A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Ducruy Jacques
Date: 2015 Aug 3, 03:22 -0700
Hello, Frank and Paul,
You'll find under an example or Borda's method for the calculation of latitude ; I use here the simplified Borda'method of Ducom.
I suppose the true lat is 40° N, declination 10°N.
First altitude : 40.1705° for true HA : 45°
second altitude : 57.1739° for true HA : 15°
ellapsed time : 2 hours or 30°
1) I suppose DR lat : 41° : I can calculate a HA with the first alt, the Dec and the DR lat => HA : 44.3875 ° ; I compute also the azimuth (with sinus formula) : 64.3609°, then the coef Cotz Z/Cos L : 0.636
2) HA of the second alt = 44.3875 - 30 = 14.3878, then the azimuth (26.8340°) and the corresponding coef Cotg Z/Cos L = 2.620
3) I compute then the latitude corresponding to Alt=57.1739, D=10 and HA : 14.3875 :
cos b = cos HA/Tang D = 79.6831
cos B = (Sin Alt cos b) / sin Decl
calculated Lat = 90 - (b - B) = 40.2435° => difference with DR Lat = 0.7565°
4) correction of latitude : (0.7565 * 2.620) / (2.620 - 0.636) = 0.9990°
=> true lat : 41° - 0.9990° = 40.0010° => OK
I suppose here that the ship do not move between the two altitudes.
I Think the method of Borda is more precise that Douwes or Dunn method (except if the 2 altitudes are the same, taken before and after noon), and the methode is better il the first altitude is taken near of prime vertical and the second near of meridian.