Annex III: Derivation of Relations between LWECPN and LDN

Annex III: Derivation of Relations between LWECPN and LDN

Where: LEPN - the average value of the energy at effective perceived noise levels in N flights;

N1, N2, N3 - the respective numbers of flights in the daytime (generally from 07：00 to 19：00), in the evening (generally from 19：00 to 22：00) and at night (generally from 22：00 to 07：00 ) .
On the basis of (Where T0=10 s) (2)

And replace 39.4 with 10×, Formula (1) may be converted as follows:

In Formula (3), represents the average noise energy in every flight. N1+3N2+10N3 represent the weighted number of flights in each day. The coefficient 3 represents the weighted number of flights in the evening, i.e., a flight in the evening is equivalent to 3 flights in the daytime, or a punishment of 5 decibels will be added for each flight in the evening. The coefficient 10 represents the weighted number of flights at night, i.e., a flight at night is equivalent to 10 flights in the daytime, or a punishment of 10 decibels will be added for each flight at night. Therefore, the numerator in the brackets represents the cumulative noise energy of all flights in a day, and the denominator 86400 is the number of seconds in a day (24×3600＝86400). Thus it can be seen the physical significance of LWECPN: i.e., the effect of aircraft noise per second on people (at the effective perceived noise level).

Where: - the sound exposure level, referring to the average value of A-weighted sound level per second converted from all noises exposed in a certain measure point in each flight;

ND, NN - the respective numbers of flights in the daytime (generally from 07：00 to 22：00) and at night (generally from 22：00 to 07：00 ).
On the basis of (t₀ = 1 s) (5)

And replace 49.4 with 10×, Formula (4) may be converted as follows:

In the formula mentioned above, represents the average noise energy in every flight. N_D+10N_N represent the weighted number of flights in each day. The coefficient 10 represents the weighted number of flights at night, i.e., a flight at night is equivalent to 10 flights in the daytime, or a punishment of 10 decibels will be added for each flight at night. Therefore, the numerator in the brackets represents the cumulative noise energy of all flights in a day, and the denominator 86400 is still the number of seconds in a day. Thus it can be seen the physical significance of L_DN: i.e., the effect of aircraft noise per second on people (at A-weighted sound level).

Theoretically, L_WECPN is based on the noisiness, with the effective perceived noise level L_EPN as the measure to assess individual noise event; while L_DN is based on the loudness, with the A-weighted sound level as the measure to assess individual noise event. Therefore, it’s unlikely to conduct accurate conversion between such two measures. However, the approximate quantitative relations between the two measures may be obtained.

Where the differences brought by pure tone modifications are ignored:

(7)

Then, the approximation relation between L_PN and L_A is^［5］:

On the basis of Formula (2), Formula (5) and the aforesaid approximation relation, the relation between L_EPN and L_SE may be derived. The derivation process is as follows:

That is: (9)

On the basis of Formula (1) (utilized to define L_WECPN), Formula (4) (utilized to define L_DN), Relation Expression (9) and the weighted rules for time intervals, it can be derived that:

As for common airports, it’s not likely that N₂/（N₁+3N₂+10N₃）≥0.1, then generally speaking:

In view of the aforesaid inequality, Formula (10) may be simplified to the following approximation relation:

The current noise assessment standard in the United States is L_DN=65dB, equivalent to 79dB after being converted to L_WECPN. Therefore, it may be deemed that the current standards implemented in China (i.e., 70dB and 75dB) are stricter than the current noise assessment standard for aircrafts in the United States.