Description
Return the leading cubic arc-minus-chord error term.
Spherical geometry distinguishes central angle, surface arc and straight chord. They coincide only in a small-angle limit, and a sphere-radius sensitivity differs from a geodesic calculation on an ellipsoid.
Return the leading cubic arc-minus-chord error term.
When to use this tool
Use Geodesic Chord Small Angle Error Term when checking a stated spherical arc, chord or radius relationship.
How to use the tool and how it works
- Enter angle, radius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cubicErrorTerm. Use the output convention below.
Return the leading cubic arc-minus-chord error term. Require radius >= 0 and abs(angle) <= 0.1 radians; cubicErrorTerm = radius*abs(angle)³/24.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angle | Central angle in radians, with absolute value at most 0.1. | Required. Finite number. |
| radius | Radius | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cubicErrorTerm | Leading asymptotic arc-minus-chord term, in length units; not a rigorous bound. | Required. Finite number. |
{
"input": {
"angle": 0,
"radius": 2
},
"output": {
"cubicErrorTerm": 0
}
}Limitations and assumptions
- This is an asymptotic term, not the exact difference or a rigorous error bound.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use endpoint coordinates and an appropriate spherical or ellipsoidal geodesic model for real geographic distance.
References
Similar or alternative tools
- Angular Chord Relative Error From Angle
Return the relative arc-to-chord shortfall.
- Geodesic Radius Relative Distance Scale
Rescale a spherical arc distance for a new radius at fixed central angle.