Block-and-Tackle Reeving Line Pull
The 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). A 20,000 lb load on 4 parts at k 0.98 needs 5,152 lb (vs the frictionless 5,000), a reeving efficiency of load / (N x pull) = 97.0%. 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 and source
frictionless_pull_lb = load_lb / parts_of_line; hauling_line_pull_lb = load_lb x (1 - k) / (1 - k^N) with k = sheave_efficiency, N = parts_of_line (= load/N when k = 1); reeving_efficiency = load_lb / (parts_of_line x hauling_line_pull_lb).
Block-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.
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