Introduction
Recently I was in Costa Rica for a holiday and I brought my sextant along for practice. I managed to get two sights in, one of the sun (Ref.1) and one of the moon (Ref.2). Due to weather/location circumstances as I explained, they were not that accurate, but the purpose was to go through and compare the various sight reduction methods and compare the various fixes obtained (Ref.3). I looked at 4 methods:
Intersecting Google Earth Great Circle Radials ( Zenith Distances)
Nautical Almanac NAO Method (Marcq St.Hilaire)
AP3270 Method (Marcq St.Hilaire)
Navigational Algorithms
In this post I will look at another method using a cellphone application iMariner. I will also give an exact geometric two altitude solution.
Scicoslab Two Altitude Solution
Figure 1 shows the 3 spherical triangles formed by the B_northpole, A_sunGP, C_moonGP and the D_fix. We know the Zenith Distances AD(pi/2-ho1) & CD(pi/2-ho2), and BA(pi/2-latA) & BC (pi/2-latC). Angle ABC is del(longA-longC). We solve triangle BAC for AC. For triangle CAD we have 3 sides so we solve for all the angles. Finally we solve BCD. Figure 2 shows the ScicosLab script file.
iMariner
The iMariner iphone application opens in the Ephemeris menu as shown in Figure 3. The various menu options are shown on the bottom. Before entering a sight, go to the More/Settings menu and enter Eye Elevation (m), Body (sun or moon in this case), Horizon, Limb and Index Error (‘). After this create a Passage in which to save the sightings. The next step is to enter the various sights taken (adjusting the settings as required before), add them to the passage just created, then chose a pair to calculate a fix.
Figure 4 shows the Sept 13th Sun Sight (Ref.1) and the Sept 15th Moon Sight (Ref.2) entries. Note the different AP_long for each sight as per the NAO method for an integer Lat & LHA.
Once the sight data is entered for a particular sight, select the Reduce menu item on the top to reduce the sight, and then save to the passage previously created.
Figure 7 shows the Costa Rica passage with the saved Sun & Moon sights. In order to generated a Fix, selected two sights from the passage. Then hit Position to get the Lat/Long of the fix. Figure 8 shows the Fix parameters of two LOPs with Azimuths & Intercepts.
| Method | NAO | iMariner |
| Sun: Heye = 2m IndxErr = +5′ Centre Limb | Sun: Hs = 41deg 58.5′ Ho = 42deg 0.1′ Lat = 3deg 32.9’N Long = 133deg 47.8’W | Sun: Hs = 41deg 58.5′ Ho=41deg 59.7′ Lat =3deg 33’N Long = 133deg 48’W |
| Sun: Az Hc Ho Intercept) | Sun: 265deg 54′ 42deg 57′ 42deg 0.1′ -56.9Nmi’ | Sun: 265deg 30′ 42deg 55.8′ 41deg 59.7′ -56.1Nmi |
| Moon: Heye = 2m IndxErr = +5′ Upper Limb | Moon: Hs = 55deg 51′ Ho = 56min 9.2′ Lat = 20deg 8′ Long = 119deg 34.8’n | Moon: Hs = 55deg 51′ Ho=56min 8.9′ Lat = 20deg 8’N Long = 119deg 34.8’W |
| Moon: Az Hc Ho Intercept) | Moon: 291.3deg 56deg 39′ 56deg 9.2min -29.8′ | Moon: 291.6deg 56deg 38.6′ 56deg 8.9′ -29.7′ |
| Fix Lat: | 10deg 24.3′ | 10deg 52.2′ |
| Fix Long: | 85deg 53′ | 85deg 55.0′ |
Figure 9 shows a comparison of NAO and iMariner. The sight reductions are identical to within a fraction of a minute, the Fix longitudes are very close, but the Fix latitudes are off a bit. This may be because iMariner is expecting the same AP for each sighting. Figure 10/11 shows the various Fixes on Google Earth.
Update
Checking with iMariner, they pointed out two fields that I had not noticed in the Fix menu. That is “Course & Distance”. This allows you to advance your first LOP in case the second sight was taken later and you moved. In my case, both sights were taken at the same location. So in this case, to get a better fix, you set Course=Distance=0, and ensure both sights have the same EP. I adjusted my Moon sight to have the same EP as the Sun sight, checking that the sextant settings were the same. Using this sight for the fix yielded a result identical to the NAO.
Please send your comments, questions and suggestions to:
contact:
References
#1. – “CelNav en Tamarindo Costa Rica – Ho1/Az1 Posicion Estimada
https://jeremyclark.ca/wp/nav/celnav-en-tamarindo-costa-rica-ho_az-posicion-estimada/
#2. – “CelNav en Tamarindo Costa Rica – Ho2/Az2”
https://jeremyclark.ca/wp/nav/celnav-en-tamarindo-costa-rica-ho2_az2/
#3. – “CelNav en Tamarindo Costa Rica – Ho1&2_Fix”
https://jeremyclark.ca/wp/nav/celnav-en-tamarindo-costa-rica-ho12_fix/
#4. – “Nautical Alamanca 2022”
https://www.amazon.ca/dp/1951116461
#5. – “Navigational Algorithms”
https://sites.google.com/site/navigationalalgorithms/Home
#6. – “HO249/AP3270”
https://www.thenauticalalmanac.com/Pub.%20No.%20249.html
