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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Double altitude method
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.

Best Regards

Jacques

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