Load and crane
Centre of gravity of a composite load (plan, 2D)
- where
- total mass (kg)
- mass of each item (kg)
- combined centre of gravity from the datum (m)
- position of each item’s centre from the datum (m)
Explain this equation
Finds where the combined centre of gravity of a load made of several parts lies in plan. Use it to position the hook, choose leg lengths and see which legs will carry more.
m₁ to m₄ are the masses of the parts, and x and y are the positions of each part's own centre, measured from a datum corner. M is the total mass, and X_g and Y_g are the coordinates of the combined centre of gravity.
Each part turns the load about the datum with a moment equal to its mass times its distance. The combined centre of gravity is the single point where the total mass would give the same moment. That is why it is the mass-weighted average position.
Sense check: a 1000 kg part at 0 and a 1000 kg part at 2 m balance at 1 m. A heavy item near one end pulls the centre of gravity towards it.
Watch out: liquids and loose contents move during the lift. The hook must end up directly above the centre of gravity or the load will tilt until it is.
Locates the combined centre of gravity of a load made of up to four parts, measured from any datum corner, so the hook can be placed over it.
Enter your values to see the result.
Good to know
Pick a datum (usually one corner of the load in plan) and measure the centre of each part from it in x and y. A uniform part’s centre is at its middle. Masses can be in any consistent unit. The hook must be directly above the combined CoG or the load will tilt until it is, and the legs will share the load unequally. For height (whether the load is top-heavy), repeat with vertical positions.
Common mistake
Assuming the CoG is in the middle of the frame or crate. Engines, tanks and unevenly packed loads are often well off-centre; ask for the CoG from the supplier and mark it on the load.
Limits
Point masses in plan; contents that can move (liquids, loose items) shift the CoG during the lift. For planning only: this does not replace a lift plan prepared by a competent person under LOLER 1998 (reg. 8) and BS 7121, and the manufacturer’s WLL markings, load charts and data always govern over this result.
Sources
- BS 7121-1:2016 Code of practice for safe use of cranes. General (lift planning, appointed person, multiple-crane lifts, ground conditions, wind)
- The Lifting Operations and Lifting Equipment Regulations 1998 (SI 1998/2307), reg. 8: every lifting operation properly planned by a competent person, appropriately supervised and carried out safely
- HSE L113 Safe use of lifting equipment. Lifting Operations and Lifting Equipment Regulations 1998. Approved Code of Practice and guidance
Results are calculations from the published methods and figures shown, and depend on the data you enter. For planning and checking only. Scaffolds must be erected to NASC TG20 or a bespoke design by competent persons, and lifting operations planned under LOLER by a competent person. Never rely on these results instead of a design, a lift plan or manufacturer ratings.