Two physics regimes, joined where the slipway meets the water:
On the ways:
a = g(sinθ − μcosθ) [constant, gravity − friction]
Afloat (vertical, draft d):
k = ρ·g·B·L·Cb [buoyancy "stiffness"]
m·d'' = m·g − k·d − c·d' [damped spring toward d_eq]
d_eq = m / (ρ·B·L·Cb) [Archimedes equilibrium]
Afloat (horizontal, drag):
m·dv/dt = −½·ρ·Cd·(B·d)·v² [quadratic hydrodynamic drag]
The hull accelerates down the greased ways under gravity, resisted only by sliding friction. The instant its keel crosses the waterline it starts displacing water: the buoyant force ρgV grows linearly with draft, acting like a stiff spring pulling the hull toward the draft where displaced weight equals hull weight (Archimedes' principle) — it overshoots and settles in a lightly damped oscillation, just as a real hull "bounces" after a stern-first launch. Meanwhile the forward speed bleeds off against quadratic water drag on the wetted beam.
- Hull mass — heavier hulls sit deeper (larger d_eq) and carry more momentum down the ways.
- Slipway angle — steeper ways mean more launch speed at the waterline.
- Beam — a wider hull has more waterplane area, so it is buoyancy-stiffer (shallower draft, faster-settling bob) but also more drag.
- Ways friction — historically Clyde yards used tallow-greased ways; less friction means a faster, harder splash.
- Water density — the Clyde is tidal and brackish; slightly denser water gives slightly more buoyancy and a shallower draft.