Table 1.

Calculation of the required measurement precisions for the cases of two profiles (in the beginning and at the end of rail).

Desired precision of coordinate differences
${\sigma }_{\Delta x}={\sigma }_{\Delta y}={\sigma }_{\Delta z}=1\text{mm}$
when measuring two points
	in the beginning of the rail		at the end of the rail
	Tleft	Tright	Tleft	Tright
horizontal direction	209°	359°	292°	315°
zenith distance	129°	115°	104°	103°
slope distance	7 m	13 m	53 m	55 m
required precision of measurements
σs	53.4″	14.6″	3.5″	3.4″
σz	62.5″	20.6″	3.4″	3.4″
σd	1.8 mm	1.3 mm	0.9 mm	0.9 mm