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:
- 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.
- 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.