Isoazimuth

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.^[1]

That is, if the initial orthodromic course θ 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°. The isoazimuth is written using the notation (X, θ).

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.

From a star

In this case the X point is the illuminating pole of the observed star, and the angle θ 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:

$cotan(Z)/cos(B) = tan(Dec)/sin(lha)-tan(B)/tan(lha)\;$

where lha is the local hour angle, and all points with latitude B and longitude L, they define the curve.

See also

• Rhumbline network
• Geography
• Mapping
• Navigational Algorithms

References

1. Flexner, W. W.. 1943. “Azimuth Line of Position”. The American Mathematical Monthly 50 (8). Mathematical Association of America: 475–84. doi:10.2307/2304185. Accessed 2016-01-24.

External links

• Navigational Algorithms http://sites.google.com/site/navigationalalgorithms/
• Institut français de navigation http://www.ifnavigation.org/