c) digital recording;
d) automatic still photographic recording;
e) cine recording; and
f) video recording.
Clearly, when a large number of parameters have to be co llected at relatively short time intervals, it may not be practicable to manually record the data. Thus the use of one of the automatic systems listed in b) to f) becomes more appropriate. The choice of a particular system may be influenced by a number of factors such as the space available, cost and availability of equipment.
For systems which optically record the flight deck instruments, care must be taken to avoid strong lighting contrast such as would be caused by sunlight, deep shadow and reflections from the glass fronts of instruments, which would make data unreadable. To avoid this, it may be necessary to provide additiona l lighting to “fill in ” the deep shadow regions. To prevent reflections from the front of instruments, it is recommended that light-colored equipment or clothing on the flight deck be avoided. Flight crews should be required to wear black or dark-colored clothing and gloves.
Furthermore, for systems which record the readings of dials it is important that the recording device be as near as possible, directly in front of the instruments to avoid parallax errors.
303(b) Magnetic Tape Recording [ETM 3.3.2] Multi-channel instrumentation tape recorders designed fo r airborne environments are employed for continuous recording of flight and engine performance parameters. Typical recorders are compact intermediate/wide band and can take both one-half-inch and one-inch magnetic tapes with a 24 to 28 volt DC power requirement. Six tape speeds as well as direct and FM recording are available in a tape recorder weighing about 60 lb (27) kg.
303(c) Automatic Still Photographic Recording [ETM 3.3.3] Photographs of the flight deck instrument panel can be taken by using a hand-held 35 mm single-lens reflex (SLR) camera with an 85 mm lens and high-speed slide film. The indications on the instruments can be read by projecting the slides onto a screen.
303(d) Cine Recording [ETM 3.3.4] Cine cameras with a one frame per second exposure rate have been used to acquire flight deck data. Care must be taken in mounting the camera to ensure that all the instruments that have to be photographed are within the field of view. Typical film cassettes containing about 2000 frames have been used with a frame counter to allow film changes to be anticipated.
303(e) Video recording [ETM 3.3.5] Flight and engine performance parameters can be recorded with a video camera, although as with cine cameras, care must be taken to ensure that all the instruments that have to be photographed are within the field of view. The recorded information is played back using freeze-frame features to obtain individual instrument readings.
TIME SYNCHRONIZATION OF MEASURED DATA [ETM 3.4] 304(a) General [ETM 3.4.1] Sections A36.2.3.2 and H36.101(d)(3) of part 36 specifies that there be precise time synchronization between noise measurements and aircraft position. Several methods have been used, such as noting the synchronization time on a clock mounted on the instrument panel which itself is recorded by the data acquisition system. One such system uses a ground camera that operates a radio transmission which, when received by an aircraft, lights two high-intensity light emitting diodes (LEDs) mounted in an analog clock attached to the instrument panel. Other methods for acquiring and processing TSPI are described in subsequent sections.
A common time base should be used to synchronize noise, aircraft tracking and meteorological measurements. TSPI data should be determined at half-second intervals throughout the sound-measuring period (i.e., within 10 dB of maximum tone corrected perceived noise level (PNLTM)) by an approved method that is independent from systems installed aboard and normally used to control the aircraft. During processing, measured TSPI data should be interpolated, over time, to the time of sound emission of each half-second acoustic data record within the 10 dB-down period. Although the simplified procedure requires adjustment of only the PNLTM record to the reference flight path, sound emission coordinates should be determined for each half-second record for use in background noise adjustment procedures and for determination of incidence-dependent free-field microphone and windscreen corrections.
304(b) TSPI Equipment and Software Approval [ETM 3.4.2] Some off-the-shelf TSPI equipment may require software enhancement to accommodate the specific installation. All TSPI equipment and software should be demonstrated to, and approved by, the FAA to ensure the system’s operational accuracy.
304(c) Continuous Time-Dode Recording [ETM 3.4.3] This method uses a time-code signal, such as IRIG B, which is a modulated audio-frequency signal used for encoding time-base data developed by the Inter-Range Instrumentation Group (IRIG). In this method, the time-code signals from individual generators that have been synchronized to a common time-base are continuously recorded by both the noise data recorder(s) and by the TSPI system during measurement test runs. Synchronization of multiple generators can be performed either physically, by interconnecting via cable, or by means of radio transmission. The transmitted continuous time-code signal can be recorded directly, or used either continuously or in bursts to maintain synchronization of an independent time-code generator which is being recorded directly. This method allows for high-quality continuous timecode recording when there are intermittent reception problems.
Note 1.— Synchronization should be accomplished at the start of each measurement day and checked at the end of each measurement day to minimize the effects of generator time drift. Any such drift should be documented and accounted for in processing.
Note 2.— GPS-based measurement systems are often used for acquisition of TSPI data. GPS receivers are capable of providing the user with precise time-base information broadcast from the GPS satellite system, in some cases eliminating the need for a separate time-keeping device in the TSPI system.
Note 3.— For noise data recording or for non-GPS-based TSPI systems, dedicated IRIG B time-code generators are available that use the GPS signal to constantly update and maintain time synchronization. Use of such a universal broadcast time-base can greatly simplify the logistics of time synchronization between measurement systems.
Note 4.— There are two available time-bases for GPS-based systems: GPS Time and Coordinated Universal Time Page 82
(UTC), whose values differ by more than 10 seconds at any given instant. Although the GPS signal includes both timebases, not all GPS receivers give the user access to both. Therefore, the user should exercise caution in identifying which time-base is used by each instrument.
Note 5.— Many acoustical data recorders provide separate annotation channels in addition to the normal data channels. These channels are often not suitable for recording a modulated time-code signal because of limitations on dynamic range or bandwidth. In such cases a normal data channel of the recorder should be dedicated to recording the time-code signal.
Note 6.— When continuous time-code recording is used, a nalysis of the recorded acoustic data can be initiated by routing the time-code channel output into a time-code reader and triggering the analyzer based on readout time.
304(d) Recording of Single Time Marker [ETM 3.4.4] This method involves transmittal and recording of a radio “hack”, or tone, usually used to indicate the “recorders on” or “overhead” time instant. This method typically requires a dedicated channel on both the noise and the TSPI recording systems. When such a system is used, analysis can be triggered manually by an operator listening for the hack, or by a detector circuit responding to the tone. When the operator wishes to start analysis at a time other than that of the time marker, a stopwatch or delay circuit can be used to delay triggering of the analyzer. When manual triggering is employed, the operator sh ould use extreme care to perform the tr iggering as accurately as possible.
Accuracy to within one-tenth of a second can be expected from a conscientious human operator.
304(e) Measurement of th e Interval Between Recorder Start and Overhead [ETM 3.4.5] This method of synchronization involves use of a stopwatch or elapsed-time indicator to measure the interval between start-up of the noise data recorder and the instant that the aircraft position is overhead the centerline noise measurement point. This method can be employed successfully as long as the operator exercises care in timing, the determination of the overhead instant is performed accurately, and the star t-up characteristics of the r ecorder (in both record and playback modes) are known and repeatab le. Some recorders have variable star t-up times that cannot be predicted.
Such recorders are not suitable for this method of synchronization.
304(f) Setting of Internal Time-Stamp Clock [ETM 3.4.6] Many digital recorders maintain a continuous internal time-of-day function by encoding time data in the recorded data stream. This method uses a digital recorder’s sub-code time, synchronized to the time-base used for the TSPI data. As with the continuous time-code recording method, synchronization by this method should be checked at the beginning and end of each measurement day and any drift accounted for in processing.
Unfortunately, the time-setting function on many recorders does not provide for the necessary precision. The “second” digits cannot be made to “tick” in synchrony with an external clock. Such recorders are unsuitable for this method of synchronization.
304(g) Additional Time-Synchronization Considerations [ETM 3.4.7] Regardless of the synchronization method used, all elements affecting time synchronization, such as analyzer start-up delay, head displacement between normal and annotation data channels on analog recorders, and delays in automated triggering circuits, should be identified, quantified and accounted for in analysis and processing. Whenever human response to a timing event is required, errors cannot be accurately predicted, and conscientious operation is required to minimize such errors. The use of automated methods is preferred. Other methods, or variants of the listed methods, may be appropriate, but the use of all methods and instrumentation is subject to prior approval by the FAA.
CALCULATION OF CONFIDENCE INTERVALS [ETM 3.5] 305(a) Introduction [ETM 3.5.1] The use of NPD curves requires that confidence intervals be determined by using a more general formulation than is used for a cluster of data points. For this more general case, confidence intervals may have to be calculated about a regression line for:
a) flight test data;
b) a combination of flight test and static test data;
c) analytical results; or
d) a combination thereof.
Items b) and c) are of particular significance for noise certification of an aircraft model range and require special care when pooling the different sources of sampling variability.
Sections 305(b) to 305(e) provide an insight into the theory of confidence interval evaluation. Application of this theory and some worked examples are provided in 305(f). A suggested bibliography is provided in Appendix 3 to this AC for those wishing to gain a greater understanding.
305(b) Confidence Int erval for the Mean of Flight Test Data [ETM 3.5.2] 305(b)(1) Confidence Interval fo r the Sample Estimate of the Mean of Clustered Measurements [ETM 3.5.2.1] If n measurements of EPNLs y1, y2,….,yn are obtained under approximately the same conditions and it can be assumed that they constitute a random sample from a normal population with true population mean, , and true standard deviation, σ, then the following statistics can be derived:
ӯ = estimate of the mean s = estimate of the standard deviation of the mean = From these and the Student’s t-distribution, the confidence interval, CI, for the estimate of the mean, ӯ, can be determined as:
௦ ܫܥ ൌ ӯ േ ݐሺଵିഀ,ఋሻ √,, మ Where ݐሺଵିഀ,ఋሻ denotes the ሺ1 െ ఈଶሻ percentile of the single-sided Student’s t-test with ߜ degrees of freedom (for a మ clustered data set ߜ ൌ ݊ െ 1 and where ߙis defined such that 100ሺ1 െ ߙሻ percent is the desired confidence level for the confidence interval. In other words it denotes the probability with which the interval will contain the unknown mean, . For noise certification purposes, 90 percent confidence intervals are generally desired and thus f ݐଽହ,ఋ is used (see Table 5 for a listing of values of ݐଽହ,ఋ for different values of ߜ .)
305(b)(2) Confidence interval for mean line obtained by regression [ETM 3.5.2.2] If n measurements of EPNL (y1, y2,….,yn ) are obtained under significantly varying values of engine-related parameter (x1, x2,….,xn ) respectively, then a polynomial can be fitted to the data by the method of least squares. For determining the mean EPNL, , the following polynomial regression model is assumed to apply:
ߤൌܤ ܤ ଵݔܤ ଶݔଶ ⋯ܤ ݔ .
The estimate of the mean line through the data of the EPNL is given by:
ݕൌܾ ܾ ଵݔܾ ଶݔଶ ⋯ܾ ݔ .
Each regression coefficient (Bi) is estimated by bi from the sample data using the method of least squares in a process summarized as follows.
Each observation (xi, yi) satisfies the equations:
ݕ ൌܤ ܤ ଵݔ ܤ ଶݔଶ ⋯. ܤ ݔ ߝ ൌܾ ܾ ଵݔ ܾ ଶݔଶ ⋯. ܾ ݔ ݁ , Where ߝ and ݁ are, respectively, the random error and residual associated with the EPNL. The random error ߝ is assumed to be a random sample from a normal population with mean zero and standard deviation . The residual (݁) is the difference between the measured value and the estima te of the value using the estimates of the regression coefficients and xi . Its root mean square value (s) is the sample estimate for . These equations are often referred to as the normal equations.
Table 5. Student's t-distribut ion (for 90 percent confidence) for various degrees of freedom Degrees of freedom () t.95, 1 6.314 2 2.920 3 2.353 4 2.132 5 2.015 6 1.943 7 1.895 8 1.860 9 1.833 10 1.812 12 1.782 14 1.761 16 1.746 18 1.734 20 1.725 24 1.711 30 1.697 60 1.671 >60 1.645 The n data points of measurements (xi, yi) are processed as follows:
Each elemental vector ሺݔሻ and its transpose ሺݔᇱሻ are formed such that:
ݔ ൌሺ 1ݔ ݔଶ..ݔ ሻ, a row vector; and ۇݔ 1 ଶ ۊݔݔᇱ ൌ ۈ ۋ ,a column vector. ۈ. ۋ ۈ. ۋ .
ݔۉی A matrix ܺ is formed from all the elemental vectors xi for i = 1, ….., n. ܺᇱ is the transpose of ܺ .A matrix ܣ is defined such that ܣ ൌܺ ᇱܺ and a matrix ܣିଵ is the inverse of ܣ In addition, ݕ ൌሺ ݕଵݕଶ …ݕሻ, and ܾ ൌሺ ܾܾଵ …ܾ ሻ, with ܾ determined as the solution of the normal equations:
ݕ ൌ ܾܺ and ݕ′ܺ ൌܾܺ′ܺ ൌܾܣ , Page 86
to give ܾ ൌܣ ିଵݕ′ܺ .
The 90 percent confidence interval CI 90 for the mean value of the EPNL estima ted with the associated value of the engine-related parameter x0 is then defined as:
ܫܥଽ ൌ ݕሺݔሻേݐ ଽହ,ఋݒݏሺݔሻ, where ݒሺݔሻ ൌ √ݔܣିଵݔᇱ .
,Thusܫܥଽ ൌ ݕሺݔሻേ.ݐ ଽହ,ఋݏ√ݔܣିଵݔᇱ where:
— ݔ ൌሺ 1 ݔݔଶ …ݔ ሻ;
— ݔᇱ is the transpose of ݔ ;
— ݕሺݔሻis the estimate of the mean value of the EPNL at the associated value of the engine-related parameter;
— .ݐଽହ, is obtained for ζ degrees of freedom. For the general case of a multiple regression analysis involving K independent variables (i.e., K + 1 coefficients) ζ is defined as ζ = n-K-1 (for the specific case of a polynomial regression analysis, for which k is the order of curve fit, there are k variables independent of the dependent variable, and so ζ = n-K-1); and ሺ௬ି௬ሺ௫ሻሻమ — ݏൌ √∑ససభ ିିଵ , the estimate of ߪ the true standard deviation.
305(c) Confidence Interval for Static-Test-Derived NPD Curves [ETM 3.5.3] When static test data are used in family certifications, NPD curves are formed by the linear combination of baseline flight regressions, baseline projected static regressions and derivative projected static regressions in the form:
EPNLDF = EPNLBF – EPNLBS + EPNLDS, or using the notation adopted above:
ݕிሺݔሻ ൌ ݕிሺݔሻ െ ݕௌሺݔሻ ݕௌሺݔሻ, where:
DF denotes derivative flight;
BF denotes baseline flight;
BS denotes baseline static; and DS denotes derivative static.
Confidence intervals for the derivative flight NPD curves are obtained by pooling the three data sets, each with their own polynomial regression. The confidence interval for the mean derived EPNL at engine-related parameter x0, i.e., for ߤிሺݔሻ, is given by:
ܫܥଽሺݔሻ ൌ ݕிሺݔሻേ ݒ′ݐ ிሺݔሻ where:
ݒிሺݔሻ ൌ√ ሺ ݏிݒிሺݔሻሻଶ ሺ ݏௌݒௌሺݔሻሻଶ ሺ ݏௌݒௌሺݔሻሻଶ with sBF, sBS, sDS, vBF (x0), vBS (x0), vDS (x0) computed as explained in 3.5.2.2 for the respective data sets indicated by the subscripts BF, BS and DS, and ݐᇱ ൌ ሺݏிݒிሺݔሻሻଶݐி ሺ ݏௌݒௌሺݔሻሻଶݐௌ ሺ ݏௌݒௌሺݔሻሻଶݐௌ ሺݏிݒிሺݔሻሻଶ ሺ ݏௌݒௌሺݔሻሻଶ ሺ ݏௌݒௌሺݔሻሻଶ where tBF, tBS, tDS are the t95, ζ values each evaluated with the respective degrees of freedom ζBF, ζBS, ζDS as they arise in the corresponding regressions.
305(d) Confidence Interval for Analytically Derived NPD Curves [ETM 3.5.4] Analysis may be used to determine the effect of changes in noise source components on certificated levels. This is accomplished by analytically determining the effect of hardware change on the noise component it generates. The resultant delta (Δ) is applied to the original configuration, and new noise levels are computed. The changes may occur on the baseline configuration or on subsequent derivative configurations. The confidence intervals for this case are computed using the appropriate method from 305(b) and 305(c).
If Δ̂ represents the analytically determined change and if it is assumed that it may deviate from the true unknown ∆by some random amount, d, such that:
߂̂ ൌ∆݀ , Where d is assumed to be normally distributed with mean zero and known variance ߬ଶ, then the confidence interval for ߤሺݔሻ ∆ is given by:
ሺݕሺݔሻ ߂ ̂ ᇱݒሻേݐ ᇱሺݔሻ, Where ݒᇱሺݔሻ ൌ√ ݒ ሺ ݔሻଶ ߬ ଶ and t’ is as above without change.
305(e) Adequacy of the Model [ETM 3.5.5] 305(e)(1) Choice of engi ne-related parameter [ETM 3.5.5.1] Every effort should be made to determine th e most appropriate engine-related parameter, x, which may be a combination of various simpler parameters.
305(e)(2) Choice of regression model [ETM 3.5.5.2] Page 88
It is not recommended in any case that polynomials of gr eater complexity than a simple quadratic be used for certification purposes, unless there is a clear basis for using a higher order polynomial.
Standard texts on multiple regression should be consulted, and the data available should be examined to show the adequacy of the model chosen.
305(f) Worked Example of the Determination of 90 percent Confidence Intervals from the Pooling of Three Data Sets [ETM 3.5.6] 305(f)(1) Introduction [ETM 3.5.6.1] This section presents an example of the derivation of the 90 percent confidence intervals arising from the pooling of three data sets. Worked examples and guidance material are presented for the calculation of confidence intervals for a clustered data set as well as for first order (i.e., straight line) and second order (i.e., quadratic) regression curves. In addition this section also shows how the confidence interval must be established for the pooling together of several data sets.
Consider the theoretical evaluation of the certification noise levels for an aircraft retrof itted with silenced engines.
The approach noise level for the “flight datum” aircraft was derived from a clustered data set of noise levels measured at nominally reference conditions, to which were added source noise corrections derived from a quadratic least-squares curve fit through a series of data points made at different e ngine thrusts. In order to evaluate the noise levels for the aircraft fitted with acoustically treated engines, a further source noise curve, assumed to be a straight least-squares regression line, was established from a series of measurements of the silenced aircraft. Each of the three databases is assumed to be made up of data unique to each base.
The clustered data set consists of six EPNL levels for the nominal datum hard wall condition. These levels have been derived from measurements which have been fully corrected to the hard wall approach reference condition.
The two curves which determine the ac oustical changes are the regression cu rves (in this example quadratic and straight-line least-squares fit curves) for the plots of EPNL against normalized thrust for the hard wall and silenced conditions. These are presented in Figure 6 where the dotted lines plotted about each line represent the boundaries of 90 percent confidence.
Each of the two curves is made up of the full set of data points obtained for each condition during a series of back-toback tests. The least-squares fits therefore have associated with them all the uncertainties contained within each data set. It is maintained that the number of data points in each of the three sets is large enough to constitute a statistical sample.
Corrected net thrust per engine
90.0
91.0
92.0
93.0
94.0
95.0
96.0
97.0
98.0
99.0
100.0 1 000 1 200 1 400 1 600 1 800 2 000 2 200 Hardwall Silenced ( = 89.93 + 0.001843 )y x EPNL Figure 6. Regression curves for plots of EPNL against normalized thrust for hard wall and silenced conditions 305(f)(2) Confidence interval for a clustered data set [ETM 3.5.6.2] The confidence interval for the clustered data set is defined as follows:
Let EPNLi be the individual values of EPNL, n = number of data points; and t = Student’s t-distribution for ( n-1) degrees of freedom (i.e., the number of degrees of freedom associated with a clustered data set).
Then the confidence interval ܫܥ ൌ ܮܰܲܧ േݐ √ ௦ , where s, the estimate of the standard deviation, is defined as:
ሺாேିாேሻమݏൌ √∑ససభ , andିଵ సభ ாேܮܰܲܧ ൌ ∑స .
Suppose that the clustered set of EPNL values consists of the following:
Run number EPNL 1 95.8 2 94.8 3 95.7 4 95.1 5 95.6 6 95.3 Then the number of data points (n) = 6, the degrees of freedom (n-1) = 5, and the Student’s t-distribution for 5 degrees of freedom = 2.015 (see Table 5 ), and so:
స ாே ܮܰܲܧ ൌ ∑సభ ൌ9 5 . 3 8, ሺாேିாேሻమݏൌ √∑ససభ ൌ 0.3869,ିଵ and the confidence interval (CI) is calculated as follows:
ܫܥ ൌ ܮܰܲܧ േݐ √ ௦ ൌ 95.38 േ 2.015 .ଷ଼ଽ ൌ 95.38 േ 0.3183√ 305(f)(3) Confidence in terval for a first order regression curve [ETM 3.5.6.3] Suppose that the regression curve for one of the source noise data sets, the silenced case, can best be represented by a straight line least-squares fit curve (i.e., a first order polynomial).
The equation for this regression line is of the general form:
Y = a + bX where Y represents the dependent variable EPNL, and X represents the independent variable, in this case normalized thrust ிಿ ఋ .
Although for higher order polynomial least-squares curves a re gression line’s coefficients (i.e., the solutions to the “normal equations”) are best established through computer matrix solutions, the two coefficients for a straight-line fit, a and b, can be determined from the following two simple formulae for the measured values of X and Y, Xi and ∆ :
స స ܽൌ ∑సభ ି ∑సభ ; and మ ܾൌ ௩ మ , where: ൌ ௌೣ ௌೣ స స ∑స ݕݔܵଶ ൌ ∑సభ െ ∑సభ మ సభ ;and Page 91
స మ ష ܵ௫ଶ ൌ ∑సభ సభ ሻଶ െሺ ∑ .
The 90 percent confidence interval about this regression line for X = x0 is then defined by:
ܫܥଽ ൌ ܻ േݏݐ √ ݔܣିଵݔᇱ where:
t = Student’s t-distribution for 90 percent confidence corresponding to (n – k - 1) degrees of freedom, where k is the order of the polynomial regression line and n is the number of data points;
ݔ ൌሺ 1 ݔሻ;
ᇱݔ ൌሺ ݔ1ሻ;
ܣିଵ is the inverse of ܣ where ܣ ൌܺ′ܺ , with ܺ and ′ܺ defined as in 305(b)(2) from the elemental vectors formed from the measured values of the independent variable ܺ; and ݏൌ√ ݅ൌ1݊െ݇െ1 Where ሺ∆ܻሻ ൌ the difference between the measured value of Y i at its associated value of X i, and the value of Y derived from the straight line least-squares fit curve for X = Xi, and n and k are defined as the number of data points and the order of the polynomial regression line, respectively.
Suppose that the data set consists of the following set of six EPNL values, together with their associated values of engine-related parameter (see Table 6). Note that it would be usual to have more than six data points making up a source noise curve, but in order to limit the size of the matr ices in this example, the number of data points has been restricted.
By plotting this data (see Figure 6) it can be seen by examination that a linear relationship between EPNL (the dependent variable Y) and ி ఋ ಿ (the independent variable X) is suggested with the following general form:
Y = a + bX.