Block-and-Tackle Reeving Line Pull

ScopeThe pull on the hauling (lead) line of a block-and-tackle or crane hoist reeved with N parts of line, and how much sheave friction costs. Frictionless, each part carries load/N; real sheaves lose a few percent each and the loss STACKS, so pull = load x (1 - k) / (1 - k^N) with k the per-sheave efficiency (~0.98 roller-bearing, 0.96 plain-bronze), and when the hauling line leaves the block over one more sheave (the usual case) that sheave costs another k: pull = load / (k + k^2 + ... + k^N). A 20,000 lb load on 4 parts at k 0.98 with the lead sheave needs about 5,258 lb (vs the frictionless 5,000), a reeving efficiency of load / (N x pull) = 95.1%. More parts multiply the advantage but stack more friction, so doubling the parts never quite halves the pull. This is the STEADY hauling pull on the lead line only, not the higher force to start the load moving. A rigging screen; the block/rope ratings, the actual sheave friction, the reeving pattern, and a qualified rigger and lift plan govern.

Formula or tablefrictionless_pull_lb = load_lb / parts_of_line; hauling_line_pull_lb = load_lb / (k + k^2 + ... + k^N) = load_lb x (1 - k) / (k (1 - k^N)) when the lead line leaves over a sheave (lead_sheave = 1, the default), or load_lb x (1 - k) / (1 - k^N) without one, with k = sheave_efficiency, N = parts_of_line (= load/N when k = 1, no lead sheave); reeving_efficiency = load_lb / (parts_of_line x hauling_line_pull_lb).

Source and editionBlock-and-tackle / hoist reeving efficiency (Wire Rope Users Manual / Crosby reeving practice; ASME B30 hoisting), by name; the block and rope ratings, the actual sheave friction, and a qualified rigger and the lift plan govern.

Free accessThe reeving-efficiency relation is public rigging mechanics; the per-sheave efficiency (~0.98 roller, 0.96 plain) is a standard published figure and the load and parts are the rig's values.

What governsEstimate. AHJ and licensed professional govern.

API field namesload_lb, parts_of_line, sheave_efficiency, lead_sheave, hauling_line_pull_lb, frictionless_pull_lb, reeving_efficiency

• Reeving pull pull = load / (k + k^2 + ... + k^N) with a lead sheave, load x (1 - k) / (1 - k^N) without; frictionless share = load/N; efficiency = load/(N x pull)block-and-tackle reeving mechanics
• Per-sheave efficiency k ~0.98 roller-bearing, ~0.96 plain-bronze sheaves; loss stacks part to part; steady pull on the lead line only (not inertia to start)Wire Rope Users Manual / Crosby / ASME B30