Train Passby Lmax at Receiver Calculator
This calculator estimates the maximum A-weighted sound level, Lmax, of a single train passby at a receiver. It works from the source reference levels SELref of the locomotives and of the rail cars, the number and length of each, the train speed S and the closest distance D from the receiver to the track.
For each group the calculator forms the total group length, finds the angle θ = atan(L / (2D)) in radians, and applies the Appendix F.3 equations of the FTA Transit Noise and Vibration Impact Assessment Manual (2018): one form for the locomotives and one for the rail cars. The total Lmax is the larger of the two group values.
It is written for rail transit noise analysts and acoustical consultants. θ is carried unrounded through the calculation and shown to 4 decimals only for reading, so the result does not drift from rounding of the angle.
Calculator
| Group | Total length (ft) | θ (rad) | Lmax (dBA) |
|---|---|---|---|
| Locomotives | — | — | — |
| Rail cars | — | — | — |
How to use the calculator
- Enter the number of locomotives and the number of rail cars as whole numbers of 0 or more. They cannot both be 0. A group with a count of 0 is left out, and its SELref and length fields are ignored.
- Enter the length of one locomotive and of one rail car in ft (needed only for a group with a count above 0, and above 0). The group lengths are Lloco = Nloco × length and Lcars = Ncars × length.
- Enter the SELref of each group present in dBA. The values come from Table 4-20 of the FTA manual or from a measurement converted with the companion source reference calculation. SELref may be any real number.
- Enter the train speed S in mph and the closest distance D from the receiver to the track in ft; both must be above 0.
- For each group the calculator finds θ = atan(L / (2D)) in radians, carried unrounded.
- Locomotives: Lmax = SELref + 10 log(S/50) − 10 log(Lloco/50) + 10 log(2θ) − 3.3. Rail cars: Lmax = SELref + 10 log(S/50) − 10 log(Lcars/50) + 10 log(2θ + sin 2θ) − 3.3, with log in base 10.
- The total Lmax is the larger of the Lmax values of the groups present. Results update as you type; the Calculate button runs the same calculation. Lmax is shown in dBA to 1 decimal, θ to 4 decimals.
Frequently asked questions
Why does the calculator carry θ unrounded?
The angle θ = atan(L/(2D)) enters Lmax through a logarithm, so rounding it shifts the result. With the inputs filled in when the page opens (1 locomotive of 70 ft, S = 43 mph, D = 125 ft), θ is 0.2730 rad and the locomotive Lmax is 84.0 dBA; with θ rounded to 0.27 the locomotive value would be 83.9 dBA. θ is shown to 4 decimals for reading only.
What happens when the number of locomotives or rail cars is 0?
That group is left out: its SELref and length fields are ignored, its Lmax, length and θ show dashes, and the total Lmax is the Lmax of the other group. The two counts cannot both be 0.
How is the total Lmax obtained from the two groups?
The total is the larger of the Lmax values of the groups present. The locomotive value uses the term 10 log(2θ) and the rail car value uses 10 log(2θ + sin 2θ); both add 10 log(S/50), subtract 10 log(L/50) for the group length L, and subtract 3.3.
Can this Lmax be used to judge noise impact?
No. Lmax here is a level at the receiver without shielding, ground or barrier corrections, and it is not an impact metric; no impact criterion is evaluated.
Disclaimer
This calculator gives an estimate only and is not a substitute for a qualified engineer. The formulas are Eq. F-6, F-7 and F-8 (Table F-3) of Appendix F.3 of FTA Report 0123, Transit Noise and Vibration Impact Assessment Manual, 2018, p. 235, with Example F-5 on p. 236.
Lmax is a level at the receiver without shielding, ground or barrier corrections and is not an impact metric. The SELref values come from Table 4-20 of the same manual or from a measurement converted with the companion source reference calculation.