Don, thanks a lot for this - it helps to have something substantial to
discuss.

> First is reflector. I changed to enhanced coatings for my own scope, and
> the obstruction % on personal scope.
> Second is refractor. Changed to best multi-coatings.
> Third is contemporary SCT. Changed to typical current coatings.
> These were all inaccurate in the on-line calculators.

It would be nice to choose from standard valuer or calulate the recipe for
your own personal telescope - and in either case, display the estimated
total loss.

> 2) FO = Math.pow(0.99,6); // EYEPIECE (4 COATED AIR-GLASS SURFACES)
>
> Changed to 6 air-to-glass surfaces for more typical widefield. This could
> be changed for a specific eyepiece if desired by changing the number after
> the comma.

same here - but for modern EPs with good coatings, I would think the total
light loss is so small that the difference between 4 and 6 coatings should
be negligible in the big context.

>
> 3) DE = 7*Math.exp(-AG*AG/20000); // DIAM EYE PUPIL IN MM
>
> This is the age-dependent diameter decrease in pupil diameter that
> predicts a certain pupil diameter at a particular age. Adjusting the
> starting point (7mm) may result in a more realistic level IF you know your
> exact pupil diameter. My own dark-adapted pupil was never as large as 7,
> and currently stands at 4.5mm. Altering this changes an assumption and
> changes limiting magnitude calculations. I experimented to find a
> realisting starting point for my pupil diamter than works in the
> calculator. I was NOT adjusting the age asumption, which might nt be a
> valid one.

Yes, Schaefer uses some age-dependent estimate of the average pupil
diameter. Robert does the right thing by letting you enter your actual
pupil, if you know it, as any serious deep sky observer will know from
measuring. If so, there is no reason for an age correction, of course. Enter
your age, and Robert's routine will calculate an estimated width - if you
know it doesn't apply to you, you can enter a true value.


>
> 4) FS=1.0; // OBSERVER'S SENSITIVITY
>
> This figure can be adjusted for the individual. I recommend playing with
> the figure if you consistently reach deeper or not as deep as the
> predictions in a variety of scopes.

Yes, this is a factor that should be brought up explicitly. However, I see
no good reason to separate this from the experience factor - they might as
well be combined to one individual sensitivity factor (equivalent to the
experience factor if you have no observations yet for a given observer, but
a factor that you could modify once you have some good data). I really doubt
the suggestion in Schaeffer's paper about individual(s) having a factor of 8
more sensitive retina than the average - the physiologic sensitivity would
vary some, surely, but I doubt by anything as much upward (neither the
number of rods nor their dark-adapted charge of rhodopsin would increase
substantially - skill in using them to best advantage can!). I think it is a
matter of training your averted vision, and the patience and time needed to
catch those 10%. This skill could be factored into the individual
sensitivity factor.
>
> 5) // CALCULATE SKY BRIGHTNESS
> if (MZ>=(7-K)) {
> BS=54; // BEST POSS. SKY BRIGHTNESS
> FS=Math.pow(10,0.4*(7-K-MZ)); // & GOOD EYESIGHT
> }
> else {
> XX=0.2*(8.68-K-MZ); // FS ASSUMED = 1
>
> Here, pupil diameter and observer sensitivity are assumed. These figures
> can be adjusted as well.

Yes, and perhaps the color correction for the limit star should be applied
as well, if known (I guess it is known for all naked-eye stars!) Perhaps you
could display the calculated bacground brightness.

>
> 6) M=M+(EX-6)*0.16; // EMPIRICAL EXPERIENCE CORRECTION
>
> Here an adjustment can be made for experience in the end factor if you
> think the difference is too great or too little.

see above - any individual should need only one factor (to be adjusted as
needed for changes in age, experience and wisdom in general ;-)

> I think the purpose for a limiting magnitude calculator is to predict the
> limit for a particular observer on a particular scope on a particular
> night.

The purpose of such a calculator can well be discussed - I believe your
definition is as good as any, but others are possible. You the observer and
your scope would be fairly constant - the background and seeing may vary
from night to night, and if you have any idea of the parameters for a
particular observing night, you may know if you should expect more or less
than your "norm" limit.
For a beginner, it might show if an intended object ought to be easy,
difficult or plain impossible - but there is nothing to prevent you from
trying, and doing so will give you yet another data point for your
individual sensitivity factor. (The inverse of Schaefer's, to get a higher
value for higher sensitivity)
For me, a didactic purpose is important, and that's why I am asking you
again as I did, and why I wish for a "transparent" algorithm - teaching what
factors are important (be it the object itself, the sky conditions, the
telescope you use, or your individual factors such as pupil size, retinal
sensitivity and more importantly, skill in using your averted vision to best
advantage) and potentially improvable.
>
> There is no harm in playing around with the assumptions IF it leads to a
> more accurate prediction. I have a fair amount of experience using a 5"
> Maksutov, 8" SCT and 12.5" newtonian, and know the average darkness of the
> site where I observe. I find that I can predict my limit +/-0.2
> magnitudes on all three scopes (as verified using limiting magnitude
> charts from Roger Clark and Brian Skiff and photomeric charts of M14,
> NGC206 and a few others), which means to me that the adjustments I made in
> the code made the calculator more accurate for me in my circumstances.

Very true! Only I think you should not need to actually modify the code, but
enter your own individual factor explicitly. If you can beat the average
test subject of Knoll's by 2 full magnitudes, it isn't unreasonable - but if
so, I would believe it is mainly a matter of acquired skill in observing by
averted vision, and giving time to let those 10% observations add to
certainty.

> Robert's calculator cleans up some of the errors in the Bogen one and is a
> little friendlier.

It is indeed, but even so, I could think of possible improvements - I have
suggested one or two like adjusting the Knoll limit for pupil size, a
binocular option, the background estimate from the NELM shown, and perhaps
even color correction for the star of your NELM estimate.

Nils Olof