Pirates of the Caribbean Underwater Boat Calculator

1. Swap lead for wood. Keep the size the same. Watch the boat's weight and whether it rises or stays down.
2. Change the depth. Deeper water squeezes the air into a smaller space, so it gives less upward push.
3. Make the boat longer in automatic mode. It captures more air, which adds time on the air dial but also more upward push. Use manual mode to compare boats holding exactly the same amount of air.
4. Change the people or their activity. A bigger body weighs more but also pushes more water aside. In this model, heavier people and harder work use oxygen faster.
5. Move the time slider. Watch oxygen go down and carbon dioxide go up.
6. Check the one-foot-longer card. Compare the extra air time with the extra boat weight and changed floating behaviour.

The depth setting measures how far below the surface the water level inside the boat sits. It does not measure the distance to the seabed.

If the upward push is bigger than the total weight, the boat and people rise unless something holds them down. If the forces match, they nearly float in place; that does not give them firm footing. A small downward force allows bottom contact in the animation. A large downward force is too heavy for its walking example.

At 20 ft (6.10 m) in seawater, the total pressure is about 1.60 times the pressure at the surface. The same air then takes up about 62% of its surface volume, if its temperature stays the same. Less air volume pushes aside less water, so it produces less upward force. See NOAA's explanation of water pressure (opens a new tab).

Here, d is the depth of the water level inside the boat; g is 9.80665 m/s²; P₀ is 101,325 Pa; ρ means density, or mass per unit volume. The volume of water pushed aside includes the solid hull, the actual gas volume and both people's full body volume. With the roof underwater, their heads also take up space that water cannot fill. This applies Archimedes' principle (opens a new tab) to the boat, air and people together.

The model uses 1,000 kg/m³ for fresh water, 1,025 kg/m³ for seawater and 1,000 kg/m³ for the human body. With trapped air held fixed, extra body mass has no net downward effect in fresh water and adds a little upward force in seawater at this assumed body density. Automatic mode also adjusts the air amount because larger bodies take up more space. The model assumes 92% of each person's body volume is below the water level inside the boat. That percentage affects the space needed for their heads and the forces on the separate parts, but not the whole system's displacement at a fixed gas volume.

The animation treats a force within ±2 kg-equivalent as nearly balanced. A downward force of more than 40 kg-equivalent is too heavy for its walking example. These are display settings, not tested limits of human strength. A kg-equivalent is the force equal to the weight of one kilogram under normal gravity. The animation does not calculate rising speed or body posture.

The starting example uses a hollow lead boat with an inside space 10 ft long, 4 ft wide and 2 ft high, and 10.45 mm walls. There are two 180 lb people, 1,500 litres of air trapped at the surface, and a 20 ft air-pocket depth in seawater. Automatic mode starts with about two-thirds of the available inside space filled with air, after allowing for the parts of the people inside it. The air shrinks to about 935 litres at the selected depth.

The hull alone weighs about 2,360 lb (1,071 kg) on land. After buoyancy is counted, the boat and people together have a net downward force of about 29.5 lb-equivalent (13.4 kg-equivalent). These are different quantities: the first is the dry boat's weight; the second is the leftover force on the whole group underwater.

A boat that balances at 20 ft may push upward much more strongly in shallow water. The example does not show how anyone could get it into position. The model also does not check the strength, grip or balance of the people holding it.

To estimate weight, the calculator treats the hull as an open rectangular shell. For inside length L, width W, height H and wall thickness t, the volume of solid hull material is (L + 2t)(W + 2t)(H + t) − LWH. Multiplying this volume by the material's density gives the hull mass.

The metal-element values follow the University of Texas density table (opens a new tab). Wood and steel are examples: wood type, moisture and the mix of metals in steel can change their density.

The picture is not a boat-building plan. Real hull shape, joints, seats and supports would change its weight. The model requires the roof to stay underwater; it does not find the final position of a boat partly above the surface. Hull strength, lead toxicity, stability, waves, gas loss and changing lung volume are not included. It also does not check whether the people can keep their mouths in the air pocket.

The main dial stops at the first of two selected gas levels. It compares carbon-dioxide pressure reaching 4.053 kPa with oxygen pressure falling to about 19.758 kPa. Gas pressure, or partial pressure, is the share of the total pressure due to that gas. In the starting example, carbon dioxide reaches its selected level first, after about 21.7 minutes.

At surface pressure, those levels equal 4% carbon dioxide and 19.5% oxygen. The first starts from the NIOSH carbon-dioxide IDLH value (opens a new tab); the second starts from OSHA's definition of oxygen-deficient air (opens a new tab). They are workplace references, not clocks that tell when a person dies. Applying equivalent gas pressures underwater is an assumption for this illustration, not a tested diving limit.

The optional comparisons use different levels, so their times differ. In the starting example, CO₂ reaches 0.5 kPa after about 2.4 minutes, and oxygen falls to 19.5% by volume after about 12 minutes. These separate checks show changes in the air. None of these times predicts when a person would faint or die, and the time before them is not a safe allowance.

The gas calculation assumes the air is fully mixed, with no fresh air entering, no CO₂ removed or dissolved in water, and fixed temperature, pressure and breathing demand. Oxygen use is estimated as 3.5 mL per kilogram per minute, multiplied by the selected activity factor (MET). It is then converted from standard temperature to surface-equivalent litres at 20°C. Carbon-dioxide production is taken as 92% of oxygen use by gas volume. These are teaching assumptions, not breathing measurements taken from people walking underwater.

For the same amount of surface air and the same breathing demand, changing depth does not change the time to the optional 19.5% oxygen-by-volume check. It does change the pressure-based times on the main dial and the CO₂ comparison, because the same gas percentage has a higher pressure deeper underwater. The tool does not calculate loss of consciousness, death, decompression or lung injury.

Real breathing rates, effort, panic, leaks and unevenly mixed air can change the result. Breathing compressed air at depth also brings pressure-related injury risks on the way up.

These links open in a new tab.

• NASA: Archimedes' principle — the water's upward push.
• NOAA: pressure and ocean depth — why pressure rises with depth.
• Smithsonian: the history of diving bells and submersibles — trapping air underwater and replenishing it.
• MythBusters: could Jack Sparrow use a rowboat as a submarine? — the show's test of the film idea, not a test of this calculator's heavy-metal boat.
• US Coast Guard: commercial diving job aid — Boyle's law and total pressure, not a test of this boat.
• University of Texas: density reference table — material densities.
• FDA-hosted exercise qualification plan — the conventional MET value used to estimate oxygen demand, not a measurement of this underwater task.
• NASA: carbon dioxide and metabolic loads — gas pressure and breathing calculations, including the 0.92 CO₂-to-oxygen ratio used here.
• NIOSH: carbon dioxide — workplace exposure guidance. Its 5,000 ppm time-weighted limit is not a safe underwater duration; 0.5 kPa here is a selected comparison point.
• NIOSH: carbon-dioxide IDLH value — the 40,000 ppm reference behind the main dial's assumed pressure comparison, not a survival-time rule.
• OSHA: oxygen-deficient atmospheres — the 19.5% workplace definition, not a diving-time limit.
• DAN Europe: breathing-gas quality — the dangers of contaminated breathing gas.

Not with an ordinary wooden rowboat as shown in the movie. Trapping air is real, but the boat and its air pocket have a strong upward push. A deliberately much heavier hollow boat can balance the forces in this calculator. That is different from showing that Jack and Will could carry, steer or breathe safely under the movie's boat.

Jack Sparrow and Will Turner walk along the bottom with an upside-down rowboat in Pirates of the Caribbean: The Curse of the Black Pearl. This calculator explores that trapped-air scene, not the ship-flipping scene in At World's End.

Air takes up space and cannot rise through the boat's closed top. Water can enter through the open bottom, but it squeezes the trapped air rather than instantly replacing it. Deeper water makes the air pocket smaller. If the boat tips enough for bubbles to escape, or air leaks out, more water can come in.

It uses the same trapped-air idea as an open-bottom diving bell. A diving bell is a heavy chamber lowered into water; its weight resists the upward push on the air pocket. A boat is not a properly equipped diving bell, and trapped air alone is not a dependable breathing supply.

In Pirates 2!, Adam and Jamie tested the rowboat-submarine idea. Their rowboat would not stay underwater as the movie suggests, even in their attempts with added weight. This calculator changes the setup by allowing a much heavier hollow-metal boat; a balanced result does not overturn that test or prove the stunt is practical. The article links to the official MythBusters clip.

There is no single answer. Boat size, trapped air and depth all matter. Wood tends to float; a heavy metal can help hold the boat down. The starting example uses a hollow lead boat weighing about 2,360 lb (1,071 kg) on land. After the water's upward push is counted, the boat and both people have a small downward push equal to the weight of about 29.5 lb (13.4 kg). Change the material and size to compare other cases.

The starting example reaches the dial's selected air warning in about 21.7 minutes. That is not a prediction of survival time. The dial calculates when carbon dioxide reaches its high-pressure comparison or oxygen reaches its low-pressure comparison, whichever happens first. People can be harmed earlier; the model cannot tell when someone would pass out or die, or how long it is safe to stay underwater.

With the starting settings and the same percentage filled with air, one extra foot adds about 151 litres of starting air. It delays the same air warning by about 2.2 minutes, from about 21.7 to 23.8 minutes. It also adds about 196 lb (89 kg) to the lead hull and makes the group nearly buoyant. The comparison updates as you change the inputs. A longer boat without any extra trapped air adds zero minutes to the air timer.

Yes, in automatic mode. Increasing the inside length, width or height captures more starting air at the same fill percentage, so the gas levels change more slowly for the same people and activity. It also changes the boat's weight and upward push. Manual mode lets you choose the trapped-air amount yourself; a larger boat with no extra air does not add time.

Not by itself. With the same inside size, trapped air, depth, people and activity, switching from wood to lead or gold changes the boat's weight and whether it rises or stays down, but not the gas timer. In real life, a harder-to-handle boat could change how hard people work; the activity control lets you compare that separately.

The dial estimates time to a carbon-dioxide pressure of 4.053 kPa or an oxygen pressure of about 19.758 kPa, whichever comes first. At surface pressure these correspond to 4% carbon dioxide and 19.5% oxygen. The carbon-dioxide value comes from NIOSH's IDLH comparison; the oxygen value starts from OSHA's oxygen-deficiency definition. Using equivalent gas pressures underwater is a modelling assumption, not a validated diving limit. The number is neither safe breathing time nor time to death.

The trapped air pushes water aside, so the water pushes the boat upward. Wood usually adds its own upward push too. Adding more wood can make the boat harder to hold underwater, not easier.

Deeper water squeezes the same trapped air into a smaller space. That smaller air pocket pushes aside less water and gives less upward lift. The depth setting measures the water level inside the boat, not the seabed. The calculation assumes the air stays at the same temperature.

A heavy metal boat can beat the water's upward push. But it may be far too heavy to lift on land, too heavy to handle underwater, or too weak to hold its shape. Lead and gold are choices for learning the physics, not suggestions for building a boat.

Not automatically. A bigger body weighs more, but it also pushes aside more water. With trapped air held fixed, those effects cancel in fresh water in this model; in seawater, extra body size adds a little upward lift. Automatic mode also adjusts the air amount because larger bodies take up more space. Heavier people use oxygen faster in the breathing calculation. Real bodies, clothing and lung volume can give different results.

These are separate from the main dial and longer-boat comparison. The carbon-dioxide time measures how long it takes to reach 0.5 kPa of carbon-dioxide pressure. The oxygen time measures how long oxygen takes to fall from 20.95% to 19.5% of the air. These are chosen points for comparing changes, not danger limits. Neither tells you when someone would die or pass out, or how long it is safe to stay.

No. Squeezing the trapped air makes it smaller; it does not add oxygen. With the same starting air and breathing demand, depth does not change the time until oxygen reaches the optional 19.5%-by-volume check. It does change the pressure-based times on the main dial and makes the carbon-dioxide pressure comparison arrive sooner.

It shows one way the weight and upward push can line up. The hollow lead boat has a 10 ft by 4 ft by 2 ft inside space and 10.45 mm walls. There are two 180 lb people, 1,500 litres of surface air and a 20 ft air-pocket depth in seawater. Automatic mode starts with about two-thirds of the available inside space filled with air. Most of the weight is balanced by the water's upward push, so the animation shows walking. It does not show how they could get such a heavy boat into position.

No. It is a hollow shell: solid lead walls with space inside for air. Filling the whole inside with lead would leave no air pocket. The calculator uses a simple rectangular shell to estimate the material volume, not the curved shape or strength of a real boat.

The above-water number is the boat's weight on land, without the people. The underwater number is the push left after the water lifts up on the boat, air and both people. Changing depth changes that upward push, not the boat's weight on land.