EXPEDITION 01 — MOUNTAIN MECHANICS

The Ascent

One cable. Two masses. A mountain to cross.

ALPINE DAWN · PROCEDURAL

0 / 120 m

MISSION / DELIVER SAFELY TO THE SUMMIT

TIME SCALE

T+ 00:00

OPERATIONAL DASHBOARD

Control the climb

● READY

ALTITUDE / m: 0.0
SPEED / m/s: 0.00
ACCEL / m/s²: 0.00
CABLE / kN: 0.00
MOTOR / °C: 8.0
ENERGY / kJ: 0.0

Scenario presets

Live variables

Live telemetry

Solid: measured solver · dashed: constant-initial-acceleration reference. Change a setting to see the curves diverge.

01 / TRACK POSITIONmetres vs seconds

02 / RAIL SPEEDm/s vs seconds

SimulationAnalytic baseline

The science — equations & limits

A taut cable constrains the passenger car and counterweight to opposite motion. The pulley rotates with angular velocity ω = v/r. All displayed forces are approximate game-scale values in SI units.

M = m₁ + m₂ + J/r² [kg]
Fᵍ = g(m₂ − m₁ sin θ) [N]
Fᵐ = τu/r [N]
Fʷ = ½ρCdA(w − v)|w − v| [N]
Fᶠ = μm₁g cos θ + 0.008m₂g [N]
Fᵇ = Fᵇ,max b [N]
a = (Fᵍ + Fᵐ + Fʷ − Fᵈ − sign(v)(Fᶠ + Fᵇ)) / M [m/s²]
C·dT/dt = Pₕ − h(T − Tₐ) [W]

Method. Fixed 1/120 s semi-implicit Euler; stiction at rest. The analytic line is x(t)=x₀+v₀t+½a₀t² or v(t)=v₀+a₀t, valid only with constant acceleration. Weather events and control inputs break that assumption.

Assumptions. Ideal massless inextensible cable, no slip, straight track, lumped thermal model, constant efficiency 78%, simplified rolling friction, wind projected along the rail, no detailed cabin suspension. Snow and scenery are stylised. These are educational approximations, not engineering or safety calculations.

Controls. Space = play/pause, B = hold brake, R = reset, up/down = throttle, M = toggle sound. The simulator pauses on hidden tabs.

PROCEDURAL SCENE · SEED 684291 · PHYSICS MODULE TESTED