Description
Compute sqrt((lineLength - verticalSeparation) × (lineLength + verticalSeparation)) with nonnegative separation no greater than line length.
A straight line, a slack line, and an ideal catenary have different geometries. Geometric projection alone does not determine tension, holding capacity, or safe anchoring conditions.
Compute sqrt((lineLength - verticalSeparation) × (lineLength + verticalSeparation)) with nonnegative separation no greater than line length.
When to use this tool
Use Anchor Horizontal Scope Projection when you need a geometric line or scope term with explicit assumptions.
How to use the tool and how it works
- Enter lineLength, verticalSeparation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read horizontalReach. Use the output convention below.
Compute sqrt((lineLength - verticalSeparation) × (lineLength + verticalSeparation)) with nonnegative separation no greater than line length.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lineLength | Line Length | Required. Finite number; minimum 0. |
| verticalSeparation | Vertical Separation | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| horizontalReach | Horizontal Reach | Required. Finite number. |
{
"input": {
"lineLength": 50,
"verticalSeparation": 30
},
"output": {
"horizontalReach": 40
}
}Limitations and assumptions
- This is a straight-line horizontal projection, not a catenary or anchor safety model; zero length is accepted.
- 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 validated mooring or anchoring analysis that includes line properties, loading, seabed contact, and environmental conditions.
References
Similar or alternative tools
- Nautical: Anchor Rode Angle Geometric
Return the horizontal leg by the Pythagorean relation and asin(vertical / length) converted to degrees.
- Mooring Catenary Endpoint Horizontal Projection
For positive catenaryParameter a and nonnegative horizontalSpan x, return a × (cosh(x/a) - 1) and a × sinh(x/a).