Slings and hitches
D/d ratio and wire rope efficiency over a pin (informational)
- where
- D/d ratio
- diameter of the pin, hook or load the rope bends round (mm)
- wire rope diameter (mm)
- rope efficiency at the bend (%)
Explain this equation
Shows how much strength a six-strand wire rope loses when it is bent round a pin, shackle or load of small diameter. It is for understanding why bend size matters, not for rating a sling.
D is the diameter of whatever the rope bends round and d is the rope diameter. r is their ratio. E is the share of the rope's straight breaking strength left at the bend.
When a rope bends, the outer wires stretch more than the inner ones and the strands crush together, so they don't share the load evenly. The tighter the bend, the worse this is. This empirical curve falls away with 1/√r.
Sense check: a rope over a pin five times its own diameter keeps about 78% of its strength. At 2:1 it keeps about 65%, and at 10:1 about 84%.
Watch out: sling makers' ratings already assume a minimum D/d. If the bend is tighter than they allow, use a bigger pin or bow, a thimble or packing.
Shows how much breaking strength a six-strand wire rope loses when bent round a pin, shackle or load of small diameter. For understanding only; the sling maker’s ratings govern.
Enter your values to see the result.
Good to know
The empirical curve E = 1 − 0.5/√(D/d) is the one used in US sling manuals for 6×19 and 6×37 rope under static load: about 65% at 2:1, 78% at 5:1, 84% at 10:1. Manufacturers’ basket and choke ratings already assume a minimum D/d (often around 5:1 for endless and grommet slings, higher for standard slings). Eyes over a hook or shackle pin are covered by the eye termination rating.
Common mistake
Bending a wire rope sling round a small pin or sharp corner and still using the full basket rating. Use a larger shackle bow, a thimble, or packing to increase D.
Limits
Static load; six-strand rope only; not for chain or textile slings, which have their own edge and bend rules. Not a rating method. 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
- Hercules Crane & Lifting Supplies, Mastering the D/d ratio (efficiency = 100 × (1 − 0.5/√(D/d)); 64.6% at 2:1, 77.6% at 5:1, 84.2% at 10:1)
- Unirope, D/d ratio and the effect on sling capacity (6-strand rope: about 25% loss at 5:1, 40% at 2:1)
- LEEA COPSULE Ed. 10, 15.5.2 Wire rope slings (BS EN 13414-1), method of use: choke hitch ×0.8, basket hitch with both ends on the hook 0–45° ×1.4, two single slings 0–45° ×1.4
- 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.