Bill Ferris wrote:
The basic formula is NELM=7.93-5*log(10^(4.316-(Ba/5))+1), which predicts the
following:

Sky
SB....... NELM
26.0..... 7.66
25.0..... 7.52
24.0..... 7.31
23.0..... 7.02
22.0..... 6.62
21.0..... 6.12
20.0..... 5.49
19.0..... 4.77
18.0..... 3.97

My initial response was that the formula is much too conservative. There
are reliable reports of observers (Curtis, O'Meara, etc.) seeing stars
as faint as mag. 8.4, naked eye. Yet, under a pristine dark sky (22.0
MPSA), the above formula predicts a NELM of just 6.62.

Two observations:

1. Because the log argument is always greater than 1, the NELM value
from this formula is bounded by 7.93.

2. This formula is almost quadratic over the range given, so it can
be approximated as follows: Add 25 to SB to get X. Subtract 25 from
SB to get Y. NELM is then approximately thrice X minus the square
of Y, divided by 20. (Not very handy, I suppose, but an item of
interest to those, like me, interested in arcane rules of thumb.)

Brian Tung
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