Topcon GTS-230 Series, Instruction Manual, Page: 126 / 163

13-1
13 CORRECTION FOR REFRACTION AND EARTH CURVATURE
13 CORRECTION FOR REFRACTION AND EARTH
CURVATURE
The instrument measures distance, taking into account correction for refraction and earth curvature.
13.1 Distance Calculation Formula
Distance Calculation Formula; with correction for refraction and earth curvature taken into account.
Follow the Formula below for converting horizontal and vertical distances.
Horizontal distance D = AC(
α
) or BE(
β
)
Vertical distance Z =BC(
α
) or EA(
β
)
D = L{cos
α
–(2
θ
–
γ
) sin
α
}
Z = L{sin
α
+(
θ
–
γ
) cos
α
}
θ
= L.cos
α
/2R........... Earth curvature
correcting item
γ
=K
•
Lcos
α
/2R....... Atmospheric
refraction
correcting item
K =0.14 or 0.2.......... Coefficient of
refraction
R =6372km.............. Radius of earth
α
( or
β
)................... Altitude angle
L .............................. Slope distance
●
The conversion formula for horizontal and vertical distances is as follows when correction for
refraction and earth curvature is not applied.
D=L
•
cos
α
Z=L
•
sin
α
Note: The coefficient of the instrument has been set at 0.14 before shipment (K=0.14).
if the "K" value is to be changed, refer to 16 “SELECTING MODE”.
Radius of earth
R
6372Km