On December 18, 1944, Admiral William Halsey's Third Fleet sailed into a compact, violent typhoon in the Philippine Sea. When the storm later named Typhoon Cobra had passed, three destroyers had capsized and sunk: USS Hull, USS Monaghan, and USS Spence. Some 790 sailors were lost. No enemy fired a shot. Those ships were defeated by wind, waves, and the unforgiving physics of ship stability.

That history is one reason ship stability sits at the heart of naval engineering. Before a warship can fight, a cargo ship can deliver, or a research vessel can do science, it has to stay upright and afloat. The principle holds whatever your specialty turns out to be. You might design hull forms, integrate combat systems, lay out machinery spaces, or plan a mid-life modernization. Your decisions will still affect where weight sits on a ship and how the hull responds to the sea.

This guide walks through the core ideas every young naval engineer should understand: why ships float, what keeps them upright, what makes them capsize, and how the U.S. Navy and international regulators set the bar for safety.

A Very Old Science With a Modern Edge

The study of ship stability began with Archimedes, who worked out the basic laws of buoyancy in the third century BC. Stability did not become a rigorous mathematical science until much later. In 1746, the French scientist Pierre Bouguer introduced the metacenter, a concept still used to measure a ship's initial stability. In 1850, the Reverend Henry Moseley added the idea of dynamic stability, which looks at the energy it takes to heel a ship over.

Today those foundations support computational fluid dynamics, probabilistic damage analysis, and full motion simulations. The tools have changed dramatically. The physics has not.

Why Ships Float: Buoyancy and Displacement

Archimedes' principle says that a floating object displaces a weight of water equal to its own weight. A ship at rest in calm water is balanced between two forces.

Gravity pulls the ship's entire weight straight down through a single point called the center of gravity (G). Where G sits depends on how weight is distributed through the ship: hull structure, machinery, fuel, weapons, stores, and crew.

Buoyancy pushes up through the center of buoyancy (B). This is the geometric center of the hull's underwater volume.

A ship sinks until the buoyant force exactly equals its weight. That weight is called displacement. Because seawater is denser than fresh water, the same ship floats a little higher in the ocean than in a river. U.S. Navy practice uses about 35 cubic feet of seawater per long ton, compared with about 36 cubic feet for fresh water. The difference is small, but for a ship already loaded close to its limits, it can matter.

The watertight volume above the waterline also matters. It is called reserve buoyancy, and it is what lets a ship absorb flooding, carry added weight, and rise over waves instead of plowing under them. Maintaining adequate reserve buoyancy is a core requirement in the Navy's Naval Ships' Technical Manual (NSTM) Chapter 096, which governs weights and stability.

Initial Stability and the Metacenter

Now push the ship a little. A gust of wind or a shifting load tilts it a few degrees. On the low side, more of the hull goes underwater. On the high side, some hull comes out. That wedge of buoyancy moves the center of buoyancy toward the low side, from B to a new point, B₁.

Draw a vertical line up through B₁. At small angles of heel, up to roughly 7 to 10 degrees, that line crosses the ship's centerline at a nearly fixed point called the transverse metacenter (M).

The vertical distance between the center of gravity and the metacenter is the metacentric height (GM). It is the single most important number for a ship's initial stability. Engineers usually measure everything from the keel (K):

GM = KM − KG

KM, the height of the metacenter above the keel, depends on the hull's shape and draft. KG, the height of the center of gravity, depends on how the ship is loaded. This split is useful to remember: hull designers largely control KM, while nearly everyone who adds, moves, or removes weight affects KG.

Why Beam Matters So Much

The distance from B to M, called the metacentric radius (BM), equals the waterplane's moment of inertia divided by the ship's underwater volume. For a simple box-shaped hull, that works out to:

BM = B² ÷ (12 × T)

Here, B is the beam and T is the draft. The waterplane's moment of inertia grows with the cube of the beam. Even after dividing by volume, BM still grows with the square of the beam. Double a box-shaped ship's beam at the same draft and BM quadruples. That is why beam is the most powerful geometric lever designers have for initial stability.

Stiff Ships, Tender Ships, and Unstable Ships

When GM is positive, M sits above G. Gravity and buoyancy combine to push a heeled ship back upright. The size of GM also shapes how the ship rolls. The roll period behaves like a pendulum's and is roughly proportional to 1 ÷ √GM.

• A stiff ship has a large GM. It resists heeling strongly but snaps back quickly, with a short, violent roll. That motion can shift cargo, fatigue structure, and make life miserable for the crew.
• A tender ship has a small GM. It rolls slowly and comfortably but has little margin against topside icing, shifting cargo, or damage.
• A ship with zero GM is in neutral equilibrium. It stays at whatever angle it is pushed to.
• A ship with negative GM has G above M. Instead of a righting moment, it experiences a capsizing moment.

Good design is not about maximizing GM. It is about finding the right balance for the ship's mission.

Weight Growth, Margins, and the Inclining Experiment

Warships rarely get lighter with age. New sensors, weapons, electronics, and habitability upgrades tend to go high in the ship, and each one raises the center of gravity and chips away at GM.

To plan for this, the Navy designs surface ships with service life allowances, which are reserves of weight and KG built in from the start. A 1996 article in the Naval Engineers Journal noted that criteria at the time generally provided a 5 to 10 percent weight margin and 0.5 to 2.5 feet of KG margin, depending on ship type. The Arleigh Burke-class destroyers (DDG 51) were originally given a 10 percent weight margin and a 1-foot KG margin. That foresight matters decades later. The DDG 51 Flight III upgrade, built around the larger AN/SPY-6(V)1 air and missile defense radar, shows how much new topside capability draws on those original margins. When margins run out, the options get expensive: adding hull blisters, or loading lead or iron ballast low in the ship to pull G back down.

Finding the Center of Gravity for Real

Calculations can only estimate where G is. To know for certain, naval architects conduct an inclining experiment, as directed by NSTM Chapter 096, after new construction or major modifications.

The ship is moored in calm, sheltered water with slack lines so it can heel freely. Tanks are either completely empty or pressed completely full, for reasons explained below. Engineers then move known weights across the deck and measure the resulting heel angle with long pendulums or electronic instruments. The math is simple:

GM = (w × d) ÷ (Δ × tan θ)

In this equation, w is the weight moved, d is the distance it was moved, Δ is displacement, and θ is the measured heel angle. KM is known from the hull geometry at the recorded draft, so subtracting GM gives the true KG.

Beyond Small Angles: The Righting Arm and the GZ Curve

GM works well for small angles, but it assumes the metacenter stays put. At larger angles, the deck edge goes under on one side and the bilge comes out on the other. The waterplane changes shape, and M moves. To judge whether a ship can survive a big roll, engineers use the righting arm (GZ).

When a ship heels, gravity still acts straight down through G, and buoyancy acts straight up through the shifted center of buoyancy. The horizontal distance between those two lines of force is GZ. Multiply it by displacement and you get the righting moment, the actual torque trying to bring the ship back upright.

Plot GZ against heel angle and you get the statical stability curve, often called the GZ curve. It is one of the most useful diagrams in naval architecture:

• The initial slope reflects GM. A steep start means a stiff ship.
• Deck edge immersion marks where the curve's growth begins to slow.
• The maximum righting arm is the angle at which the ship fights hardest to right itself.
• The point of vanishing stability is where GZ drops back to zero. Roll past it, and the ship will keep going over.

For moderate angles, before the deck edge immerses, engineers often use the wall-sided formula. It assumes the hull's sides are vertical where they meet the waterline:

GZ = sin θ × (GM + ½ BM tan² θ)

The extra term accounts for the center of buoyancy rising as the ship heels. Because of it, the true righting arm grows faster than GM alone would predict.

Two Hidden Dangers: Free Surface Effect and Angle of Loll

Free Surface Effect

A partly filled tank, called a slack tank, is one of the quietest threats to a ship's stability. When the ship heels, the liquid inside sloshes toward the low side and shifts its weight outboard, working against the righting arm. In effect, it raises the center of gravity. This virtual rise is called the free surface correction (FSC):

FSC = (i × ρ) ÷ Δ

For a rectangular tank, i = (length × breadth³) ÷ 12. The ρ term is the density of the liquid in the tank.

Consider a 10,000-tonne ship with one slack seawater tank that is 12 meters long and 8 meters wide. That tank alone reduces GM by about 0.05 meters. Now make the tank 16 meters wide. Because breadth is cubed, the loss jumps eightfold, to about 0.42 meters. That is enough to erase much of the GM of many ships.

The fix is elegantly simple: subdivide. One longitudinal bulkhead down the middle of a tank cuts the free surface effect to one quarter. Dividing it into three sections cuts it to one ninth. This is why tank layout is a stability decision as much as a machinery or arrangement decision.

Angle of Loll

If G rises high enough, from topside weight, ice buildup, or flooding, GM can turn negative. The ship cannot sit upright. Any small disturbance tips it to one side. As it leans, the hull's underwater shape changes and the center of buoyancy moves outboard until it lines up under G again. The ship settles at a steady list called the angle of loll. Using the wall-sided formula with GZ set to zero:

tan θ = √(2 × |GM| ÷ BM)

A lolling ship looks like a ship with an off-center weight, and that resemblance is dangerous. An untrained crew might shift weight to the high side to level it. With negative GM, the ship can then flop violently to the opposite side, carrying enough momentum to capsize. The correct response is to lower the center of gravity: press up slack tanks, or add ballast low in the ship, typically starting on the low side. That may briefly worsen the list, but once GM turns positive again, the ship can be brought upright safely.

How the Navy Sets the Bar: DDS 079-1

In 1962, naval architects T.H. Sarchin and L.L. Goldberg published "Stability and Buoyancy Criteria for U.S. Naval Surface Ships" through the Society of Naval Architects and Marine Engineers. Their work drew on hard wartime experience, and it became the basis for the Navy's Design Data Sheet (DDS) 079-1. That document remains the core intact and damage stability standard for conventional U.S. surface ships.

DDS 079-1 checks a ship against a series of hazards: beam winds combined with rolling, lifting heavy weights over the side, high-speed turns, and crew crowding to one side. The best known is the beam wind and rolling criterion. Engineers draw a wind heeling arm curve, based on the ship's exposed profile, on top of the GZ curve. They then compare the ship's reserve of righting energy with the energy the wind can put in. The restoring energy must be at least 1.4 times the capsizing energy. For ocean-going ships, the design wind is 100 knots.

Surviving Damage

Intact stability covers normal operations. Warships also have to survive collisions and combat damage. The Navy has traditionally used a deterministic approach: assume a specific extent of damage, such as a given length of hull opened to the sea, and require the ship to survive it. Commercial rules have increasingly moved to a probabilistic approach that estimates overall survival chances across many damage scenarios.

Either way, watertight subdivision is key. Designers space transverse bulkheads so that flooding a compartment does not sink the ship past its margin line, a safety line drawn at least 3 inches below the bulkhead deck at the side. Asymmetric flooding is especially dangerous because it adds a heeling moment on top of lost buoyancy. Some ships use cross-flooding arrangements that let water reach the opposite side and reduce the list.

Back to Typhoon Cobra

Typhoon Cobra shows how these concepts combine in the real world. Spence was running low on fuel. Fuel in the lower tanks acts as ballast, so its absence raised her center of gravity. Her crew began ballasting with seawater, but too late. Hull and Monaghan were older Farragut-class destroyers that had received substantial wartime additions such as anti-aircraft guns and radar, much of it high in the ship. Those additions ate into their stability margins before the storm ever arrived.

Hurricane-force winds and huge seas then pushed all three ships through extreme rolls. Water poured down stacks and ventilation openings, knocking out electrical power and steering. The flooding added weight and free surface effect at the worst possible moment. Each of those factors appears in this article. Together, they proved fatal.

New Threats: Parametric Rolling and Next-Generation Criteria

Some modern hull forms have fine, narrow midbodies to cut drag and heavy flare at the bow and stern to add deck space. These hulls can suffer parametric rolling, a resonance that can produce dangerous rolls even in head or following seas.

The mechanism comes straight from BM depending on the waterplane. When a wave trough sits amidships, the flared ends dig into the crests, the waterplane grows, and GM spikes. When a crest sits amidships, the ends lift out, the waterplane shrinks, and GM drops. If the ship meets waves at about twice its natural roll frequency, those swings in stability pump energy into each roll. Rolls can build dramatically within a few wave cycles. The best-known case is the post-Panamax container ship APL China, which lost and damaged hundreds of containers in a North Pacific storm in 1998. The standard operational fix is to change course or speed to break the resonance.

Cases like these showed that a ship proven stable in calm water is not necessarily safe in a seaway. In response, the International Maritime Organization (IMO) spent more than a decade developing the Second Generation Intact Stability Criteria, released as interim guidelines in 2020. The Navy's Carderock Division contributed to the effort. The criteria address five dynamic failure modes:

• parametric rolling
• pure loss of stability on a wave crest
• surf-riding and broaching
• the "dead ship" condition after a loss of power
• excessive acceleration in very stiff ships

Designs move through progressively more detailed levels of assessment. The final level is a direct stability assessment using advanced motion simulations. The shift from static rules toward high-fidelity dynamic modeling is one of the biggest changes in the field in decades.

When Things Go Wrong: Stability in Salvage

Stability knowledge does not stop at the design office. The Navy's Supervisor of Salvage (SUPSALV) uses a software tool called POSSE, the Program of Ship Salvage Engineering, to analyze damaged and grounded ships in near real time. Salvage engineers model flooding, grounding forces, tides, and hull strength together. They then plan how to offload cargo and shift ballast to refloat a ship without capsizing it or breaking its back.

Why Ship Stability Matters for Your Career

Ship stability is not just a course you pass and forget. It shapes nearly every naval engineering decision:

• Combat systems engineers adding a radar are adding weight high in the ship.
• Machinery and auxiliary engineers laying out tanks are making free surface decisions.
• Structural engineers set the watertight boundaries that damage stability depends on.
• Program managers spend weight and KG margins that must last a ship's entire service life.

The good news is that the fundamentals are learnable, and they reward mastery. Get comfortable with GM, GZ curves, free surface corrections, and the logic behind the Navy's criteria, and you will understand why ships are shaped and loaded the way they are. For a deeper dive, Principles of Naval Architecture from SNAME remains a standard reference. The Naval Engineers Journal has published decades of technical papers on stability, weight control, and survivability.

As Typhoon Cobra showed, the margins engineers calculate on paper translate directly into the safety of the sailors who take these ships to sea.

Main image caption: The Vietnam People’s Navy ship, HQ-274, and the Vietnam Maritime Search and Rescue Coordination Centre ship SAR 274, conduct a search and rescue exercise with Arleigh burke-class guided-missile destroyer USS Shoup (DDG 86) in the South China Sea, Aug. 5, 2026. Shoup and Carrier Strike Group Five are forward-deployed to the U.S. 7th Fleet area of operations. U.S. 7th Fleet, the Navy's largest forward-deployed numbered fleet, routinely interacts and operates with allies and partners in preserving a free and open Indo-Pacific. (U.S. Navy photo by Mass Communication Specialist 2nd Class Lillian Olen)