...
running...
How to use
Pick a preset, then change depth, loads, speed and acceleration limits, jerk smoothing and rope diameter. The rope is a spring, so a sudden start makes the loaded skip bounce on it and the tension graph rings; jerk smoothing or a thicker rope reduces that. Power goes negative when the load drives the motor as a generator. Use the time scale slider to speed up the cycle.
The science
Motion profile. The drum pays the rope at a prescribed speed: acceleration at a to the maximum speed v, cruise, then deceleration (a triangle if the shaft is short, H < v2/a). The velocity is smoothed with a moving average of width tj, which limits jerk and keeps the travelled distance equal to H.
Elastic rope. The rope between the sheave and the skip is a spring of stiffness k = E A / L (steel rope modulus about 110 GPa, metallic fill 0.55) with light damping, so the skip of mass m follows:
m u'' = T - m g, T = k (s - u) + c (s' - u'), f_bounce = sqrt(k/m) / (2 pi)
In a rigid rope the tension would be m (g + a); the elastic rope adds an oscillation around it after any step in acceleration.
Counterweight and power. A counterweight of mass m_cw hangs on the other side of the drum, so the motor force is F = T - m_cw (g - a) and the power P = F v. For a rigid rope the energy over a trip is (m - m_cw) g H; negative power means the load is regenerating. A good counterweight halves the motor size.
Simplifications. One skip on one rope, the counterweight rope rigid and massless, constant rope stiffness across the trip step, no drum inertia, no rope mass, no guide friction, dwell times fixed (6 s load or dump, 15 s settle), rough rope breaking load. Educational model, not a hoist design tool. Integration is RK4 at 5 ms.