Leica Geosystems TPS1100 Professional Series - User Manual - Manual (Page 155)

155
TPS1100 - User Manual 2.2.1en Technical specifications
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In the distance-measuring program
"Averaging", the following values are
displayed:
D
= slope distance as arithmetic
mean of all measurements
s = standard deviation of a single
measurement
n = number of measurements
These values are calculated as
follows:
Reduction formulae
= displayed slope distance [m]
D
0
= uncorrected distance [m]
ppm = scale correction [mm/km]
mm = prism constant [mm]
The instrument calculates slope
distance, horizontal distance and
height difference in accordance with
the following formula. Earth curvature
and mean refraction coefficient
(k = 0.13) are taken into account
automatically. The calculated hori-
zontal distance relates to the station
height, not to the reflector height.
∑ = sum
D
i
= single measurement
The standard deviation S
D
of the
arithmetic mean of the distance can
be calculated as follows:
= Y - A · X · Y
= X + B · Y 2
s =
∑ n
i = 1
(D
i
- D)²
n - 1
=
∑ n
i = 1
D
i
² -
n - 1
( ∑ D
i
)²
n
S
D
=
s
n
= horizontal distance [m]
= height difference [m]
Y = · |sin ζ |
X = · cos ζ
ζ = vertical-circle reading
A =
1 - k / 2
R
= 1.47 · 10 -7 [m -1 ]
k = 0.13
R = 6.37 · 10 6 m
B =
1 - k
2R
= 6.83 · 10 -8 [m -1 ]
Instrument
Reflector
Mean sea level
Height measurement
ζ
1100Z36
= D
0
· (1 + ppm · 10 -6 ) + mm
D =
1
n
· ∑ n
i = 1
D
i