BIZOMAT MAKEOS · Mechanics
Three-Leg Sling Load Share (3D Leg Geometry, Tensions, Angles)
For a three-leg sling to lift points that are not symmetric, how is the load shared between the legs, how long is each leg, and is any leg overloaded or too steep?
Check of a three-leg bridle with the hook directly above the load’s centre of gravity and the lift points at any positions: leg lengths and angles from vertical from the point coordinates (as the cylindrical and spherical coordinates tool), and the tension in each leg by solving the three equilibrium equations of the hook (as the simultaneous equations tool), checked for slack legs, the leg working load limit and the largest angle from vertical.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load (with rigging below the hook) | kN | Weight of the load and everything below the hook. |
| Lift points from the hook (z negative below) | ||
| Point 1 x | mm | Horizontal x position of lift point 1 from the hook, which sits directly above the centre of gravity. |
| Point 1 y | mm | Horizontal y position of lift point 1. |
| Point 1 z | mm | Vertical position of lift point 1 (negative: below the hook). |
| Point 2 x | mm | x of lift point 2. |
| Point 2 y | mm | y of lift point 2. |
| Point 2 z | mm | z of lift point 2. |
| Point 3 x | mm | x of lift point 3. |
| Point 3 y | mm | y of lift point 3. |
| Point 3 z | mm | z of lift point 3. |
| Limits | ||
| Working load limit of each leg | kN | Working load limit of each leg at the angle used. |
| Largest leg angle from vertical | ° | Steepest leg angle from vertical your rigging rules allow. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load (with rigging below the hook)
- What it is
- The total weight hanging from the hook, expressed as a force: the load itself plus shackles, spreaders and any other rigging below the hook.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every leg tension scales in direct proportion to the load; the leg angles do not change.
- Get it right
- Enter a force in kN, not a mass in kg: multiply a mass in tonnes by 9.81 to get kN.
Lift points from the hook (z negative below)
What this means: Point 1 x
- What it is
- The horizontal distance of lift point 1 along the x axis, measured from the vertical line through the hook, which sits directly above the load’s centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Put the origin directly below the hook at the centre of gravity; positions measured from a corner of the load give wrong tensions.
What this means: Point 1 y
- What it is
- The horizontal distance of lift point 1 along the y axis, at right angles to x, measured from the vertical line through the hook and centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep one sign convention for all three points: positive y on one side of the centre of gravity, negative on the other.
What this means: Point 1 z
- What it is
- The vertical distance from the hook down to lift point 1, typed as a negative number because the lift point is below the hook.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to -1 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type it as a negative number measured from the hook down to the lift point; a positive value would put the point above the hook and is rejected.
What this means: Point 2 x
- What it is
- The horizontal distance of lift point 2 along the x axis, measured from the vertical line through the hook, which sits directly above the load’s centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same origin and axes as for point 1; mixing references between points gives wrong tensions.
What this means: Point 2 y
- What it is
- The horizontal distance of lift point 2 along the y axis, at right angles to x, measured from the vertical line through the hook and centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep one sign convention for all three points: positive y on one side of the centre of gravity, negative on the other.
What this means: Point 2 z
- What it is
- The vertical distance from the hook down to lift point 2, typed as a negative number because the lift point is below the hook.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to -1 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type it as a negative number measured from the hook down to the lift point; a positive value would put the point above the hook and is rejected.
What this means: Point 3 x
- What it is
- The horizontal distance of lift point 3 along the x axis, measured from the vertical line through the hook, which sits directly above the load’s centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same origin and axes as for points 1 and 2; mixing references between points gives wrong tensions.
What this means: Point 3 y
- What it is
- The horizontal distance of lift point 3 along the y axis, at right angles to x, measured from the vertical line through the hook and centre of gravity.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If the centre of gravity falls outside the triangle of the three lift points, one leg goes slack and the tool reports it.
What this means: Point 3 z
- What it is
- The vertical distance from the hook down to lift point 3, typed as a negative number because the lift point is below the hook.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to -1 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type it as a negative number measured from the hook down to the lift point; a positive value would put the point above the hook and is rejected.
Limits
What this means: Working load limit of each leg
- What it is
- The rated working load limit of one sling leg, from the sling tag or test certificate; the tension calculated in each leg is compared with it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the single-leg rating, not the multi-leg assembly rating on the tag, which already assumes equal sharing at a set angle.
What this means: Largest leg angle from vertical
- What it is
- The largest angle between any leg and the vertical that your rigging procedure or sling rating allows; the leg with the largest angle is checked against it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from vertical, not from horizontal: an angle of 60° from vertical is 30° from horizontal.
Method and formulas
- Leg length = distance from the hook to each lift point; angle from vertical from the spherical coordinates of the point (as the cylindrical and spherical coordinates tool).
- Hook equilibrium: Σ Tᵢ uᵢ = (0, 0, −W) with uᵢ the unit vector along each leg, solved as three simultaneous equations (as the simultaneous equations tool).
- A negative tension means that leg goes slack: the centre of gravity lies outside the triangle of lift points.
- Example: the legs carry 12.806, 12.667 and 12.667 kN at 38.66°, 37.864° and 37.864° from vertical.
Limitations
- Hook directly over the centre of gravity and rigid legs of the lengths given; stretch and hook shift redistribute load.
- Three legs only: a four-leg bridle is statically indeterminate and is usually rated on two legs.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan a lift with three uneven lift points
- Check which leg of a bridle carries most
- Find leg lengths for a level lift
Who it is for
- Riggers
- Lifting supervisors
- Lifting engineers
What you get
- Leg lengths and angles from vertical
- Tension in each leg
- Checks for slack, overload and angle
Interpreting the result
- The leg nearest the centre of gravity and the steepest legs carry most: shorten or re-position to even them out.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 43–45, 122–127, 153–163. Topic reference; no source tables or recommended settings are reproduced.
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Open the Three-Leg Sling Load Share (3D Leg Geometry, Tensions, Angles) calculator