Description
Estimate trigonometric height difference with instrument/target heights and a curvature/refraction term.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Estimate trigonometric height difference with instrument/target heights and a curvature/refraction term.
When to use this tool
Use this tool when you need to estimate trigonometric height difference with instrument/target heights and a curvature/refraction term.
How to use the tool and how it works
- Enter slantDistanceMeters, elevationDegrees, instrumentHeightMeters, targetHeightMeters, earthRadiusMeters, refractionCoefficient using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.horizontalDistanceMeters, result.heightDifferenceMeters, result.curvatureRefractionMeters, using the stated boundary, ordering, sign and absence conventions.
Resolve horizontal distance d=slantDistance×cos(elevation). Add slantDistance×sin(elevation), instrument height minus target height, and (1−k)d²/(2R) to obtain height difference; report the curvature/refraction term separately.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| slantDistanceMeters | Observed nonnegative slope distance in meters, at most 100,000. | Finite numeric value satisfying the stated comparisons. |
| elevationDegrees | Signed ray elevation from the horizontal in degrees, with magnitude at most 89.9999°. | Finite numeric value satisfying the stated comparisons. |
| instrumentHeightMeters | Signed instrument height above its station reference in meters, within ±100. | Finite numeric value satisfying the stated comparisons. |
| targetHeightMeters | Signed target height above its station reference in meters, within ±100. | Finite numeric value satisfying the stated comparisons. |
| earthRadiusMeters | Explicit spherical reference radius in meters, 10⁶–10⁷. | Finite numeric value satisfying the stated comparisons. |
| refractionCoefficient | Dimensionless coefficient k from zero up to but excluding one. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.horizontalDistanceMeters | Horizontal projection of the slant distance, in meters. |
| result.heightDifferenceMeters | Signed station height difference including instrument/target and curvature/refraction terms, in meters. |
| result.curvatureRefractionMeters | Positive modeled (1−k)d²/(2R) heighting term in meters. |
{
"input": {
"slantDistanceMeters": 1000,
"elevationDegrees": 0,
"instrumentHeightMeters": 1,
"targetHeightMeters": 1,
"earthRadiusMeters": 1000000,
"refractionCoefficient": 0
},
"output": {
"result": {
"horizontalDistanceMeters": 1000,
"heightDifferenceMeters": 0.5,
"curvatureRefractionMeters": 0.5
}
}
}Limitations and assumptions
- Slant distance is 0–100,000 m, R 10⁶–10⁷ m, k in [0,1), and instrument/target heights within ±100 m. Elevation excludes the poles under the tool’s angular guard. Atmospheric variation and observation uncertainty are not modeled.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
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