USCG Exam Prep · ⚖️ Interactive Trainer
Vessel Stability — GM, GZ & Free Surface
Stability is easier to feel than to memorize. Heel a vessel with a slider and watch G, B, M and the righting arm move — then the numbers make sense.
Tested on the 100/200-Ton Master and MMC Deck General exams. Binnacle School has 267 Deck General questions in the bank.
What it is
Transverse stability is what rights a vessel after it heels. The metacentric height GM = KM − KG measures initial stability; the righting arm GZ = GM·sin θ (at small angles) is the lever that returns her upright. Slack tanks reduce stability through the free-surface effect, and an off-center weight produces a steady angle of list.
How the USCG tests it
Deck General stability questions ask you to compute GM from KM and KG, find the new KG after loading or shifting weight, apply a free-surface correction, and calculate the angle of list from a transverse moment. The interactive trainer shows the heeling vessel — with the center of buoyancy moving to the low side — alongside a live GZ curve, then drills the calculations.
Key concepts
Metacentric height: the height of the metacenter above the keel minus the height of the center of gravity. Positive GM means initial stability; larger GM is 'stiff', smaller is 'tender'.
GZ = GM·sin θ at small angles; the righting moment = displacement × GZ. The GZ curve shows how the lever grows and then falls as she heels.
A slack tank's liquid shifts as she rolls, raising G virtually and reducing GM by the free-surface correction (proportional to tank breadth cubed). Press up or empty tanks to remove it.
An off-center weight gives a steady heel: tan(list) = (w·d) / (displacement × GM). List is a static offset; roll is dynamic.
Worked example
KM = 24.0 ft, KG = 22.0 ft. What is GM, and is she stiff or tender?
GM = KM − KG = 24.0 − 22.0 = 2.0 ft. That is positive and moderate — comfortably stable. A very large GM would be 'stiff' (a fast, jerky roll); a small GM near zero would be 'tender' (a slow, lazy roll and little reserve).
Practice Stability hands-on
The interactive trainer generates a fresh problem every time and checks your work against exam-accurate math. Free with a Binnacle School account, on web and iOS.
Frequently asked questions
What is metacentric height (GM)?
GM is the distance between a vessel's center of gravity (G) and its metacenter (M), found from GM = KM − KG. It measures initial stability: positive GM means she returns upright after heeling.
What is the free-surface effect?
Liquid in a partly filled (slack) tank flows to the low side as the vessel rolls, which acts like raising the center of gravity and reduces GM. It is worst in wide tanks and is why you press up or empty slack tanks.
What is the difference between list and roll?
List is a steady angle of heel from an off-center weight or negative GM; roll is the dynamic motion back and forth in a seaway. The exam tests the list calculation, tan(list) = w·d / (displacement·GM).