# BUOYANCY

## CONCEPT

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.

## HOW IT WORKS

### Archimedes Discovers Buoyancy

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 valueas will be shownto 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 valueArchimedes, Hero of Alexandria (c. 65-125 a.d.), and a few othersthere 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.

### Buoyancy and Weight

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 propertiesmost notably, gravityunknown 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 fluidthat 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 forcethe product of mass multiplied by accelerationthat 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" didand hence, it will also experience the same buoyant force pushing it up from the bottom. This means that buoyant force is equal to the weightVdg of displaced fluid.

Buoyancy is always a double-edged proposition. If the buoyant force on an object is greater than the weight of that objectin other words, if the object weighs less than the amount of water it has displacedit 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 weightnot a good thing if one wants an object to float.

## REAL-LIFE APPLICATIONS

### Staying Afloat

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 riverboats grounded on sandbarsby 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 densityon 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%.

### Ships at Sea

Because water itself is relatively dense, a high-volume, low-density object is likely to displace a quantity of water more denseand heavierthan 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 lightthat is, too much volume and too little densitywill 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 weightthe 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.

### Down to the Depths

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 sinkin 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.

#### PERILS OF THE DEEP.

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 differentbut equally frighteningeffects.

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 narcosisoften 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 sicknessknown 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.

#### BATHYSPHERE, SCUBA, AND BATHYSCAPHE.

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 otherJacques 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 buoyancynot so much that it causes him to surface.

As for the bathyscaphea 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 bathyscaphethere could only be two, since the pressurized chamber was just 79 in (2.01 m) in diameterreleased 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.

#### REACHING NEW DEPTHS.

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.

#### FILMING TITANIC.

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 sidethe 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.

### Into the Skies

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 1953and as Jacques and Walsh did in an even greater way in 1960Piccard 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 forceand 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 envelopethe part of the balloon holding buoyant gasesto 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 Eartha far cry from the first days of ballooning two centuries earlier.

#### THE FIRST BALLOONS.

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 buoyancybelow the ocean and even more so in the airhas 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 creaturesa sheep, a rooster, and a duckand 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 eighteenth1794, specifically, when France created a balloon corps.

#### HOW A BALLOON FLOATS.

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 idealexcept 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 airspecifically, 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 nonattractivethat 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.

#### AIRSHIPS.

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 ideathe prototype for an airshipbecame 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 flighta man whose name, along with blimp and dirigible, became a synonym for the airshipwas 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 problemsnot 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.

#### THE LIMITATIONS OF LIGHTER-THAN-AIR TRANSPORT.

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 viableeven 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.

#### BLIMPS AND BALLOONS: ON THE CUTTING EDGE?.

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 stadiumand 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 Earthoffer 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). <http://www.aquaholic.com/gasses/laws.htm> (March 12, 2001).

"Buoyancy" (Web site). <http://www.uncwil.edu/nurc/aquarius/lessons/buoyancy.htm> (March 12, 2001).

"Buoyancy Basics" Nova/PBS (Web site). <http://www.pbs.org/wgbh/nova/lasalle/buoybasics.html> (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.

## KEY TERMS

### ARCHIMEDES'S PRINCIPLE:

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.

### BALLAST:

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

### BUOYANCY:

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

### DENSITY:

Mass divided by volume.

### DISPLACEMENT:

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.

### FLUID:

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

### FORCE:

The product of mass multiplied by acceleration.

### MASS:

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.

### PRESSURE:

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.)

### SPECIFIC GRAVITY:

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.

### VOLUME:

The amount of three-dimensional space occupied by an object. Volume is usually measured in cubic units.

### WEIGHT:

A force equal to mass multiplied by the acceleration due to gravity (32ft/9.8 m/sec2). For an object immersed influid, weight is the same as volume multiplied by density multiplied by gravitational acceleration.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"Buoyancy." Science of Everyday Things. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"Buoyancy." Science of Everyday Things. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/science/news-wires-white-papers-and-books/buoyancy

"Buoyancy." Science of Everyday Things. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/news-wires-white-papers-and-books/buoyancy

# Buoyancy

Buoyancy is the tendency of an object to float in a fluid, such as air or water. The principle of buoyancy was first discovered by Greek mathematician Archimedes (c. 287212 b.c.) and is therefore often called Archimedes' Principle. Legend has it that Archimedes was working on a problem given to him by the king of ancient Syracuse, Hieron II. The king had paid a goldsmith to make him a new crown but suspected that some metal other than gold had been used in the crown. He asked Archimedes to find out if his suspicions were correctbut without destroying the crown.

One day, perhaps while pondering the problem, Archimedes stepped into his bath and noticed the overflow of water. He suddenly realized that the volume of water that had flowed out of the bath had to be equal to the volume of his own body that was immersed. His problem was solved. Later historians claim that Archimedes was so excited with his discovery that he ran naked through the streets of Syracuse shouting "Eureka!" ("I've found it!").

Archimedes began performing experiments with objects in liquids. He immersed the crown and measured the amount of water it displaced. Then he immersed an equal weight of gold in the

water. If the crown were pure gold, it would displace the same amount of water. But the crown displaced more water than the gold, indicating it was made of a mixture of gold and silver, which is a bulkier substance. The king had the deceitful goldsmith executed.

## What causes buoyancy?

Suppose that you put a block of wood into a container of water. Two competing forces are at work. One force is the downward pressure of the wood on the water. That force is caused by the mass of the wood. The second force is the upward pressure of the water on the block. If the downward pressure of the wood is greater than the upward pressure of the water, the wood sinks. Otherwise, it floats.

The formal statement of Archimedes' Principle is this: the buoyant force acting on an object placed in a fluid is equal to the weight of the fluid displaced by the object. Suppose that the wood block in the example above has a volume of 1 cubic foot. A cubic foot of water weighs about 62.4 pounds. Therefore, water pushes upward on the wooden block with a force of 62.4 pounds.

But a cubic foot of most kinds of wood weighs about 40 to 50 pounds. So water pushes upward more strongly than the wood pushes downward, and the wood floats. If you substituted a block of lead for the wood, the result would be different. A cubic foot of lead weighs about 1,200 pounds. The block of lead pushes downward much more strongly than the water it displaces and it, therefore, will sink.

## Practical applications

The principle of buoyancy is used in many forms of transportation. Some sailing ships are made out of materials that are less dense than water and that would, therefore, float under any circumstances. But how can a ship made out of steel float? Steel has a density of 487 pounds per cubic foot, so it would be expected to sink if placed into water.

The reason steel ships float is that they are not constructed of solid pieces of steel. Instead, they consist of hollow shells made of steel. Inside the shell is air, which is much less dense than water or steel. A hollow block of steel and air has an overall density that is less than that of water; therefore, it can float.

Airships such as balloons and dirigibles operate on the same principle. Some material (such as plastic or cloth) is filled with a gas that is less dense than air. The gases most commonly used are hydrogen and helium. The total package of balloon plus gas weighs less than the air it displaces and is, therefore, pushed upward by the air.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"Buoyancy." UXL Encyclopedia of Science. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"Buoyancy." UXL Encyclopedia of Science. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/buoyancy

"Buoyancy." UXL Encyclopedia of Science. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/buoyancy

## buoyancy

buoyancy The condition that arises from the difference between the density of a given parcel of air or gas and that of the surrounding air. It is this that makes a hydrogen- or helium-filled balloon or airship float or rise through the atmosphere. If an air parcel is warmer than its surroundings, the density difference implies an upwards-directed force acting upon that parcel of air and it will rise, with positive buoyancy. When a parcel of air is colder than its surroundings the reverse condition causes it to sink, with downward (negative) buoyancy. See thermal.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyancy." A Dictionary of Ecology. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyancy." A Dictionary of Ecology. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/buoyancy-0

"buoyancy." A Dictionary of Ecology. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/buoyancy-0

## buoyancy

buoyancy Condition arising from the difference between the density of a given parcel of air or gas and that of the surrounding air. It is this that makes a hydrogen- or helium-filled balloon or airship float or rise through the atmosphere. Also, if an air parcel is warmer than its surroundings, the density difference implies an upwards directed force acting upon that parcel of air and it will rise, with positive buoyancy. When a parcel of air is colder than its surroundings the reverse condition causes it to sink, with downward (negative) buoyancy. See THERMAL.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyancy." A Dictionary of Earth Sciences. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyancy." A Dictionary of Earth Sciences. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/buoyancy

"buoyancy." A Dictionary of Earth Sciences. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/buoyancy

## buoyant

buoy·ant / ˈboi-ənt; ˈboōyənt/ • adj. able or apt to stay afloat or rise to the top of a liquid or gas. ∎  (of a liquid or gas) able to keep something afloat. ∎ fig. (of an economy, business, or market) involving or engaged in much activity: car sales were not buoyant. ∎ fig. cheerful and optimistic: the conference ended with the party in a buoyant mood. DERIVATIVES: buoy·an·cy n. buoy·ant·ly adv.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyant." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyant." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyant-0

"buoyant." The Oxford Pocket Dictionary of Current English. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyant-0

## buoyancy

buoyancy Upward pressure exerted on an object by the fluid in which it is immersed. The object is subjected to pressure from all sides. The result of all these pressures is a force acting upwards that is equal to the weight of the fluid displaced. See also Archimedes' principle

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyancy." World Encyclopedia. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyancy." World Encyclopedia. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/buoyancy

"buoyancy." World Encyclopedia. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/buoyancy

## buoyancy

buoyancy (boi´ənsē, bōō´yən–), upward force exerted by a fluid on any body immersed in it. Buoyant force can be explained in terms of Archimedes' principle.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyancy." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyancy." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/buoyancy

"buoyancy." The Columbia Encyclopedia, 6th ed.. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/buoyancy

## buoyant

buoyant XVI. — OF. bouyant or Sp. boyante light-sailing, prp. of boyar float. f. boya buoy; see -ANT.
Hence buoyancy XVIII.

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyant." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyant." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyant-1

"buoyant." The Concise Oxford Dictionary of English Etymology. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyant-1

## buoyancy

buoyancy •radiancy •immediacy, intermediacy •expediency • idiocy • saliency •resiliency • leniency •incipiency, recipiency •recreancy • pruriency • deviancy •subserviency • transiency • pliancy •buoyancy, flamboyancy •fluency, truancy •constituency • abbacy • embassy •celibacy • absorbency •incumbency, recumbency •ascendancy, intendancy, interdependency, pendency, resplendency, superintendency, tendency, transcendency •candidacy •presidency, residency •despondency • redundancy • infancy •sycophancy • argosy • legacy •profligacy • surrogacy •extravagancy • plangency • agency •regency •astringency, contingency, stringency •intransigency • exigency • cogency •pungency •convergency, emergency, insurgency, urgency •vacancy • piquancy • fricassee •mendicancy • efficacy • prolificacy •insignificancy • delicacy • intricacy •advocacy • fallacy • galaxy •jealousy, prelacy •repellency • valency • Wallasey •articulacy • corpulency • inviolacy •excellency • equivalency • pharmacy •supremacy • clemency • Christmassy •illegitimacy, legitimacy •intimacy • ultimacy • primacy •dormancy • diplomacy • contumacy •stagnancy •lieutenancy, subtenancy, tenancy •pregnancy •benignancy, malignancy •effeminacy • prominency •obstinacy • pertinency • lunacy •immanency •impermanency, permanency •rampancy • papacy • flippancy •occupancy •archiepiscopacy, episcopacy •transparency • leprosy • inerrancy •flagrancy, fragrancy, vagrancy •conspiracy • idiosyncrasy •minstrelsy • magistracy • piracy •vibrancy •adhocracy, aristocracy, autocracy, bureaucracy, democracy, gerontocracy, gynaecocracy (US gynecocracy), hierocracy, hypocrisy, meritocracy, mobocracy, monocracy, plutocracy, technocracy, theocracy •accuracy • obduracy • currency •curacy, pleurisy •confederacy • numeracy •degeneracy • itinerancy • inveteracy •illiteracy, literacy •innocency • trenchancy • deficiency •fantasy, phantasy •intestacy • ecstasy • expectancy •latency • chieftaincy • intermittency •consistency, insistency, persistency •instancy • militancy • impenitency •precipitancy • competency •hesitancy • apostasy • constancy •accountancy • adjutancy •consultancy, exultancy •impotency • discourtesy •inadvertency • privacy •irrelevancy, relevancy •solvency • frequency • delinquency •adequacy • poignancy

Pick a style below, and copy the text for your bibliography.

• MLA
• Chicago
• APA

"buoyancy." Oxford Dictionary of Rhymes. . Encyclopedia.com. 28 May. 2017 <http://www.encyclopedia.com>.

"buoyancy." Oxford Dictionary of Rhymes. . Encyclopedia.com. (May 28, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyancy

"buoyancy." Oxford Dictionary of Rhymes. . Retrieved May 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/buoyancy

## buoyant

buoyantabeyant, mayn't •ambient, circumambient •gradient, irradiant, radiant •expedient, ingredient, mediant, obedient •valiant • salient • resilient • emollient •defoliant • ebullient • suppliant •convenient, intervenient, lenient, prevenient •sapient •impercipient, incipient, percipient, recipient •recreant • variant • miscreant •Orient • nutrient •esurient, luxuriant, parturient, prurient •nescient, prescient •omniscient • insouciant • renunciant •officiant • negotiant • deviant •subservient • transient •affiant, Bryant, client, compliant, defiant, giant, pliant, reliant •buoyant, clairvoyant, flamboyant •fluent, pursuant, truant •affluent • effluent • mellifluent •confluent • circumfluent • congruent •issuant • continuant • constituent •lambent • absorbent •incumbent, recumbent •couchant • merchant • hadn't •ardent, guardant, regardant •pedant •appendant, ascendant, attendant, codependent, defendant, descendant, descendent, intendant, interdependent, pendant, pendent, splendent, superintendent, transcendent •antecedent, decedent, needn't, precedent •didn't • diffident • confident •accident • dissident •coincident, incident •oxidant • evident •improvident, provident •president, resident •strident, trident •co-respondent, correspondent, despondent, fondant, respondent •accordant, concordant, discordant, mordant, mordent •rodent •imprudent, jurisprudent, prudent, student •couldn't, shouldn't, wouldn't •impudent •abundant, redundant •decadent • verdant • infant • elephant •triumphant • sycophant • elegant •fumigant • congregant • litigant •termagant • arrogant • extravagant •pageant •cotangent, plangent, tangent •argent, Sargent, sergeant •agent • newsagent • regent •astringent, contingent, stringent •indigent • intelligent • negligent •diligent • intransigent • exigent •cogent •effulgent, fulgent, indulgent •pungent •convergent, detergent, divergent, emergent, insurgent, resurgent, urgent •bacchant • peccant • vacant • piquant •predicant • mendicant • significant •applicant • supplicant • communicant •lubricant • desiccant • intoxicant •gallant, talent •appellant, propellant, propellent, repellent, water-repellent •resemblant •assailant, inhalant •sealant • sibilant • jubilant •flagellant • vigilant • pestilent •silent •Solent, volant •coolant • virulent • purulent •ambulant, somnambulant •coagulant • crapulent • flatulent •feculent • esculent • petulant •stimulant • flocculent • opulent •postulant • fraudulent • corpulent •undulant •succulent, truculent •turbulent • violent • redolent •indolent • somnolent • excellent •insolent • nonchalant •benevolent, malevolent, prevalent •ambivalent, equivalent •garment • clement • segment •claimant, clamant, payment, raiment •ailment •figment, pigment •fitment • aliment • element •oddment •dormant, informant •moment • adamant • stagnant •lieutenant, pennant, subtenant, tenant •pregnant, regnant •remnant • complainant •benignant, indignant, malignant •recombinant • contaminant •eminent •discriminant, imminent •dominant, prominent •illuminant, ruminant •determinant • abstinent •continent, subcontinent •appurtenant, impertinent, pertinent •revenant •component, deponent, exponent, opponent, proponent •oppugnant, repugnant •immanent •impermanent, permanent •dissonant • consonant • alternant •covenant • resonant • rampant •discrepant • flippant • participant •occupant • serpent •apparent, arrant, transparent •Arendt •aberrant, deterrent, errant, inherent, knight-errant •entrant •declarant, parent •grandparent • step-parent •godparent •flagrant, fragrant, vagrant •registrant • celebrant • emigrant •immigrant • ministrant • aspirant •antiperspirant • recalcitrant •integrant • tyrant • vibrant • hydrant •migrant, transmigrant •abhorrent, torrent, warrant •quadrant • figurant • obscurant •blackcurrant, concurrent, currant, current, occurrent, redcurrant •white currant • cross-current •undercurrent •adherent, coherent, sederunt •exuberant, protuberant •reverberant • denaturant •preponderant • deodorant •different, vociferant •belligerent, refrigerant •accelerant • tolerant • cormorant •itinerant • ignorant • cooperant •expectorant • adulterant •irreverent, reverent •nascent, passant •absent •accent, relaxant •acquiescent, adolescent, albescent, Besant, coalescent, confessant, convalescent, crescent, depressant, effervescent, erubescent, evanescent, excrescent, flavescent, fluorescent, immunosuppressant, incandescent, incessant, iridescent, juvenescent, lactescent, liquescent, luminescent, nigrescent, obsolescent, opalescent, pearlescent, phosphorescent, pubescent, putrescent, quiescent, suppressant, tumescent, turgescent, virescent, viridescent •adjacent, complacent, obeisant •decent, recent •impuissant, reminiscent •Vincent • puissant •beneficent, maleficent •magnificent, munificent •Millicent • concupiscent • reticent •docent •lucent, translucent •discussant, mustn't •innocent •conversant, versant •consentient, sentient, trenchant •impatient, patient •ancient • outpatient •coefficient, deficient, efficient, proficient, sufficient •quotient • patent •interactant, reactant •disinfectant, expectant, protectant •repentant • acceptant •contestant, decongestant •sextant •blatant, latent •intermittent •assistant, coexistent, consistent, distant, equidistant, existent, insistent, persistent, resistant, subsistent, water-resistant •instant •cohabitant, habitant •exorbitant • militant • concomitant •impenitent, penitent •palpitant • crepitant • precipitant •competent, omnicompetent •irritant • incapacitant • Protestant •hesitant • visitant • mightn't • octant •remontant • constant •important, oughtn't •accountant • potent •mutant, pollutant •adjutant • executant • disputant •reluctant •consultant, exultant, resultant •combatant • omnipotent • impotent •inadvertent •Havant, haven't, savant, savante •advent •irrelevant, relevant •pursuivant • solvent • convent •adjuvant •fervent, observant, servant •manservant • maidservant •frequent, sequent •delinquent • consequent •subsequent • unguent • eloquent •grandiloquent, magniloquent •brilliant • poignant • hasn't •bezant, omnipresent, peasant, pheasant, pleasant, present •complaisant • malfeasant • isn't •cognizant • wasn't • recusant •doesn't