Load weight and centre of gravity: the two numbers every lift depends on

Every rigging calculation starts from two numbers: how much the load weighs and where its centre of gravity (CoG) is. Sling tensions, crane utilisation, ground pressure and hardware sizes all follow from them. If either is wrong, every number after it is wrong too, however carefully it is calculated.

1. Establishing the weight

Use the most reliable source available, in this order of preference:

1. Weighed: a certified weighbridge ticket, load-cell reading or crane load indicator reading from a previous lift.
2. Manufacturer’s data: the nameplate, shipping documents or certified weight on the general arrangement drawing.
3. Calculated: volume × density from the drawings, with an allowance for the parts you cannot see.
4. Estimated: never use an estimate alone for a planned lift. Confirm it by one of the methods above.

When the weight is calculated rather than weighed, add a contingency according to your company procedure. Many procedures use a few percent to around 10%, more for items with internals, residual fluids, insulation or fireproofing. Always add the weight of everything below the hook: slings, shackles, spreader beam, hook block and any attached load cell.

Typical densities

Worked examples: weight from dimensions

Steel plate 3.0 m × 1.5 m × 25 mm: volume = 3.0 × 1.5 × 0.025 = 0.1125 m³, so mass = 0.1125 × 7,850 ≈ 883 kg.

Steel pipe 610 mm outside diameter (24 in), 12.7 mm wall, 12 m long. The mass per metre of a tube is ρ × π × (D − t) × t:

7,850 × π × (0.610 − 0.0127) × 0.0127 ≈ 187 kg/m, so a 12 m joint weighs about 2,245 kg before coating, lining or contents.

2. Centre of gravity of an assembly

The CoG is the point where the whole weight can be treated as acting. For an assembly of parts, take moments about a convenient datum in each direction:

x̄ = Σ(Wᵢ × xᵢ) ÷ ΣWᵢ    ȳ = Σ(Wᵢ × yᵢ) ÷ ΣWᵢ    (and z̄ for height)

Example: a pump skid. Datum at one corner of the skid.

x̄ = 15.6 ÷ 9.0 = 1.73 m; ȳ = 7.5 ÷ 9.0 = 0.83 m. The CoG is well off the geometric centre of the 4.0 m × 1.8 m frame (2.0 m, 0.9 m), towards the heavy pump. Lifting from the frame centre would tilt the skid.

Do not forget the vertical position (z̄). A high CoG makes a load top-heavy, which matters when slings are short, when lifting from below the CoG, or when a load is turned over.

3. Finding the CoG by weighing

When drawings are unreliable, weigh the item at two support points a known distance apart. If the reactions are R₁ and R₂ and the supports are L apart, the CoG lies at a distance x = R₂ × L ÷ (R₁ + R₂) from support 1.

Example: load cells read 3.6 t and 5.4 t at supports 4.0 m apart. Weight = 9.0 t; CoG = 5.4 × 4.0 ÷ 9.0 = 2.4 m from the 3.6 t support. Repeat across the other axis, or with three or four load cells, to locate the CoG in plan.

4. When the hook is not above the CoG

A freely suspended load always rotates until its CoG is directly below the hook. If the hook is not set over the CoG, the load tilts as it leaves the ground and swings sideways towards the hook. On a tight site that sideways swing is often what causes contact with people or structure. Before every lift:

• Mark the CoG on the load or on the lift drawing.
• Position the hook over the CoG and keep the hoist line plumb at the moment of lift-off.
• Choose sling lengths so the load hangs level (Chapter 2), or use adjustable rigging such as chain blocks or adjustable spreader lugs.
• Lift a few centimetres, stop and check level and stability before continuing.

Treat a load whose weight or CoG is not verified as an unknown load. Under LOLER and BS 7121 the person planning the lift must be satisfied that both are known with enough confidence for the lift being made.

5. Weight control on projects

On a large project, weights change from the first estimate to the item that arrives on site. A weight control report tracks every heavy item through those stages so that the crane and rigging chosen early on are still adequate on the day. Each line of the report records the item, its weight, its CoG in three directions and, importantly, the status of the weight:

The figures above are examples of common practice, not a rule; use your company procedure. The contingency is reduced as the status improves, but it should never be dropped to zero on a calculated weight. Drawings miss welds, paint, galvanising (around 3–6% on light sections), loose items, sand in skids, trapped water and late design changes.

Two things are easily forgotten:

• Contents. Water left from a hydrotest, process residue, catalyst, lube oil in a gearbox or ballast in a tank. A 3 m³ sump of water adds 3 t.
• Additions after weighing. Insulation, fireproofing, ladders, platforms, piping spools and temporary steelwork for transport (sea fastening, saddles) may be fitted after the item was weighed at the factory.

6. Weights of common shapes

Most heavy items can be broken into a few simple shapes. Calculate each, add them, then take moments for the CoG (Section 2). Use the mean diameter for thin shells, which is accurate to well under 1% for normal wall thicknesses.

Worked example: a horizontal tank

A carbon steel tank has a cylindrical shell of 2.4 m outside diameter, 16 mm wall, 10 m long, closed by two hemispherical heads of the same thickness.

• Shell: 7,850 × π × (2.4 − 0.016) × 0.016 × 10 = 7,850 × 1.198 m³ ≈ 9,407 kg.
• Heads: the two hemispheres together make one spherical shell, mean radius r_m = (2.4 − 0.016) ÷ 2 = 1.192 m. Volume = 4π × 1.192² × 0.016 = 0.286 m³, so mass ≈ 2,243 kg.
• Total steel ≈ 11,650 kg. Add nozzles, saddles, lifting lugs and internals: with a 5% allowance the lift weight is about 12.2 t, plus the rigging.

Because the tank is symmetrical, the CoG is at mid-length on the axis. That changes as soon as anything is attached to one end, such as a manway with a davit, a platform or a heavy nozzle: take moments as for the skid.

7. Finding the CoG height by tilting

Weighing at two supports gives the CoG in plan, but not its height. The height can be found by repeating the weighing with the item tilted. Raise end B by a known angle θ while it stays on the load cells. If the CoG is a height z above the line joining the support points, raising B moves the CoG horizontally towards A, and the reading at B falls:

z = (R_B,level − R_B,tilted) × L ÷ (W × tan θ)   where L is the horizontal distance between the supports when level.

Example. The 9.0 t item from Section 3 (supports 4.0 m apart). Level, R_B = 5.40 t. With end B raised 5°, R_B = 5.05 t. Then z = (5.40 − 5.05) × 4.0 ÷ (9.0 × tan 5°) = 1.40 ÷ 0.787 = 1.78 m above the support line.

The method is sensitive to small reading errors. Here a change of only 0.35 t gives the whole answer, so an error of 0.05 t in either reading moves z by about 0.25 m. Use the largest tilt that is safe, accurate load cells, and repeat the reading. Make sure the item cannot slide on its supports and that loose or liquid contents are drained, because they move when the item tilts.

8. Single-point lifts, top-heavy loads and moving contents

When an item hangs from one lift point, it rotates until the CoG is directly below the hook. If the lug is a horizontal distance e from the CoG and a height h above it, the load hangs at a tilt of φ = tan⁻¹(e ÷ h). A lug 0.3 m off the CoG and 1.2 m above it gives tan⁻¹(0.25) = 14.0°. The closer the lug is to the CoG in height, the more a small offset tilts the load.

Lift points below the CoG. If a load is lifted from points below its CoG, it is in unstable balance: any small tilt moves the CoG outwards, and the load tries to turn over. This is common with tall, narrow items picked from base lugs. The rigging must then hold the load upright, for example a spreader with slings long enough that the hook is well above the CoG, or additional restraint slings. For a two-leg bridle from base lugs, the load is stable only if the CoG is below the point where the sling legs’ lines meet, which in practice is the hook. Check the geometry, do not assume it.

Liquids and loose contents. A partly filled tank or a box of loose parts has a CoG that moves when the item tilts, always in the direction that increases the tilt. Drain or secure contents before lifting; if that is impossible, treat the CoG as a range and check the rigging and crane for both ends of it.

9. Common mistakes

• Using the shipping weight, which may exclude items packed separately, or the dry weight of an item that still contains water from testing.
• Forgetting the rigging: a spreader, four slings, shackles and a load cell can add 1–3 t on a medium lift.
• Taking the CoG at the geometric centre of an asymmetric skid or module.
• Calculating the CoG in plan but ignoring its height, then lifting from lugs that are below it.
• Accepting a single load-cell reading without checking that the sum of the reactions matches the expected weight.
• Not updating the lift plan after late additions to the item.

10. Field checklist

• Weight source recorded (weighed, certified, calculated, estimated) and the contingency stated.
• Contents drained, or included in the weight and CoG.
• All rigging, the spreader and the hook block added to the load weight used for the crane.
• CoG marked on the lift drawing in plan and height, and on the item itself where practical.
• Hook position set over the marked CoG; trial lift a short distance to confirm level and stability.
• If the item tilts more than expected on trial lift, stop: land it, re-check weight and CoG, adjust the rigging.

11. Self-check questions

General guidance only. It does not replace the manufacturer's data, the applicable standards or the judgement of a competent person.

References

Technical references consulted for this chapter. The text and worked examples are original to LiftPlan Pro.

• J. Keith Anderson, Rigging Engineering Calculations (Industrial Training International).
• Rigging Handbook, 2nd edition (Bechtel Equipment Operations, 2002).
• LOLER 1998 (UK) and its Approved Code of Practice; BS 7121-1 general requirements for lifting operations.

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