NATARAJADry-docking, grounding & the rolling test
Learning outcomes & permitted supports
- Find the upthrust P at the critical instant from the trim to be lost, MCTC and the blocks' distance from F
- Account for the stability P costs — by the KM method and the KG method, and say why both are honest
- State the docking preconditions (small trim, sound GM, no slack tanks) from the physics, not the checklist
- Treat an accidental grounding as the same arithmetic with the tide as the dock
- Estimate GM with a stopwatch: T = 2π·k/√(g·GM), and name the approximation inside k ≈ 0.35B
Supports in this lab: Calculator. Box-form hydrostatics for the live theatre; the P and GM formulas are the general ship's, entered with given particulars. Golden 840/840.
The water leaves; the blocks push back
She enters with a little stern trim, touches the after blocks first, and from that moment a force P grows under her sternframe while the falling water takes her trim away. P is real weight taken off the water — and stability pays for it.
| W · KM · GM afloat | 12177.0 t · 7.66 m · 1.26 m |
|---|---|
| MCTC (box) | 221.4 t·m/cm |
| Trim change so far | 30.6 cm of 60.0 cm |
| Upthrust P = trim·MCTC / l | 123.2 t |
| GM effective — KM method | 1.182 m (GM − P·KM/W) |
| GM effective — KG method | 1.194 m (rise of G with P at the keel) |
| P that takes GM to zero | 2001.8 t |
Two methods, one physics: take P's moment about M and you write GM − P·KM/W; treat P as weight landed at the keel and G rises by P·KG/(W−P). They differ at second order in P/W — the golden suite bounds the gap (< 5 cm at the P/W a docking sees). The exam wants either, WITH its reasoning.
GM with a stopwatch — the rolling test
A ship rolls with period T = 2π·k/√(g·GM). Time a few rolls, take k ≈ 0.35·B (the honest approximation in this method), and GM falls out — the check a master runs when something feels tender and there is no time for an inclining.
| Rolling period | 13.3 s |
|---|---|
| GM recovered from that period | 0.9000 m — the inverse, exactly |
| Read it | moderate — the working range |