Intercept method: Difference between revisions

Revision as of 17:54, 14 March 2013

Revision as of 05:48, 19 March 2014

Line 31:

: {{math|size=large|sin(Hc) {{=}} sin(lat) · sin(dec) + cos(lat) · cos(dec) · cos(LHA)}}

: <math>\mathrm{tan(ZZn) = \frac{sin(LHA)}{sin(lat) \cdot cos(LHA) - cos(lat) \cdot tan(dec)}}</math>

or, alternatively,

: <math>\mathrm{ cos(ZZn) = \frac{sin(dec) - sin(lat) \cdot sin(Hc)}{cos(lat) \cdot cos(Hc)}}</math>

Where

:''Hc'' = Computed altitude

:''Zn'' = Computed azimuth

:''lat'' = Latitude

:''dec'' = Declination

Line 48 ⟶ 49:

: <math>\mathrm{ haversin(\overline{Hc}) = haversin(LHA) \cdot cos(lat) \cdot cos(dec) + haversin(lat \pm dec) }</math>

Where {{overline|Hc}} is the zenith distance, or complement of Hc: {{overline|Hc}} = 90° - Hc.

{{overline|Hc}} = 90° - Hc.

The relevant formula for Z is

The relevant formula for ZZn is

: <math>\mathrm{ hav(Z) = \frac{ cos(lat - Hc) - sin(dec)}{2 \cdot cos(lat) \cdot cos(Hc)} }</math>

: <math>\mathrm{ hav(ZZn) = \frac{ cos(lat - Hc) - sin(dec)}{2 \cdot cos(lat) \cdot cos(Hc)} }</math>

When using such tables or a computer or scientific calculator, the navigation triangle is solved directly, so any assumed position can be used. Often the dead reckoning DR position is used. This simplifies plotting and also reduces any slight error caused by plotting a segment of a circle as a straight line.