg(Ft/Ft,ref ) + Allg(Ve/Ve,ref)−10 lg(Vf/Vf,ref)−10 lg(H/Href),(44)
where the Ft,Ve,Vf, and flyover altitude Hhave to be determined for the cutback conditions in the flyover measuring
point with the equations developed in section IIB. The reference EPNL values are EPNLref,fo = 74 EPNdB for twins
and EPNLref,fo = 79 EPNdB for quads.
V. Approach measuring point
Approach noise consists of engine noise and airframe noise. The engine noise is determined by the thrust required
to maintain a stable slope of 3 degrees. Since the distance of the aircraft to the measuring point is always 120 m
no distance correction is required. Estimates of the engine noise contribution at approach similar to equation 42
yield values that are much lower than the measured EPNL values. This problem can be resolved by reducing the
slope Al= 65 in equation 42 to a smaller value, e.g., Al= 10 for effective jet speeds below a certain limit, e.g.,
Ve<150 m/s, but this is not included in the following correlations. As examples, the effective jet speeds on approach
were estimated at Ve≈106,123,151 m/s for the Boeing 787-8, the Airbus A380 and Boeing 747-8, respectively.
The approach noise levels are plotted in figure 12 as function of MTOM. The figure includes a line describing the
certification limit of ICAO Annex 16, Chapter 3 reduced by 8 EPNdB. It can be seen that the Boeing 787-8 reaches
already roughly -9 EPNdB.
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Figure 12. Certification noise levels EPNL for approach as function of MTOM (logarithmic scale). The line indicates the current certifica-
tion limit of chapter 3 minus 8 EPNdB.
The noise levels are plotted in figure 13 as function of maximum landing mass MLM, which is a more reasonable
parameter then the MTOM. It can be seen that the noise levels rise approximately with MLM0.6. The figure contains
the noise data of three aircraft that have two engine options, the A320, A321, A380, and 787-8. The fact that the
different engines have noise levels differing by up to 2 EPNdB indicates that engine noise has still an important
influence on the approach noise.
Figure 13. Approach EPNL as function of maximum landing mass MLM (logarithmic scale). A trendline indicates that the noise levels rise
approximately with MLM0.6.
The noise levels are found to be proportional to the wing loading and the wing span. To demonstrate this, the noise
levels are adjusted for the influence of loading pwand span b. The loading-adjusted approach certification noise levels
EPNLldg =EPNLmeas −10 lg(pw/pw,ref ),(45)
are shown in figure 14 as a function of wing span. The reference value for the wing loading was chosen as pw,ref =
6000 Pa. An approach noise estimate proportional to span is plotted as dashed line.
Similarly, the span-adjusted approach certification noise levels
EPNLspan =EPNLmeas −10 lg(b/bref),(46)
are plotted in figure 15 as function of wing loading. The reference span bref = 40 m was chosen. It can be seen that
the noise increases roughly proportionally to the wing loading.
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Figure 14. Approach EPNL adjusted for wing loading as function of wing span. Dashed line is wing loading adjusted airframe noise
estimate.
Figure 15. Approach EPNL adjusted for wing span as function of wing loading. Dashed line is wing span adjusted airframe noise estimate.
The loading and span-adjusted certification noise levels
EPNLnorm =EPNLmeas −10 lg(pw/pw,ref )−10 lg(b/bref),(47)
are plotted in figure 16 as function of approach airspeed. The aircraft with noise levels higher than 95 EPNdB in this
figure are likely dominated by engine noise. Even the quietest aircraft, the 787-8, has different certification levels
for the two engine options. It can be concluded that airframe noise alone would yield an EPNLnorm of even less than
93 EPNdB. No trend with airspeed can be observed if the engine noise dominated 747-400 with CF6-80C2 engine17
is excluded. The airframe noise is apparently independent of approach speed in the speed range used in the final
approach. Some increase of airframe noise at higher speeds is offset by the shorter duration of the noise signal.
The primary explanation for the independence of approach noise on airspeed may be the decreasing lift coefficient
when airspeed is increased. Slat noise is normally considered to be proportional to V5
f. But this is based on wind-
tunnel experiments that were carried out with constant angle-of-attack. The situation during an approach is, however,
that the lift remains constant, which requires that the lift coefficient cl∝V−2
f. To achieve this the angle-of-attack
decreases when the airspeed is increased. It could even be explainable if slat-noise were proportional to VfΓ/c, with
the wing circulation Γand the wing chord c. Slat noise would then be independent of airspeed Vf.
The independence of the EPNL values on airspeed also indicates that landing gear noise does not play a significant
role at the airspeeds of the final approach. Cavity tones as airframe noise source may also be present in some cases,
but these tones can always be removed and are not considered a physical limit.
One can conclude that the approach certification noise levels can be correlated by
EPNLapp =EPNLapp,ref + 10 lg(b/bref ) + 10 lg(pw/pw,ref).(48)
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Figure 16. Approach EPNL adjusted for wing span and wing loading as function of airspeed. It is apparent that airspeed has no explicit
influence.
The reference values are bref = 40 m and pw,ref = 6000 Pa. It can be seen from figure 16 that EPNLapp,ref =
94 EPNdB would correlate almost all newer aircraft within ±2EPNdB. Exceptions are likely dominated by engine
noise. Achievements in the noise reduction technology for airframe noise would yield smaller values for EPNLapp,ref
for future aircraft designs.
The scaling relation 48 is apparently new, since wing loading was to the author’s knowledge not included in
previous airframe noise predictions schemes. The independence of the noise levels on airspeed requires that landing
gear noise is negligible in the final approach and that slat and flap noise depend on the lift coefficient of the wing.
A final correlation of approach noise levels has to include an engine noise component, probably with a formula
similar to equations 42 and 44 but with a smaller slope Al= 10 for effective jet speeds Ve<150 m/s.
VI. Conclusions
The noise levels for all three certification points can be predicted with the aid of the correlations fairly well within
±2EPNdB or better. The correlations may be used to determine the sensitivities of the noise levels to various design
parameters, e.g., fan-pressure ratio (influencing the bypass ratio) and wing loading. The cumulative noise margin of
any arbitrary aircraft design can be estimated. The correlations should be extremely valuable if the noise levels of
derivative aircraft have to be predicted. The correlations might also be used to demonstrate, which values for the
aircraft design parameters would lead to extremely quiet aircraft without regard to economical feasibility.
Airframe noise on the final approach was found to be proportional to wing loading and wing span and to be
independent of flight speed. This is a scaling relation that can only be valid if landing gear noise is negligible on the
final approach. The increase of slat noise with increasing airspeed to the power 5 is at least partially offset by the
benefit due to the associated decrease of the lift coefficient of the wing and the shortened duration of the flyover time
history.
There is still room for fine-tuning the equations, especially those describing the engine performance at reduced
power, which is needed for the cutback and approach conditions. Modeling engine noise at approach must be improved
and has to include combustion noise. Also the optimization procedure of section IIB2 on page 7 needs to be automated.
VII. Acknowledgments
The work was started as member of an independent expert panel for the Committee on Aviation Environmental
Protection (CAEP) of ICAO. The critical discussions with the co-members Dennis Huff, Alain Jozelson, Brian Tester,
Yuri Khaletskiy and with Jeff Berton of NASA Glenn and Pierre Lempereur of Airbus and Fredi Holste of Rolls-Royce
Deutschland were very valuable and are appreciated. The discussions with Willem Franken and Guy Readman of the
European Aviation Safety Agency (EASA) about details of the noise certification procedures are also appreciated.
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