Tidewatch: The Barge Passage

Equations (SI units)

m = 7,800 kg + cargo mass [kg]

d_eq = m / (ρ × 8 m × 3 m) [m] — closed-form static draft, for an upright box hull.

h = clamp(η − keelY, 0, 1.30 m) [m]

F_b = ρ × 9.81 m/s² × 24 m² × h [N]

m × a_y = F_b − m × g − c × v_y [N]

c = 2 × 0.85 × sqrt(m × ρ × g × 24 m²) [kg/s] — approximate linear damping.

T = 0.68 m − tideRate × (30t / 3600) + correction [m], with t in solver seconds and tideRate in m/h.

η = T + (A + extraWave) × sin(2πt / 4 s) [m]

under-keel gap = keelY + chartDepth + routeOffset [m]; freeboard = 1.30 m − max(0, η − keelY) [m].

Assumptions and honest limits

• Rectangular 8 × 3 × 1.30 m hull, uniform mass; no roll, trim, leaks, squat or real navigation dynamics.
• One sinusoidal, spatially uniform wave. Tides are accelerated 30× to make changes visible; not a real voyage timetable.
• Loading and route changes are discrete game events. Throttle-related wave changes are illustrative, not a validated wake law.
• The numerical vertical solver uses semi-implicit Euler at 1/120 s; static predictions are Archimedes' closed form.

What you can try

• Increase cargo by 2,500 kg. Predict the extra draft before observing it.
• Reduce charted depth to 0.85 m and compare direct vs deep route.
• Set waves to zero and check that the actual draft settles onto the dashed prediction.
• Call window.__selfTest() in the console for the independent numerical check.