I (3-2.1)
i5o
The process however, can be instable if one uses a very large
stepsize, e.g. a step size of 10,000 km. Therefore the prodecure takes
a maximum step size of 500 km. The step size and the accuracy
of the results are other points to be questioned.
The procedure computes first the geodesic in n steps, with a step
size h of about 500 kmif the length of the line is less than 500 km
then n 1. After computing To, Ai and s, in an iteration process,
the procedure is repeated with 2n steps. If the difference between
the azimuth An, computed in n steps, and the azimuth Am com
puted in 2n steps, is less than 8, then the process stops. Otherwise
the process is repeated with qw steps until (3.2.1) is fulfilled.
s is the accuracy of 91.
A test has been built in for extreme requirements that cannot be
reached by the computer, e.g. to compute a geodesic of 10,000 km
with s 0.000001".
Mostly after one to three repetitions the required accuracy has
been reached. This procedure has been tested on several geodesies,
also in extreme places and directions.
The TR4 computes a geodesic of 100 km in about a second. A line
of 1000 km with an accuracy of 0.0001" in latitude can be computed
in about 10 seconds.
4. Other Computations on the Ellipsoid
4.1 Intersection by azimuths.
Given are the coordinates of the points Pi and P2 and the angles
ai and ot2 measured in Pi and P2. The problem is to compute the
coordinates of P3 on a given ellipsoid (figure 6).
First we compute the geodesic P1-P2 with the method described
in 3.1. Now we have in Pi and P2 the starting values of the geodesic
|Ao« Ao2»| 8
8 e. sin (s/a)
Figure 6.
