Some quick and dirty PostGIS:
Get the longest line for your polygons
create table test.tatortlongestline as
select st_longestline(t.geom, t.geom) as geom, t.tatort
from indata.tatort as t
where lanskod = '01';
Get the orientation of those lines
create table test.tatortlongestangle as
select tl.geom, st_azimuth(st_startpoint(tl.geom), st_endpoint(tl.geom))
from test.tatortlongestline as tl;
A little bit shortened:
drop table if exists test.tatortlongestangle2;
create table test.tatortlongestangle2 as
select tl.*, st_azimuth(st_startpoint(tl.geom), st_endpoint(tl.geom)) as orientation
from (
select st_longestline(t.geom, t.geom) as geom, t.tatort
from indata.tatort as t
where lanskod = '01'
) as tl;