Why a four-leg sling is rated on three legs

Because the standard does not let you assume four legs are sharing. On a rigid load with fixed-length legs, three of them find the load first and the fourth is a passenger until one of the three yields, so EN 13414 and EN 1492 give a four-leg sling the same mode factor as a three-leg one. That is the rule, and it is visible as a number rather than a principle. It is also only one of three reasons that dividing the load by the number of legs gives you an answer that is too small — the angle does more damage than the count, and the third one, the sideways squeeze, is the one nobody calculates at all. SLING does all three in the browser.

The mode factors, which say it plainly

Three legs and four legs carry the same two numbers. That is the whole of it: a four-leg assembly is permitted to lift no more than a three-leg one of the same size. You are not being given a fourth leg's worth of capacity, and if you have bought a four-leg sling expecting twice a two-leg sling, the arithmetic above is where that expectation ends.

You will read elsewhere that this is because three points define a plane and a three-leg sling is therefore mathematically superior. That is a true statement about geometry and it is not the reason. The reason is that four fixed legs on a rigid load cannot be shown to share, once you allow for the tolerance in their lengths and the stiffness of what you are lifting, so a standard that has to be safe for every case assumes they do not.

The angle does more damage than the count

A leg at an angle carries the load divided by the cosine of that angle. That sounds mild and it is not. The same two-tonne load on the same two-leg sling, measured at five angles:

At sixty degrees a two-leg sling has stopped sharing anything. Each leg is carrying the entire load. Sixty degrees is the limit in the standard, and this is precisely why it is the limit — not because something dramatic happens at sixty-one, but because by then the second leg has bought you nothing.

Put the same two tonnes on four legs and the worst leg carries 1,333 kg at sixty degrees, against the 500 kg that dividing by four would have told you. At thirty degrees it is 770 kg. In every case the honest number is larger than the obvious one, and never by a comfortable margin.

The number nobody calculates

Every degree of angle turns part of the lift into horizontal force, pulling the tops of the load inwards. It is the same trigonometry, it takes no extra information, and it appears on no sling chart.

In the table above, at sixty degrees the two legs are squeezing that load inwards with 1,732 kg from each side — eighty-seven per cent of the load's own weight, applied horizontally to something that was designed to be stood on, not squashed. That is what folds a crate, buckles a fabricated frame, pops the cladding off a machine and bends a door out of true on the way to the lorry. The lift succeeds. The thing you lifted arrives damaged, and nobody connects the two, because the sling did not fail and nothing dropped.

Spreader beams exist for this reason and are usually explained as a way of keeping the angle down. They are, and keeping the angle down is a way of keeping this number down.

An off-centre load is worse than either

Legs share by moments, not by goodwill. If the centre of gravity is not in the middle, the near leg takes more, and a load twice as far from one leg as the other puts two-thirds of itself on the near one.

The same two tonnes, two legs, sixty degrees, with the centre of gravity half a metre off centre: the worst leg carries 2,833 kg. Dividing the load by two legs said 1,000 kg. The real figure is 1,833 kg higher, and the squeeze has gone to 2,454 kg — a hundred and twenty-three per cent of the load's own weight.

Off-centre is not an unusual case. A motor at one end of a skid, a transformer in a cabinet, a pump on a baseplate: most things are heavier at one end than the other, and the lift is planned as though they are not.

What to do with the numbers

1. Work to the worst leg, not the average. The average leg tension is a number with no safety meaning. What matters is the one carrying the most.
2. Measure the angle, or measure the geometry. Hook height above the eyes and the distance between attachment points give the angle exactly; estimating it by eye reliably underestimates it, because a sling looks steeper from below than it is.
3. Check the load, not only the sling. If the squeeze figure is a meaningful fraction of what you are lifting, it is a question for whoever knows the load's structure, and the honest answer may be a spreader beam.
4. Find the centre of gravity before the lift, not during it. A load that swings level on the first inch was planned properly. One that does not has told you your leg tensions are wrong, at the worst possible moment to learn it.

What this is and is not

SLING is arithmetic against published figures: the mode factors and the sixty-degree limit come from EN 13414 and EN 1492, and everything else is trigonometry you could do on paper if you had the time and never do. It runs in the browser and nothing is uploaded, which for a lift plan attached to a job on somebody else's site is worth knowing.

It is not a lift plan, it does not know the condition of your sling, it has not seen its certificate, and it cannot tell you whether the attachment points will hold. Those belong to a competent person, and the arithmetic is there to inform that person rather than to replace them.

Alongside: BALANCE finds the centre of gravity of a made-up load, PALLET works out what fits and what it weighs, and TORQUE does the equivalent honesty for a bolted joint — the range of tension one torque setting really produces, which is wider than anybody expects.