Description
Check a supplied rise against a semicircular span relation.
Architectural curves, stairs and roof planes can be described by ideal radii, angles, linear slopes and reference heights. Arc length differs from chord length, and a plan diagonal differs from a sloping member’s length. These local geometry terms do not evaluate structural capacity or building requirements.
Check a supplied rise against a semicircular span relation.
When to use this tool
Use Vault Semicircular Rise Span Check when checking the stated ideal curve, tread, slope or reference-plane term.
How to use the tool and how it works
- Enter span, rise, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read expectedRise, residual, semicircular. Inspect semicircular before interpreting the associated values.
Check a supplied rise against a semicircular span relation. Require span > 0, rise/tolerance >= 0; expectedRise = span/2, residual = rise-expected, semicircular tests abs(residual) <= tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| span | Span | Required. Finite number; strictly above 0. |
| rise | Rise | Required. Finite number; minimum 0. |
| tolerance | Caller-supplied comparison tolerance; it is not automatically a measurement uncertainty. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expectedRise | Expected Rise | Required. Finite number. |
| residual | Signed observed/calculated-minus-reference difference under the operation specified above. | Required. Finite number. |
| semicircular | Semicircular | Required. Boolean. |
{
"input": {
"span": 6,
"rise": 2.8,
"tolerance": 0.1
},
"output": {
"expectedRise": 3,
"residual": -0.20000000000000018,
"semicircular": false
}
}Limitations and assumptions
- This is one numerical geometric condition, not structural analysis or proof that an actual vault is semicircular.
- 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 a complete spatial design, verified dimensions and qualified professional review for structural, accessibility and construction decisions.
References
Similar or alternative tools
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