MCTC (Moment to Change Trim one Centimetre) is the trimming moment — measured in tonne-metres — required to change a vessel’s trim by exactly one centimetre.
The Actual Formula
MCTC = (W × GML) / (100 × L)
Where:
- W = the vessel’s displacement (total weight)
- GML = longitudinal metacentric height (a stability value from the vessel’s hydrostatic data)
- L = length (typically length between perpendiculars)
- 100 = conversion factor (relating meters to centimeters)
Vessel-specific hydrostatic tables in the stability booklet provide the correct MCTC for the current displacement, rather than requiring this to be calculated from scratch aboard ship.
Practical Use: Calculating Weight Shift to Correct Trim
MCTC is used directly when planning to correct or adjust trim by shifting weight (cargo or ballast) fore or aft — the calculation determines how far a given weight needs to move (or how much weight needs to move a given distance) to achieve a specific trim change.
The core relationship: Trimming Moment = Weight × Distance moved (from the ship’s center of flotation)
Trim change (in cm) = Trimming Moment / MCTC
This lets a Chief Officer calculate, for instance, exactly how many tonnes of ballast need to be transferred between forward and aft tanks (or how far a given weight needs to be shifted) to correct an unwanted trim condition by a specific amount.
MCTC vs TPC: Different Calculations, Different Purposes
- TPC (Tonnes Per Centimetre) — weight needed to change draft (vertical) by 1cm
- MCTC — moment needed to change trim (fore-and-aft tilt) by 1cm
Both are essential loading calculations but address different aspects of a vessel’s floating condition — draft change versus trim change — and both are used together during real loading planning.
Why This Matters Practically
Getting trim right isn’t just about appearance — trim affects propeller immersion, under-keel clearance at bow or stern (whichever end has less clearance), and visibility from the bridge. MCTC calculations give a Chief Officer a precise, real tool for correcting trim to within a specific target, rather than adjusting ballast by guesswork and rechecking repeatedly.
Exam Relevance
MCTC’s correct formula and its practical application in trim correction calculations are core, heavily-tested Ship Stability topics in deck officer competency exams.