TS12P, Technical Data
71
7.10
Reduction Formulas
Measurements
Reflector types
The reduction formulas are valid for measurements to all reflector types:
• measurements to prisms, to reflector tape and reflectorless measurements.
Formulas
The instrument calculates the slope distance, horizontal distance, height difference in
accordance with the following formulas:
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.
a) Mean Sea Level
b) Instrument
c) Reflector
Slope distance
Horizontal distance
Height difference
c
a
b
TS_110
Displayed slope distance [m]
D
0
Uncorrected distance [m]
ppmAtmospheric scale correction [mm/km]
mm Additive constant of the reflector [mm]
Horizontal distance [m]
Height difference [m]
Y
* |sin
|
X
* cos
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 * 10
6
m (radius of the earth)
TS_111
= D0 · ( 1 + ppm · 10
-6
) + mm
TS_112
= Y - A · X · Y
TS_113
= X + B · Y
2
