Leica TS11 User Manual page 207

Formulas
TS11/TS15, Technical Data
The instrument calculates the slope distance, horizontal distance, height difference
in accordance with the following formulas:
= D 0 · ( 1 + ppm · 10
TS_111
= Y - A · X · Y
TS_112
2
= X + B · Y
TS_113
Earth curvature (1/R) and mean refraction coefficient (k) (if enabled on the Refrac-
tion page in Main Menu: Config...\Instrument Settings...\TPS Corrections) are auto-
matically taken into account when calculating the horizontal distance and height
difference. The calculated horizontal distance relates to the station height and not
to the reflector height.
Displayed slope distance [m]
-6
) + mm
D Uncorrected distance [m]
0
ppm Atmospheric scale correction [mm/km]
mm Additive constant of the reflector [mm]
Horizontal distance [m]
Height difference [m]
Y * |sinζ|
X * cosζ
ζ
Vertical circle reading
A (1 - k/2)/R = 1.47 * 10-7 [m-1]
B (1 - k)/2R = 6.83 * 10-8 [m-1]
k 0.13 (mean refraction coefficient)
R 6.378 * 106 m (radius of the earth)
207