Friction (Koepe) Hoist Traction and Slip Limit
Whether the ropes of a friction hoist will slip on the drive wheel.
Example
You enter
- Loaded-side conveyance weight, empty (lb) 20000
- Payload (lb) 30000
- Opposite side: empty conveyance or counterweight (lb) 20000
- Head ropes, all together (lb per ft) 24
- Tail (balance) ropes, all together (lb per ft, 0 if none) 24
- Hoisting depth (ft) 3000
- Rope-to-liner friction coefficient (about 0.25) 0.25
- Wrap angle on the wheel (degrees, 180 typical) 180
- Acceleration or braking rate (ft/s², 0 to skip) 3
You get
- Slip limit ratio 2.1933
- Static ratio 1.3261
- Dynamic ratio 1.5988
- Max acceleration ft s2 7.928
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeThe tension ratio between the two sides cannot exceed e^(mu theta), 2.19 at a friction coefficient of 0.25 and a half wrap. A 30,000 lb payload on balanced 20,000 lb conveyances at 3,000 ft with matching tail ropes stands at a ratio of 1.33, rises to 1.60 at 3 ft/s2, and slips at 7.9 ft/s2; without tail ropes it slips standing still. Checks both ends of the wind. First principles; the hoist regulations govern.
Formula or tableSlip limit T1/T2 = e^(mu theta), theta in radians. Loaded conveyance at the bottom: T_loaded = conveyance + payload + head rope x depth, T_other = opposite side + tail rope x depth; at the top the head and tail ropes swap sides. Static ratio = larger/smaller at the worse position; dynamic ratio = T_hi (1 + a/g) / (T_lo (1 - a/g)), g = 32.174 ft/s2; slip acceleration a/g = (limit x T_lo - T_hi)/(limit x T_lo + T_hi).
Source and editionThe capstan (Euler-Eytelwein) belt-friction relation applied to a friction hoist's rope tensions by statics, cited by name; a first-principles screen.
Free accessTextbook mechanics; the friction coefficient, weights and rates are the user's inputs. No regulatory traction limit is asserted.
What governsEstimate. AHJ and licensed professional govern.
API field namesloaded_conveyance_lb, payload_lb, opposite_side_lb, head_rope_lb_ft, tail_rope_lb_ft, depth_ft, friction_coefficient, wrap_deg, acceleration_ft_s2, slip_limit_ratio, static_ratio, dynamic_ratio, max_acceleration_ft_s2
- Friction coefficient entered; about 0.25 is commonly used for tread liners, lower for wet or greased ropesthe hoist manufacturer
- Rope weights all head ropes together and all tail ropes together, in lb per ft, over the full hoisting depthscope of this tile
- Dynamic case the heavy side accelerating upward, or being braked on the way down, at the entered rateNewton's second law