Description
Check leveling closure against an explicitly caller-defined square-root-distance allowance.
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.
Check leveling closure against an explicitly caller-defined square-root-distance allowance.
When to use this tool
Use this tool when you need to check leveling closure against an explicitly caller-defined square-root-distance allowance.
How to use the tool and how it works
- Enter closureMm, distanceKm, coefficientMmPerSqrtKm, gradeDefinition using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.allowedMm, result.withinCallerTolerance, result.excessMm, result.gradeDefinition, using the stated boundary, ordering, sign and absence conventions.
Calculate allowedMm=coefficientMmPerSqrtKm×sqrt(distanceKm), compare abs(closureMm) inclusively, and report excess=max(0,abs(closure)−allowed). Echo the caller’s gradeDefinition.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| closureMm | Signed observed leveling-loop closure in millimeters, magnitude≤10⁶. | Finite numeric value satisfying the stated comparisons. |
| distanceKm | Positive separation/route length in kilometers, with the operation-specific bound stated above. | Finite numeric value satisfying the stated comparisons. |
| coefficientMmPerSqrtKm | Positive caller tolerance coefficient in mm per square root of km, at most 1000. | Finite numeric value satisfying the stated comparisons. |
| gradeDefinition | Nonblank caller-supplied name/definition of the tolerance convention; no official grade is inferred. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.allowedMm | Caller coefficient times square root of route kilometers, in millimeters. |
| result.withinCallerTolerance | Whether absolute leveling closure is ≤allowedMm. |
| result.excessMm | Nonnegative amount by which absolute closure exceeds the allowance, in millimeters. |
| result.gradeDefinition | Unmodified caller-supplied tolerance definition. |
{
"input": {
"closureMm": 3,
"distanceKm": 4,
"coefficientMmPerSqrtKm": 2,
"gradeDefinition": "illustrative caller criterion"
},
"output": {
"result": {
"allowedMm": 4,
"withinCallerTolerance": true,
"excessMm": 0,
"gradeDefinition": "illustrative caller criterion"
}
}
}Limitations and assumptions
- Distance lies in (0,10⁵] km, coefficient in (0,1000] mm/√km and closure within ±10⁶ mm; gradeDefinition must be nonblank. The grade is caller-defined, not a verified jurisdictional standard. The coefficient’s operative unit is mm/√km.
- 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
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