Vessel Stability and Trim

The center of buoyancy (B) is the centroid of the underwater volume of the hull — the point through which the upward buoyant force acts. The center of gravity (G) is the point through which the entire downward weight of the vessel acts. The metacenter (M) is the point where a vertical line through the shifted center of buoyancy intersects the vessel centerline when heeled at small angles. For a vessel to be stable, M must be above G. These three points — B, G, and M — are the fundamental reference points for all stability calculations on the USCG exam.

Metacentric height (GM) is the vertical distance from the center of gravity (G) to the metacenter (M). Positive GM means M is above G — the vessel is stable and will return to upright after heeling. The formula is GM = KM minus KG, where K is the keel. Neutral GM (GM = 0) means G and M coincide — the vessel has no initial restoring tendency. Negative GM means G is above M — the vessel is unstable and will either capsize or settle at a loll angle. A large positive GM means a stiff vessel with a short, jerky roll. A small positive GM means a tender vessel with a slow, comfortable roll. The USCG exam requires you to recognize how loading changes affect GM.

The righting moment is the force that returns a heeled vessel to upright. It equals the vessel's displacement multiplied by the righting arm GZ. GZ is the horizontal distance between the line of action of buoyancy (upward through B) and the line of action of gravity (downward through G) at any given heel angle. When GZ is positive, the vessel tends to return upright. When GZ is zero, the vessel is in neutral equilibrium or at the capsize point. When GZ is negative, the vessel will capsize. The GZ curve plots righting arm against heel angle. The area under the GZ curve represents dynamic stability — resistance to being capsized by waves or gusts.

Free surface effect is the loss of effective stability caused by liquid in a partially filled tank. When the vessel heels, the liquid shifts to the low side, raising the effective center of gravity and reducing GM. The free surface correction (FSC) is subtracted from solid GM: GM corrected = GM solid minus FSC. FSC = (i times density of liquid) divided by (V times density of seawater), where i is the second moment of area of the free surface and V is the displacement volume. Free surface effect is worst when tanks are approximately 50 percent full because the free surface is at its widest. Wide, shallow tanks cause more free surface effect than narrow, deep tanks. The USCG exam tests the correct action: keep tanks either full or empty to minimize free surface effect.

List is a permanent heel caused by an off-center weight — the center of gravity (G) has shifted to one side of the centerline. The vessel has positive GM and positive righting arm on the low side. To correct list: shift weights from the low side to the high side, or add weight to the high side. Loll is caused by negative GM — G has risen above M. The vessel has no tendency to return to upright; instead it settles at an angle (the loll angle) on a random side where GZ equals zero. Attempting to correct loll by moving weight to the high side is extremely dangerous and can capsize the vessel. The correct action for loll is to lower G by adding low ballast, emptying high tanks, filling double-bottom tanks, or removing high cargo. Never shift weight to the high side of a lolling vessel first.

Trim is the difference between the forward draft and the aft draft — it describes the longitudinal tilt of the vessel. A vessel trimmed by the stern has a greater aft draft than forward draft, which is the normal running condition for most power vessels. A vessel trimmed by the head has a greater forward draft and is generally undesirable — it increases resistance and reduces maneuverability. Trim is calculated as: Trim = Draft Aft minus Draft Forward. If the result is positive, the vessel is trimmed by the stern; if negative, trimmed by the head. List, by contrast, is a transverse lean — a side-to-side tilt caused by off-center weight. Trim is a fore-and-aft issue; list is a port-starboard issue.

Adding weight raises the center of gravity if the added weight is above G, and lowers G if added below G. The shift in G is: GG1 = (w times d) divided by (W plus w), where w is the added weight, W is the original displacement, and d is the vertical distance between the old G and the center of the new weight. Adding weight increases displacement and draft. Removing weight has the opposite effect — if high cargo is discharged, G lowers and stability improves; if low ballast is discharged, G rises and stability decreases. The exam frequently tests loading sequences: loading heavy cargo high in the ship worsens stability, while loading it low improves stability. Always verify the corrected GM after any significant loading change.

The downflooding angle is the angle of heel at which water can enter the vessel through openings that cannot be closed watertight — ventilators, companion hatches, portlights, or machinery exhausts. Once water enters through these openings, it floods compartments rapidly and can sink the vessel. The downflooding angle is the practical limit of the positive stability range — even if the GZ curve shows positive righting arm beyond this point, the vessel will flood before it can recover. Damage stability calculations must show that the vessel remains afloat with adequate freeboard after flooding of specified compartments, and that the downflooding angle is not exceeded. The USCG exam tests the concept that the downflooding angle limits the effective range of stability.

Damage stability refers to a vessel's ability to remain afloat and upright after flooding of one or more compartments due to collision, grounding, or structural failure. Under 46 CFR Subchapter S and T, passenger vessels must demonstrate damage stability — the ability to survive flooding of the most critical single compartment (one-compartment standard) or sometimes two compartments. After flooding, the vessel must: maintain positive GM; have a waterline that does not submerge the margin line (a line 3 inches below the freeboard deck at the side); and not heel beyond a specified angle. Watertight subdivision — bulkheads, watertight doors, and compartmentalization — is the primary means of achieving adequate damage stability.

A stability letter (also called a stability booklet or stability approval letter) is issued by the USCG or a recognized classification society and certifies that the vessel meets the applicable stability requirements for its operating area and type. It contains the vessel's hydrostatic curves, GZ curves for various loading conditions, maximum allowable KG at each displacement, and operating instructions. The master is required to load the vessel within the limits specified in the stability letter. Loading outside these limits invalidates the stability approval and creates legal and safety liability. For vessels under 46 CFR Subchapter T, the stability letter must be kept aboard and available for USCG inspection.

Load lines are marks on a vessel's hull indicating the maximum allowable draft in various sea and seasonal conditions. The Plimsoll mark (a circle with a horizontal line through it) is the reference mark. Additional marks indicate Fresh Water (F), Tropical Fresh (TF), Tropical (T), Summer (S), Winter (W), and Winter North Atlantic (WNA) load lines. Loading a vessel below the applicable load line is illegal and dangerous — insufficient freeboard means less reserve buoyancy and reduced range of positive stability. Load line requirements are established under the International Load Line Convention and 46 CFR Part 42 for ocean-going vessels. Inland passenger vessels are governed by Subchapter S freeboard requirements.

Displacement hulls move through the water and are supported entirely by buoyancy. Their stability comes from hull form and the relationship between B, G, and M. They have predictable hydrostatic stability curves and relatively long GZ curves. Planing hulls, at speed, rise up and are partially supported by dynamic lift — hydrodynamic forces generated by the hull bottom running over the water surface. At planning speeds, form stability is reduced because less hull is submerged. At rest or low speeds, planing hulls behave like displacement hulls. The USCG exam tests that planing hull vessels can be more susceptible to capsize when passengers move suddenly at slow speed, and that their stability at rest must be evaluated like a displacement hull. Planing hull vessels generally have high beam-to-draft ratios, providing good initial stability but potentially short GZ curves.

The USCG captain's exam tests these formulas: GM = KM minus KG (basic metacentric height). KM = KB plus BM (metacentric height above keel). BM = I divided by V (metacentric radius). GM corrected = GM solid minus FSC (with free surface). GZ = GM times sine of heel angle (for small angles). Righting moment = Displacement times GZ. G shift from weight addition: GG1 = (w times d) divided by (W plus w). G shift from weight removal: GG1 = (w times d) divided by (W minus w). G shift from weight transfer: GG1 = (w times d) divided by W. Trim = Draft Aft minus Draft Forward. Change in trim from shifting weight: change in trim = (w times d) divided by MCT1in (moment to change trim one inch). Know which direction G moves for each scenario.

The angle of vanishing stability (AVS) is the angle of heel at which the GZ righting arm curve crosses zero after reaching its maximum. Beyond the AVS, GZ becomes negative — the vessel will capsize and not return to upright without external assistance. A healthy vessel should have an AVS greater than 90 degrees. On a GZ curve diagram, the AVS is the second point where the curve intersects the x-axis (the first being at 0 degrees upright). The area under the GZ curve represents dynamic stability. A vessel with a high AVS and large area under its GZ curve has excellent reserve stability. The USCG exam may show a GZ curve and ask you to identify the AVS, the angle of maximum GZ, and regions of positive and negative stability.

When a weight is added off the longitudinal center of flotation (LCF), the vessel trims to accommodate the moment. The change in trim is calculated using the moment to change trim one inch (MCT1in), which is a hydrostatic value from the vessel's stability tables: Change in trim (inches) = (w times d) divided by MCT1in, where w is the weight in long tons and d is the distance in feet from the LCF to the center of the added weight. If the weight is added aft of the LCF, the vessel trims by the stern; forward of the LCF, the vessel trims by the head. To find the change in draft at each end, the trim change is apportioned: change in aft draft = (l forward times change in trim) divided by vessel length, and change in forward draft = (l aft times change in trim) divided by vessel length.

On a small vessel, passengers and crew represent a significant percentage of total displacement. Moving people from centerline to one side raises G (people are usually high in the vessel) and shifts G off centerline, creating a list. On very small vessels, the USCG and vessel stability rules account for passenger weight by specifying a heel angle that must not be exceeded when all passengers move to one side. The exam tests the 10-degree passenger heel criterion: a vessel must not heel more than 10 degrees (or to the point of water on deck, whichever is less) when all passengers move to one side. Passenger weight is taken at 140 pounds per person for USCG calculations unless otherwise specified.