EDM Slope Reduction
07-28-2017, 10:18 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,146 Joined: Dec 2013
EDM Slope Reduction
The program EDMSLOPE calculates the following:

* curvature correction due to the Earth
* horizontal distance from observer to reflector at both elevation of the observer and at sea level
* change of in elevation from observer to reflector

Given:

* slope distance between observer to reflector
* height of both the observer and reflector’s instruments
* the elevation the observer
* zenith angle: angle from directly above to the slope distance line

Notes:

All measurements are given in feet. Assume that the correction factor due to light refraction is negligible. The radius of Earth is approximately 20,902,231 feet.

Formulas (see diagram above)

C = asin((90* sin Z * S)/(π * radius))

H = (S * sin(Z – C))/cos(Z)

E = (S * cos Z / cos C) + M – F

HP Prime Program EDMSLOPE

Code:
EXPORT EDMSLOPE() BEGIN // 2017-07-26 EWS // in feet // Radius of Earth: // based off 6371 km, to nearest // integer LOCAL R:=20902231; // Degrees HAngle:=1; LOCAL Z,S,M,D,F; INPUT({Z,S,M,D,F},"EDM Slope Reduction",{},{"Zenith Angle", "Slope Distance (ft)", "Instrument Height (ft)", "Elevation (ft)", "Reflector Height (ft)"}); // Curvature correction LOCAL C:=ASIN((90*SIN(Z)*S)/(π*R)); // Horizontal dist-elevation LOCAL H:=(S*SIN(Z-C))/COS(C); // Horizontal dist-Sea level LOCAL L:=H*R/(R+D); // Elevation change LOCAL E:=S*COS(Z)/COS(C)+M-F; PRINT(); PRINT("Curvature correction"); PRINT(C); PRINT("Horizontal dist-elevation"); PRINT(H); PRINT("Horizontal dist-Sea level"); PRINT(L); PRINT("Elevation change"); PRINT(E); END;

Example

Observer: D = 1,238.32 feet, instrument height = M = 3.5 feet
Slope distance: S = 1,474 feet, at a zenith angle of 86.11°
Reflector height = F = 3 feet

Results:
Curvature correction = C = 0.1154831691
Horizontal Distance-Elevation = H = 1,470.40255 ft
Horizontal Distance-Sea Level = L = 1,470.315444 ft
Elevation Change = E = 100.4980742 ft

Sources:

TI Programmable 58/59 Surveying – Texas Instruments 1977
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