Product Manual

8.10 Reduction Formulas
c
a
b
TS_110
a Mean Sea Level
b Instrument
c Reflector
Slope distance
Horizontal distance
Height difference
The instrument calculates the slope distance, horizontal distance, height difference in accordance
with the following formulas:
002425_002
= D
0
· ( 1 + ppm · 10
-6
) + AC
Displayed slope distance [m]
D
0
Uncorrected distance [m]
ppm Atmospheric scale correction [mm/km]
AC Additive constant of the reflector [m]
TS_112
= Y - A · X ·
Y
TS_113
= X + B · Y
2
Horizontal distance [m]
Height difference [m]
Y * |sinz|
X * cosz
z
Vertical circle reading
A
(1 - k / 2) / R = 1.47 * 10
-7
[m
-1
]
B
(1 - k) / (2 * R) = 6.83 * 10
-8
[m
-1
]
k 0.13 (mean refraction coefficient)
R
6.378 * 10
6
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 difference. The calculated horizontal distance
relates to the station height and not to the reflector height.
The reduction formulas are valid for measurements to all reflector types:
Formulas
Reflector types
64 Technical Data