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M 1 Ldn = 10 log 10( LAE , j +Wj )/10 86, 400 j = 1
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where LAE,j = sound exposure level produced by the jth aircraft passby during the day Wj = time-of-day weighting for the jth aircraft pass-by (0 dB if it occurred between 7 am and 10 pm, 10 dB if it occurred between 10 pm and 7 am) M = number of aircraft noise events during 24-h period The application of this equation to determine the DNL of several aircraft flyovers at various times during the day is illustrated by Example Problem 14-3
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Example Problem 14-3 The following sound exposure levels of five aircraft flyovers were measured over the course of a 24-h period: 812 dB at 6:03 am, 951 dB at 10:32 am, 792 dB at 2:15 pm, 888 dB at 7:33 pm, and 712 dB at 10:05 pm
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To compute the DNL, we must substitute into Eq (14-10) The sound exposure levels at 6:03 am and 10:05 pm must be increased by the time of day weighting of 10 dB since these flyovers occurred between 10:00 pm and 7:00 am 1 Ldn = 10 log (1091 2/10 + 1095 1/10 + + 108 1 2/10 ) 86, 400 = 10 log 63,97885 = 481 dB To find the aircraft which has the greatest and least contribution to the daynight average sound level the (LAE,j + Wj)/10 value of the quantity 10 must be evaluated for each aircraft Clearly, by adding the time of day weighting, we see that the aircraft flyover at 10:32 am is the greatest contributor and the aircraft flyover at 2:15 is least contributor to the day-night average sound exposure level
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A useful rule of thumb for estimating the contribution of DNL to a single daytime (7 am to 10 pm) noise event may be obtained by simplifying Eq (14-10) for the condition, where M is equal to 1 The approximation shown in Eq (14-11) is accurate to within 05 dB
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where LAE is the sound exposure level of a single aircraft pass-by The use of Eqs (14-10) and (14-11) to compute the DNL of a single daytime noise event is illustrated by Example Problem 14-4
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Example Problem 14-4 Let us determine the DNL produced by a single daytime noise event with a sound exposure level of 105 dB Using Eq (14-10), we have 1 Ldn = 10 log (10105 0/10 ) 86, 400 = 10 log 366,004 = 556 dB Using Eq (14-11), we have Ldn 105 50 55 dB If this noise event were added to the noise events in Example Problem 14-3, we would find that the DNL was increased to 563 dB or there would be an increase of 07 dB
Environmental reporting criteria often require annual average values of DNL Both airport and atmospheric factors contribute to day-to-day variability in the DNL observed at a particular location near the airport In cases where average values must be computed from measurements, the averaging must be done on a sound energy
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basis Equation (14-12) shows the formula for computing the annual average value 1 365 L /10 Ldn , annual = 10 log 10 dn ,i 365 i = 1
(14-12)
where Ldn,i is the DNL for the ith day of the year This equation assumes 365 individual DNL values are to be used in the averaging process For conditions where the number of days differs from 365 (leap years, missing data, etc) the available number of data points should be used in the summation and the number 365 replaced by the actual number of data points used Representative values of DNL range from a low of 40 to 45 dB in extremely quiet isolated locations to highs of 80 or 85 dB immediately adjacent to a busy truck route or just off the end of a runway at an active military air base The US Environmental Protection Agency (EPA) identified this measure as the most appropriate means of evaluating community (including aircraft) noise in 1974 [28] Most other public agencies dealing with noise exposure, including the FAA, the Department of Defense, and the Department of Housing and Urban Development (HUD), have also adopted DNL in their guidelines and regulations
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