How to Find Leg Tension from Sling Length and Height

Why this matters

A two-leg bridle does not split a load in half. Each leg carries its half of the weight plus a sideways pull, and the flatter the legs run, the bigger that sideways share gets. A crew that picks a 2,000 lb rooftop unit on two slings rated for 1,000 lb each, reasoning that each sling only holds half, has put every sling past its rating before the load leaves the curb.

The correction factor is a single division you can do on the tailgate with a tape and nothing else: leg length over vertical height. This card walks through measuring both, applying the factor, and what changes when the load is off center or hangs on more than two legs. Why angle eats capacity is owned by Why Sling Angle Costs More Capacity Than Anyone Expects; this card is the arithmetic you do before the pick.

Every measurement here is taken with the load on the ground and the slings slack or laid out. Nobody measures, adjusts or stands under a suspended load, and nobody puts a hand between a sling and the load as it takes tension. Lifts made with a crane in construction fall under 29 CFR 1926 Subpart CC, which has its own rigger and signal-person qualification rules; in general industry, sling use is 29 CFR 1910.184, and in construction the rigging equipment rules are at 29 CFR 1926.251.

The bridle and the two measurements

                 HOOK
                  *
                 /|\
                / | \
     leg L=10ft/  |  \leg L=10ft
              /   |H  \
             /    |8ft \
            /     |     \
   PICK A  *------+------*  PICK B
           |<-6ft->|<-6ft->|
           spread 12 ft between picks

  factor = L / H = 10 / 8 = 1.25
  angle from horizontal: sin = H / L = 0.8, 53.1 deg

• L, leg length: from the bearing point in the hook to the bearing point at the pick, along the sling. Include any shackle or hook in the leg, because hardware adds length.
• H, vertical height: from the hook's bearing point straight down to the level of the pick points.

The factor L / H is the same number as 1 / sin of the sling angle measured from horizontal, which is why tension tables printed by angle give the same answer. Using lengths means you never need a protractor.

Step 1: Get the load weight from a document, not a guess

Use the nameplate, the shipping weight on the bill of lading, the manufacturer's submittal, or a scale ticket. Add anything that comes up with it: a curb adapter strapped to the unit, a spreader bar, the slings and shackles if they are heavy relative to the load.

Why first: every later number scales with this one. A load that weighs 20 percent more than the guess makes every leg 20 percent heavier than the figure you checked against the sling tag.

What breaks if you skip it: a package unit with refrigerant, an economizer and a factory heat kit can weigh well over its base model's catalog figure. The nameplate or the shipping weight carries the configured number.

Example: the rooftop unit's shipping label reads 1,940 lb, the curb adapter shipped bolted to it adds 60 lb. Load W = 2,000 lb.

Step 2: Measure leg length and spread on the ground

Lay the slings out from the planned hook position to each pick point, or measure the sling and its hardware with a tape. Then measure the spread between pick points straight across.

You usually cannot measure H directly without the load hanging, and you should not try. Compute it from the right triangle: H = square root of (L squared minus half-spread squared).

Example: each leg is a 10 ft sling with its shackle, L = 10 ft. The lifting lugs are 12 ft apart, so half-spread is 6 ft. H = square root of (10 x 10 - 6 x 6) = square root of (100 - 36) = square root of 64 = 8 ft.

What breaks if you skip it: measuring H with a tape while the load is hanging puts a body under it, which is the one thing every rigging rule forbids.

Step 3: Divide for the factor

Factor = L / H, both in the same unit. Feet over feet cancel, leaving a plain number.

Example: 10 ft / 8 ft = 1.25.

Sanity check: the factor is always 1.0 or more. Exactly 1.0 means vertical legs, which only happens with a single vertical sling or a spreader bar. 2.0 means the legs sit at 30 degrees from horizontal. If you get a number under 1, you divided the wrong way.

Step 4: Share the load across the legs that actually carry it, then multiply

Leg tension = (W / number of carrying legs) x factor.

Example: (2,000 lb / 2) x 1.25 = 1,000 lb x 1.25 = 1,250 lb in each leg.

Check it from the other direction. The vertical part of each leg's pull has to hold up 1,000 lb. Tension times sin of the angle is that vertical part: 1,250 lb x 0.8 = 1,000 lb. The sideways part is 1,250 x 0.6 = 750 lb in each leg, pulling the lugs toward each other. Those two sideways pulls cancel against each other, which is why the load hangs still, but each lug and each sling still feels the full 1,250 lb.

On three or four legs, assume two carry it. A four-leg bridle on a rigid load is almost never shared evenly: leg lengths differ by a few inches, lugs sit at slightly different heights, and the load settles onto the two diagonal legs. The safe working assumption is that any two legs may carry the whole weight. For the same 2,000 lb load on four 10 ft legs at an 8 ft height, the even-share answer would be (2,000 / 4) x 1.25 = 625 lb a leg; size every leg for (2,000 / 2) x 1.25 = 1,250 lb.

Step 5: Compare against the sling's rated load for the hitch and the hardware

The sling's tag gives its rated capacity for each hitch type. Compare the leg tension from Step 4 against the vertical rating for that sling in the hitch it is actually in. A basket or choker hitch rates lower than vertical, and the tag says by how much.

Then check every piece in the leg: the shackle's working load limit, the lifting lug, the hook. The weakest piece sets the leg's capacity.

Example: the slings are tagged 1,600 lb vertical, the shackles are rated well above that. 1,250 lb is under 1,600 lb, with 1,600 - 1,250 = 350 lb in hand. The lugs on the unit are marked by the manufacturer for this lift.

What breaks if you skip it: a tag can be right for the sling and wrong for the shackle. A sling rated far above the load, hung on a shackle sized for a smaller sling, is only as strong as the shackle.

When the load is off center

The geometry above assumes the center of gravity sits midway between the pick points. When it does not, the hook moves over the center of gravity as the load comes up, and the leg nearer the center of gravity takes more of the weight.

Work it in two parts. First the vertical share, by lever: the near leg carries W x (distance from the far pick to the CG) / spread.

Take the same 2,000 lb load and 12 ft spread, but with the CG 4 ft from pick A and 8 ft from pick B. Vertical share on A = 2,000 x 8 / 12 = 1,333 lb. On B = 2,000 x 4 / 12 = 667 lb. Those add to 2,000 lb.

Then each leg's own factor. With the hook over the CG and rigged to an 8 ft height, leg A runs 4 ft out and 8 ft down: L = square root of (16 + 64) = 8.94 ft, factor 8.94 / 8 = 1.118. Leg B runs 8 ft out: L = square root of (64 + 64) = 11.31 ft, factor 11.31 / 8 = 1.414.

• Leg A tension = 1,333 x 1.118 = 1,490 lb.
• Leg B tension = 667 x 1.414 = 943 lb.

Check the sideways pulls balance: leg A pulls 1,333 x 4 / 8 = 667 lb sideways, leg B pulls 667 x 8 / 8 = 667 lb. They match, so the numbers close.

The near leg is now carrying 1,490 lb against the 1,250 lb the centered calculation gave, about 19 percent more, still under the 1,600 lb tag in this case. A crew that rigged off the centered number and then found the unit's compressor end dipping would be relying on a margin they never calculated. The manufacturer's rigging diagram usually marks the CG; where it does not, the unit's weight distribution sheet or a test lift of an inch or two, with everyone clear, shows which end is heavy.

What would change the answer

• Shorter slings on the same lugs. With 8 ft legs and the same 12 ft spread, H = square root of (64 - 36) = square root of 28 = 5.29 ft, factor = 8 / 5.29 = 1.51, and each leg of a centered 2,000 lb load sees 1,000 x 1.51 = 1,510 lb. Shortening the slings by 2 ft added 260 lb to every leg. Below a 30 degree angle from horizontal (factor 2.0), ASME B30.9 in substance says the angle should not be used unless a qualified person or the sling manufacturer recommends it; check the edition your employer or the site works to.
• A spreader bar. Vertical legs from a spreader take the factor to 1.0, so each leg of the 2,000 lb load carries 1,000 lb, and the bar takes the sideways compression instead. The bar's own rating then becomes the check.
• Lugs at different heights. If pick A sits lower than pick B, the two legs have different heights and different factors even when their slings are the same length. Measure each leg's own L and H.

How to know you got it right

Write the four numbers on the lift plan or the job ticket before the pick: W, L, H, and the leg tension, with the sling tag rating beside it. Recompute the tension from the angle as a check: if the factor is 1.25, sin of the angle is 0.8, and tension times 0.8 should give back the vertical share. If the two ways disagree, a measurement is wrong.

The usual slip is dividing H by L and getting 0.8, then multiplying the half-load by it, which produces 800 lb a leg and a sling choice that is 450 lb light. A factor under 1 is the tell.

References

• 29 CFR 1910.184, Slings (general industry); 29 CFR 1926.251, Rigging equipment for material handling (construction)
• 29 CFR 1926 Subpart CC, Cranes and Derricks in Construction (rigger and signal-person qualification)
• ASME B30.9, Slings, in the edition your employer or site specifies
• See related: Why Sling Angle Costs More Capacity Than Anyone Expects
• See related: Write the Calculation Down: The Field Math Habit