**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

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