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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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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American Institute of Aeronautics and Astronautics

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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