HP Prime and TI-84 Plus
CE: EDM Slope Reduction
Introduction
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)
L
= H * (radius / (radius + D))
E
= (S * cos Z / cos C) + M – F
HP Prime
Program EDMSLOPE
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;
TI-84 Plus CE Program EDMSLOPE
"2017-07-26
EWS"
"IN
FEET"
20902231→R
Degree
Input
"ZENITH ANGLE: ",Z
Input
"SLOPE DIST (FT): ",S
Input
"INSTRUMENT (FT): ",M
Input
"ELEVATION (FT): ",D
Input
"REFLECTOR (FT): ",F
sin^-1((90*sin(Z)*S)/(π*R))→C
(S*sin(Z-C))/cos(C)→H
H*R/(R+D)→L
S*cos(Z)/cos(C)+M-F→E
Disp
"CURVATURE CORR.",C
Disp
"HORIZ-ELEVATION",H
Pause
Disp
"HORIZ-SEA LEVEL",L
Disp
"ELEVATION CHANGE",E
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
Eddie
This
blog is property of Edward Shore, 2017
