Hoist Rope Tension
Calculate the resultant force in an elevator's hoist rope, F = (Q + M_car − M_counterweight)·g, from the payload Q, the car mass and the counterweight mass (kg). The result, in newtons, is the unbalanced effort the steel ropes must transmit, already net of the counterweight's balancing effect. It is the basis for sizing the ropes (number, diameter and safety factor, typically ≥ 12 in elevator codes) and the traction sheave. When the load is such that car + load ≈ counterweight, the force tends to zero (balanced system). Enter the load, the car mass and the counterweight mass.
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Hoist rope tension
The steel ropes of a traction elevator do not carry the full weight of the car plus its load — the counterweight balances most of it, and the ropes run over a traction sheave linking the two sides. The resulting force the ropes transmit is the imbalance: F = (Q + M_car − M_counterweight)·g. When car plus load match the counterweight, the force tends to zero (balanced system, the ideal load condition). That load, together with the self-weight of the ropes and dynamic effects (acceleration), drives the rope sizing: how many ropes, their diameter and the safety factor (elevator codes demand very high factors, typically ≥ 12, given that human lives ride on them). It also governs the traction available at the sheave (the friction between rope and sheave groove, which must never slip — the traction principle) and the sizing of the brake. Enter the load, the car mass and the counterweight mass.
Related Tools
Counterweight Mass
Calculate an elevator's counterweight mass, M_cw = M_car + factor × Q_max, from the car mass, the balancing factor (typically 0.40 to 0.50) and the maximum load Q_max (kg). The result, in kg, is the mass that balances the car plus a fraction of the payload, so the motor works with the smallest average imbalance. A factor of 0.45 (45%) is common: it fully balances the car and 45% of the rated load, minimizing motor work both with a full and an empty car. Enter the car mass, the balancing factor and the maximum load.
Wire Rope Safety Factor
Calculate a wire rope's safety factor, SF = breaking load ÷ working load, from the minimum breaking load (MBL, N) and the applied working load (N). Wire ropes, used in cranes, elevators, cableways, bridges, lifting and mooring, work with HIGH safety factors — far higher than static structures — for several reasons: the load is rarely static (there are impacts, accelerations, swings), the rope wears and loses strength over use (wires break, corrosion and fatigue occur), and a rupture is catastrophic (load drop, life risk). Codes prescribe minimum safety factors per application: typically 5 for general load lifting, 6-8 for people-carrying ropes (elevators, cableways), 3-4 for static stays and moorings, and specific values per use. The safety factor is the ratio between the load that would break the rope (its rated strength, from the maker) and the load it actually carries in service. Checking that the real safety factor meets the code minimum is the basic safety check of any wire-rope application — and the rope must be DISCARDED when wear reduces its strength enough for the factor to fall below the limit. Enter the breaking load and the working load.
Wire Rope Working Load Limit (WLL)
Calculate a wire rope's allowable working load, WLL = MBL ÷ SF, from the minimum breaking load (MBL, N) and the required safety factor. The working load (WLL — Working Load Limit, or SWL — Safe Working Load) is the MAXIMUM load that can be safely applied to a rope, fitting or lifting equipment — the information STAMPED on slings, shackles, hooks and equipment plates, and what the operator uses to decide whether a given load can be lifted. It is obtained by dividing the breaking load (the real strength that would break the component) by the code safety factor (5 for general lifting, more for special situations). Respecting the WLL is an absolute safety rule in lifting and material-handling: exceeding the working load dangerously approaches the component to rupture, eliminating the safety margin covering dynamic effects, wear and uncertainties. The WLL is not the rope's strength — it is the SAFE fraction of it. Every rigging operation starts by checking that the load to lift is below the WLL of each component in the load line (rope, slings, shackles, hook, eye), since the chain is only as strong as its weakest link. Enter the breaking load and the safety factor.
Tensile Strength from Brinell Hardness
Estimate a carbon steel's tensile strength (Rm) from the Brinell hardness, Rm ≈ 3.45·HB, in MPa. There is a remarkably robust empirical correlation between hardness and strength in steels, which lets you estimate strength from a hardness test — fast, cheap and almost non-destructive — instead of a tensile test. Useful in inspection and quality control. Enter the Brinell hardness (HB).
Drawbar Pull
Calculate the available drawbar pull of a tractor, F = W × μ, multiplying the weight on the driving wheels W (kN) by the traction coefficient μ of the tire-soil pair. The result, in kN, is the pulling effort the tractor can exert on implements (plow, harrow, planter) — limited by soil grip, not engine power. The traction coefficient depends on soil and tire type (0.5 to 0.7 on firm soil; much less on loose or wet soil). Increasing the adhesive weight (ballast) raises the available force. Enter the adhesive weight and the traction coefficient.
Number of Elevators Required
Calculate the number of elevators required, N = peak demand ÷ capacity per elevator, dividing the peak transport demand (people in 5 min) by the handling capacity of a single elevator (people in 5 min). The result is the minimum number of elevators in the group to meet peak demand. In practice, round up and also check the resulting traffic interval (waiting quality). Peak demand comes from the building population times the peak percentage (12-15% in offices). Undersizing causes queues and long waits. Enter the peak demand and the capacity per elevator.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.