The noise protection area as a criterion for the problem of aircraft

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SECOND EUROPEAN ROTORCRAFT AND POWERED LIFT AIRCRAFT FORUM

Paper No. 40

THE NOISE PROTECTION AREA AS A CRITERION FOR THE PROBLEM OF AIRCRAFT NOISE DURING THE TAKE-OFF OF VTOL AIRCRAFT

V. Nitsche

Institut fur Flugtechnik Technische Hochschule Darmstadt

Darmstadt, Germany

September 20 - 22, 1976

Buckeburg, Federal Republic of Germany

Deutsche Gesellschaft fur Luft- und Raumfahrt e.v. Postfach 510645, D-5000 Koln, Germany

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THE NOISE PROTECTION AREA AS A CRITERION FOR THE PROBLEM OF AIRCRAFT NOISE DURING THE TAKE-OFF OF VTOL AIRCRAFT

V.Nitsche

Institut fUr Flugtechnik,Technische Hochschule Darmstadt

1. Introduction

Noise requireaents more and more influence the perfor-mance of take-off and landing of commercial airplanes. As a measure for the acoustic situation in the vicinity of airports, noise regions can be determined, which are enclosed by a curve

of constant noise annoyance. The German aircraft noise law of 1971[1) uses the mean annoyance level, which is called the noise inde%

Q,

and which can be obtained by taking the inte-gral mean value of the instantaneous noise levels of all

flights during a long time, and defines as the noise protection area that area, in which the noise Index

Q

is greater than

67 dBA. Herein the spectral content and the long time effects of the noises are considered, but more important characteristic ~arameters are aissing, e.g. the maximum perceived noise level

L2].

In the following, the noise protection area correspon-ding to the German law against aircraft noise is computed for the take-off of VTOL-aircraft. Moreover, the noise protection areas are computed taking into consideration the maximum per-ceived noise level; the noise protection area is now defined as that area, in which either the noise index

Q

is greater than 67 dBA or the maximum perceived noise level Qmax is greater than 95 dBN or both is the case. Besides, the effect of different flight path profiles (height of the vertical ascent, transition flight path angle) on the noise protection area is investigated with the aim to determine noise optimal VTOL-flight paths. An important effect is the engine noise characteristic. Therefore it is investigated how tar the noise optimal flight trajectories are effected by a more or less simplification of the engine noise characteristics. 2. Calculation of the take-off flight profile

In this study, calculations are performed for a typical VTOL-aircratt with seperate lift and cruise engines. The take-ott weight is W•550 000 N and the thrust/weight ratio is

Tmax/W•i.i. Since the emphasis-is on performance the pitching degree of freedom is disregarded. The longitudinal motion can then be discribed by the following equations:

mV=-CD(~

•lt)

~sv2-wsin'(

+t[

T(V ,h)cos (6'+oc)-N( V ,h) sin(<T +"') Je _( 1) mVi":s-Ct(«, 1!,)isv2-Wcos y-

-f[

T(V ,h)sin(G' +ilC)+N(V ,h) cos (G'+<X) Je ( 2)

eoi

The drag and lift coefficient CD and CL are prescribed depen-dent on the angle of attack "' and the flap angle

-rz..

The thrust T of the engines is the net thrust, which decreases with

increasing forward speed V because of the increasing ram drag, and which decreases proportional to air density with increasing height. That component of the ram drag which is pe~pendicular

to the engine axis acts as an external force on the aircraft. E denotes the number of engines and G' is the angle of rotation of the thrust vector. The motion of the aircraft is controllable by the variables T, G' , 0(. and "'1..

In the following three equations, representing the

integral VTOL flight performances, the tangential acceleration

V

is the essential variable:

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duration of flight _t ₌

l

_V(V)dV distance X =

J

VT VdV ~ 0 Y\ V J (3) fuel consumption

£

VTmf(V)dV mf .. V(V)

Therefore the VTOL take-off is considered then optimal, when the control variables of the aircraft mentioned above, at any time or at any rate of speed are chosen so that the tangential acceleration is a maximum. The control variables as well as

their first derivative with respect to time are restricted, because of constructional reasons and passenger comfort. The integrals are to be taken for the total VTOL section of the take-ott, beginning at V•O and ending with the speed VT at the end of the transition.

To simplify the problem, the trajectories are separated into two parts: the vertical ascent to a certain height hv and the transition on a flight path with constant angle ~T (see figure 2). The demand for maximum acceleration means, that the vertical ascent has to be flown with maximum thrust. The

acceleration during this ascent decreases because of the decreasing thrust with increasing height and because of the increasing ram drag. This ram drag acts as a damping factor which increases with decreasing jetvelocity. To calculate the optimal acceleration during the transition flight, the control variables in discrete straight flight path segments of constant time duration are combined so, that the equations (i) and (2) are satisfied and the demanded acceleration is at its maximum value. The climbing flight following the end of the transition

js flown on the steepest possible flight path with regard to flight performance with maximum continous thrust of the cruise engines and with the lift engines ott.

For each of the take-off flight trajectories, which are prescribed by the parameters hv and ~T now exist optimal states of the control variables with regard to flight performance, and resulting forward speed and acceleration throughout the

trajectory. From the manifold of this flight trajectories, that trajectory is selected, which gives the minimum value for the noise protection area. To compute the noise protection areas, a VTOL airport is assumed, which has an annual transport

capacity of 4.5 Mill. passengers and 30.000 t of freight, half of which is transported by the departing aircraft, each of which can carry maximal 100 passengers or 10 t of freight. The load factor is assumed to be 80

%.

To calculate the effective number of flights per time unit, it is considered that the annoyance of flight movements during daytime hours, from 0600 to 2200 hours, is weighted with the factor 1 and for flight movements during the nighttime hours the annoyance is weighted with the factor

5.

Moreover it is assumed, that the frequency

of the flight movements during the nighttime hours is reduced inversely proportional to the weighting factor.

3. The acoustic assumptions

The aircraft used in the study is propelled by 12 lift engines with a bypass ratio of 10, and 2 cruise engines with a bypass ratio of 6.5. For each of the- two types of engine~ a different noise characteristic is used which are computed by procedures described in Ref. [3]. Figure 3 shows the noise

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characteristic of one lift engine. For a cruise engine a corresponding noise characteristic is valid with the

difference, that the low frequent jet noise is little more emphasized compared with the fan noise because of the lower bypass ratio. The essential features of jet noise and fan noise referring to spectral characteristics, directivity charcteristics and thrust reduction can be seen in figure 3. To study the effect of a more or less simplified engine noise characteristic, the following cases are defined:

Case 1: This is the case, which includes the complete noise characteristic shown in figure 3, that is directivity

characteristic in relation to the engine axis, different spectral characteristics in different directions, and the effect of thrust reduction on the spectral characteristics. Case 2a: The directivity characteristic is taken into account,

that is, each engine produces in different directions different overall sound pressure levels. The spectral characteristic however is disregarded. The atmospheric ab-sorption rate~ is assumed to be O.OOi dB/m corresponding to the frequency of the maximal jet noise emission. This case is lateron called "with directivity, without spectral characteristics, jet noise".

Case 2b: Like in case 2a, however is the atmospheric absorption rate J assumed to be

J

a 0.016 dB/m, which corresponds to the fundamental fan blade passage frequency. This case is lateron called •with directivity, without spectral characteristics, fan noise".

Case 3a: The directivity characteristic is disregarded but the spectral characteristic is taken into account, i.e. each engine produces in any direction noise with the same spectral content. The characteristic frequency spectrum of the engine is assumed to be that of the direction of maximum jet noise. This case is called "without directivity, with spectral characteristics, jet noise•.

Case 3b: Like in case 3a, however is the characteristic fre-quency spectrua of each engine assumed to be that of the direction of maximum fan noise emission. This case is called

"without directivity, with spectral characteristics, fan noise". Case 4a: Directivity and spectral characteristics are

dis-regarded. Each lift engine (cruise engine) produces an overall sound pressure level ot 113 dB (118 dB) in a distance of 45.7 m, which corresponds to the overall sound pressure level of the maximum jet noise. The atmospheric absorption rateo is that

ot case 1a. This case 4a is called "without directivity, with-out spectral characteristic, jet noise",

Case 4b: Like in case 4a, however the overall sound pressure levels of the engines are these ot the maximum tan noise;

for the lift engine 103.9 dB and for the cruise engine i05.1 dB in a distance of 45.7 m. The atmospheric absorption rateo is that of case ib. Case 4b is called "without directivity, with-out spectral characteristics, fan noise".

The energy and intensity of the noise decrease with increasing distance r from the noise source because of the spherical spreading and the atmospheric absorption. The

atmospheric absorption rateJ depends on the noise frequency and the atmosperic conditions. In this study a relative

humidity of the air of 75 ~and an air temperatur of 30°C on the ground as well as a gradient of the humidity of -10

%

and

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a temperatur gradient of

-4.5°C

per km of increasing height is assumed. The sound pressure level of one frequency band j in one direction i in the distance r is:

Qij=Qrefij+kij log(T/Tref)-20log(r/rref)-Jij(r-rref) (4) In this, Qrefii is the noise level of the j-th frequency band in the i-th di~ection at the reference distance rref for

reference thrust Tref• The factor kij describes the noise attenuation due to thrust reduction, which has different values depending on direction and fre~uency. By summing up n frequency bands on an energy basis {in this study n=8 octave bands are used), one can compute the overall sound pressure level in many points in the surroundings of the airport.

To include the time behaviour of the noise in the calculation of the aircraft noise annoyance, and with this the duration and the number of the noise events during a reference time the mean annoyance level is used in Germany called the noise index Q [4], [5]. This noise index Q is generally defined as follows:

Q

=

13.3log

{...L

~

10 Q(t)/13 • 3 dt} (5) to

1

₀

In this, Q(t) is the time dependend overall noise level in dBA (or dBN) and t0 is the total time of observation. The

factor 13.3 means, that the noise index~ is increased by 4 dB per dubling of the noise duration. Because the flight trajectories are given in time discrete segments (m segments of ~tk duration), the noise index

Q

was discretized with reference to the flight path and computed piecewise:

~

=

13.3log{~f:

J{

jt:

10°· 1 Qij(t)JiO/i3.3 dt} (6) 0 ks1 0 j=1

In this, N denotes the number of take-offs during the reference time to. Qij(t) is the momentary overall noise level corres-ponding t.o equation (4), which includes the levels of all engines of the aircraft.

Having computed the noise annoyance in many points around the airport by using the noise index

Q

or the maximum perceived noise level Qmax, one can get by interpolation a curve of constant noise annoyance, which is the boundary of the noise protection area.

4. The noise protection areas

As mentioned above, two,different definitions of the noise protection area are used in this study. On the one hand, the noise index

Q

is the boundary of the noise protection area, which corresponds to the German law against aircraft noise. This noise protection area is called the simple noise protec-tion area. On the other hand, the noise protecprotec-tion area is that area, in which either the noise index

Q

or the maximum perceived noise.leve1 Qmax exceed given values. That. noise protection area is called the extended noise protection area. The value for the maximum perceived noise level is Qmax =

95 dBN and for the noise index

Q

=

67 dBA. All areas are shown as relative areas, i.e. in each case the respective

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trajectory with h¥

=

0 m and YT = 0° for the simple noise protection area

(Q

= 67 dBA).

Figure 4 shows the results of the systematic computations for the relative noise protection areas in dependence of the vertical ascent hv and the transition flight path angleYT for the different, in chapter 3 des-cribed simplifications of the engine noise characteristics.

In case 1, that is the case which considers all the noise features of figure 3, it can be seen, that increasing vertical ascent hv results in almost linearly increasing of the simple noise protection area. This at first astonish-ing fact has the followastonish-ing reasons: The formation of the simple noise protection area is essentially affected by the low frequent jet noise. Since the atmospheric absorption rate is very small for low frequencies, an increasing distance from the noise source to the ground with increasing height hv gives a small decreasing of the noise level - however mainly along the ground track of the climbout path -, on the other hand, the duration of the noise integration increases. The integral mean value of the noise level, which is the noise index

Q,

contains a strong effect of the vertical ascent hv• Within the considered values o! hv, this effect increases with increasing hv• This is valid for the transition flight path angler T • oo as well as !or Y"T • 120. The noise protection areas for~T • 120 are about 70 ~larger than for~T

=

oo, because of the increasing horizontal distance until reaching

the end of transition, i.e. until the lift engines are turned

ott. .

When the maximum perceived noise level is taken into account to obtain the extended noise protection area described above, this maximum perceived noise level is the defining

criterion !or the noise protection area, when the vertical ascent hv is small, because the curve of constant maximum per-ceived noise level Qmax = 95 dBN lies completely outside the curve of constant noise index

0 =

67 dBA. With increasing ver-tical ascent hv the extended noise protection area decreases until reaching a minimum for a height of about hv

=

80 m. Further increasing the vertical ascent hv results in increas-ing of the extended noise protection area, because now the noise index

Q

is the defining criterion !or the boundaries of the

extended noise protection area. Increasing the transition flight path angle~T results in an increasing of the extended noise protection area, again as an effect of the increasing horizon-tal distance to the end or the transition, but the minimum value is now at a height hv • o. From the case 1 in figure 4 it can be concluded, that a vertical ascent to a height hv =

80 m and a subsequent transition flight on a flight path angle of 't T • oo is noise optimal with respect to the extended noise protection area, if the complete noise characteristics of

figure 3 are used •

. Case 2, which is also represented in figure 4, shows the effect

of

neglected spectral characteristics of the engine noise. If the noise energy is concentrated in one frequency band, corresponding to the frequency band of maximum jet noise, the duration of the noise increases because of the very low atmospheric absorption rate. This means, that the effect of the duration is overestimated against the effect of the distance from tne noise source to the ground when computing the noise index Q. Therefore the size of the simple noise protection area is increasing stronger with increasing vertical ascent hv than in case 1. That stronger increase results in shifting the

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height hv of minimal extended noise protection area to hv =

o.

An increase of the transition flight path angle t"T again re-sults in increasing the noise protection areas, because of the increasing horizontal distance until the lift engines are

turned off. For case 2a it can be concluded, that a vertical ascent of hv

=

0 and a subsequent transition on a flight path angle ~T = 0 is the noise optimal take-oft trajectory.

In case 2b, the noise energy is concentrated in one frequency band corresponding to the frequency band of maximum fan noise emission. Now the duration effect is underestimated against the distance effect, because of the rather high

atmospheric absorption rate. Therefore, in case 2b, a vertical ascent hv =300m and a subsequent transition with~T

=

0 is the noise optimal take-off trajectory with respect to the extended noise protection area.

Case 3 shows the effect of neglected directivity characteristics compared with case 1. If the jet noise is assumed to be the characteristic noise for all directions, (case 3a), this means, that the acoustic power of the engine is

overestimated, because in all directions exept one, the noise level is actually lower. This results in too large computed absolute noise protection areas (see Ao in figure 4, case 3a). Since the distance from the flight path to the boundary of the noise protection .area is now very great, the duration of the noise increases to a large extend·· while the aircraft flies along its flight path, so that the curve of constant noise index ~ = 67 dBA on the ground lies completely outside the curve of constant maximum perceived noise level Qmax = 95 dBN. This is valid for all heights hv• Therefore, in case 3a, the extended noise protection area is identical to the simple noise protection area. Because of the low frequent noise in this

case 3a, the noise protection area increases with increas-ing vertical ascent hv due to the increasincreas-ing noise duration. In this case, a take-off trajectory with hv = 0 and~T = 0 is the noise optimal trajectory.

If the high frequent fan noise is the characteristic spectrum - case 3b -, the effect of increasing distance with increasing vertical ascent hv is overestimated, especially for the maximum perceived noise level Qmax = 95 dBN and~T =

i2°, so that the noise optimal take-off trajectory is a vertical ascent to hv = 300 m and a subsequent transition flight on a flight path angle oft"T

=

12o.

Finally, in case 4 the directivity as well as the spec-tral characteristics are neglected. Looking on figure 4, it is obvious, that the results for case 4 almost agree with the results of case 3. The reason for this is, that for the low frequent jet noise as well as for the high frequent fan noise one respectively frequency band is dominant in the prescribed engine noise characteristics. Therefore the omission of all other frequency bands has no great effect.

5.

Conclusions

The aim of the present study was to compute noise optimal VTOL take-off trajectories with respect to the noise protection area, and how far a simplification of the used engine noise characteristics has an effect on the optimal take-off trajectory. The investigation shows, that the ~imple noise protection area", this is the noise protection area which corresponds to the German law against aircraft noise

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with the noise index

Q

= 67 dBA as the boundary, has a minimum value, when the height of the vertical ascent hv =

0 m, and the flight path angle ~T of the subsequent transi-tion is

rT

=

0°. This is independend of each of the simpli-fications made in this study.

However, far outside of the simple noise protection area, maximum perceived noise levels of more than 95 dBN can occur. Therefore the definition of the noise protection area is extended by the maximum perceived noise level in the described manner. If now this "extended noise protection area" is computed, using a complete engine noise

charac-teristic, the take-off trajectory is noise optimal when the aircraft ascend vertically to a height of about hv = 80 m

and fly the subsequent transition on a flight path angle~T=0°.

However, it has to be emphasized, that a change in the num-ber of flights per time unit results in changing the optimal vertical ascent; that is increasing the frequency of the flight movements decreases the noise optimal vertical ascent hv.

When the engine noise characteristic is simplified by neglecting particular peculiarities, it is shown, that take-off trajectories with different flight path parameters hv and YT are determined as noise optimal, such as: hv = Om and ~T = oo; hv =300m and YT

=

0°; hv =350m andrT = 12°. Hereby statements- concerning noise-optimal VTOL take-off

trajectories can be adulterated heavily. To get safe state-ments, it is necessary to take into account complete engine noise characteristics.

6. References

1. Anon., Gesetz zum Schutz gegen den Fluglarm. Bundesgesetz-blatt Nr. 28(1971), Teil I,

s.

282-286.

2. W.Btirck, Zur Entstehung des Fluglarms, tiber seine meatech-nische Erfassung und die akustischen Kenn- und·Meagroaen, die Wirkung auf den Menschen und Minderungs- oder Schutz-maanahmen. Vortrag auf dem DGLR-Symposium Flugtechnik und Umweltforschung.

3. D.G.DunnandN.A.Peart, Aircraft Noise Source and Contour Estimation. NASA CR-114649 (1973).

4. W.Btirck, et al, Fluglarm, seine Messung und Bewertung, seine Berticksichtigung bei der Siedlungsplanung, Maanah-men zu seiner Minderung.

Gutachten erstattet im Auftrag des Bundesministers ftir Gesundheitswesen, Gottingen (1965).

5. E.Koppe, et al, fiber die Methoden zur Ermittlung von

Larmschutzbereichen nach dem Gesetz zum Schutz gegen Flug-larm. Jahrbuch 1974 der DGLR, S. 279-289.

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Figure 1 Force2s acting on the aircraft_

h<Zight h wrtical asc<Znt transition <Znd of transition

~

Figur<2 2

Take-off flight path shape

climb

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601-l-...--...--...--...--..--~ _____ ~ 0.013 IUS Q.5 1 2 4 I ---- - - - kHI c .Q

_....

v

.e

_1J ~

120+---dB

110-t---.91 (i:

i

CD*-""-"'

...

.-:: 110+-_..._~

120.J----1 2 4 a kHz

..

~ 6 '4>•160° 1 2 4 8 kHz 1 2 4 1 k H z 1 2

'

8kHz dB 1 1 cp • so• 1 2

'

8kHz 11 dB100

v

go 8Q 10 .... 100" "" 1 2

'

I kHz <II •120" 1 2 4 1 k H z .... 140° 1 2 4 8 kHz

Figurcz 3

Dirczctivity and spczctral charactczristics of oncz

lift czngincz at a distanccz of 45. 7m

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{within thea curvca Q = 67d8A

- - - Arrza of tha simplca noisQ protcaction arcaa - - · - - Arrza within tha curw Omax = 95 dBN

{ within tha CUI"VQS Q = 67d8A and Q max= 95 dBN Ar<aa of thQ czxtcandQd noiSQ protcaction arrza

y

For ooch CCSQ Ao is tha OOSQ prot<action anza for Q = 67d8A end hv=O,yr =0

Ao=1,25km2

I I

I

50+---+---+1

---j-+----1 YT=0° Ol+-~---L-L--L~ 0

500

hv

[m]

250 A/Ao

[ "fo]

v

200 1/

150

100 50 0

0 / '

v

:/·

/f ../"'

/ j

I

~-.

I

'\{

I\

I

\ ~-_• I

\

I

_•

Yr=12°

I

500

hv

[mJ

Casrz 1 with rzngifl(Z noiSQ dirrzctivity charact<aristics with cangifl(Z noisg sp<atral charactrzristics

Figurrz 4

Rrzlativrz noise protrzction arrzas as a function

of thrz hflight of thfZ wrtical ascrznt hv for

two transition flight path anglqs YT

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a)J~t Noisa 0 I 0 hv [m] 500 250-.----,----.---,---,..,,.--, A/Ao 200+--+--JC---+

[ "'o]

15Q+.L-+--#'-+----:.---l 100~+---l--l----l----i Ao = 10,88km2 50+--l--l---l--+--1 a)~tNoisa hv

[m]

500 250 r---.---.----.-...,-,..-A/Ao 200+-+--JI'~~#=--1

[ %]

150~-h~~~--i 100 -T-+--l----1---l----l A₀=11,70 km2 50 I a)mNois~ hv

[m]

500 250 A/A ₀ 2 00 [0/o 1

J

50

1 00 50

-TI

I

_I Yr=Oo Yr=12o !

1

><J.J

_...

_{1,_}

!"---....,.:::

...

I I Ao=2,94km2

I I

I I b) Fan Noisa 0 I I I I 0

5 )o

250 A/Ao 200

[

"/~] 150 100 50 hv

[m]

Yr=1~

I

t:--l

I ;/yr=Oo

I

v.1::l

I'.

1/

i

Ao= 1,45km2

I

b) Fan Noisa 0 0 I I I

500

hv

[m]

250 A/Ao 200

[%]

150 100 50

I

Yr=1:20

__jj_

II Yr=Oo

,

...

_·.::z:

::--;;::

/,.. Ao=1,86km2

. I I I

I

I I I b) Fan Noisa I I I 500 hv[m] Cas~ 2 with dir~ctivity charact~ristics without spactral charact~ristics Casa 3 without dir~ctivity charact~ristics with spactral charact~ristics Cas~ 4 without dir~ctivity charactrzristics without spactral charactrzristics

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characteristic o~ one lift engine. For a cruise engine a corresponding noise characteristic is valid with the

dif~erence, that the l.ow frequent jet noise is little more emphasized compared with the fan noise because of the lower bypass ratio. The essential features of jet noise and fan noise referring to spectral characteristics, directivity charcteristics and thrust reduction can be seen in figure 3. To study the effect o~ a more or less simpli~ied engine noise characteristic, the ~ollowing cases are defined:

Case 1: This is the case, which includes the complete noise characteristic shown in figure 3, that is directivity

characteristic in relation to the engine axis, different spectral characteristics in dif~erent directions, and the effect of thrust reduction on the spectral characteristics. Case 2a: The directivity characteristic is taken into account,

that is, each engine produces in di~ferent directions different overall sound pressure levels. The spectral characteristic however is disregarded. The atmospheric ab-sorption rate6 is assumed to be 0.001 dB/m corresponding to the frequency o~ the maximal jet noise emission. This case is lateron called "with directivity, without spectral characteristics, jet noise".

Case 2b: Like in case 2a, however is the atmospheric absorption rate J assumed to be d • 0,016 dB/m, which corresponds to the fundamental tan blade passage frequency. This case is lateron called •with directivity, without spectral characteristics, fan noise•.

Case 3a: The directivity characteristic is disregarded but the spectral characteristic is taken into account, i.e. each engine produces in any direction noise with the same spectral content. The characteristic frequency spectrum o~ the engine is assumed to be that of the direction o~ maximum jet noise. This case is called "without directivity, with spectral characteristics, jet noise".

Case 3b: Like in case 3a, however is the characteristic fre-quency spectrua o~ each engine assumed to be that o~ the direction of maximum fan noise emission. This case is called "without directivity, with spectral characteristics, fan noise". Case 4a: Directivity and spectral characteristics are

dis-regarded. Each li~t engine (cruise engine) produces an overall sound pressure level o~ 113 dB (118 dB) in a distance of 45.7 m, which corresponds to the overall sound pressure level of the maximum jet noise. The atmospheric absorption rate~ is that

o~ case 1a. This case 4a is called "without directivity, with-out spectral characteristic, jet noise",

Case 4b: Like in case 4a, however the overall sound pressure levels of the engines are these o~ the maximum !an noise:

for the lift engine 103.9 dB and for the cruise engine 105.1 dB in a distance of 45.7 m. The atmospheric absorption rate6 is that o~ case 1b. Case 4b is called "without directivity, with-out spectral characteristics, ~an noise•.

The energy and intensity o~ the noise decrease with increasing distance r !rom the noise source because o~ the spherical spreading and the atmospheric absorption. The

atmospheric absorption rateJ depends on the noise frequency and the atmosperic conditions. In this study a relative

humidity of the air of 75 ~and an air temperatur of 30°C on the ground as well as a gradient of the humidity of -10

%

and

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a temperatur gradient of -4.5°C per km of increasing height is assumed. The sound pressure level of one frequency band j in one direction i in the distance r is:

Qij=Qrefij+kij log(T/Tref)-20log(r/rref)-Jij(r-rref) (4) In this, Qrefij is the noise level of the j-th frequency band in the i-th di~ection at the reference distance rref for

reference thrust Tref• The factor kij describes the noise attenuation due to thrust reduction, which has different values depending on direction and frequency. By summing up n frequency bands on an energy basis (in this study n=S octave bands are used), one can compute the overall sound pressure level in many points in the surroundings of the airport.

To include the time behaviour of the noise in the calculation of the aircraft noise annoyance, and with this the duration and the number of the noise events during a reference time the mean anaoyance level is used in Germany called the noise index~

[4], [5].

This noise index

Q

is generally defined as follows:

Q

=

i:;.:nog

{...!..

~

iO Q(t)/n.:; dt} (5) to )₀

In this, Q(t) is the time dependend overall noise level in dBA (or dBN) and t0 is the total time of observation. The

factor i:;.:; means, that the noise index ~ is increased by 4 dB per dubling of the noise duration. Because the flight trajectories are given in time discrete segments (m segments of ~tk duration), the noise index

Q

was discretized with reference to the flight path and computed piecewise:

~

= i:;.:;log{f

1:;

J{

1:_

100.i Qij(t)Ji0/i3.:; dt} (6) 0 k=1 0 j=i

In this, N denotes the number of take-offs during the reference time to. Qij(t) is the momentary overall noise level corres-ponding t_o equation ( 4), which includes the levels of all engines of the aircraft.

Having computed the noise annoyance in many points around the airport by using the noise index

Q or the maximum

perceived noise level Qmax, one can get by interpolation a curve of constant noise annoyance, which is the boundary of the noise protection area.

4. The noise protection areas

As mentioned above, two- different definitions of the noise protection area are used in this study. On the one hand,

the noise index

Q

is the boundary of the noise protection area, which corresponds to the German law against aircraft noise. This noise protection area is called the simple noise protec-tion area. On the other hand, the noise protecprotec-tion area is that area, in which either the noise index

Q

or the maximum perceived noise_leve~ Qmax exceed given values. That_ noise protection area is called the extended noise protection area. The value for the maximum perceived noise level is Qmax = 95 dBN and for the noise index

Q

= 67 dBA. All areas are shown as relative areas, i.e. in each case the respective

(15)

trajectory with h¥ ,. 0 m and YT = 0° for the simpl·e noise protection area (~,. 67 dBA).

In case 1, that is the case which considers all the noise features of figure 3, it can be seen, that increasing vertical ascent hv results in almost linearly increasing of the simple noise protection area. This at first astonish-ing fact has the followastonish-ing reasons: The formation of the simple noise protection area is essentially affected by the low frequent jet noise. Since the atmospheric absorption rate is very small for low frequencies, an increasing distance from the noise source to the ground with increasing height hv gives a small decreasing ot the noise level - however mainly along the ground track of the climbout path -, on the other hand, the duration of the noise integration increases. The integral mean value of the noise level, which is the noise index ~. contains a strong effect of the vertical ascent hv• Within the considered values of hv, this effect increases with increasing hv• This is valid for the transition flight path angleY"T a oo as well as for Y"T

=

120, The noise protection

areas for~T • 120 are about 70 ~larger than for (T

=

oo, because of the increasing horizontal distance until reaching the end of transition, i.e. until the lift engines are turned

ott. ·

criterion for the noise protection area, when the vertical ascent hv is small, because the curve of constant maximum per-ceived noise level Qmax = 95 dBN lies completely outside the curve of constant noise index~ a 67 dBA. With increasing

ver-tical ascent hv the extended noise protection area decreases until reaching a minimum tor a height ot about hv = 80 m. Further increasing the vertical ascent hv results in increas-ing of the extended noise protection area, because now the noise index

Q

is the defining criterion for the boundaries of the

extended noise protection area. Increasing the transition flight path angle~T results in an increasing of the extended noise protection area, again as an effect of the increasing horizon-tal distance to the end of the transition, but the minimum value is now at a height hv

=

0. From the case 1 in figure 4 it can be concluded, that a vertical ascent to a height hv

=

80 m and a subsequent transition flight on a flight path angle ofY"T • oo is noise optimal with respect to the extended noise protection area, if the complete noise characteristics of

. Case 2, which is also represented in figure 4, shows the effect

of

neglected spectral characteristics of the engine noise. If the noise energy is concentrated in one frequency band, corresponding to the frequency band of maximum jet noise, the duration of the noise increases because of the very low atmospheric absorption rate. This means, that the effect of the duration is overestimated against the effect of the distance from tge noise source to the ground when computing the noise index Q. Therefore the size of the simple noise ~rotection area is increasing stronger with increasing vertical ascent hv than in case 1. That stronger increase results in shifting the

(16)

height hv o! minimal extended noise protection area to hv = 0.

An increase ot the transition !light path anglerT ·again re-sults in increasing the noise protection areas, because ot the increasing horizontal distance until the li!t engines are

turned otf. For case 2a it can be concluded, that a vertical ascent of hv = 0 and a subsequent transition on a flight path angle ~T = 0 is the noise optimal take-off trajectory.

In case 2b, the noise energy is concentrated in one frequency band corresponding to the frequency band of maximum fan noise emission, Now the duration e!!ect is underestimated against the distance effect, because ot the rather high

atmospheric absorption rate. Therefore, in case 2b, a vertical ascent hv =300m and a subsequent transition with~T = 0 is

the noise optimal take-of! trajectory with respect to the extended noise protection area.

Case 3 shows the effect ot neglected directivity characteristics compared with case 1. If the jet noise is assumed to be the characteristic noise tor all directions, ~ase 3a), this means, that the acoustic power of the engine is

overestimated, because in all directions exept one, the noise level is actually lower. This results in too large computed absolute noise protection areas (see

Ao

in figure 4, case 3a). Since the distance !rom the !light path to the boundary of the noise protection area is now very great, the duration of the noise increases to a large extend·while the aircraft !lies along its flight path, so that the curve ot constant noise index ~ = 67 dBA on the ground lies completely outside the curve ot constant maximum perceived noise level Qmax • 95 dBN. This is valid tor all heights hv• Therefore, in case 3a, the extended noise protection area is identical to the simple noise protection area. Because of the low frequent noise in this

case 3a, the noise protection area increases with increas-ing vertical ascent hv due to the increasincreas-ing noise duration. In this case, a take-ott trajectory with hv

=

o

andrT =

o

is the noise optimal trajectory.

I t the high frequent tan noise is the characteristic spectrum - case 3b -, the effect of increasing distance with increasing vertical ascent hv is overestimated, especially for the maximum perceived noise level Qmax = 95 dBN and liT

=

i2°, so that the noise optimal take-of! trajectory is a

vertical ascent to hv

=

300 m and a subsequent transition flight on a flight path angle ofl(T

=

12°.

Finally, in case 4 the directivity as well as the spec-tral characteristics are neglected. Looking on figure 4, it is obvious, that the results tor case 4 almost agree with the results of case 3. The reason for this is, that for the low frequent jet noise as well as for the high frequent tan noise one respectively frequency band is dominant in the prescribed engine noise characteristics. Therefore the omission of all other frequency bands has no great effect.

5. Conclusions

The aim of the present study was to compute noise optimal VTOL take-otf trajectories with respect to the noise protection area, and how tar a simplification of the used engine noise characteristics has an effect on the optimal take-otf trajectory. The investigation shows, that the ~imple noise protection area", this is the noise protection area which corresponds to the German law against aircraft noise

(17)

Q

= 67 dBA as the boundary, has a minimum value, when the height of the vertical ascent hv = 0 m, and the flight path angle~T of the subsequent transi-tion is ~T

=

oo. This is independend of each of the simpli-fications made in this study.

However, far outside of the simple noise protection area, maximum perceived noise levels of more than 95 dBN can occur. Therefore the definition of the noise protection area is extended by the maximum perceived noise level in the described manner. If now this "extended noise protection area" is computed, using a complete engine noise charac-teristic, the take-off trajectory is noise optimal when the aircraft ascend vertically to a height of about hv = 80 m

and fly the subsequent transition on a flight path angle~T=0°.

However, it has to be emphasized, that a change in the num-ber of flights per time unit results in changing the optimal vertical ascent; that is increasing the frequency of the flight movements decreases the noise optimal vertical ascent hv.

When the engine noise characteristic is simplified by neglecting particular peculiarities, it is shown, that

take-off trajectories with different flight path parameters hv andYT are determined as noise optimal, such as: hv =Om and

~T • oo; hv ~ jOO m and YT • oo; hv = 350 m and ~T = 12°. Hereby statements- concerning noise-optimal VTOL take-off

6. References

s.

282-286.

2. W.Btirck, Zur Entstehung des Fluglarms, tiber seine meatech-nische Erfassung und die akustischen Kenn- und·Meagroaen, die Wirkung auf den Menschen und Minderungs- oder Schutz-maanahmen. Vortrag auf dem DGLR-Symposium Flugtechnik und Umweltforschung.

). D.G.DunnandN.A.Peart, Aircraft Noise Source and Contour Estimation. NASA CR-114649 (1973).

4. W.Btirck, et al, Fluglarm, seine Messung und Bewertung, seine Berticksichtigung bei der Siedlungsplanung, Maanah-men zu seiner Minderung.

5. E.Koppe, et al, tlber die Methoden zur Ermittlung von

(18)

flignt /:Jot

Figurcz 1

Forc~s

acting on thcz aircraft.

h<Zight h

varticol

OSCI2nt transition <Znd of transition

~

Flgur~

2 Takcz-off flight path shapcz

climb

(19)

c: .Q

_....

u

.e

_"C

£,

if

cjl •ISO• I 2 4 I kHt

..

~ 1 2 4 a I 2 4 8 kHz dB I 101) 10 8 _!()-6 dB11 100

....

10 1248kHz I 2

'

8kHz

-

"

<1>•80" ---1 2 4 I kHz

v

"'

"'•100" I 2

'

• ktlt 1 2 • 8 ktlt I 2 4 8 kHt

Figure 3

Directivity and spectral characteristics of one

lift engine at a distance of 45. 7m

(20)

{within th~ curv~ Q = 67dBA

- - -

~a

of thtz

simp!~

noisa

prot~ction ar~a

- - · - - Ar~a within th<Ol curw Omax = 95 dBN

{ withn th<Ol ~s Q = 67dBA and Q max= 95 dBN ....---- Aroo of

t~ 12Xt~d~

noisa promction

ar~a

y

For ooch co~ Ao is thtz noisa promction ~a for

0

= 67dBA end hv=O,yr =0

Ao=1,25km2

I I

50+-~--rl _,--+-~ YT=0° 0+-~--~~-~~ 0

500

hv

[m]

250 A/Ao

[ "'o]

200

150 100 50

I

/;

I

0

0 /

_:/'

A

L"

~/

I

_I

t',

I

~

I\

I

\

''·

• '

\

I

_• Yr=12°

I

500 hv

[m]

Casa 1 with angi~ noisa dir~ctivity characmristics with ~i~ noisa spfltral charactClristics

Figurrz 4

Rrzlativrz noise protrzction arrzas as a function

of thrz hrzight of

thtZ

wrtical ascrznt hv for

two transition flight path anglas YT

(21)

·100-¥--+--1---+--l--1 Ao= 1,81km2 a) Jcrt NoiS<Z

0

I 0 hv

[m]

500 2501~---.-~~~~ A/Ao

200+-+-~---1-[ "fo]

150Y--+-2PS.+-_j.._--i 100.,L-+---I----l---l---l Ao =10,88km2 50+--+--+--+--4--t a)J<zt NoiS<Z hv

[m]

500 A/Ao 200+--+--¥+---'~

[ %]

150~~~---r-'-!!....,-::.--1 100 -F---1--+--I--+----1 A₀=11,70 km2 50+--+I-+--ll-l--l a) J<zt Noiscz

00

hv

[m]

500 250 A/A ₀ 2 00

[ot o]

1 50 1

,...,...

~~ 50

T-I

I Yr=Oo Yr=12o

1 P<

ft

!'-...

t-~ _1-.

...

1.1

Ao=2,94km 2

I

I b) Fan NoiS<Z I I I I 0 0 500 hv

[m]

250 A/Ao 200

[

"(~] 150 100 50 Yr=1~

I

I I ;?r=Oo ~

I

,J.

~,::::;ii

_"'

/ '

Ao= 1,45km2

I

b)~

NoiS<Z 0

0

I I I 500 hv

[m]

250 A/Ao 200

[%]

150 100 50

I

Yr=12"

_jj

11 Yr=Oo

,

...

_~::z,:--... I

,

... Ao=1,86km2

I

I b)

Fan

NoiS<Z I I I [ ] 500 hv

m

Cascz 2 with dirczctivity charactczristics without spactral charactczristics CaS<Z 3 without dirczctivity charactczristics with spczctral charactczristics Cascz 4 without diractivity charactczristics without spczctral charact12ristics

(22)

trajectory with hl!: • Om and 'r'"T

=

0° for the simple noise protection area (Q

=

67 dBA).

In case i, that is the case which considers all the noise features of figure 3, it can be seen, that increasing vertical ascent hv results in almost linearly increasing

ot the simple noise protection area. This at first astonish-ing fact has the followastonish-ing reasons: The formation ot the simple noise protection area is essentially affected by the low frequent jet noise. Since the atmospheric absorption rate is very small tor low frequencies, an increasing distance from the noise source to the ground with increasing height hv gives a small decreasing of the noise level - however mainly along the ground track ot the climbout path -, on the other hand, the duration of the noise integration increases. The integral mean value of the noise level, which is the noise index

Q,

contains a strong effect ot the vertical ascent hv• Within the considered values of hv, this effect increases with

increasing hv• This is valid for the transition flight path angle y- T "' oo as well as for Y"T • 120. The noise protection areas tor~T • 120 are about 70% larger than for ~T

=

oo, because ot the increasing horizontal distance until reaching the end of transition, i.e. until the lift engines are turned

ott.

criterion tor the noise protection area, when the vertical ascent hv is small, because the curve of constant maximum per-ceived noise level Qmax

=

95 dBN lies completely outside the curve of constant noise index

Q

= 67 dBA. With increasing ver-tical ascent hv the extended noise protection area decreases until reaching a minimum tor a height of about hv

=

80 m. Further increasing the vertical ascent hv results in increas-ing of the extended noise protection area, because now the noise index

Q

is the defining criterion tor the boundaries of the

extended noise protection area. Increasing the transition flight path angle~T results in an increasing of the extended noise protection area, again as an effect of the increasing horizon-tal distance to the end of the transition, but the minimum value is now at a height hv • o. From the case 1 in figure 4

it can be concluded, that a vertical ascent to a height hv =

80 m and a subsequent transition flight on a flight path angle ofYT • oo is noise optimal with respect to the extended noise protection area, if the complete noise characteristics of

. Case 2, which is also represented in figure 4, shows the effect o! neglected spectral characteristics of the engine noise. If the noise energy is concentrated in one frequency band, corresponding to the frequency band of maximum jet noise,

the duration ot the noise increases because of the very low atmospheric absorption rate. This means, that the effect of the duration is overestimated against the effect of the distance · from tge noise source to the ground when computing the noise index Q. Therefore the size of the simple noise protection area is increasing stronger with increasing vertical ascent hv than in case 1. That stronger increase results in shifting the

(23)

height hv ot ~inimal extended noise protection area to hv = 0,

An increase of the transition !light path anglerT again re-sults in increasing the noise protection areas, because ot the increasing horizontal distance until the lift engines are

turned off. For case 2a it can be concluded, that a vertical ascent of hv

=

0 and a subsequent transition on a !light path

angle~T = 0 is the noise optimal take-of! trajectory, In case 2b, the noise energy is concentrated in one frequency band corresponding to the frequency band of maximum fan noise emission. Now the duration effect is underestimated against the distance effect, because of the rather high

atmospheric absorption rate. Therefore, in case 2b, a vertical ascent hv = )00 m and a subsequent transition with~T = 0 is the noise optimal take-of! trajectory with respect to the extended noise protection area.

Case ) shows the effect ot neglected directivity characteristics compared with case 1. I! the jet noise is assumed to be the characteristic noise !or all directions, ~ase )a), this means, that the acoustic power of the engine is

overestimated, because in all directions exept one, the noise level is actually lower. This results in too large computed absolute noise protection areas (see

Ao

in figure 4, case )a). Since the distance !rom the !light path to the boundary ot the noise protection area is now very great, the duration of the noise increases to a large extend while the aircraft !lies along its flight path, so that the curve of constant noise index ~

=

67 dBA on the ground lies completely outside the curve of constant maximum perceived noise level Qmax

=

95 dBN. This is valid !or all heights hv• Therefore, in case )a, the extended noise protection area is identical to the simple noise protection area. Because of the low frequent noise in this

case 3a, the noise protection area increases with increas-ing vertical ascent hv due to the increasincreas-ing noise duration. In this case, a take-ott trajectory with hv

=

0 and¥"T

=

0. is the noise optimal trajectory,

It the high frequent !an noise is the characteristic spectrum - case )b -, the ettect of increasing distance with increasing vertical ascent hv is overestimated, especially for the maximum perceived noise level Qmax

=

95 dBN and )iT

=

i2°, so that the noise optimal take-ott trajectory is a

vertical ascent to hv

=

)00 m and a subsequent transition !light on a !light path angle ofltT

=

120,

Finally, in case 4 the directivity as well as the spec-tral characteristics are neglected. Looking on figure 4, it is obvious, that the results tor case 4 almost agree with the results ot case ), The reason tor this is, that !or the low frequent jet noise as well as !or the high frequent !an noise one respectively frequency band is dominant in the prescribed engine noise characteristics. Therefore the omission of all other frequency bands has no great effect.

5.

Conclusions

The aim of the present study was to compute noise optimal VTOL take-ott trajectories with respect to the noise protection area, and how far a simplification of the used engine noise characteristics has an effect on the optimal take-of! trajectory. The investigation shows, that the ~imple

noise protection area", this is the noise protection area which corresponds to the German law against aircraft noise

(24)

Q

=

67 dBA as the boundary, has a

minimum value, when the height of the vertical ascent hv

=

0 m, and the flight path angle~T of the subsequent transi-tion is ~T

=

oo, This is independend of each of the simpli-fications made in this study,

However, far outside of the simple noise protection area, maximum perceived noise levels of more than 95 dBN can occur. Therefore the definition of the noise protection area is extended by the maximum perceived noise level in

the described manner. If now this "extended noise protection area" is computed, using a complete engine noise

charac-teristic, the take-off trajectory is noise optimal when the aircraft ascend vertically to a height of about hv

=

80 m

and fly the subsequent transition on a flight path angle~T=0°. However, it has to be emphasized, that a change in the

num-ber of flights per time unit results in changing the optimal vertical ascent; that is increasing the frequency of the

flight movements decreases the noise optimal vertical ascent hv.

When the engine noise characteristic is simplified by neglecting particular peculiarities, it is shown, that take-off trajectories with different flight path parameters hv and YT are determined as noise optimal, such as: hv

=

Om and tT

=

QO; hy ~ 300 m and YT

=

0°; hv

=

350 m and rT

=

12°. Hereby statements- concerning noise-optimal VTOL take-off

6. References

s.

282-286.

2. W.Btirck, Zur Entstehung des Fluglarms, tiber seine meBtech-nische Erfassung und die akustischen Kenn- und MeBgroBen, die Wirkung auf den Menschen und Minderungs- oder Schutz-maBnahmen. Vortrag auf dem DGLR-Symposium Flugtechnik und Umweltforschung.

3. D.G.Dunn andN.A.Peart, Aircraft Noise Source and Contour Estimation. NASA CR-114649 (1973).

4. W.Btirck, et al, Fluglarm, seine Messung und Bewertung, seine Berticksichtigung bei der Siedlungsplanung, MaBnah-men zu seiner Minderung.

5. E.Koppe, et al, ttber die Methoden zur Ermittlung von

(25)

Figurcz 1 Forcczs acting on thcz aircraft .

hczight h vczrticot osccznt transition cznd of transition

~

Figurcz 2

Takcz-off flight path shapcz

climb

(26)

&o+-....-...-...-...-.,-...j o.ou G.25 Q.5 1 2 4 • --- - - - - 1<111

120-t---dB

110-t---ioo~~~ 110+--..._~ 120-+---~ dB 110-.---., 100 110 10 70 1 2 4 a kHz •• :zo-ljl. 160" 1 2 4 8 kHz 1 2 4 8 k H z 1 2 4 8 k H z dB 1

»r---,

101)-»~---'"' 8 _'7~ f--- -- Y • so• &,~-.--.-.,...,..-.,..-,...j 1 2 4 8 k H z dB11~---, 1:v~ RJI 10 .. •100" 1 2 4 1 k H z ojl •120° 1 2 4 8 kHz <I>. 140° 1 2 4 8 k H z

Figur(l 3

Dir(lctivity and sp(lctral charact(lristics of

on(l