The isoazimuth is the locus of the points on the Earth's surface whose initial orthodromic course with respect to a fixed point is constant. That is, if the initial orthodromic course Z from the starting point S to the fixed point X is 80 degrees, the associated isoazimuth is formed by all points whose initial orthodromic course with respect to point X is 80° (with respect to true north). The isoazimuth is written using the notation isoz(X, Z) . The isoazimuth is of use when navigating with respect to an object of known location, such as a radio beacon. A straight line called the azimuth line of position is drawn on a map, and on most common map projections this is a close enough approximation to the isoazimuth. On the Littrow projection, the correspondence is exact. This line is then crossed with an astronomical observation called a Sumner line, and the result gives an estimate of the navigator's position.
Isoazimutal on the spherical Earth Let X be a fixed point on the Earth of coordinates latitude: B 2 {\displaystyle B_{2}} , and longitude: L 2 {\displaystyle L_{2}} . In a terrestrial spherical model, the equation of isoazimuth curve with initial course C passing through point S(B, L) is:
tan ( B 2 ) cos ( B ) = sin ( B ) cos ( L 2 − L ) + sin ( L 2 − L ) / tan ( C ) {\displaystyle \tan(B_{2})\cos(B)=\sin(B)\cos(L_{2}-L)+\sin(L_{2}-L)/\tan(C)\;}
Isoazimutal of a star In this case the X point is the illuminating pole of the observed star, and the angle Z is its azimuth. The equation of the isoazimuthal curve for a star with coordinates (Dec, GHA), - Declination and Greenwich hour angle -, observed under an azimuth Z is given by:
cot ( Z ) / cos ( B ) = tan ( D e c ) / sin ( L H A ) − tan ( B ) / tan ( L H A ) {\displaystyle \cot(Z)/\cos(B)=\tan(Dec)/\sin(LHA)-\tan(B)/\tan(LHA)\;}
where LHA is the local hour angle, and all points with latitude B and longitude L, they define the curve.
See also Great circle Rhumb line Cartography Navigational algorithms
References
External links Navigational Algorithms http://sites.google.com/site/navigationalalgorithms/ Institut français de navigation https://web.archive.org/web/20140103212146/http://www.ifnavigation.org/ Le segment capable sphérique. Navigation Nº.116 Vol.XXIX, Institut français de navigation, octubre/1981. (in French)