Elevator Traction Roping Ratio, Torque, and Rope Tension

The roping ratio is a mechanical advantage and it trades force for speed exactly as any block and tackle does. A 2 to 1 arrangement halves the tension each rope carries -- allowing smaller ropes or fewer of them -- and doubles the rope speed, so the machine turns twice as fast for the same car speed and can be a smaller, faster unit. That is why 2 to 1 dominates in geared and machine-room-less installations while 1 to 1 is common on high-speed gearless machines where rope speed would otherwise become excessive. A car running 500 fpm on 2 to 1 roping over a 30 in sheave puts 1,000 fpm through the ropes and turns the machine at 127 rpm; on 1 to 1 the same car speed turns it at 64 rpm, half the speed and twice the torque for the same power. THE ARITHMETIC ERROR WORTH PREVENTING is computing motor torque from the car load and the sheave radius without dividing by the ratio. A 2,000 lb unbalanced load on that 2 to 1 machine is 1,250 ft-lb at the sheave; skip the division and you get 2,500, double the truth, and a drive or brake diagnosed against that number looks undersized when it is correct. Rope tension goes the same way: five ropes on 2 to 1 each carry the suspended load divided by ten, against divided by five on 1 to 1, which is the reason 2 to 1 allows smaller ropes -- and the reason those ropes travel twice as far per trip and wear accordingly, and the sheave sees twice the rope passes, which is the fatigue driver in the grooves. Kinematics and statics only. It does not size a machine, motor, brake, or drive, evaluate traction, sheave groove pressure, or the bending fatigue that sheave diameter imposes on the ropes, or account for compensation, rope weight variation over the travel, or the inertia of the rotating masses, which matter for acceleration and brake sizing. The governor and safeties are arranged for the CAR's speed, not the rope speed, and the counterweight overbalance sets the unbalanced load this uses. Elevator equipment is life-safety: ASME A17.1, the equipment manufacturer's data, the elevator authority having jurisdiction, and a licensed elevator mechanic govern.

rope speed = ratio x car speed; sheave torque = (unbalanced load / ratio) x sheave radius; machine rpm = rope speed x 12 / (pi x sheave diameter); tension per rope = suspended load / (ratio x rope count); power = unbalanced load x car speed / 33,000.

The roping-ratio relations as standard elevator machine-room practice, by name, with ASME A17.1 and the equipment manufacturer's data named. Kinematics and statics only; the machine, brake, and drive are sized by the manufacturer, and traction is a separate required check.

Block-and-tackle kinematics on the user's own machine data; no manufacturer rating table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: roping_ratio, car_speed_fpm, sheave_diameter_in, unbalanced_load_lb, suspended_load_lb, rope_count, machine_rated_torque_ftlb, alternative_roping_ratio, rope_speed_fpm, sheave_rpm, sheave_torque_ftlb, tension_per_rope_lb, power_hp, alt_sheave_torque_ftlb

• 2 to 1 halves tension and doubles rope speed which is why it allows smaller ropes and why those ropes wear twice as fastelevator machine-room practice
• Torque must be divided by the ratio omitting it overstates a 2 to 1 machine's torque by a factor of twoelevator machine-room practice
• The governor sees car speed not rope speed, regardless of the suspension ropingASME A17.1