Crane Hook / Lifting Sling Angle Load Calculator mechanism

Model scope

The idealized tension equation is conditionally correct, but the instrument needs explicit validation and labeling before release. It should distinguish force from mass, define the angle convention, reject zero or near-zero angles, identify when geometry is not symmetric, and avoid presenting required sling rating as computable from tension alone.

• T=W/(n·sin(theta)) is the standard idealized result only for a centered, purely vertical load with n identical legs, equal angles measured from the horizontal, and equal load sharing.
• The supplied leg spread geometry is not used by the formula; arbitrary geometry, off-center load, unequal leg lengths, or unequal angles require vector equilibrium and may produce unequal tensions.
• The required sling rating cannot be determined from tension alone. It requires sling type, hitch configuration, material, diameter, working-load-limit tables, design or safety factor, connection details, and applicable code.
• The input named W must be a force, not a mass. If mass is supplied, gravitational acceleration and its units must be specified and applied before using the formula.
• The angle reference must be enforced as degrees from horizontal. An angle from vertical would require T=W/(n·cos(theta)) instead.

Units and conventions

• W is force in newtons (N) or another explicitly consistent force unit; it is not mass in kilograms.
• theta is an angle in degrees measured upward from the horizontal sling direction.
• n is a positive integer representing identical, symmetrically arranged sling legs with equal tension.
• sin(theta) is dimensionless, so tension has the same force units as W.
• For mass inputs, standard test conversion uses g=9.81 m/s^2, giving W=m·g.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "total_weight_W": 12000,
    "weight_unit": "N",
    "number_of_legs_n": 2,
    "sling_angle_theta": 30,
    "angle_unit": "degrees",
    "angle_reference": "horizontal",
    "leg_spread_geometry": "symmetric; equal angles; centered vertical load"
  },
  "expected_outputs": {
    "tension_per_leg": 12000,
    "tension_unit": "N",
    "required_sling_rating": "not determinable from this formula alone"
  },
  "working": "sin(30°)=0.5. n·sin(theta)=2·0.5=1. T=W/(n·sin(theta))=12000/1=12000 N per leg."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes hazards at the zero-angle denominator, requires rejection of negative or out-of-domain angles rather than trusting raw arithmetic, and has a substantial result ambiguity if the angle reference is not enforced as measured from horizontal.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json