Description
For positive catenaryParameter a and nonnegative horizontalSpan x, return a × (cosh(x/a) - 1) and a × sinh(x/a).
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.
For positive catenaryParameter a and nonnegative horizontalSpan x, return a × (cosh(x/a) - 1) and a × sinh(x/a).
When to use this tool
Use Mooring Catenary Endpoint Horizontal Projection when you need a geometric line or scope term with explicit assumptions.
How to use the tool and how it works
- Enter catenaryParameter, horizontalSpan. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read heightAboveLowest, arcLength. Use the output convention below.
For positive catenaryParameter a and nonnegative horizontalSpan x, return a × (cosh(x/a) - 1) and a × sinh(x/a).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| catenaryParameter | Catenary Parameter | Required. Finite number; strictly above 0. |
| horizontalSpan | Horizontal Span | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| heightAboveLowest | Height Above Lowest | Required. Finite number. |
| arcLength | Arc Length | Required. Finite number. |
{
"input": {
"catenaryParameter": 10,
"horizontalSpan": 5
},
"output": {
"heightAboveLowest": 1.276259652063807,
"arcLength": 5.210953054937474
}
}Limitations and assumptions
- These coordinates are measured from the ideal catenary's lowest point; the parameter is supplied and seabed contact, elasticity, and load limits are omitted.
- 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.
- Chain Scope Depth Angle Term
Divide chainLength by positive depth for scope and return asin(depth / chainLength) in radians.