Mooring Load

Solve horizontal two-line tension-only equilibrium for summed caller cage loads and fixed anchor bearings; distinct from windage drag, and catenaries, pretension, vertical load, waves and line strength are excluded.

Description

A planar two-line mooring balance resolves the force needed in each line to oppose supplied external loads.

A planar two-line mooring balance resolves the force needed in each line to oppose supplied external loads. A tensile line cannot supply a compressive force.^[1]

When to use Mooring Load

Use this tool to solve horizontal two-line tension-only equilibrium for summed caller cage loads and fixed anchor bearings; distinct from windage drag, and catenaries, pretension, vertical load, waves and line strength are excluded.

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.

How to use Mooring Load and understand its results

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.
Enter externalHorizontalForcesNewtons, anchorDirectionsDegrees using the field table and calculation rules, then run the tool.
Read resultantExternalForceNewtons, lineTensionsNewtons, equilibriumResidualMagnitudeNewtons. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
externalHorizontalForcesNewtons	External horizontal forces newtons	list of list of number	Required
anchorDirectionsDegrees	Anchor directions degrees	list of number	Required

Enter nonempty two-component force rows in newtons and exactly two line angles measured counterclockwise from positive X in degrees. The tool sums loads and solves the 2×2 equilibrium system. Near-parallel directions with determinant magnitude below 10⁻¹⁰ are rejected, as are materially negative tensions; tiny roundoff negatives are clipped to zero. Return tensions and residual magnitude.

[cos a₁ cos a₂; sin a₁ sin a₂] × tensions = −ΣexternalForces

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
resultantExternalForceNewtons	Resultant external force newtons	list of number
lineTensionsNewtons	Line tensions newtons	list of number
equilibriumResidualMagnitudeNewtons	Equilibrium residual magnitude newtons	number

json

{
  "input": {
    "externalHorizontalForcesNewtons": [
      [
        100,
        0
      ]
    ],
    "anchorDirectionsDegrees": [
      150,
      210
    ]
  },
  "output": {
    "resultantExternalForceNewtons": [
      100,
      0
    ],
    "lineTensionsNewtons": [
      57.73502691896259,
      57.73502691896256
    ],
    "equilibriumResidualMagnitudeNewtons": 3.552713678800501e-15
  }
}

Limitations and assumptions

The model is two dimensional and excludes pretension, catenary shape, vertical forces and dynamic amplification. It does not compare tensions with line or anchor capacity.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Cage Drag Force: Sum signed collinear water-current drag across independently calibrated cage panels; area/coefficient must use consistent net-solidity basis and shielding/deformation are external. For a complementary task, use Net Fouling Loss: Measure area-weighted net opening loss from panel porosity measurements; no hydraulic flow or drag change is inferred merely from loss of open area.

References

Mooring Load — tool.io

Similar or alternative tools

Cage Drag Force
Sum signed collinear water-current drag across independently calibrated cage panels; area/coefficient must use consistent net-solidity basis and shielding/deformation are external.
Net Fouling Loss
Measure area-weighted net opening loss from panel porosity measurements; no hydraulic flow or drag change is inferred merely from loss of open area.