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when was buoyancy discovered?

Buoyancy (/ˈbɔɪənsi, ˈbuːjənsi/),[1][2] or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid.

For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a non-inertial reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction.[3]

Buoyancy also applies to fluid mixtures, and is the most common driving force of convection currents. In these cases, the mathematical modelling is altered to apply to continua, but the principles remain the same. Examples of buoyancy driven flows include the spontaneous separation of air and water or oil and water.

The center of buoyancy of an object is the center of gravity of the displaced volume of fluid.

Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 BC.[4] For objects, floating and sunken, and in gases as well as liquids (i.e. a fluid), Archimedes' principle may be stated thus in terms of forces:

—with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.[5]

More tersely: buoyant force = weight of displaced fluid.

Archimedes' principle does not consider the surface tension (capillarity) acting on the body,[6] but this additional force modifies only the amount of fluid displaced and the spatial distribution of the displacement, so the principle that buoyancy = weight of displaced fluid remains valid.

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). In simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. This is also known as upthrust.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water.

Assuming Archimedes' principle to be reformulated as follows,

then inserted into the quotient of weights, which has been expanded by the mutual volume

yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes.:

(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)

Example: If you drop wood into water, buoyancy will keep it afloat.

Example: A helium balloon in a moving car. During a period of increasing speed, the air mass inside the car moves in the direction opposite to the car's acceleration (i.e., towards the rear). The balloon is also pulled this way. However, because the balloon is buoyant relative to the air, it ends up being pushed "out of the way", and will actually drift in the same direction as the car's acceleration (i.e., forward). If the car slows down, the same balloon will begin to drift backward. For the same reason, as the car goes round a curve, the balloon will drift towards the inside of the curve.

The equation to calculate the pressure inside a fluid in equilibrium is:

where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:

Here δij is the Kronecker delta. Using this the above equation becomes:

Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function:

Then:

Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field. Let the z-axis point downward. In this case the field is gravity, so Φ = −ρfgz where g is the gravitational acceleration, ρf is the mass density of the fluid. Taking the pressure as zero at the surface, where z is zero, the constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is

So pressure increases with depth below the surface of a liquid, as z denotes the distance from the surface of the liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater. This difference in pressure causes the upward buoyancy force.

The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:

The surface integral can be transformed into a volume integral with the help of the Gauss theorem:

where V is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body, since the fluid doesn't exert force on the part of the body which is outside of it.

The magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume V surrounded by a liquid. The force the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude:

where ρf is the density of the fluid, Vdisp is the volume of the displaced body of liquid, and g is the gravitational acceleration at the location in question.

If this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to

Though the above derivation of Archimedes principle is correct, a recent paper by the Brazilian physicist Fabio M. S. Lima brings a more general approach for the evaluation of the buoyant force exerted by any fluid (even non-homogeneous) on a body with arbitrary shape.[7] Interestingly, this method leads to the prediction that the buoyant force exerted on a rectangular block touching the bottom of a container points downward! Indeed, this downward buoyant force has been confirmed experimentally.[8]

The net force on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy force and the object's weight

If the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink. Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.

In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore;

and therefore

showing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent of the gravitational field regardless of geographic location.

It can be the case that forces other than just buoyancy and gravity come into play. This is the case if the object is restrained or if the object sinks to the solid floor. An object which tends to float requires a tension restraint force T in order to remain fully submerged. An object which tends to sink will eventually have a normal force of constraint N exerted upon it by the solid floor. The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent weight is defined.

If the object would otherwise float, the tension to restrain it fully submerged is:

When a sinking object settles on the solid floor, it experiences a normal force of:

Another possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and apparent weight of that object in the water (in Newtons). To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies:

The final result would be measured in Newtons.

Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum. The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for objects of very low average density such as a balloon or light foam).

A simplified explanation for the integration of the pressure over the contact area may be stated as follows:

Consider a cube immersed in a fluid with the upper surface horizontal.

The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side.

There are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero.

The upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.

Similarly, the downward force on the cube is the pressure on the top surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface.

As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.

This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.

This analogy is valid for variations in the size of the cube.

If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended to an arbitrary number of cubes.

An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence.

Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.

A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up.

Rotational stability is of great importance to floating vessels. Given a small angular displacement, the vessel may return to its original position (stable), move away from its original position (unstable), or remain where it is (neutral).

Rotational stability depends on the relative lines of action of forces on an object. The upward buoyancy force on an object acts through the center of buoyancy, being the centroid of the displaced volume of fluid. The weight force on the object acts through its center of gravity. A buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment'.

The stability of a buoyant object at the surface is more complex, and it may remain stable even if the center of gravity is above the center of buoyancy, provided that when disturbed from the equilibrium position, the center of buoyancy moves further to the same side that the center of gravity moves, thus providing a positive righting moment. If this occurs, the floating object is said to have a positive metacentric height. This situation is typically valid for a range of heel angles, beyond which the center of buoyancy does not move enough to provide a positive righting moment, and the object becomes unstable. It is possible to shift from positive to negative or vice versa more than once during a heeling disturbance, and many shapes are stable in more than one position.

The atmosphere's density depends upon altitude. As an airship rises in the atmosphere, its buoyancy decreases as the density of the surrounding air decreases. In contrast, as a submarine expels water from its buoyancy tanks, it rises because its volume is constant (the volume of water it displaces if it is fully submerged) while its mass is decreased.

As a floating object rises or falls, the forces external to it change and, as all objects are compressible to some extent or another, so does the object's volume. Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands.

If an object at equilibrium has a compressibility less than that of the surrounding fluid, the object's equilibrium is stable and it remains at rest. If, however, its compressibility is greater, its equilibrium is then unstable, and it rises and expands on the slightest upward perturbation, or falls and compresses on the slightest downward perturbation.

Submarines rise and dive by filling large ballast tanks with seawater. To dive, the tanks are opened to allow air to exhaust out the top of the tanks, while the water flows in from the bottom. Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth. Most military submarines operate with a slightly negative buoyancy and maintain depth by using the "lift" of the stabilizers with forward motion.[citation needed]

The height to which a balloon rises tends to be stable. As a balloon rises it tends to increase in volume with reducing atmospheric pressure, but the balloon itself does not expand as much as the air on which it rides. The average density of the balloon decreases less than that of the surrounding air. The weight of the displaced air is reduced. A rising balloon stops rising when it and the displaced air are equal in weight. Similarly, a sinking balloon tends to stop sinking.

Underwater divers are a common example of the problem of unstable buoyancy due to compressibility. The diver typically wears an exposure suit which relies on gas-filled spaces for insulation, and may also wear a buoyancy compensator, which is a variable volume buoyancy bag which is inflated to increase buoyancy and deflated to decrease buoyancy. The desired condition is usually neutral buoyancy when the diver is swimming in mid-water, and this condition is unstable, so the diver is constantly making fine adjustments by control of lung volume, and has to adjust the contents of the buoyancy compensator if the depth varies.

If the weight of an object is less than the weight of the displaced fluid when fully submerged, then the object has an average density that is less than the fluid and when fully submerged will experience a buoyancy force greater than its own weight.[9] If the fluid has a surface, such as water in a lake or the sea, the object will float and settle at a level where it displaces the same weight of fluid as the weight of the object. If the object is immersed in the fluid, such as a submerged submarine or air in a balloon, it will tend to rise. If the object has exactly the same density as the fluid, then its buoyancy equals its weight. It will remain submerged in the fluid, but it will neither sink nor float, although a disturbance in either direction will cause it to drift away from its position. An object with a higher average density than the fluid will never experience more buoyancy than weight and it will sink. A ship will float even though it may be made of steel (which is much denser than water), because it encloses a volume of air (which is much less dense than water), and the resulting shape has an average density less than that of the water.

[5]
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According to the Roman architect Vitruvius, the Greek mathematician and philosopher Archimedes first discovered buoyancy in the 3rd century B.C. while puzzling over a problem posed to him by King Hiero II of Syracuse. King Hiero suspected that his gold crown, made in the shape of a wreath, was not actually made of pure gold, but rather a mixture of gold and silver.

Allegedly, while taking a bath, Archimedes noticed that the more he sank into the tub, the more water flowed out of it. He realized this was the answer to his predicament, and rushed home while crying “Eureka!” (“I’ve found it!”) He then made two objects – one gold and one silver – that were the same weight as the crown, and dropped each one into a vessel filled to the brim with water.

Archimedes observed that the silver mass caused more water to flow out of the vessel than the gold one. Next, he observed that his "gold" crown caused more water to flow out of the vessel than the pure gold object he had created, even though the two crowns were of the same weight. Thus, Archimedes demonstrated that his crown indeed contained silver.

Though this tale illustrates the principle of buoyancy, it may be a legend. Archimedes never wrote down the story himself. Furthermore, in practice, if a tiny amount of silver were indeed swapped for the gold, the amount of water displaced would be too small to reliably measure.

Prior to the discovery of buoyancy, it was believed that an object’s shape determined whether or not it would float.

The buoyant force arises from differences in hydrostatic pressure – the pressure exerted by a static fluid. A ball that is placed higher up in a fluid will experience less pressure than the same ball placed further down. This is because there is more fluid, and therefore more weight, acting on the ball when it is deeper in the fluid.

Thus, the pressure at the top of an object is weaker than the pressure at the bottom. Pressure can be converted to force using the formula Force = Pressure x Area. There is a net force pointing upward. This net force – which points upwards regardless of the object’s shape – is the buoyancy force.

The hydrostatic pressure is given by P = rgh, where r is the density of the fluid, g is acceleration due to gravity, and h is the depth inside the fluid. The hydrostatic pressure does not depend on the shape of the fluid.

The Archimedes principle states that the buoyant force exerted on an object that is submerged partially or completely in a fluid is equal to the weight of the fluid that is displaced by the object.

This is expressed by the formula F = rgV, where r is the density of the fluid, g is acceleration due to gravity, and V is the volume of fluid that is displaced by the object. V only equals the volume of the object if it is completely submerged.

The buoyant force is an upward force that opposes the downward force of gravity. The magnitude of the buoyant force determines whether an object will sink, float, or rise when submerged in a fluid.

Several other observations can be drawn from the formula, as well.

A cube with a volume of 2.0 cm3 is submerged halfway into water. What is the buoyant force experienced by the cube?

A cube with a volume of 2.0 cm3 is submerged fully into water. What is the buoyant force experienced by the cube?

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The principle of buoyancy holds that the buoyant or lifting force of an object submerged in a fluid is equal to the weight of the fluid it has displaced. The concept is also known as Archimedes's principle, after the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 b.c.), who discovered it. Applications of Archimedes's principle can be seen across a wide vertical spectrum: from objects deep beneath the oceans to those floating on its surface, and from the surface to the upper limits of the stratosphere and beyond.

There is a famous story that Sir Isaac Newton (1642-1727) discovered the principle of gravity when an apple fell on his head. The tale, an exaggerated version of real events, has become so much a part of popular culture that it has been parodied in television commercials. Almost equally well known is the legend of how Archimedes discovered the concept of buoyancy.

A native of Syracuse, a Greek colony in Sicily, Archimedes was related to one of that city's kings, Hiero II (308?-216 b.c.). After studying in Alexandria, Egypt, he returned to his hometown, where he spent the remainder of his life. At some point, the royal court hired (or compelled) him to set about determining the weight of the gold in the king's crown. Archimedes was in his bath pondering this challenge when suddenly it occurred to him that the buoyant force of a submerged object is equal to the weight of the fluid displaced by it.

He was so excited, the legend goes, that he jumped out of his bath and ran naked through the streets of Syracuse shouting "Eureka!" (I have found it). Archimedes had recognized a principle of enormous value—as will be shown—to shipbuilders in his time, and indeed to shipbuilders of the present.

Concerning the history of science, it was a particularly significant discovery; few useful and enduring principles of physics date to the period before Galileo Galilei (1564-1642.) Even among those few ancient physicists and inventors who contributed work of lasting value—Archimedes, Hero of Alexandria (c. 65-125 a.d.), and a few others—there was a tendency to miss the larger implications of their work. For example, Hero, who discovered steam power, considered it useful only as a toy, and as a result, this enormously significant discovery was ignored for seventeen centuries.

In the case of Archimedes and buoyancy, however, the practical implications of the discovery were more obvious. Whereas steam power must indeed have seemed like a fanciful notion to the ancients, there was nothing farfetched about oceangoing vessels. Shipbuilders had long been confronted with the problem of how to keep a vessel afloat by controlling the size of its load on the one hand, and on the other hand, its tendency to bob above the water. Here, Archimedes offered an answer.

Why does an object seem to weigh less underwater than above the surface? How is it that a ship made of steel, which is obviously heavier than water, can float? How can we determine whether a balloon will ascend in the air, or a submarine will descend in the water? These and other questions are addressed by the principle of buoyancy, which can be explained in terms of properties—most notably, gravity—unknown to Archimedes.

To understand the factors at work, it is useful to begin with a thought experiment. Imagine a certain quantity of fluid submerged within a larger body of the same fluid. Note that the terms "liquid" or "water" have not been used: not only is "fluid" a much more general term, but also, in general physical terms and for the purposes of the present discussion, there is no significant difference between gases and liquids. Both conform to the shape of the container in which they are placed, and thus both are fluids.

To return to the thought experiment, what has been posited is in effect a "bag" of fluid—that is, a "bag" made out of fluid and containing fluid no different from the substance outside the "bag." This "bag" is subjected to a number of forces. First of all, there is its weight, which tends to pull it to the bottom of the container. There is also the pressure of the fluid all around it, which varies with depth: the deeper within the container, the greater the pressure.

Pressure is simply the exertion of force over a two-dimensional area. Thus it is as though the fluid is composed of a huge number of two-dimensional "sheets" of fluid, each on top of the other, like pages in a newspaper. The deeper into the larger body of fluid one goes, the greater the pressure; yet it is precisely this increased force at the bottom of the fluid that tends to push the "bag" upward, against the force of gravity.

Now consider the weight of this "bag." Weight is a force—the product of mass multiplied by acceleration—that is, the downward acceleration due to Earth's gravitational pull. For an object suspended in fluid, it is useful to substitute another term for mass. Mass is equal to volume, or the amount of three-dimensional space occupied by an object, multiplied by density. Since density is equal to mass divided by volume, this means that volume multiplied by density is the same as mass.

We have established that the weight of the fluid "bag" is Vdg, where V is volume, d is density, and g is the acceleration due to gravity. Now imagine that the "bag" has been replaced by a solid object of exactly the same size. The solid object will experience exactly the same degree of pressure as the imaginary "bag" did—and hence, it will also experience the same buoyant force pushing it up from the bottom. This means that buoyant force is equal to the weight—Vdg —of displaced fluid.

Buoyancy is always a double-edged proposition. If the buoyant force on an object is greater than the weight of that object—in other words, if the object weighs less than the amount of water it has displaced—it will float. But if the buoyant force is less than the object's weight, the object will sink. Buoyant force is not the same as net force: if the object weighs more than the water it displaces, the force of its weight cancels out and in fact "overrules" that of the buoyant force.

At the heart of the issue is density. Often, the density of an object in relation to water is referred to as its specific gravity: most metals, which are heavier than water, are said to have a high specific gravity. Conversely, petroleum-based products typically float on the surface of water, because their specific gravity is low. Note the close relationship between density and weight where buoyancy is concerned: in fact, the most buoyant objects are those with a relatively high volume and a relatively low density.

This can be shown mathematically by means of the formula noted earlier, whereby density is equal to mass divided by volume. If Vd = V(m/V), an increase in density can only mean an increase in mass. Since weight is the product of mass multiplied by g (which is assumed to be a constant figure), then an increase in density means an increase in mass and hence, an increase in weight—not a good thing if one wants an object to float.

In the early 1800s, a young Mississippi River flat-boat operator submitted a patent application describing a device for "buoying vessels over shoals." The invention proposed to prevent a problem he had often witnessed on the river—boats grounded on sandbars—by equipping the boats with adjustable buoyant air chambers. The young man even whittled a model of his invention, but he was not destined for fame as an inventor; instead, Abraham Lincoln (1809-1865) was famous for much else. In fact Lincoln had a sound idea with his proposal to use buoyant force in protecting boats from running aground.

Buoyancy on the surface of water has a number of easily noticeable effects in the real world. (Having established the definition of fluid, from this point onward, the fluids discussed will be primarily those most commonly experienced: water and air.) It is due to buoyancy that fish, human swimmers, icebergs, and ships stay afloat. Fish offer an interesting application of volume change as a means of altering buoyancy: a fish has an internal swim bladder, which is filled with gas. When it needs to rise or descend, it changes the volume in its swim bladder, which then changes its density. The examples of swimmers and icebergs directly illustrate the principle of density—on the part of the water in the first instance, and on the part of the object itself in the second.

To a swimmer, the difference between swimming in fresh water and salt water shows that buoyant force depends as much on the density of the fluid as on the volume displaced. Fresh water has a density of 62.4 lb/ft3 (9,925 N/m3), whereas that of salt water is 64 lb/ft3 (10,167 N/m3). For this reason, salt water provides more buoyant force than fresh water; in Israel's Dead Sea, the saltiest body of water on Earth, bathers experience an enormous amount of buoyant force.

Water is an unusual substance in a number of regards, not least its behavior as it freezes. Close to the freezing point, water thickens up, but once it turns to ice, it becomes less dense. This is why ice cubes and icebergs float. However, their low density in comparison to the water around them means that only part of an iceberg stays atop the surface. The submerged percentage of an iceberg is the same as the ratio of the density of ice to that of water: 89%.

Because water itself is relatively dense, a high-volume, low-density object is likely to displace a quantity of water more dense—and heavier—than the object itself. By contrast, a steel ball dropped into the water will sink straight to the bottom, because it is a low-volume, high-density object that outweighs the water it displaced.

This brings back the earlier question: how can a ship made out of steel, with a density of 487 lb/ft3 (77,363 N/m3), float on a salt-water ocean with an average density of only about one-eighth that amount? The answer lies in the design of the ship's hull. If the ship were flat like a raft, or if all the steel in it were compressed into a ball, it would indeed sink. Instead, however, the hollow hull displaces a volume of water heavier than the ship's own weight: once again, volume has been maximized, and density minimized.

For a ship to be seaworthy, it must maintain a delicate balance between buoyancy and stability. A vessel that is too light—that is, too much volume and too little density—will bob on the top of the water. Therefore, it needs to carry a certain amount of cargo, and if not cargo, then water or some other form of ballast. Ballast is a heavy substance that increases the weight of an object experiencing buoyancy, and thereby improves its stability.

Ideally, the ship's center of gravity should be vertically aligned with its center of buoyancy. The center of gravity is the geometric center of the ship's weight—the point at which weight above is equal to weight below, weight fore is equal to weight aft, and starboard (right-side) weight is equal to weight on the port (left) side. The center of buoyancy is the geometric center of its submerged volume, and in a stable ship, it is some distance directly below center of gravity.

Displacement, or the weight of the fluid that is moved out of position when an object is immersed, gives some idea of a ship's stability. If a ship set down in the ocean causes 1,000 tons (8.896 · 106 N) of water to be displaced, it is said to possess a displacement of 1,000 tons. Obviously, a high degree of displacement is desirable. The principle of displacement helps to explain how an aircraft carrier can remain afloat, even though it weighs many thousands of tons.

A submarine uses ballast as a means of descending and ascending underwater: when the submarine captain orders the crew to take the craft down, the craft is allowed to take water into its ballast tanks. If, on the other hand, the command is given to rise toward the surface, a valve will be opened to release compressed air into the tanks. The air pushes out the water, and causes the craft to ascend.

A submarine is an underwater ship; its streamlined shape is designed to ease its movement. On the other hand, there are certain kinds of underwater vessels, known as submersibles, that are designed to sink—in order to observe or collect data from the ocean floor. Originally, the idea of a submersible was closely linked to that of diving itself. An early submersible was the diving bell, a device created by the noted English astronomer Edmund Halley (1656-1742.)

Though his diving bell made it possible for Halley to set up a company in which hired divers salvaged wrecks, it did not permit divers to go beyond relatively shallow depths. First of all, the diving bell received air from the surface: in Halley's time, no technology existed for taking an oxygen supply below. Nor did it provide substantial protection from the effects of increased pressure at great depths.

The most immediate of those effects is, of course, the tendency of an object experiencing such pressure to simply implode like a tin can in a vise. Furthermore, the human body experiences several severe reactions to great depth: under water, nitrogen gas accumulates in a diver's bodily tissues, producing two different—but equally frightening—effects.

Nitrogen is an inert gas under normal conditions, yet in the high pressure of the ocean depths it turns into a powerful narcotic, causing nitrogen narcosis—often known by the poetic-sounding name "rapture of the deep." Under the influence of this deadly euphoria, divers begin to think themselves invincible, and their altered judgment can put them into potentially fatal situations.

Nitrogen narcosis can occur at depths as shallow as 60 ft (18.29 m), and it can be overcome simply by returning to the surface. However, one should not return to the surface too quickly, particularly after having gone down to a significant depth for a substantial period of time. In such an instance, on returning to the surface nitrogen gas will bubble within the body, producing decompression sickness—known colloquially as "the bends." This condition may manifest as itching and other skin problems, joint pain, choking, blindness, seizures, unconsciousness, and even permanent neurological defects such as paraplegia.

French physiologist Paul Bert (1833-1886) first identified the bends in 1878, and in 1907, John Scott Haldane (1860-1936) developed a method for counteracting decompression sickness. He calculated a set of decompression tables that advised limits for the amount of time at given depths. He recommended what he called stage decompression, which means that the ascending diver stops every few feet during ascension and waits for a few minutes at each level, allowing the body tissues time to adjust to the new pressure. Modern divers use a decompression chamber, a sealed container that simulates the stages of decompression.

In 1930, the American naturalist William Beebe (1877-1962) and American engineer Otis Barton created the bathy-sphere. This was the first submersible that provided the divers inside with adequate protection from external pressure. Made of steel and spherical in shape, the bathysphere had thick quartz windows and was capable of maintaining ordinary atmosphere pressure even when lowered by a cable to relatively great depths. In 1934, a bathysphere descended to what was then an extremely impressive depth: 3,028 ft (923 m). However, the bathysphere was difficult to operate and maneuver, and in time it was be replaced by a more workable vessel, the bathyscaphe.

Before the bathyscaphe appeared, however, in 1943, two Frenchmen created a means for divers to descend without the need for any sort of external chamber. Certainly a diver with this new apparatus could not go to anywhere near the same depths as those approached by the bathy-sphere; nonetheless, the new aqualung made it possible to spend an extended time under the surface without need for air. It was now theoretically feasible for a diver to go below without any need for help or supplies from above, because he carried his entire oxygen supply on his back. The name of one of inventors, Emile Gagnan, is hardly a household word; but that of the other—Jacques Cousteau (1910-1997)—certainly is. So, too, is the name of their invention: the s elf-c ontained u nderwater b reathing a pparatus, better known as scuba.

The most important feature of the scuba gear was the demand regulator, which made it possible for the divers to breathe air at the same pressure as their underwater surroundings. This in turn facilitated breathing in a more normal, comfortable manner. Another important feature of a modern diver's equipment is a buoyancy compensation device. Like a ship atop the water, a diver wants to have only so much buoyancy—not so much that it causes him to surface.

As for the bathyscaphe—a term whose two Greek roots mean "deep" and "boat"—it made its debut five years after scuba gear. Built by the Swiss physicist and adventurer Auguste Piccard (1884-1962), the bathyscaphe consisted of two compartments: a heavy steel crew cabin that was resistant to sea pressure, and above it, a larger, light container called a float. The float was filled with gasoline, which in this case was not used as fuel, but to provide extra buoyancy, because of the gasoline's low specific gravity.

When descending, the occupants of the bathyscaphe—there could only be two, since the pressurized chamber was just 79 in (2.01 m) in diameter—released part of the gasoline to decrease buoyancy. They also carried iron ballast pellets on board, and these they released when preparing to ascend. Thanks to battery-driven screw propellers, the bathyscaphe was much more maneuverable than the bathysphere had ever been; furthermore, it was designed to reach depths that Beebe and Barton could hardly have conceived.

It took several years of unsuccessful dives, but in 1953 a bathyscaphe set the first of many depth records. This first craft was the Trieste, manned by Piccard and his son Jacques, which descended 10,335 ft (3,150 m) below the Mediterranean, off Capri, Italy. A year later, in the Atlantic Ocean off Dakar, French West Africa (now Senegal), French divers Georges Houot and Pierre-Henri Willm reached 13,287 ft (4,063 m) in the FNRS 3.

Then in 1960, Jacques Piccard and United States Navy Lieutenant Don Walsh set a record that still stands: 35,797 ft (10,911 m)—23% greater than the height of Mt. Everest, the world's tallest peak. This they did in the Trieste some 250 mi (402 km) southeast of Guam at the Mariana Trench, the deepest spot in the Pacific Ocean and indeed the deepest spot on Earth. Piccard and Walsh went all the way to the bottom, a descent that took them 4 hours, 48 minutes. Coming up took 3 hours, 17 minutes.

Thirty-five years later, in 1995, the Japanese craft Kaiko also made the Mariana descent and confirmed the measurements of Piccard and Walsh. But the achievement of the Kaiko was not nearly as impressive of that of the Trieste's twoman crew: the Kaiko, in fact, had no crew. By the 1990s, sophisticated remote-sensing technology had made it possible to send down unmanned ocean expeditions, and it became less necessary to expose human beings to the incredible risks encountered by the Piccards, Walsh, and others.

An example of such an unmanned vessel is the one featured in the opening minutes of the Academy Award-winning motion picture Titanic (1997). The vessel itself, whose sinking in 1912 claimed more than 1,000 lives, rests at such a great depth in the North Atlantic that it is impractical either to raise it, or to send manned expeditions to explore the interior of the wreck. The best solution, then, is a remotely operated vessel of the kind also used for purposes such as mapping the ocean floor, exploring for petroleum and other deposits, and gathering underwater plate technology data.

The craft used in the film, which has "arms" for grasping objects, is of a variety specially designed for recovering items from shipwrecks. For the scenes that showed what was supposed to be the Titanic as an active vessel, director James Cameron used a 90% scale model that depicted the ship's starboard side—the side hit by the iceberg. Therefore, when showing its port side, as when it was leaving the Southampton, England, dock on April 15, 1912, all shots had to be reversed: the actual signs on the dock were in reverse lettering in order to appear correct when seen in the final version. But for scenes of the wrecked vessel lying at the bottom of the ocean, Cameron used the real Titanic.

To do this, he had to use a submersible; but he did not want to shoot only from inside the submersible, as had been done in the 1992 IMAX film Titanica. Therefore, his brother Mike Cameron, in cooperation with Panavision, built a special camera that could with stand 400 atm (3.923 · 107 Pa)—that is, 400 times the air pressure at sea level. The camera was attached to the outside of the submersible, which for these external shots was manned by Russian submarine operators.

Because the special camera only held twelve minutes' worth of film, it was necessary to make a total of twelve dives. On the last two, a remotely operated submersible entered the wreck, which would have been too dangerous for the humans in the manned craft. Cameron had intended the remotely operated submersible as a mere prop, but in the end its view inside the ruined Titanic added one of the most poignant touches in the entire film. To these he later added scenes involving objects specific to the film's plot, such as the safe. These he shot in a controlled underwater environment designed to look like the interior of the Titanic.

In the earlier description of Piccard's bathyscaphe design, it was noted that the craft consisted of two compartments: a heavy steel crew cabin resistant to sea pressure, and above it a larger, light container called a float. If this sounds rather like the structure of a hot-air balloon, there is no accident in that.

In 1931, nearly two decades before the bathyscaphe made its debut, Piccard and another Swiss scientist, Paul Kipfer, set a record of a different kind with a balloon. Instead of going lower than anyone ever had, as Piccard and his son Jacques did in 1953—and as Jacques and Walsh did in an even greater way in 1960—Piccard and Kipfer went higher than ever, ascending to 55,563 ft (16,940 m). This made them the first two men to penetrate the stratosphere, which is the next atmospheric layer above the troposphere, a layer approximately 10 mi (16.1 km) high that covers the surface of Earth.

Piccard, without a doubt, experienced the greatest terrestrial altitude range of any human being over a lifetime: almost 12.5 mi (20.1 km) from his highest high to his lowest low, 84% of it above sea level and the rest below. His career, then, was a tribute to the power of buoyant force—and to the power of overcoming buoyant force for the purpose of descending to the ocean depths. Indeed, the same can be said of the Piccard family as a whole: not only did Jacques set the world's depth record, but years later, Jacques's son Bertrand took to the skies for another record-setting balloon flight.

In 1999, Bertrand Piccard and British balloon instructor Brian Wilson became the first men to circumnavigate the globe in a balloon, the Breitling Orbiter 3. The craft extended 180 ft (54.86) from the top of the envelope—the part of the balloon holding buoyant gases—to the bottom of the gondola, the part holding riders. The pressurized cabin had one bunk in which one pilot could sleep while the other flew, and up front was a computerized control panel which allowed the pilot to operate the burners, switch propane tanks, and release empty ones. It took Piccard and Wilson just 20 days to circle the Earth—a far cry from the first days of ballooning two centuries earlier.

The Piccard family, though Swiss, are francophone; that is, they come from the French-speaking part of Switzerland. This is interesting, because the history of human encounters with buoyancy—below the ocean and even more so in the air—has been heavily dominated by French names. In fact, it was the French brothers, Joseph-Michel (1740-1810) and Jacques-Etienne (1745-1799) Montgolfier, who launched the first balloon in 1783. These two became to balloon flight what two other brothers, the Americans Orville and Wilbur Wright, became with regard to the invention that superseded the balloon twelve decades later: the airplane.

On that first flight, the Montgolfiers sent up a model 30 ft (9.15 m) in diameter, made of linen-lined paper. It reached a height of 6,000 ft (1,828 m), and stayed in the air for 10 minutes before coming back down. Later that year, the Montgolfiers sent up the first balloon flight with living creatures—a sheep, a rooster, and a duck—and still later in 1783, Jean-François Pilatre de Rozier (1756-1785) became the first human being to ascend in a balloon.

Rozier only went up 84 ft (26 m), which was the length of the rope that tethered him to the ground. As the makers and users of balloons learned how to use ballast properly, however, flight times were extended, and balloon flight became ever more practical. In fact, the world's first military use of flight dates not to the twentieth century but to the eighteenth—1794, specifically, when France created a balloon corps.

There are only three gases practical for lifting a balloon: hydrogen, helium, and hot air. Each is much less than dense than ordinary air, and this gives them their buoyancy. In fact, hydrogen is the lightest gas known, and because it is cheap to produce, it would be ideal—except for the fact that it is extremely flammable. After the 1937 crash of the airship Hindenburg, the era of hydrogen use for lighter-than-air transport effectively ended.

Helium, on the other hand, is perfectly safe and only slightly less buoyant than hydrogen. This makes it ideal for balloons of the sort that children enjoy at parties; but helium is expensive, and therefore impractical for large balloons. Hence, hot air—specifically, air heated to a temperature of about 570°F (299°C), is the only truly viable option.

Charles's law, one of the laws regarding the behavior of gases, states that heating a gas will increase its volume. Gas molecules, unlike their liquid or solid counterparts, are highly nonattractive—that is, they tend to spread toward relatively great distances from one another. There is already a great deal of empty space between gas molecules, and the increase in volume only increases the amount of empty space. Hence, density is lowered, and the balloon floats.

Around the same time the Montgolfier brothers launched their first balloons, another French designer, Jean-Baptiste-Marie Meusnier, began experimenting with a more streamlined, maneuverable model. Early balloons, after all, could only be maneuvered along one axis, up and down: when it came to moving sideways or forward and backward, they were largely at the mercy of the elements.

It was more than a century before Meusnier's idea—the prototype for an airship—became a reality. In 1898, Alberto Santos-Dumont of Brazil combined a balloon with a propeller powered by an internal-combustion instrument, creating a machine that improved on the balloon, much as the bathyscaphe later improved on the bathysphere. Santos-Dumont's airship was non-rigid, like a balloon. It also used hydrogen, which is apt to contract during descent and collapse the envelope. To counter this problem, Santos-Dumont created the ballonet, an internal airbag designed to provide buoyancy and stabilize flight.

One of the greatest figures in the history of lighter-than-air flight—a man whose name, along with blimp and dirigible, became a synonym for the airship—was Count Ferdinand von Zeppelin (1838-1917). It was he who created a lightweight structure of aluminum girders and rings that made it possible for an airship to remain rigid under varying atmospheric conditions. Yet Zeppelin's earliest launches, in the decade that followed 1898, were fraught with a number of problems—not least of which were disasters caused by the flammability of hydrogen.

Zeppelin was finally successful in launching airships for public transport in 1911, and the quarter-century that followed marked the golden age of airship travel. Not that all was "golden" about this age: in World War I, Germany used airships as bombers, launching the first London blitz in May 1915. By the time Nazi Germany initiated the more famous World War II London blitz 25 years later, ground-based anti-aircraft technology would have made quick work of any zeppelin; but by then, airplanes had long since replaced airships.

During the 1920s, though, airships such as the Graf Zeppelin competed with airplanes as a mode of civilian transport. It is a hallmark of the perceived safety of airships over airplanes at the time that in 1928, the Graf Zeppelin made its first transatlantic flight carrying a load of passengers. Just a year earlier, Charles Lindbergh had made the first-ever solo, nonstop transatlantic flight in an airplane. Today this would be the equivalent of someone flying to the Moon, or perhaps even Mars, and there was no question of carrying passengers. Furthermore, Lindbergh was celebrated as a hero for the rest of his life, whereas the passengers aboard the Graf Zeppelin earned no more distinction for bravery than would pleasure-seekers aboard a cruise.

For a few years, airships constituted the luxury liners of the skies; but the Hindenburg crash signaled the end of relatively widespread airship transport. In any case, by the time of the 1937 Hindenburg crash, lighter-than-air transport was no longer the leading contender in the realm of flight technology.

Ironically enough, by 1937 the airplane had long since proved itself more viable—even though it was actually heavier than air. The principles that make an airplane fly have little to do with buoyancy as such, and involve differences in pressure rather than differences in density. Yet the replacement of lighter-than-air craft on the cutting edge of flight did not mean that balloons and airships were relegated to the museum; instead, their purposes changed.

The airship enjoyed a brief resurgence of interest during World War II, though purely as a surveillance craft for the United States military. In the period after the war, the U.S. Navy hired the Goodyear Tire and Rubber Company to produce airships, and as a result of this relationship Goodyear created the most visible airship since the Graf Zeppelin and the Hindenburg: the Goodyear Blimp.

The blimp, known to viewers of countless sporting events, is much better-suited than a plane or helicopter to providing TV cameras with an aerial view of a stadium—and advertisers with a prominent billboard. Military forces and science communities have also found airships useful for unexpected purposes. Their virtual invisibility with regard to radar has reinvigorated interest in blimps on the part of the U.S. Department of Defense, which has discussed plans to use airships as radar platforms in a larger Strategic Air Initiative. In addition, French scientists have used airships for studying rain forest treetops or canopies.

Balloons have played a role in aiding space exploration, which is emblematic of the relationship between lighter-than-air transport and more advanced means of flight. In 1961, Malcolm D. Ross and Victor A. Prother of the U.S. Navy set the balloon altitude record with a height of 113,740 ft (34,668 m.) The technology that enabled their survival at more than 21 mi (33.8 km) in the air was later used in creating life-support systems for astronauts.

Balloon astronomy provides some of the clearest images of the cosmos: telescopes mounted on huge, unmanned balloons at elevations as high as 120,000 ft (35,000 m)—far above the dust and smoke of Earth—offer high-resolution images. Balloons have even been used on other planets: for 46 hours in 1985, two balloons launched by the unmanned Soviet expedition to Venus collected data from the atmosphere of that planet.

American scientists have also considered a combination of a large hot-air balloon and a smaller helium-filled balloon for gathering data on the surface and atmosphere of Mars during expeditions to that planet. As the air balloon is heated by the Sun's warmth during the day, it would ascend to collect information on the atmosphere. (In fact the "air" heated would be from the atmosphere of Mars, which is composed primarily of carbon dioxide.) Then at night when Mars cools, the air balloon would lose its buoyancy and descend, but the helium balloon would keep it upright while it collected data from the ground.

"Buoyancy" (Web site). (March 12, 2001).

"Buoyancy" (Web site). (March 12, 2001).

"Buoyancy Basics" Nova/PBS (Web site). (March 12, 2001).

Challoner, Jack. Floating and Sinking. Austin, TX: Raintree Steck-Vaughn, 1997.

Cobb, Allan B. Super Science Projects About Oceans. New York: Rosen, 2000.

Gibson, Gary. Making Things Float and Sink. Illustrated by Tony Kenyon. Brookfield, CT: Copper Beeck Brooks, 1995.

Taylor, Barbara. Liquid and Buoyancy. New York: Warwick Press, 1990.

A rule of physics which holds that the buoyant force of an object immersed in fluid is equal to the weight of the fluid displaced by the object. It is named after the Greekmathematician, physicist, and inventor Archimedes (c. 287-212 b.c.), who first identified it.

A heavy substance that, by increasing the weight of an object experiencing buoyancy, improves its stability.

The tendency of an objectimmersed in a fluid to float. This can be explained by Archimedes's principle.

Mass divided by volume.

A measure of the weight of the fluid that has had to be moved out of position so that an object can be immersed. If a ship set down in the ocean causes 1,000 tons of water to be displaced, it is said to possess a displacement of 1,000 tons.

Any substance, whether gas or liquid, that conforms to the shape of itscontainer.

The product of mass multiplied by acceleration.

A measure of inertia, indicating the resistance of an object to a change in itsmotion. For an object immerse in fluid, mass is equal to volume multiplied by density.

The exertion of force over a two-dimensional area; hence the formula for pressure is force divided byarea. The British system of measures typically reckons pressure in pounds per square inch. In metric terms, this is measured in terms of newtons (N) per square meter, a figure known as a pascal (Pa.)

The density of an object or substance relative to the density of water; or more generally, the ratio between the densities of two objects or substances.

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