NavList:

David Pike, you wrote:
"Ho=Ha – R + P in A +/- SD"

Right. And I agree that these things would become second nature after a little practice. Also the calculator steps are so very short that they should be as easy as any short table lookup.

My setup for an example was: "at 12:07:16 UT today (19 Oct 2024), I observe the altitude of the Moon's Upper Limb: 18°57'. I have no index correction. My height of eye is 3.1 meters (10 feet). Air temp is 8°C and pressure is 1035 mb. I'll spare you an almanac lookup and specify that the HP of the Moon at this time is 60.4'. What are the steps to get the Ho using only simple calculator equations?"

I think I'll write up all the corrections in minutes of arc for variety from the N.A. directions. Dip is easy to calculate:
  dip = 0.97 × √(height of eye in feet) m.o.a., or dip = 1.76 × √(height of eye in meters) m.o.a.

For refraction, the N.A. gives a variant of a popular formula that has some issues. I prefer to stick with the short, pure equation that's valid for altitudes above 15°:
  R₀ = 0.97 / tan(H) m.o.a., where H is altitude in degrees (above 15°).
That's easy, and in fact R₀ = 1 / tan(H) will give quite adequate results. Next is the factor for unusual weather. On a calculator, this is also very easy! We tend to skip over it because it formerly required learning a slightly exotic table, but there's nothing to it on a calculator. The factor, ƒ, multiplies the baseline refraction. For temp, T, in °C and pressure, P, in mb:
  ƒ = 0.28 P / (T + 273).
In the example as given, this factor is only slightly off-standard. It's a factor of 1.03. Given that the baseline refraction, R₀, is 2.9' in the case in question, bumping that up by 3% is negligible. But now we know!

Next up is the Moon's parallax in altitude correction which is
  PA = HP × cos(H).
The altitude so far (up to this point in the clearing process) is 18°51' or 18.85°. The HP (from almanac data, as given above) is 60.4. So the parallax in altitude is 57.2'. Taking out parallax elevates the Moon, reminding us that the PA should always be added to the Moon's altitude. And finally we need to subtract the Moon's SD which is just 0.2724×60.4' or 16.5' (the SD of the Moon is always 27.24% of the Moon's HP at any moment of UT). So the last two corrections combine as +57.2-16.5 or +40.7' which I can now round to 41'. So finally I get
  Ho = 19°32'.
Of course that agrees with your calculation to the 'minute of arc' precision we were working under. Phew! :)

There are little tricks that some navigators may like in this process. Maybe the most obvious is to combine the SD and the PA into one step since they both multiply the HP... But that's all there is to it. It really just isn't all that complicated. The mystery of the Moon, for altitudes anyway, is not so bad after all, right?

Frank Reed