NavList:

Dear Lance,

Reply to your queries here.

From your data, 02AUG2022   S42°49.4' E147°15.7'  Moon LL, sea horizon, T = 12.5°C P = 1007 hPa, HoE = 2.9 m

1 - Own reverse engineering data for instrument error = 0.0' , I am getting (hopeflly no typos) :

(1.1) - 01:02:06 UTC Hs = 12°51.6' / Z = 070.6°  Hc = 13°54.1'           

(1.2) - 01:55:07 UTC Hs = 21°37.8' / Z = 060.7°  Hc = 22°39.4'

(1.3) - 04:12:17 UTC Hs = 39°16.7' / Z = 027.2°  Hc = 40°10.9'

(1.4) - 05:55:58 UTC Hs = 43°05.7' / Z = 353.5°  Hc = 43°57.9'

Overall own Hc accuracy is +/- 4" , i.e. +/- 0.75' due to using truncated ELP Series, which translates into maximum overall errors not exceeding 0.1' due to round-off errors when rounding to the closest 0.1' .

Hs values hereabove obtained through 3D reverse engineering Hc values onto the WGS84 Ellipsoid.

We are to remember that in the Real World, most often the Dip correction remains the factor with the greatest uncertainty.

2 - Preliminary discussion :

(2.1) - These first 3 Hc's hereabove exactly match FER's values to +/- 0.1'  Hence no reason to question your own Hc's values

(2.2) - Most probably a typo in your 4th Hc value. If no error in your 05:55:58 UTC value, you should rather get Hc = 43°57.4' (vs. your published 43°57.9')

(2.3) - With HoE = 2.90m, then Dip correction is extremely close from -3.0' . Hence your "Dip + Index" correction = -3.0' + (-1.0') = -4.0' ... you are OK here.

(2.4) - For UT's Mean value 05:30 UTC, Moon HP = 55.9' . This is the tabular value you are expected to use throughout.

3 - Solving Hs values here-above with US Nautical Almanac (for the Year 1983) for HP = 55.9' and comparing them with computer results:

(3.1) - LL Hs = 12°51.6'  Dip = -3.0'  ⇾ 12°48.6' ⇾ Corr. 1 = +62.7' , Corr. 2 = +2.7'  / Σ Corr. = +65.4' , Hc = 12°48.6' + 65.4' = 13°54.0'    (vs. 13°54.1' here-above)

(3.2) - LL Hs = 21°37.8'  Dip = -3.0'  ⇾ 21°34.8' ⇾ Corr. 1 = +61.8' , Corr. 2 = +2.8'  / Σ Corr. = +64.6' , Hc = 21°34.8' + 64.6' = 22°39.4'    (vs. 22°39.4' here-above)

(3.3) - LL Hs = 39°16.7'  Dip = -3.0'  ⇾​​​​​​​ 39°13.7' ⇾ Corr. 1 = +54.1' , Corr. 2 = +3.1'  / Σ Corr. = +57.2' , Hc = 39°13.7' + 57.2' = 40°10.9'     (vs. 40.10.9' here-above)

(3.4) - LL Hs = 43°05.7'  Dip = -3.0'  ⇾​​​​​​​ 43°02.7' ⇾ Corr. 1 = +51.8' , Corr. 2 = +3.2'  / Σ Corr. = +55.0' , Hc = 43°02.7' + 55.0' = 43°57.7'     (vs. 43°57.9' here-above)

4 - Lessons learnt :

(4.1) -  The best results achievable with our 2D Tabular Corrections (US Nautical Almanac or Éphémérides Nautiques which are slightly different) fall within 0.2' / 0.3' of the true 3D results.

Here a comparison of the (1.1, 1.2, 1.3, 1.4) results with the (3.1, 3.2, 3.3, and 3.4) results again confirms that.

 (4.2) - Performing the Moon Tabular correction requires extreme care, especially since you generally have no easy independent cross-checking of your tabular corrections.

Moon heights tabular correction errors are certainly rather frequent and this probably also explains why our Lady Moon has long been / is regarded as a bit "unreliable" by a number of Navigators.

As a personal example, I have archived over 250 Moon observations - from 1974 until 1987 - corrected through French or US tables then. Through carefully reprocessing them much later with a computer I have observed that for 1/3 of them my intercepts differed by 0.5 NM or more. Then very carefully reprocessing all Moon Observations through the same tables, I had to admit that about one third of the time, my earlier/initial use of these tables was not optimal as regards the best results which could be derived from them. I later discovered that - as just mentioned - these are 2D corrections tables which already have built-in limits reaching up to 0.3' of error.

Hope it helps,

Antoine M. "Kermit" Couëtte