Leica TS13 User Manual page 78

Formulas
Distance measuring
program Averaging
78
b
a
TS_110
The instrument calculates the slope distance, horizontal distance, height differ-
ence in accordance with the following formulas:
= D 0 · ( 1 + ppm · 10
002425_002
Displayed slope distance [m]
D Uncorrected distance [m]
0
ppm Atmospheric scale correction [mm/km]
AC Additive constant of the reflector [m]
= Y - A · X · Y
TS_112
2
= X + B · Y
TS_113
Horizontal distance [m]
Height difference [m]
Y * |sinz|
X * cosz
z
Vertical circle reading
A
(1 - k / 2) / R = 1.47 * 10
B
(1 - k) / (2 * R) = 6.83 * 10
k 0.13 (mean refraction coefficient)
R
6
6.378 * 10 m (radius of the earth)
Earth curvature (1/R) and mean refraction coefficient (k) are automatically
taken into account when calculating the horizontal distance and height differ-
ence. The calculated horizontal distance relates to the station height and not
to the reflector height.
In the distance measuring program Averaging, the following values are dis-
played:
D Slope distance as arithmetic mean of all measurements
s Standard deviation of a single measurement
n Number of measurements
c
a
b
c
-6
) + AC
-7 -1
[m ]
-8 -1
[m ]
Mean Sea Level
Instrument
Reflector
Slope distance
Horizontal distance
Height difference
Technical Data