Computations in Airplane Noise Study (16 Responses)

This post reviews and makes available airplane noise data supplied by Massport. It offers background for the conversation about airplane noise in Belmont and Watertown.

A couple of things come out of the data. The data drive home, first-of-all, that the FAA’s 65 DNL threshold for noise compatibility with residential land use is simply a very high threshold. Areas experiencing noise above that DNL are areas that most people would experience as unmistakeably noisy, much noisier by any measure than Belmont or Watertown. The data also yield a practical insight: Flights departing from runway 33L are very concentrated over two narrow corridors in Belmont and Watertown, but spreading them out by as much as 1000 meters in either direction would not make a detectable difference in experienced noise levels.

The Data

MassPort’s recent Belmont Noise Monitoring Report concluded that the noise levels related to flight operations in Belmont are far under those recognized as incompatible with residential land use by the FAA. I’ve been interested to better understand the computations underlying MassPort’s conclusions, given that some residents do feel disturbed by the noise. MassPort was kind enough to furnish the detail data underlying the report.

The detail data came in two Excel files:

  • A file containing actual second by second measurements. This is a big file — 2.3 million records for 27 days at 86,400 seconds per day. Too big to post for download, but I’m happy to share the disk with anyone interested.
  • A file correlating noise events to flight operations at Logan. During the study period, 2071 Logan flights correlated to identifiable noise events at the monitoring site. You can download the flight operations file here.

tracks-image2
The report and the underlying data do correlate well and appear to provide very useful information about the intensity of the airplane noise in an affected location.

  • The report is based on a noise measurement device installed in a well chosen location. The device was installed in the back yard of a home in Belmont where the residents have been particularly disturbed by the airplane noise. The location is, in fact, close to the flight path for many planes. The radar/earth image above is copied from page 9 of the report. The image shows that the monitoring location lies at the southeastern edge of the path for runway 33L departures that branches over Belmont. The monitoring location is also 0.5 miles northwest of the edge of the path that branches over Watertown. The radar/earth image shows a dense area of flight tracks for each path branch which is roughly half a mile wide, with some tracks going well outside that dense area. (The image on page 9 shows a distance scale if you zoom in on it).
  • The report covers a relevant period — during the 27 days of the report, the usage of runway 33L was relatively heavy — 24% of airport departures as compared to under 20% in each of the last 7 full years.
  • The second-by-second detail does correlate as it should with the flight operations data. One can look at the second-by-second noise level increasing as a plane approaches and reaching a peak level that matches with LMAX column in the flight operations file.
  • I was able to closely reproduce the computation of SEL or “Sound Exposure Level” in the flight operations file for a selected flight. The SEL is the noise level in decibels that would result if all the noise energy from the single flight — which might actually be audible for a minute or so — were concentrated into one second. Page 8 of a Virginia Tech training document shows how the SEL computation is done:.
    1. scale up from the decibel number for each second of the flyover to noise energy for that second (divide decibel level by 10 and then exponentiate 10 to that number);
    2. add that energy across all the seconds of the flyover (or closely approximate that by using only the seconds during which the noise level is within 10 decibels of the peak);
    3. scale the sum back to decibels (take the log base 10 of the sum and multiply it by 10).
  • I was able to exactly reconstruct the computation of day night noise level from the SEL values. The day-night noise level is the average noise energy from flight operations (with a 10 decibel up-adjustment for noise between 10PM and 7AM). DNL can be derived from the SEL’s for each flyover as follows:
    1. scale the SEL for each fly over back to energy (divide by 10 and exponentiate 10 to that number);
    2. sum that energy across all fly overs and then divide by the number of seconds in the period (27 days * 24 hours * 3600 seconds ) for an average energy;
    3. scale that average energy back to decibels (take the log base 10 of the average and multiply by 10).
  • In SQL, that computation reads as follows: SELECT 10 * ln( sum( 1 / ( 27 *86400 ) * exp( ln( 10 ) * ( sel + if( hour( eventstarttime ) >21 OR hour( eventstarttime ) <7, 10, 0 ) ) /10 ) ) ) / ln( 10 ) FROM flightevents. Applying that query to the flight operations file (that you can download above and then import into your favorite database for querying) yields a total flight operations DNL of 44.5 decibels — exactly the flight operations DNL computed in the report. Selecting only 33L departures, I got a DNL of 44.1 decibels, again, exactly as in the report. I was also able to validate the all-operations daily DNL levels at page 8 of the report.

The accuracy of the report does, of course, depend on the accuracy of the association between flight operations and measured noise events. That association is done entirely by MassPort using radar data and we have no ability to verify that association. On the other hand, we have no reason to doubt it, as the data do hang together well.

Noise intensity by hour

One question that comes up in conversation about the noise issue is the intensity of noise during certain hours. The data supplied by MassPort allows us to compute DNL by individual hour. The table below shows the DNL by hour for the noisiest 30 individual hours during the period.

Date Hour Count MaxLMAX MaxSEL Hourly DNL
2014-Mar-16 6 18 70.7 81.5 63.3
2014-Mar-13 6 8 70.7 80.6 61.2
2014-Mar-09 23 4 68.2 78.2 56.8
2014-Feb-24 22 6 69.0 77.8 56.6
2014-Mar-08 23 4 70.6 80.8 56.2
2014-Feb-25 22 7 65.3 77.6 55.3
2014-Mar-12 22 3 66.7 77.2 54.9
2014-Mar-20 17 16 75.2 87.3 54.9
2014-Mar-13 22 6 67.6 77.3 54.8
2014-Mar-02 8 16 74.9 86.0 54.6
2014-Mar-16 22 5 65.5 77.1 54.2
2014-Mar-15 17 15 74.2 86.3 54.0
2014-Mar-20 19 20 73.5 83.6 53.8
2014-Mar-16 5 4 63.3 73.9 53.6
2014-Mar-20 16 17 73.7 81.0 53.5
2014-Mar-03 22 7 61.6 73.4 53.4
2014-Mar-08 6 2 63.3 76.3 52.7
2014-Mar-20 15 17 71.0 79.3 52.6
2014-Mar-09 22 3 62.0 74.3 52.5
2014-Mar-20 20 16 68.9 81.4 52.4
2014-Mar-09 6 4 67.3 74.2 52.3
2014-Mar-16 13 13 78.8 84.8 52.3
2014-Mar-17 5 6 64.9 72.3 52.0
2014-Feb-27 23 2 64.2 76.5 51.8
2014-Mar-13 7 11 74.2 83.7 51.6
2014-Mar-02 11 18 67.5 77.2 51.5
2014-Mar-09 15 15 75.7 84.4 51.2
2014-Mar-13 15 14 68.1 81.7 51.2
2014-Mar-02 9 20 65.8 78.8 51.1
2014-Mar-02 7 14 66.1 79.2 51.1

What this table shows is that even in the busiest hours of the 27 days in question, the DNL did not exceed the 65 decibel level deemed to merit remedy by the FAA. And note that the very highest DNL’s are all in night hours so that, in the DNL computation they are  boosted 10 decibels.  The highest single-hour unboosted DNL was March 20 at 5PM with a DNL of 54.9, 10 decibels lower than the 65 level.  10 decibels of DNL is a very different hourly noise level — equating to either a 10 decibel (very noticeable) increase for each noise event in the hour or a 10 fold increase in traffic.  For more hourly detail in spreadsheet form, click here.

The FAA’s 65 decibel DNL threshold, which is computed as an annual average, is simply a very high threshold.   To put it fully in perspective, consider the following three statements that are all mathematically true.

  • To reach the annual 65 DNL threshold, Belmont would have to have traffic equal to its worst single day-time hour during every single night hour (from 10PM to 7AM) and would also have to have a 10-fold increase in traffic over that worst single day-time hour during every single day-time hour 365 days per year.
  • To reach the annual 65 DNL threshold, Belmont would have to have 100 times as many flights as it does — Belmont’s DNL is under 45.  To achieve a 20 decibel increase, Belmont would have to have 100 times as much sound energy.
  • To reach the annual 65 DNL threshold with Belmont’s current traffic level, it would have to be 10 times closer to the airport than it is, in other words it would have to be under a mile away from the end of the runway. Only certain parts of East Boston and Winthrop are that close.  Of course, in those locations, people hear all the planes Belmont hears at a noise level 20 decibels higher (because the planes are under 1/10 as high), but they additionally hear a lot of other air traffic. They also can hear airport ground operations.

The comparisons for Watertown, if measured, would be very similar to the comparisons for Belmont.

Flights by aircraft type (33L Departures)

The flight operations file contains 2071 records, consistent with the report. It identifies 1534 of them as 33L departures, also consistent with the report. The data confirm that 33L departures are almost all of the noise problem — the DNL for events other than 33L departures is only 34.0, well below the ambient DNL. Only 25 of the non-33L events had a peak one second noise level (“LMAX”) greater than 65. Focusing on the 33L departures, 10 aircraft types account for 1229 (80%) of the departures and have comparable LMAX averages:

Type Count Avg LMAX
E190 390 61.4
A320 290 59.8
A319 127 59.3
E170 103 56.8
B738 98 62.1
CRJ9 59 55.1
B737 50 61.1
B752 43 58.3
B712 40 58.0
B733 29 63.9

MD88s account for only 17 flight events, but 12 of the top 20 most noisy events based on LMAX (13 of the top 20 based on SEL).

Flights by POCA Altitude (33L Departures)

The average altitude at Point of Closest Approach for flight events in the file is 1861.4 meters or 6107.0 feet for 33L departures. This is a little different than the report which states an average altitude of 6269 feet. I can’t explain this by backing out the elevation of the monitoring station — it was under 15 meters (50 feet) above sea level. Note: The Point of Closest Approach Distance (POCADistance) is consistently within 1 meter of the squareroot of the sum of the squares of the POCAAltitude and POCARange (if POCAAltitude is adjusted down by 20 meters, a few meters more than the true elevation of the monitoring station). This is the correct mathematical relationship for distance to have to altitude and range.

Altitude (meter range) Count Average LMAX
800 1 56.5
900 2 53.0
1000 5 64.1
1100 8 62.9
1200 17 61.1
1300 32 61.2
1400 110 59.0
1500 124 61.5
1600 200 60.8
1700 230 59.9
1800 184 60.0
1900 183 59.8
2000 146 59.7
2100 98 60.1
2200 66 58.9
2300 41 58.3
2400 22 58.3
2500 22 57.1
2600 14 58.1
2700 9 57.1
2800 7 54.3
2900 3 55.3
3000 3 54.9
3100 1 57.2
3300 1 56.4
3400 1 51.2
3500 1 49.5
3700 1 53.5
3800 1 50.7
4000 1 55.9

83% of the flights (1275 of 1534) fall within the 1400 to 2200 meter altitude range.

Flights by POCA Range (33L Departures)

Looking at the table below, it emerges that there are two Point of Closest Approach ranges with high traffic, one with roughly 200 flights ranging 300-500 meters from the monitoring site and a second with roughly 700 flights ranging 1100 to 1400 meters from the site. Based on the graphic reproduced above, it appears that the first peak may correspond to the Belmont path and the second peak to the Watertown path. There is a smaller third peak around 1800 meters which appears to correspond to the Arlington path.

The numbers in the left column of the chart below each represent the low end of a 100 meter range for horizontal range at closest approach (POCA).

Horizontal Range (meter range) Count Average LMAX
0 3 64.6
100 2 64.7
200 20 63.3
300 91 62.2
400 99 62.7
500 50 62.1
600 25 62.5
700 22 57.4
800 25 57.9
900 34 58.8
1000 51 59.9
1100 143 59.2
1200 496 60.1
1300 209 59.7
1400 35 60.2
1500 10 61.6
1600 12 57.7
1700 19 57.3
1800 66 58.3
1900 54 57.0
2000 12 57.8
2100 9 56.0
2200 6 55.5
2300 6 56.9
2400 6 56.6
2500 10 54.6
2600 5 54.9
2700 6 54.1
2800 1 58.7
2900 6 53.3
3000 1 58.0
It is striking that the maximum noise levels (average LMAX) associated with flights on the Belmont path (range 300-500 meters away) are only 2 to 3 decibels louder than those on the Watertown path (range 1100-1400 meters away). This is a noise level difference that the human ear can barely detect. This makes sense mathematically, because most of the distance from the noise source plane to the monitoring device is in the altitude. At the altitude of 1800 meters, going from 300 to 1300 meters of horizontal range only adds 400 meters to the total distance (use the pythagorean theorem from high school math), a 22% distance increase which translates into a 32% noise energy reduction (energy inversely proportional to square of distance), which in turn translates into a 2 decibel noise reduction (10 * log10 of the energy ratio). By the same computation, the difference is even smaller moving from 0 to 1000 meters of range — roughly a 1 decibel change.

Worth noting: the altitude differences among locations in Watertown and Belmont are too small to make a difference: The top of Oakley Country club is at 65 meters and the Belmont Hill Club is at 87 meters as compared to the average POCA altitude which is 1800 to 1900 meters. Note also: The particularly noisy few flights in the 0-200m range happen to include noisy MD88’s and are noisy for that reason, not because of their being directly overhead.

Flights by destination by POCA range (33L Departures)

The following table allocates flights by destination to the ranges identified above and the allocation does appear to make sense geographically, with Watertown(?) getting most of the eastern seaboard destinations, Belmont(?) getting more of the southwestern destinations and Arlington(?) getting the most westerly destinations.

Destination Total 1100-1400m 0-600m 1700-2000m
(Watertown?) (Belmont?) (Arlington?)
New York LaGuardia 115 102 1 0
DC National 112 101 0 0
Philadelphia 111 90 0 10
New York JFK 84 69 1 2
Atlanta 76 0 69 0
Newark 73 62 1 2
Baltimore 64 53 1 0
Charlotte 57 56 0 0
Raleigh/Durham 54 42 0 1
Orlando 52 27 1 2
Fort Myers 52 37 1 0
Fort Lauderdale 46 29 0 2
Miami 41 28 0 2
DC Dulles 40 0 37 0
Houston 38 2 10 18
Pittsburgh 38 0 0 35
Richmond 28 18 1 0
Dallas 26 0 23 1
West Palm Beach 25 16 0 0
Teterboro (NJ) 23 1 17 0
Cincinatti 20 0 1 19
LA 18 1 7 8
Indianapolis 18 0 4 10
Norway 17 11 1 0
JSJ(?) 15 7 0 1
Jacksonville 15 12 0 0
Tampa 15 8 0 1
Columbus 14 1 12 0
Memphis 14 1 11 0
Houston 13 0 13 0
La Desirade (Caribbean) 11 5 0 1
Saint Louis 10 0 10 0

Note that the 32 destinations shown above account for 1335 flights, 87% of the 1534 33L departures in the study. The selected ranges account for a total of 83% of the flights to those destinations, with the Watertown track alone accounting for 58%. The following is the query generating this table: SELECT arrivalairport, count( eventid ) , sum( if( pocarange >1100 AND pocarange <1400, 1, 0 ) ) AS watertown, sum( if( pocarange <600, 1, 0 ) ) AS belmont, sum( if( pocarange >1700 AND pocarange <2000, 1, 0 ) ) AS arlington FROM `flightevents` WHERE departurerunway = ’33l’ GROUP BY arrivalairport ORDER BY count( eventid ) DESC.

Selecting the top 10 destinations on the Watertown track, all easternboard destinations, and recomputing the range table for only the 774 flights to those destinations, it is striking that 400 of the 774 fall within the 1200-1300 meter POCA range and 639 fall within the 1100-1400 meter range — in other words, the flights are following a very consistent path as intended under the RNAV system. SQL for this query is: SELECT floor( POCArange /100 ) , count( eventid ) , avg( lmax ) FROM flightevents WHERE departurerunway = ’33L’ AND (arrivalairport = ‘LGA’ OR arrivalairport = ‘DCA’ OR arrivalairport = ‘PHL’ OR arrivalairport = ‘JFK’ OR arrivalairport = ‘EWR’ OR arrivalairport = ‘BWI’ OR arrivalairport = ‘CLT’ OR arrivalairport = ‘RDU’ OR arrivalairport = ‘MCO’ OR arrivalairport = ‘RSW’ ) GROUP BY floor( POCArange /100 )

Please note, this thread is not open for comment at this time.

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