September 2011 

NASA/TM–2011-217177 

On INM’s Use of Corrected Net Thrust for the 

Prediction of Jet Aircraft Noise 

Gerry L. McAninch and Kevin P. Shepherd 

Langley Research Center, Hampton, Virginia 
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September 2011 

NASA/TM–2011-217177 

On INM’s Use of Corrected Net Thrust for the 

Prediction of Jet Aircraft Noise 

Gerry L. McAninch and Kevin P. Shepherd 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
1

Abstract

The Federal Aviation Administration’s (FAA) Integrated Noise Model1 (INM) employs 

a prediction methodology that relies on corrected net thrust (Fn δ a ) as the sole 

correlating parameter between aircraft and engine operating states and aircraft 

noise. Thus aircraft noise measured for one set of atmospheric and aircraft operating 

conditions is assumed to be applicable to all other conditions as long as the corrected 

net thrust remains constant. This hypothesis is investigated under two primary 

assumptions: (1) the sound field generated by the aircraft is dominated by jet noise, 

and (2) the sound field generated by the jet flow is adequately described by Lighthill’s 

theory of noise generated by turbulence. 

The analysis shows that the correlating parameter Fn δ a employed by the INM 

prediction methodology can be reconciled with relative jet velocity, the independent 

variable used in Lighthill's jet noise theory. The ratio of INM predictions to those 

made using Lighthill’s theory can be separated into two factors, one dependent on 

atmospheric conditions and the other dependent on aircraft performance parameters. 

The factor that depends on atmospheric conditions is generally very near unity. Thus 

prediction errors will be small, even under the most extreme temperature and altitude 

conditions. The one that depends on aircraft performance parameters indicates that 

small deviation of the Mach number of the prediction flight from the Mach number of 

the aircraft during the data collection flight will yield relatively large prediction 

errors. The INM prediction will under predict the acoustic field if the prediction flight 

Mach number is less than the data collection flight Mach number, and over predict 

the acoustic field if the prediction flight's Mach number is greater than the data 

collection flight's Mach number.

Introduction

The Federal Aviation Administration’s (FAA) Integrated Noise Model1 (INM) employs a prediction 

methodology based on the procedures developed by the Society of Automotive Engineers (SAE) and

presented in SAE’s Aerospace Information Report (AIR) 1845, “Procedure for the Calculation of 

Airplane Noise in the Vicinity of Airports2

.” The procedures presented in that report were developed 

for the prediction of aircraft noise near airports, primarily airports located near sea level and 

particularly noise generated by aircraft flying into or out of those airports.

There is some indication3,4 that INM predictions are in error both for locations more distant from 

airports and for aircraft taking off from airports located at a considerable altitude above sea level. 

These differences between measured and predicted levels could be due to any of several factors

including incorrect modeling of: (1) aircraft flight performance, (2) sound propagation through the 

atmosphere, or (3) the noise source itself. One hypothesis, perhaps viewed most correctly as falling 

within the third category, is that this error in the prediction of the noise levels by INM is due to INM’s 

use of corrected net thrust as the sole correlating parameter between engine state and aircraft noise. In 

the following this hypothesis is investigated under two primary assumptions: (1) the sound field 

generated by the aircraft is dominated by jet noise, and (2) the acoustic field generated by the jet flow 

is adequately described by Lighthill’s theory of noise generated by turbulence. The assumption that

the atmospheric properties depend only on the altitude is also employed. Further assumptions, which 

do not constrain the conclusions of this analysis in any essential way, will be introduced as required.
2

Airplanes and Flights (Real and Imaginary) A Note on Notation

In the following it is necessary to differentiate between two quite different aircraft "flights." The first 

requires flying a real airplane and deploying real microphones to measure the acoustic field generated

by that airplane. The atmospheric properties, aircraft performance parameters, and data collected from 

these flights are indicated by a subscript "d" in all that follows, and these flights are referred to as data 

collection flights. The second requires only imaginary airplanes generating imaginary acoustic fields 

that are sampled by imaginary microphones. For these "flights," the data previously collected is used 

to predict the acoustic field that would be generated by a particular airplane flying a given trajectory

through a prescribed atmosphere. The atmospheric properties, aircraft performance parameters, and 

predicted acoustic field variables for these "flights" though generally displayed without a subscript

will be subscripted with the letter "a" when required for clarity. These flights are referred to as 

prediction flights.

The Fundamental Assumption of INM

Consider an aircraft flying at an altitude z = za above sea level with its engine developing net thrust Fn. 

Let P(z) be the atmospheric pressure, PSLST be the sea level atmospheric pressure on a standard day,

and δ(z) = P(z) PSLST . Then, P(za) = Pa is the atmospheric pressure at the aircraft's altitude, 

δ(za ) = Pa PSLST = δa , and the corrected net thrust is defined as

Fc(Pa,Fn ;PSLST ) = Fn

δa

(1)

The INM noise data is presented in so-called Noise-Power-Distance (NPD) tables in which noise 

levels are tabulated for a range of engine "power" settings and a range of aircraft to observer distances.

Significantly, INM expresses the engine "power" setting as Fn/δa, i.e., as corrected net thrust. 

Therefore, the engine's corrected net thrust determines entirely the INM prediction of the noise level at 

a given distance from the aircraft. Notably there is no further adjustment for airport altitude even 

though altitude variation affects both atmospheric density and temperature, and both of these may 

reasonably be expected to affect the sound field as, for example, the ambient density appears explicitly

and the ambient temperature implicitly (through the sound speed) in Lighthill's jet noise equation (see 

Equation (2) below). Further, apart from an adjustment for the flyover duration, there is no accounting 

for aircraft speed in the INM noise-tables even though the acoustic source strength may depend on 

aircraft speed.

Therefore, the fundamental assumption of the method employed by INM for the prediction of aircraft 

noise is: The acoustic source strength of a given aircraft is a function of corrected net thrust alone.

A Relationship Between Jet Noise and Corrected Net Thrust

Whereas the methodology employed by INM predicts the acoustic field of an aircraft, Lighthill's jet 

noise theory predicts the acoustic field of a turbulent jet flow. However, when the sound field 

generated by an aircraft is dominated by jet noise it follows that the INM prediction of the acoustic 

field caused by that aircraft is in essence a prediction of the sound field produced by the turbulent jet 

flow generated by that aircraft's engine and therefore that the two predictions are in some sense

comparable. One further incongruity remains however: The methodology employed by INM uses

Fn δa as the sole correlating parameter for its prediction of the acoustic field; Lighthill’s jet noise 

theory expresses that field as a function of the relative jet velocity, Uj = vj - Ua, where vj is the jet 
3

exhaust speed and Ua is the aircraft speed. Therefore in addition to the assumption that jet noise 

dominates the acoustic field, the comparison of a prediction by INM with the prediction of the same 

acoustic field by Lighthill's jet noise theory requires the reconciliation of the correlating parameter

Fn δa used by INM with the independent variable Uj used by Lighthill's theory.

In the following, this reconciliation is accomplished by algebraic manipulation of the four equations:

(1) Lighthill's jet noise equation; (2) the equation governing the thrust of a jet engine (Newton's 

second law); (3) the mass conservation equation applied to the jet flow; and (4) the definition of 

corrected net thrust, Equation (1), to produce a form of Lighthill's equation in which the primary 

independent variable Uj has been eliminated in favor of INM's correlation parameter Fn δa . If the 

two primary assumptions of this study are valid, evaluation of this equation for the conditions under 

which the data in the INM tables was acquired will reproduce that data. Then enforcing INM's 

fundamental assumption will reproduce the INM NPD tables. The analysis that follows carries out 

this procedure thereby providing the analytical representation of the INM NPD tables. That analytical 

representation is then compared directly with the analytical prediction of the acoustic field given by 

Lighthill's theory of jet noise thus determining the fidelity of the INM prediction.

Let

Ai be the jet engine inlet cross-sectional area

Aj be the jet engine exhaust cross-sectional area

ca be the sound speed at the altitude at which the aircraft is flying

co be the sound speed at the altitude of the observer

s o h( x - x )   be a proportionality function 

o x

 be the observer location

s x

 be the source location

s o x - x

  be the distance between the source and the observer

ρa be the mass density of the atmosphere at the altitude at which the aircraft is flying

ρj be the mass density of the jet exhaust flow

and ρo be the mass density of the atmosphere at the altitude of the observer, then the mean-squared

acoustic pressure, p 2

, generated by a jet flow at a given location as predicted by Lighthill’s jet noise 

theory is5

2 j 2 8

'Lighthill' s o 5 j j o o

a a

A

p = h( x - x ){[ ] U }( c )

c

ρ ρ

ρ

  (2)

Assuming one-dimensional flow through the engine, application of Newton’s second law to that flow 

provides the equation

Fn = ρaUaAi

(vj - Ua ) = ρaUaAi

Uj (3)

and neglecting fuel flow which is generally a small percentage of the total mass flow conservation of 

mass requires that

ρaUaAi = ρ j

vjAj (4)
4

Eliminating vj between Equations (3) and (4), and solving the resulting equation for ρj, yields

ρ j = ρaAi

(1 +

Fn

RD

)Aj

(5)

where

RD = ρaUa

2

Ai (6)

is the ram drag. Solving Equation (3) for the relative jet velocity, Uj = vj – Ua, yields

 Uj = Fn

ρaUaAi

(7)

Finally, employing Equations (5) and (7) to eliminate ρj and Uj from Equation (2) provides the 

equation

6

2 n

'Lighthill' s o 35 2 o o

aa i j 2 2 D

D

n

1 F p = h( x - x ){[ ] }( c ) cAA R R (1 + ) F

ρ

ρ

  (8)

Given the net thrust, Fn, being developed by a jet engine, Equation (8) provides the estimate of the 

mean-squared acoustic pressure, p 2

, in the acoustic field generated by that engine as obtained by 

application of Lighthill’s jet noise theory. However, INM uses corrected net thrust rather than net 

thrust as the independent variable. Therefore Equation (1) is employed to write Equation (8) in the 

form

4

2 6 a n

'Lighthill' s o 35 2 o o

D Dn 2 -1 2 aa i j a

a aa

1 F p = h( x - x ){( ) ( ) }( c ) cAA R RF ( ) [1 + ( ) ]

δ

ρ ρ δ

δ δδ

  (9)

This is the form of Lighthill’s theory of sound generated by turbulence that is most convenient for the 

current study. Note, however, that except for the use of a different primary independent variable: Uj in 

Equation (2), Fn in Equation (8), and Fn/δa in Equation (9), there is no fundamental difference between 

these three equations; they are simply different forms of Lighthill's equation, and Equation (9) is as 

general as Equation (2). That this cannot be true for the INM prediction method will become clear 

before the current analysis is completed.

The Analytical Representation of the INM Noise Tables

The next step in the quest for an analytical representation of the INM noise tables is to realize that 

those tables represent a severely limited subset of the set of all predictions possible by application of 

Equation (9). That subset is, in fact, precisely the subset represented by realizations for which 

acoustic data have been obtained and that are then presented in the INM tables. Denoting the 

members of that set by subscripting the physical parameters with the letter “d,” for data, we obtain
5

4

2 6 d nd

d s o 35 2 od od

Dd 2 Dd nd -1 2 dd i j d

d dd

1 F p = h( x - x ){( ) ( ) }( c ) cAA R RF ( ) [1 + ( ) ]

δ

ρ ρ δ

δ δδ

  (10)

Application of Equation (10) is restricted to combinations of aircraft, aircraft flights, weather 

conditions, and source and receiver locations for which acoustic data have been acquired; this equation 

takes the place of the raw data from which the INM NPD tables are produced, and as currently 

employed Equation (10) can replicate any of the data used to construct the INM NPD tables but it 

cannot predict any realization not directly represented in that data set. The set of raw data used to 

construct the INM NPD noise tables and Equation (10) both lack predictive capability. The INM NPD 

tables are not so restricted; they do in fact provide a predictive capability. That capability is obtained, 

however, only by invoking the fundamental assumption of INM introduced earlier: the acoustic source 

strength for the NPD noise table entry with corrected net thrust Fnd δ d is the acoustic source strength 

for any prediction flight of the given aircraft for which Fn δ a = Fnd δ d . Invoking this assumption

not only gives the INM NPD tables whatever predictive capability they possess, it also places

Equation (10) in the form

4

2 6 d n

'INM' s o 35 2 o o

Dd 2 Dd n -1 2 dd i j a

d da

1 F p = h( x - x ){( ) ( ) }( c ) cAA R R F ( ) [1 + ( ) ]

δ

ρ ρ δ

δ δδ

  (11)

(where a ρc correction has been applied) and endows this final equation with the same predictive 

capability as the INM NPD tables.

Under the assumptions adopted for the current study, that jet noise dominates the acoustic field and 

that Lighthill's jet noise theory adequately models jet noise, Equation (11) is the desired result, the 

analytical representation of the INM NPD tables, that is Equation (11) provides the mean-squared 

acoustic pressure, p 'INM'

2 , as a function of the corrected net thrust, Fn δ a , as would be predicted by 

INM. Note that the state of the aircraft and its engine is represented solely by the quantity Fn δa , and 

that all other relevant quantities in Equation (11): δd when not part of the expression

Fnd δ d (= Fn δa ), ρd, cd, and RDd, in all cases, are unchanged from their values for the data 

collection flight as represented in Equation (10) even if, as is generally true, other values of these 

parameters are more appropriate for a given prediction flight.

Comparing the Noise Estimates of INM and Lighthill

Equations (9) and (11) both claim to predict the acoustic field for a turbulent jet flow or, equivalently,

for an aircraft for which the acoustic field is dominated by jet noise. If these two models are to 

provide the same estimate of the acoustic field the ratio

D n -1 2

2 4 35

'INM' d a a d D 2 a a

2 4 35

Dd n -1 2 'Lighthill' a d d Dd a

d a

R F [1 + ( ) ]

p c R = {( )( ) } p cR R F [1 + ( ) ]

δρ δ δ δ

δρ δ

δ δ

(12)
6

must be unity, an equality that does not hold in most cases thereby implying that Equation (11) and

hence the prediction methodology used in INM is not as general as Lighthill's theory, Equation (9). 

Although the right-hand-side of Equation (12) cannot be reduced to unity it can be simplified

considerably. Define the parameters

ξ ≡ PdRD

PaRDd

(13)

and

η ≡ PaRDd

PdFn

(14)

Then, minor algebraic manipulation employing the ideal gas law, P = ρRT, the isentropic relation c2 = 

γRT, the relations δa = Pa/PSLST, and δd = Pd/PSLST, the parameters ξ and η and the notation Ta = T(za),

places Equation (12) in the form

2 1

'INM' d d 2 2

2

'Lighthill' a a

p TP (1 + ) = [( ) ( )][ ] p T P (1 + )

ξ ξη

η

(15)

Alternate Forms For ξ and η

Employing the ideal gas law, the definition of ram drag, and the isentropic relation, c2 = γRT, we 

have

ξ = Ma

2

Md

2 (16)

where Ma = Ua/ca, and Md = Ud/cd, are the Mach number of the aircraft for the prediction and data 

collection flights, respectively. Another alias for ξ is obtained by employing INM's fundamental 

assumption, Fnd δ d = Fn δa . The definitions of δa and δd may be used to write this equation as 

Pd Pa = Fnd Fn , thereby showing that ξ = FndRD (FnRDd ). Now, for most INM data collection 

flights the aircraft is in constant speed level flight, consequently the equation Fnd = ρdUd

2

AwCDd 2, 

were Aw is the aircraft's wing area, and CDd is the aircraft's drag coefficient during the data collection 

flight, must apply. If for the prediction flight the aircraft is also to be in steady level flight, the 

equation Fn = ρaUa

2

AwCDa 2, where CDa is the drag coefficient for the aircraft during the given 

segment of the prediction flight, also applies. Utilizing these equations and the equation for ram drag 

we may write ξ = CDd CDa . 

A similar analysis may be employed to find two alternate aliases for η. The definition of δ implies 

that Pa Pd = δ a δ d . Therefore, we may write η = δaRDd (δ dFn ) = RDd [δ d (Fn δa )], and 

INM's fundamental assumption implies that this may be written as η = RDd [δ d (Fnd δ d )] or more 

simply as η = RDd Fnd . Employing the definitions of ram drag and net thrust, this may be written 

as η = Ud (vjd - Ud ), where Ud and vjd are the aircraft speed and the jet exhaust speed for the data 
7

collection flight, respectively. This is the first alternate form and shows that η is fully determined by 

the conditions of the data collection flight. 

The second alternate form is obtained by assuming that the data collection flight was a constant speed 

flight at a constant altitude. Thus, Fnd = ρdUd

2

AwCDd 2, which, coupled with the definition of ram 

drag in the formRDd = ρdUd

2

Ai required for the present purposes, and the equation η = RDd Fnd

shows that η = 2Ai (AwCDd ). The previous alias for η implied that η depends only on conditions 

of the data collection flight. This representation shows that, for constant speed flight at a fixed 

altitude, except for fixed aircraft parameters, i.e., wing area and engine inlet area, η depends only on 

the drag coefficient of the aircraft during the data collection flight, and that η decreases as the drag 

coefficient increases.

These results are summarized in Table I.

Table I. Parameter Aliases

Parameter Definition No Further 

Assumptions 

Required*

Fundamental Assumption 

of INM

Fn δa = Fnd δ d

Fundamental 

Assumption Plus 

Constant Velocity

Level Flight

ξ PdRD (PaRDd ) Ma

2 Md2 CDd CDa

η PaRDd (PdFn ) Ud (vjd - Ud ) 2Ai (AwCDd )

*Derived using only the ideal gas law, the isentropic relation, and defined quantities.

The form ξ = Ma

2 Md

2 shows that ξ > 1 if the Mach number of the aircraft for the prediction flight 

is greater than the Mach number of the aircraft during the data collection flight, while the form 

ξ = CDd CDa implies that ξ ≥ 1, for a fixed aircraft weight, if the aircraft configuration is 

“cleaner” (e.g. retracted landing gear and flaps) for the prediction flight that it was for the data 

collection flight. Neither of these conclusions is easily obtained from the definition 

ξ ≡ PdRD (PaRDd ). Also since both ξ and η are positive the conditions presented in Table II must 

hold.

Table III provides the wing area, Aw, and the number of engines and fan diameter, hence an estimate

of the total engine inlet area, for four typical aircraft. From this data it is possible to obtain an estimate 

of the quantity Cdη, which is also presented in the table. These estimates are remarkably consistent.

Table II. Simple Relations Between Mach Numbers, Drag Coefficients, ξ

and [ξ(1 + ξη)/(1 + η)]2

General Conditions Steady Level Flight ξ [

ξ(1 + ξη)

(1 + η) ]

2

Ma < Md CDd < CDa < 1 < 1

Ma = Md CDd = CDa = 1 = 1

Ma > Md CDd > CDa > 1 > 1
8

Table III. Typical Values of 2Ai/Aw = Cdη

Aircraft Wing 

Area6

(M2)

Typical 

Engine7

Number of 

Engines

Fan 

Diameter7

(M)

Total Inlet 

Area* (M2) Cdη = 2Ai

Aw

747 511 PW4152 4 2.36 17.5 0.07

757 185.25 PW2037 2 1.99 6.2 0.07

767 283.3 JT9D 2 2.36 8.7 0.06

MD-80 118 JT8D 2 1.17 2.2 0.04

* Total inlet area ≈ πD2

Ne

4 , where Ne is the number of engines and D is the fan diameter.

If it is assumed that the drag coefficient of a typical aircraft is in the range 

0.02 < CD ≤ 0.1, it will appear that 0.4 ≤ η ≤ 3.5, for the aircraft listed above. The parameter η will 

decrease if the drag coefficient is increased, by, for example, increasing the aircraft angle of attack,

deploying slats and/or the landing gear, or increasing aircraft weight. Assuming that the quantity 

2Ai Aw may be as large as 0.1 for some aircraft suggests that it is not unreasonable to assume that 

0.01 ≤ η ≤ 5 for a reasonable range of transport aircraft under most flight conditions.

Although ξ and η are defined in terms that involve atmospheric properties, the analysis presented here 

shows that in the case of constant velocity flight at a fixed altitude they actually depend on aircraft 

performance parameters alone.

The value of the function p 'INM'

2 p 'Lighthill'

2 (Equation (15)) depends on the two factors

G = (

Td

Ta

)

1

2 (

Pd

Pa

) (17)

and

H = [

ξ(1 + ξη)

(1 + η) ]

2 (18)

the first of which depends on atmospheric conditions alone, and the second of which depends on 

aircraft performance parameters alone. These two factors will now be investigated in turn.

Effect of Atmospheric Conditions 

For the purposes of the current study we consider atmospheric temperature variation of the form

T(z) = T - z sl  (19)

Here, Tsl is the sea level temperature, and  = - dT dz is the temperature lapse rate. For this 

temperature profile, it may be shown that8
9

g

sl R

sl sl

P(z) T - z = ( ) P T

 

(20)

where Psl is the sea level pressure, and therefore that

a

a

1 2g + R

d d 2 sla 2R

sla sla sla a a

TP T G = ( ) ( )( ) T P T - z





 (21)

Here, Tsla, Psla, are the sea level atmospheric temperature, pressure, respectively, and a  is the lapse 

rate for the prediction flight, g = 9.8 meter/second2

, is the acceleration due to gravity, and 

R = 287 meter2 (° Kelvin second2

), is the gas constant for air. Employing Equation (21) places 

Equation (15) in the form

a

a

1 2g + R 2

'INM' d d 2 sla 2R 2

2

'Lighthill' sla sla sla a a

p TP T (1 + ) = ( ) ( )( ) [ ] p T P T - z (1 + )

ξ ξη

η





 (22)

which, for the following discussion, is written in the form

10 *Log10

p 'INM'

2

p 'Lighthill'

2 = 10*Log10(G) + 10 *Log10(H) (23)

where Equations (17), (18) and (21) have been employed. In all cases it will be assumed that Psla = 

PSLST as the variation in sea level pressure is a very small percentage of PSLST, and is assuredly 

negligible for the purposes of the current discussion.

Data collection flights are generally flown at an altitude of approximately 1,000 feet, and the sea level 

temperature for these flights is, or is corrected to, 77 °F = 298.15 °K. If it is assumed that the 

lapse rate at the time of the flight was the standard lapse rate, 1.98 °K/1,000 feet, and that the data 

collection flight was at an altitude of 1,000 feet, the temperature at the aircraft's altitude is 

Td = 296.17 °K, the value used for all of the following. Also, for prediction flights with a standard 

lapse rate, a a (2g + R ) (2R ) 5.75   ≈ ; the value used for the following calculations.
10

Figure 1. Effect of sea level temperature on INM prediction error, 

 10*Log10 (G). Prediction flight altitude is between sea level and 2,000 feet.

Figure 1 presents the quantity 10*Log10 (G) as a function of sea level temperature for prediction 

flights at altitudes of 0, 1,000 and 2,000 feet above sea level. As expected, the point Tsla = 77 °F

and 0 dB falls on the curve for 1,000 feet, indicating that there is no error at the point at which the 

INM data is obtained. Clearly, for prediction flights within 1,000 feet of the altitude of the data 

collection flight the error due to this factor is small, its extremes for the temperature range considered, 

0 °F ≤ Tsla ≤ 120 °F, being 0.6 dB at Tsla = 0 °F and za = 2,000 ft., and minus 0.4 dB at 

Tsla = 120 °F and za = 0 ft. Note that for a fixed sea level temperature the error increases with 

increasing altitude of the prediction flight, and that the error decreases for a constant prediction flight 

altitude as the sea level temperature increases. Thus INM predictions are expected to under-predict 

measured levels for low altitude and hot conditions, i.e. negative values in Figure 1.

Figure 2 presents the quantity 10*Log10 (G) as a function of sea level temperature, again for 

0 °F ≤ Tsla ≤ 120 °F, for prediction flights at altitudes of 3000, 4,000 and 5,000 feet above sea 

level. Again the error is reasonably small, being less than 1.2 dB over-prediction throughout the 

region 0 °F ≤ Tsla ≤ 120 °F, and 3,000 feet ≤ za ≤ 5,000 feet. Again, for a fixed sea level 

temperature the error increases with increasing altitude of the prediction flight, and decreases for a 

constant prediction flight altitude as the sea level temperature increases.

-0.4

-0.2

2E-15

0.2

0.4

0.6

0 20 40 60 80 100 120

INM Error (dB)

Due to Atmospheric Properties

Sea Level Temperature

Prediction Flight

Altitude (Feet)

2,000

1,000

0

(77, 0)
11

Figure 2. Effect of sea level temperature on INM prediction of flyover noise, 

 10*Log10 (G). Prediction flight altitude is between 3,000 feet and 5,000 feet.

On occasion, INM is employed to predict noise levels for aircraft at altitudes greater than 5,000 feet. 

Therefore, Figure 3 presents the quantity 10 *Log10 (G) as a function of sea level temperature, again 

for 0 °F ≤ Tsla ≤ 120 °F, for prediction flights at altitudes of 10,000, 20,000 and 30,000 feet above 

sea level. Clearly, for prediction flights at an altitude below 10,000 feet the error is reasonably small, 

being less than 3 dB throughout the region. Figure 3 suggests that this factor is 5 - 7 dB at za = 30,000 

feet, implying that measured levels are expected to be significantly below predicted ones for cruise 

altitudes.

Figure 3. Effect of sea level temperature on INM prediction of flyover noise, 

 10*Log10 (G). Prediction flight altitude is between 10,000 feet and 30,000 feet.

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

INM Error (dB)

Due to Atmospheric Properties

Sea Level Temperature (F)

Prediction Flight

Altitude (Feet)

5,000

4,000

3,000

1

3

5

7

0 20 40 60 80 100 120

INM Error (dB)

Due to Atmospheric Properties

Sea Level Temperature (F)

Prediction Flight

Altitude (Feet)

30,000

20,000

10,000
12

Figure 4. Effect of sea level temperature on INM prediction of flyover noise, 

 10*Log10 (G). Prediction flight altitude is between 5,431 feet and 7,431 feet.

Figure 4 presents the quantity 10*Log10(G) as a function of sea level temperature for prediction flight 

altitudes of 5,431, 6,431, and 7,431 feet, as would be applicable for the prediction of an aircraft flying 

into or out of Denver International, which is at an altitude of 5,431 feet. Again, the error is relatively 

small being less than 1.8 dB for the entire range of sea level temperature and prediction flight altitude 

considered.

Potential errors in the INM prediction due to performance parameters captured in the function H(ξ,η)

is considered in the next section.

Effect of Aircraft Performance Parameters

Figure 5 through 7 display the function 10*Log10 (H(ξ,η)) for η = 0.04, 0.25, 0.5, 1.5 and 5. 

Remember that η is determined by the data flight parameters (η = RDd Fnd ). Since 

ξ = (Ma Md )

2

, it is convenient to use ξ = Ma Md as the independent variable.

Most prediction flights for aircraft near an airport will have Ma Md ≈ 1. Figure 5 presents 

10*Log10 (H) for 0.95 ≤ Ma Md ≤ 1. As shown, for this range of Ma Md INM will underpredict measured levels by less than 2 dB for all reasonable values of η. Note that the magnitude of 

the error increases with increasing η for all Ma Md < 1, and that it increases as Ma Md decreases 

if Ma Md < 1. 

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-30 20 70 120

INM Error (dB)

Due to Atmospheric Properties

Sea Level Temperature (F)

Prediction Flight

Altitude (Feet)

5,431

6,431

7,431
13

Figure 5. The function 10*Log10(H) for 0.95 ≤ Ma Md ≤ 1.

Figure 6 presents 10 *Log10 (H) for 1 ≤ Ma Md ≤ 1.05. In this region INM will over-predict 

measured levels by no more than 1.6 dB. The magnitude of the error increases with increasing η and

Ma/Md. The results presented in Figures 5 and 6 suggest that in general the magnitude of the error 

increases as η increases and as Ma Md increases. However, for realistic values of η, the error in the 

INM prediction due to performance parameters is less than ± 1.6 dB if the prediction flight Mach 

number differs from the data collection flight Mach number by ± 5% or less, as is likely for low 

altitude flights, i.e., operations into or out of airports located near sea level.

Figure 6. The function 10*Log10(H) for 1 ≤ Ma Md ≤ 1.05. 

For aircraft at much higher altitudes than the data collection flights, the Mach number will typically be 

considerably greater than the Mach number of the data collection flight. Thus, Figure 7 presents 

-2

-1.5

-1

-0.5

0

0.95 0.96 0.97 0.98 0.99 1

INM Error (dB)

Due to Performance Parameters

Ma/Md

η

5

1.5

0.5

0.25

0.04

0

0.5

1

1.5

2

1 1.01 1.02 1.03 1.04 1.05

INM Error (dB)

Due to Performance Parameters

Ma/Md

η

5

1.5

0.5

0.25

0.04
14

10*Log10 (H) for 1 ≤ Ma Md ≤ 3.5. It is clear that the error increases rather rapidly with 

increasing Ma/Md if Ma/Md > 1. Hence INM is likely to significantly over predict noise from high 

altitude flights.

Figure 7. The function 10*Log10(H) for 1 ≤ Ma Md ≤ 3.5. 

Conclusions

The current analysis shows:

1. The correlating parameter Fn δ a employed by the INM prediction methodology can be reconciled 

with relative jet velocity, vj - Ua the independent variable used in Lighthill's jet noise theory.

2. Errors in the INM prediction can be separated into two factors, one that depends on atmospheric 

conditions and one that depends on aircraft performance parameters.

3. The factor that depends on atmospheric conditions is generally very near unity. Thus prediction 

errors will be small, even under the most extreme temperature and altitude conditions. The one that 

depends on aircraft performance parameters indicates that small deviations of the Mach number for the 

prediction flight from the Mach number of the aircraft during the data collection flight will yield 

relatively large prediction errors. The INM prediction will under predict the acoustic field if the 

prediction flight Mach number is less than the data collection flight Mach number, and over predict 

the acoustic field if the prediction flight's Mach number is greater than the data collection flight's 

Mach number. Thus, INM is expected to significantly over predict noise levels from high altitude 

cruise conditions.

0

15

30

45

1 1.5 2 2.5 3 3.5

INM Error (dB)

Due to Performance Parameters

Ma/Md

η

5

1.5

0.5

0.25

0.04
15

References

1. Fleming, G. G., Olmstead, J. R., D’Aprile, J. R., Gerbi, P. J., Gulding, J. M., and 

 Plante, J. A., “INM Technical Manual,” Federal Aviation Administration, 800 

 Independence Avenue, S.W., Washington, DC 20591 (1997).

2. “Procedure for the Calculation of Airplane Noise in the Vicinity of Airports,” 

 Aerospace Information Report AIR 1845, Society of Automotive Engineers, Inc. 400 

 Commonwealth Drive, Warrendale, PA 15096 (1986).

3. "Examining INM Accuracy Using Empirical Sound Monitoring and Radar Data," Miller, 

Nicholas P., Anderson, Grant S., et. all, NASA/CR-2000-210113 (2000).

4. "Validation of Aircraft Noise Models at Lower Levels of Exposure," Page, Juliet A., et. al, 

NASA Contractor Report 198315 (1996).

5. Lilley, G. M., Jet Noise Classical Theory and Experiments. In Hubbard, H. H., 

 Aeroacoustics of Flight Vehicles: Theory and Practice, Vol. 1: Noise Sources. NASA 

 RP 1258, Vol. 1 (1991).

6. Taylor, John W. R., Janes All The World's Aircraft 1989-90

7. Hunecke, Klaus, Jet Engines, Motor Books International, Osceola, WI, (2003)

8. Owczarek, Jerzy A., Introduction To Fluid Mechanics, pp. 42-47, International 

 Textbook Company, Scranton Pennsylvania, (1968).
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Technical Memorandum

 4. TITLE AND SUBTITLE

On INM's Use of Corrected Net Thrust for the Prediction of Jet

Aircraft Noise

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McAninch, Gerry L.; Shepherd, Kevin P.

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NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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14. ABSTRACT

The Federal Aviation Administration’s (FAA) Integrated Noise Model (INM) employs a prediction methodology that relies on 

corrected net thrust as the sole correlating parameter between aircraft and engine operating states and aircraft noise. Thus 

aircraft noise measured for one set of atmospheric and aircraft operating conditions is assumed to be applicable to all other 

conditions as long as the corrected net thrust remains constant. This hypothesis is investigated under two primary assumptions:

(1) the sound field generated by the aircraft is dominated by jet noise, and (2) the sound field generated by the jet flow is 

adequately described by Lighthill’s theory of noise generated by turbulence. 

15. SUBJECT TERMS

Aircraft noise; Community noise; Jet noise

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