Reduction Formulas - Leica MS50 User Manual

7.14
Measurements
Reflector types
Formulas
MS50/TS50/TM50, Technical Data

Reduction Formulas

b
a
TS_110
The reduction formulas are valid for measurements to all reflector types:
• measurements to prisms, to reflector tape and reflectorless measurements.
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) 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.
c
a) Mean Sea Level
b) Instrument
c) Reflector
Displayed slope distance [m]
-6
) + mm
D Uncorrected distance [m]
0
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
B (1 - k)/2R = 6.83 * 10
k 0.13 (mean refraction coefficient)
R 6.378 * 10
Slope distance
Horizontal distance
Height difference
-7 -1
[m ]
-8 -1
[m ]
6
m (radius of the earth)
97