Mine Hoist Rope Factor of Safety and Depth Limit

Because the rope hangs from the sheave, the whole of it is carried at the top where the factor of safety is checked. A four-rope hoist with 1,400 ft of 1.8 lb/ft rope carries 10,080 lb of rope -- every rope hangs the full length, so the count multiplies -- against a 4,200 lb cage and eight people at 180 lb. That is 15,720 lb suspended, and THE ROPE IS 64% OF IT. Four ropes breaking at 128,000 lb each give a factor of safety of 32.6. Leave the rope out and the same arithmetic reads 90.8, which looks far safer than the truth and is the error this exists to prevent. DEPTH, NOT PAYLOAD, IS WHAT CONSUMES THE MARGIN. Double the shaft to 2,800 ft and the rope weight doubles to 20,160 lb, the suspended load reaches 25,800, and the factor falls to 19.8 for the same cage and the same eight people. Nothing about the load the hoist was bought to carry has changed. THE SECOND HALF MATTERS MORE IN PRACTICE. A rope with an adequate factor of safety can still be due for retirement, because ropes are retired on CONDITION and on TIME rather than on calculated stress: broken wires per rope lay, loss of diameter, corrosion, distortion, and in many jurisdictions a maximum service life regardless of condition. A rope that passes this arithmetic and fails the broken-wire count comes out of service, and no factor of safety argument changes that. A static calculation. It does not model dynamic loads from acceleration, deceleration, emergency braking, or shock, all of which add substantially and which the statutory factors are partly there to cover; it does not evaluate friction hoist traction, which is a separate and governing check on a Koepe installation, or rope stretch, sheave and drum diameter-to-rope ratios and their effect on rope life, attachments and terminations, or the brake system. It does not perform the statutory rope inspection. Hoisting people is among the most heavily regulated activities in mining: MSHA, the applicable ASME and state hoisting requirements, the hoist and rope manufacturers, and the mine's hoisting plan govern.

rope weight = rope count x length x weight per foot; total suspended load = conveyance + payload + that rope weight; factor of safety = (count x breaking strength) / the total; the depth at which the factor reaches a minimum inverts the same relation.

The suspended-load factor of safety by name, with the statutory minimum entered because it varies by service and depth and is highest for personnel hoisting, and with the rope retirement criteria named as independent of it. MSHA, the applicable ASME and state hoisting requirements, and the mine's hoisting plan govern.

Division on the user's own conveyance, rope, and payload data against a minimum they supply; no statutory table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: conveyance_lb, people_count, person_weight_lb, rope_length_ft, rope_weight_per_ft, rope_count, rope_breaking_lb, minimum_fs, rope_weight_lb, payload_lb, total_load_lb, rope_share_pct, factor_of_safety, fs_without_rope, depth_at_limit_ft

• The rope count multiplies the rope weight every rope hangs the full length; dropping the count is dropping the ropestatics
• Depth consumes the margin, not payload the same cage and people at twice the depth is a materially lower factorhoisting practice
• Retirement is on condition and time a passing factor of safety does not extend a rope's life by one dayMSHA hoisting requirements