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A standard Brunton compass, used commonly by geologists and surveyors to obtain a bearing in the field. In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
The calculation is essentially the conversion of the equatorial polar coordinates of Mecca (i.e. its longitude and latitude) to its polar coordinates (i.e. its qibla and distance) relative to a system whose reference meridian is the great circle through the given location and the Earth's poles and whose polar axis is the line through the ...
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
As is shown in Figure 1, the rangekeeper defines the "y axis" as the LOS and the "x axis" as a perpendicular to the LOS with the origin of the two axes centered on the target. An important aspect of the choice of coordinate system is understanding the signs of the various rates. The rate of bearing change is positive in the clockwise direction.
To calculate the azimuth of the Sun or a star given its declination and hour angle at a specific location, modify the formula for a spherical Earth. Replace φ 2 with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east).
Many automated Aids to Navigation, such as a VORTAC, use the Rho-Theta data as the primary method to calculate relative position of an aircraft to the reference beacon(s). Rho-Theta methodology is a key component in Area Navigation (RNAV). [1] The term "Rho-Theta" consists of the two Greek letters corresponding to Rho and Theta: [2] [3] [4]
Traverse tables use three values for each of the crooked course segments – the Distance (Dist.), Difference of Latitude (D.Lat., movement along N–S axis) and the Departure (Dep., movement along E–W axis), the latter two calculated by the formulas: Difference of latitude = distance × cos θ Departure = distance × sin θ
In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3,60°). In blue, the point (4,210°). By measuring bearings and distances, local polar coordinates are recorded. The orientation of this local polar coordinate system is defined by the 0° horizontal circle of the total station (polar