Bessel Helmert Tab

In the Bessel-Helmert Tab you can calculate distances and directions on the ellipsoid.

Geodesics and Azimuths

Ellipsoidal geometry is used. In this geometry "straight lines" are the geodetic lines/geodesics, i.e. the shortest line from one point to another on the ellipsoid. Thus, 'angle' refers to angles between crossing geodesics and 'direction' to the directions of geodesics (see below).

From each point  on the ellipsoid (except the north pole), the geodesic to the north pole is used as reference for other geodesics passing through that point: The direction of a geodesic in a point is called an azimuth and is measured as the angle between the reference direction (towards north) and the geodesic.

When two points (Stn1 and Stn2) on the ellipsoid are connected by a geodesic, the azimuths of the geodesic connecting the points are called the "Forward" and the "Backward" azimuth respectively. The forward azimuth is measured in Stn1 as the azimuth towards Stn2. The backward azimuth is the azimuth of the geodesic from Stn 2 towards Stn1.
Calculation Mode
For a setup of two points connected by a geodesic, you can use this widget to calculate unknown elements from given elements.
The Bessel Helmert calculation has two modes, each corresponding to the calculation type:
  1. Based on coordinates for two points, calculate the ellipsoidal distance (the length of the geodesic) between the points and calculate the forward and backward azimuths.
  2. From distance and forward azimuth from one coordinated point, calculate the coordinates of the other point.
Buttons in the lower left corner are used to toggle the mode selection.

Coordinate systems

In both modes, you must select the input system for the coordinates of the two stations - ellipsoid parameters are taken from this system. The geometric calculations (distance and azimuth) will be performed on the corresponding ellipsoid.
It is also possible to define a custom ellipsoid by specifying semi-major axis and inverse flattening. The coordinate system will always be geographic in this case.