The science
The car (mass mc) on a slope of angle θ and the hanging counterweight (mw) are joined by a taut massless cable over a pulley of inertia I, giving one degree of freedom with equivalent mass M = mc + mw + I/r². Along the slope: M a = g(mw - mc sinθ) + F_motor + F_wind - F_roll - F_fric - F_brake, with Coulomb friction (stiction at rest) and an icy-rail factor 0.52. The motor warms as C dT/dt = P_loss - h (T - T_amb) (Newton cooling), integrated with semi-implicit Euler at 120 Hz.
Simplifications: cable is inextensible and always taut, one lumped motor temperature, constant drivetrain efficiency 78 %, a deterministic gust instead of turbulence, rolling losses fitted by hand. Numbers are illustrative, not a certified design.
Made with ChatGPT · 2D companion of the 3D page; same solver and numbers.