Description
Reduce ground distance to grid distance using a supplied projection scale and representative elevation factor.
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.
Reduce ground distance to grid distance using a supplied projection scale and representative elevation factor.
When to use this tool
Use this tool when you need to reduce ground distance to grid distance using a supplied projection scale and representative elevation factor.
How to use the tool and how it works
- Enter groundDistanceMeters, ellipsoidalHeightMeters, curvatureRadiusMeters, projectionPointScale using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.elevationFactor, result.combinedFactor, result.gridDistanceMeters, using the stated boundary, ordering, sign and absence conventions.
Calculate elevationFactor=R/(R+h), combinedFactor=elevationFactor×projectionPointScale, and gridDistance=groundDistance×combinedFactor.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| groundDistanceMeters | Nonnegative representative ground distance in meters, at most 10⁶. | Finite numeric value satisfying the stated comparisons. |
| ellipsoidalHeightMeters | Signed height above the reference ellipsoid in meters; the operation-specific height bounds apply. | Finite numeric value satisfying the stated comparisons. |
| curvatureRadiusMeters | Representative Earth curvature radius in meters, 10⁶–10⁷. | Finite numeric value satisfying the stated comparisons. |
| projectionPointScale | Positive dimensionless projection scale at the representative point, at most two. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.elevationFactor | Dimensionless R/(R+h) ground-to-ellipsoid factor. |
| result.combinedFactor | Elevation factor times projection point scale. |
| result.gridDistanceMeters | Ground distance multiplied by combined factor, in meters. |
{
"input": {
"groundDistanceMeters": 1000,
"ellipsoidalHeightMeters": 100,
"curvatureRadiusMeters": 1000000,
"projectionPointScale": 1
},
"output": {
"result": {
"elevationFactor": 0.9999000099990001,
"combinedFactor": 0.9999000099990001,
"gridDistanceMeters": 999.9000099990001
}
}
}Limitations and assumptions
- Ground distance is 0–10⁶ m, height within ±10⁵ m, R 10⁶–10⁷ m and projection scale in (0,2]. This representative single-factor reduction does not identify a State Plane zone or account for scale variation along the line.
- 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
Similar or alternative tools
- UTM Point Scale Factor k0 Gamma Series Calculator
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- Ellipsoidal Height h from H plus N Calculator
Convert orthometric height to ellipsoidal height using a supplied compatible geoid undulation.