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Upwelling
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The replacement by deep water moving upwards of surface water driven offshore by wind
If the wind blows parallel to the coast in the southern hemisphere (such as along the coast of Peru, where the wind blows North), then Ekman transport can produce a net movement of surface water 90° to the left. This may result in coastal upwelling.
If the wind blows parallel to the coast in the northern hemisphere (such as the coast of California, where the wind blows South), then Ekman transport can produce a net movement of surface water 90° to the right. This may result in coastal upwelling.
Upwelling is an oceanographic phenomenon that involves wind-driven motion of dense, cooler, and usually nutrient-rich water towards the ocean surface, replacing the warmer, usually nutrient-depleted surface water. The nutrient-rich upwelled water stimulates the growth and reproduction of primary producers such as phytoplankton. Due to the biomass of phytoplankton and presence of cool water in these regions, upwelling zones can be identified by cool sea surface temperatures (SST) and high concentrations of chlorophyll-a.[1][2]
The increased availability of nutrients in upwelling regions results in high levels of primary production and thus fishery production. Approximately 25% of the total global marine fish catches come from five upwellings that occupy only 5% of the total ocean area.[3] Upwellings that are driven by coastal currents or diverging open ocean have the greatest impact on nutrient-enriched waters and global fishery yields.[3][4]
Contents
1 Mechanisms
2 Types
2.1 Coastal
2.1.1 Equatorial
2.1.2 Southern Ocean
2.1.3 Other sources
3 Variations
4 High productivity
5 Threats to upwelling ecosystems
6 References
7 External links
Mechanisms[edit]
The three main drivers that work together to cause upwelling are wind, Coriolis effect, and Ekman transport. They operate differently for different types of upwelling, but the general effects are the same.[5] In the overall process of upwelling, winds blow across the sea surface at a particular direction, which causes a wind-water interaction. As a result of the wind, the water is transported a net of 90 degrees from the direction of the wind due to Coriolis forces and Ekman transport. Ekman transport causes the surface layer of water to move at about a 45 degree angle from the direction of the wind, and the friction between that layer and the layer beneath it causes the successive layers to move in the same direction. This results in a spiral of water movement down the water column. Then, it is the Coriolis forces that dictate which way the water will move; in the Northern hemisphere, the water is transported to the right of the direction of the wind. In the Southern Hemisphere, the water is transported to the left of the wind.[6] If this net movement of water is divergent, then upwelling of deep water occurs to replace the water that was lost.[1][5]
Types[edit]
Areas of upwelling in red
The major upwellings in the ocean are associated with the divergence of currents that bring deeper, colder, nutrient rich waters to the surface. There are at least five types of upwelling: coastal upwelling, large-scale wind-driven upwelling in the ocean interior, upwelling associated with eddies, topographically-associated upwelling, and broad-diffusive upwelling in the ocean interior.
Coastal[edit]
Coastal upwelling is the best known type of upwelling, and the most closely related to human activities as it supports some of the most productive fisheries in the world. Wind-driven currents are diverted to the right of the winds in the Northern Hemisphere and to the left in the Southern Hemisphere due to the Coriolis effect. The result is a net movement of surface water at right angles to the direction of the wind, known as the Ekman transport (See also Ekman Spiral). When Ekman transport is occurring away from the coast, surface waters moving away are replaced by deeper, colder, and denser water.[4] Normally, this upwelling process occurs at a rate of about 5–10 meters per day, but the rate and proximity of upwelling to the coast can be changed due to the strength and distance of the wind.[1][7]
Deep waters are rich in nutrients, including nitrate, phosphate and silicic acid, themselves the result of decomposition of sinking organic matter (dead/detrital plankton) from surface waters. When brought to the surface, these nutrients are utilized by phytoplankton, along with dissolved CO2 (carbon dioxide) and light energy from the sun, to produce organic compounds, through the process of photosynthesis. Upwelling regions therefore result in very high levels of primary production (the amount of carbon fixed by phytoplankton) in comparison to other areas of the ocean. They account for about 50% of global marine productivity.[8] High primary production propagates up the food chain because phytoplankton are at the base of the oceanic food chain.[9]
The food chain follows the course of:
Phytoplankton → Zooplankton → Predatory zooplankton → Filter feeders → Predatory fish [4] → Marine birds, marine mammals [10]
Worldwide, there are five major coastal currents associated with upwelling areas: the Canary Current (off Northwest Africa), the Benguela Current (off southern Africa), the California Current (off California and Oregon), the Humboldt Current (off Peru and Chile), and the Somali Current (off Somalia and Oman). All of these currents support major fisheries. The four major eastern boundary currents in which coastal upwelling primarily occurs are the Canary Current, Benguela Current, California Current, and Humboldt Current.[11] The Benguela Current is the eastern boundary of the South Atlantic subtropical gyre and can be divided into a northern and southern sub-system with upwelling occurring in both areas. The subsystems are divided by an area of permanent upwelling off of Luderitz, which is the strongest upwelling zone in the world. The California Current System (CCS) is an eastern boundary current of the North Pacific that is also characterized by a north and south split. The split in this system occurs at Point Conception, California due to weak upwelling in the South and strong upwelling in the north. The Canary Current is an eastern boundary current of the North Atlantic Gyre and is also separated due to the presence of the Canary Islands. Finally, the Humboldt Current or the Peru Current flows west along the coast of South America from Peru to Chile and extends up to 1,000 kilometers offshore.[8] These four eastern boundary currents comprise the majority of coastal upwelling zones in the oceans.
Equatorial[edit]
Effects of equatorial upwelling on surface chlorophyll concentrations in the Pacific ocean
Upwelling at the equator is associated with the Intertropical Convergence Zone (ITCZ) which actually moves, and consequently, is often located just north or south of the equator. Easterly (westward) trade winds blow from the Northeast and Southeast and converge along the equator blowing West to form the ITCZ. Although there are no Coriolis forces present along the equator, upwelling still occurs just north and south of the equator. This results in a divergence, with denser, nutrient-rich water being upwelled from below, and results in the remarkable fact that the equatorial region in the Pacific can be detected from space as a broad line of high phytoplankton concentration.[3]
Southern Ocean[edit]
Upwelling in the Southern Ocean
Large-scale upwelling is also found in the Southern Ocean. Here, strong westerly (eastward) winds blow around Antarctica, driving a significant flow of water northwards. This is actually a type of coastal upwelling. Since there are no continents in a band of open latitudes between South America and the tip of the Antarctic Peninsula, some of this water is drawn up from great depths. In many numerical models and observational syntheses, the Southern Ocean upwelling represents the primary means by which deep dense water is brought to the surface. In some regions of Antarctica, wind-driven upwelling near the coast pulls relatively warm Circumpolar deep water onto the continental shelf, where it can enhance ice shelf melt and influence ice sheet stability.[12] Shallower, wind-driven upwelling is also found in off the west coasts of North and South America, northwest and southwest Africa, and southwest and south Australia, all associated with oceanic subtropical high pressure circulations (see coastal upwelling above).
Some models of the ocean circulation suggest that broad-scale upwelling occurs in the tropics, as pressure driven flows converge water toward the low latitudes where it is diffusively warmed from above. The required diffusion coefficients, however, appear to be larger than are observed in the real ocean. Nonetheless, some diffusive upwelling does probably occur.
Other sources[edit]
Local and intermittent upwellings may occur when offshore islands, ridges, or seamounts cause a deflection of deep currents, providing a nutrient rich area in otherwise low productivity ocean areas. Examples include upwellings around the Galapagos Islands and the Seychelles Islands, which have major pelagic fisheries.[3]
Upwelling can also occur when a tropical cyclone transits an area, usually when moving at speeds of less than 5 mph (8 km/h). The churning of a cyclone eventually draws up cooler water from lower layers of the ocean. This causes the cyclone to weaken.
Artificial upwelling is produced by devices that use ocean wave energy or ocean thermal energy conversion to pump water to the surface. Ocean wind turbines are also known to produce upwellings.[13] Ocean wave devices have been shown to produce plankton blooms.[14]
Variations[edit]
Unusually strong winds from the east push warm (red) surface water towards Africa, allowing cold (blue) water to upwell along the Sumatran coast
Upwelling intensity depends on wind strength and seasonal variability, as well as the vertical structure of the water, variations in the bottom bathymetry, and instabilities in the currents.
In some areas, upwelling is a seasonal event leading to periodic bursts of productivity similar to spring blooms in coastal waters. Wind-induced upwelling is generated by temperature differences between the warm, light air above the land and the cooler denser air over the sea. In temperate latitudes, the temperature contrast is greatly seasonably variable, creating periods of strong upwelling in the spring and summer, to weak or no upwelling in the winter. For example, off the coast of Oregon, there are four or five strong upwelling events separated by periods of little to no upwelling during the six-month season of upwelling. In contrast, tropical latitudes have a more constant temperature contrast, creating constant upwelling throughout the year. The Peruvian upwelling, for instance, occurs throughout most of the year, resulting in one of the world's largest marine fisheries for sardines and anchovies.[4]
In anomalous years when the trade winds weaken or reverse, the water that is upwelled is much warmer and low in nutrients, resulting in a sharp reduction in the biomass and phytoplankton productivity. This event is known as the El Nino-Southern Oscillation (ENSO) event. The Peruvian upwelling system is particularly vulnerable to ENSO events, and can cause extreme interannual variability in productivity.[4]
Changes in bathymetry can affect the strength of an upwelling. For example, a submarine ridge that extends out from the coast will produce more favorable upwelling conditions than neighboring regions. Upwelling typically begins at such ridges and remains strongest at the ridge even after developing in other locations.[4]
High productivity[edit]
Since upwelling regions are important sources of marine productivity, and they attract hundreds of species throughout the trophic levels, the diversity of these systems has been a focal point for marine research. While studying the trophic levels and patterns typical of upwelling regions, researchers have discovered that upwelling systems exhibit a wasp-waist richness pattern. In this type of pattern, the high and low trophic levels are well-represented by high species diversity. However, the intermediate trophic level is only represented by one or two species. This trophic layer, which consists of small, pelagic fish usually makes up about only three to four percent of the species diversity of all fish species present. The lower trophic layers are very well-represented with about 500 species of copepods, 2500 species of gastropods, and 2500 species of crustaceans on average. At the apex and near-apex trophic levels, there are usually about 100 species of marine mammals and about 50 species of marine birds. The vital intermediate trophic species however are small pelagic fish that usually feed on phytoplankton. In most upwelling systems, these species are either anchovies or sardines, and usually only one is present, although two or three species may be present occasionally. These fish are an important food source for predators, such as large pelagic fish, marine mammals, and marine birds. Although they are not at the base of the trophic pyramid, they are the vital species that connect the entire marine ecosystem and keep the productivity of upwelling zones so high[11]
Threats to upwelling ecosystems[edit]
A major threat to both this crucial intermediate trophic level and the entire upwelling trophic ecosystem is the problem of commercial fishing. Since upwelling regions are the most productive and species rich areas in the world, they attract a high number of commercial fishers and fisheries. On one hand, this is another benefit of the upwelling process as it serves as a viable source of food and income for so many people and nations besides marine animals. However, just as in any ecosystem, the consequences of over-fishing from a population could be detrimental to that population and the ecosystem as a whole. In upwelling ecosystems, every species present plays a vital role in the functioning of that ecosystem. If one species is significantly depleted, that will have an effect throughout the rest of the trophic levels. For example, if a popular prey species is targeted by fisheries, fishermen may collect hundreds of thousands of individuals of this species just by casting their nets into the upwelling waters. As these fish are depleted, the food source for those who preyed on these fish is depleted. Therefore, the predators of the targeted fish will begin to die off, and there will not be as many of them to feed the predators above them. This system continues throughout the entire food chain, resulting in a possible collapse of the ecosystem. It is possible that the ecosystem may be restored over time, but not all species can recover from events such as these. Even if the species can adapt, there may be a delay in the reconstruction of this upwelling community.[11]
The possibility of such an ecosystem collapse is the very danger of fisheries in upwelling regions. Fisheries may target a variety of different species, and therefore they are a direct threat to many species in the ecosystem, however they pose the highest threat to the intermediate pelagic fish. Since these fish form the crux of the entire trophic process of upwelling ecosystems, they are highly represented throughout the ecosystem (even if there is only one species present). Unfortunately, these fish tend to be the most popular targets of fisheries as about 64 percent of their entire catch consists of pelagic fish. Among those, the six main species that usually form the intermediate trophic layer represent over half of the catch.[11]
During an El Niño, wind indirectly drives warm water to the South American coast, reducing the effects of cold upwelling
Besides directly causing the collapse of the ecosystem due to their absence, this can create problems in the ecosystem through a variety of other methods as well. The animals higher in the trophic levels may not completely starve to death and die off, but the decreased food supply could still hurt the populations. If animals do not get enough food, it will decrease their reproductive viability meaning that they will not breed as often or as successfully as usual. This can lead to a decreasing population, especially in species that do not breed often under normal circumstances or become reproductively mature late in life. Another problem is that the decrease in the population of a species due to fisheries can lead to a decrease in genetic diversity, resulting in a decrease in bio-diversity of a species. If the species diversity is decreased significantly, this could cause problems for the species in an environment that is so variable and quick-changing; they may not be able to adapt, which could result in a collapse of the population or ecosystem.[11]
Another threat to the productivity and ecosystems of upwelling regions is El Niño-Southern Oscillation (ENSO) system, or more specifically El Niño events. During the normal period and La Niña events, the easterly trade winds are still strong, which continues to drive the process of upwelling. However, during El Niño events, trade winds are weaker, causing decreased upwelling in the equatorial regions as the divergence of water north and south of the equator is not as strong or as prevalent. The coastal upwelling zones diminish as well since they are wind driven systems, and the wind is no longer a very strong driving force in these areas. As a result, global upwelling drastically decreases, causing a decrease in productivity as the waters are no longer receiving nutrient-rich water. Without these nutrients, the rest of the trophic pyramid cannot be sustained, and the rich upwelling ecosystem will collapse.[15]
References[edit]
^ Jump up to: a b c Anderson DM, Prell WL. (1993). A 300 KYR record of upwelling off Oman during the late quaternary: evidence of the Asian southwest monsoon. Paleoceanography, 8(2): 193-208.
Jump up ^ Sarhan T, Lafuente JG, Vargas M, Vargas JM, Plaza F. (1999). Upwelling mechanisms in the northwestern Alboran Sea. Journal of Marine Systems, 23: 317-331.
^ Jump up to: a b c d Jennings, S., Kaiser, M.J., Reynolds, J.D. (2001) "Marine Fisheries Ecology." Oxford: Blackwell Science Ltd. ISBN 0-632-05098-5
^ Jump up to: a b c d e f Mann, K.H., Lazier, J.R.N. (2006) Dynamics of Marine Ecosystems: Biological-Physical Interactions in the Oceans. Oxford: Blackwell Publishing Ltd. ISBN 1-4051-1118-6
^ Jump up to: a b Bakun A. (1990). Global climate change and intensification of coastal ocean upwelling. Science, 247: 198-201.
Jump up ^ Chelton DB, Schlax MG, Freilich MH, Milliff RF. (2004). Satellite measurements reveal persistent small-scale features in ocean winds. Science, 303:978-983.
Jump up ^ Bakun A, Nelson CS. (1991). The seasonal cycle of wind-stress curl in subtropical eastern boundary current regions. Journal of Physical Oceanography, 21: 1815-1834.
^ Jump up to: a b Blanchette CA, Wieters EA, Briotman BR, Kinlan BP, Schiel DR. (2009). Trophic structure and diversity in rocky intertidal upwelling ecosystems: a comparison of community patterns across California, Chile, South Africa, and New Zealand. Progress in Oceanography. doi:10.1016/j.pocean.2009.07.038
Jump up ^ Lalli, C.M., Parsons, T.R. (1997) "Biological Oceanography: An Introduction" Oxford: Elsevier Publications. ISBN 0-7506-3384-0
Jump up ^ Brodeur RD, Ware DM. (2007). Long-term variability in zooplankton biomass in the subarctic Pacific ocean. Fisheries Oceanography, 1(1): 32-38.
^ Jump up to: a b c d e Cury P, Bakun A, Crawford RJM, Jarre A, Quinones RA, Shannon LJ, Verheye HM. (2000). Small pelagics in upwelling systems: patterns of interaction and structural changes in “wasp-waist” ecosystems. ICES Journal of Marine Science, 57:603-618.
Jump up ^ Greene, Chad A.; Blankenship, Donald D.; Gwyther, David E.; Silvano, Alessandro; Wijk, Esmee van (2017-11-01). "Wind causes Totten Ice Shelf melt and acceleration". Science Advances. 3 (11): e1701681. doi:10.1126/sciadv.1701681. ISSN 2375-2548.
Jump up ^ https://wiki.met.no/_media/windfarms/brostrom_jms_2008.pdf On the influence of large wind farms on the upper ocean circulation. Göran Broström, Norwegian Meteorological Institute, Oslo, Norway
Jump up ^ US Research project, NSF and Oregon State University Archived August 4, 2009, at the Wayback Machine.
Jump up ^ Rasmussen EM, Carpenter TH. (1982). Variations in tropical sea surface temperature and surface wind fields associated with the outer Oscillation/El Nino. Monthly Weather Review, 110: 354-384.
External links[edit]
Wind Driven Surface Currents: Upwelling and Downwelling
Animation demonstrates the upwelling process.
Coastal Upwelling
On the influence of large wind farms on the upper ocean circulation. Göran Broström, Norwegian Meteorological Institute, Oslo, Norway
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Free fall
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
For other uses, see Free fall (disambiguation).
"Freeflight" redirects here. For the album by Ahmad Jamal, see Freeflight (album).
Free fall of an apple
Play media
Commander David Scott conducting an experiment during the Apollo 15 moon landing.
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
An object in the technical sense of the term "free fall" may not necessarily be falling down in the usual sense of the term. An object moving upwards would not normally be considered to be falling, but if it is subject to the force of gravity only, it is said to be in free fall. The moon is thus in free fall.
In a uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body equally and this is weightlessness, a condition that also occurs when the gravitational field is zero (such as when far away from any gravitating body).
The term "free fall" is often used more loosely than in the strict sense defined above. Thus, falling through an atmosphere without a deployed parachute, or lifting device, is also often referred to as free fall. The aerodynamic drag forces in such situations prevent them from producing full weightlessness, and thus a skydiver's "free fall" after reaching terminal velocity produces the sensation of the body's weight being supported on a cushion of air.
Contents
1 History
2 Examples
3 Free fall in Newtonian mechanics
3.1 Uniform gravitational field without air resistance
3.2 Uniform gravitational field with air resistance
3.3 Inverse-square law gravitational field
4 Free fall in general relativity
5 Record free fall parachute jumps
6 Surviving falls
7 See also
8 References
9 External links
History[edit]
In the Western world prior to the 16th century, it was generally assumed that the speed of a falling body would be proportional to its weight—that is, a 10 kg object was expected to fall ten times faster than an otherwise identical 1 kg object through the same medium. The ancient Greek philosopher Aristotle (384–322 BC) discussed falling objects in Physics (Book VII) which was perhaps the first book on mechanics (see Aristotelian physics).
The Italian scientist Galileo Galilei (1564–1642) subjected the Aristotelian theories to experimentation and careful observation. He then combined the results of these experiments with mathematical analysis in an unprecedented way.
According to a tale that may be apocryphal, in 1589–92 Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse (stopwatches having not yet been invented). This he repeated "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat." In 1589–92, Galileo wrote De Motu Antiquiora, an unpublished manuscript on the motion of falling bodies.
Examples[edit]
Examples of objects in free fall include:
A spacecraft (in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory (ballistics) going up for some minutes, and then down).
An object dropped at the top of a drop tube.
An object thrown upward or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight).
Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g {\displaystyle g} .
Since all objects fall at the same rate in the absence of other forces, objects and people will experience weightlessness in these situations.
Examples of objects not in free fall:
Flying in an aircraft: there is also an additional force of lift.
Standing on the ground: the gravitational force is counteracted by the normal force from the ground.
Descending to the Earth using a parachute, which balances the force of gravity with an aerodynamic drag force (and with some parachutes, an additional lift force).
The example of a falling skydiver who has not yet deployed a parachute is not considered free fall from a physics perspective, since he experiences a drag force that equals his weight once he has achieved terminal velocity (see below). However, the term "free fall skydiving" is commonly used to describe this case in everyday speech, and in the skydiving community. It is not clear, though, whether the more recent sport of wingsuit flying fits under the definition of free fall skydiving.
Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of 2 h / g {\displaystyle {\sqrt {2h/g}}} , where h is the height and g is the free-fall acceleration due to gravity.
Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (195 km/h or 122 mph[1]) for a human skydiver. The terminal velocity depends on many factors including mass, drag coefficient, and relative surface area and will only be achieved if the fall is from sufficient altitude. A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time he will have fallen around 450 m (1,500 ft).[1]
Free fall was demonstrated on the moon by astronaut David Scott on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the moon's surface. The hammer and the feather both fell at the same rate and hit the ground at the same time. This demonstrated Galileo's discovery that, in the absence of air resistance, all objects experience the same acceleration due to gravity. (On the Moon, the gravitational acceleration is much less than on Earth, approximately 1.6 m/s2.)
Free fall in Newtonian mechanics[edit]
Main article: Newtonian mechanics
Uniform gravitational field without air resistance[edit]
This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below).
v ( t ) = v 0 − g t {\displaystyle v(t)=v_{0}-gt\,}
y ( t ) = v 0 t + y 0 − 1 2 g t 2 {\displaystyle y(t)=v_{0}t+y_{0}-{\frac {1}{2}}gt^{2}}
where
v 0 {\displaystyle v_{0}\,} is the initial velocity (m/s).
v ( t ) {\displaystyle v(t)\,} is the vertical velocity with respect to time (m/s).
y 0 {\displaystyle y_{0}\,} is the initial altitude (m).
y ( t ) {\displaystyle y(t)\,} is the altitude with respect to time (m).
t {\displaystyle t\,} is time elapsed (s).
g {\displaystyle g\,} is the acceleration due to gravity (9.81 m/s2 near the surface of the earth).
Uniform gravitational field with air resistance[edit]
Acceleration of a small meteoroid when entering the Earth's atmosphere at different initial velocities.
This case, which applies to skydivers, parachutists or any body of mass, m {\displaystyle m} , and cross-sectional area, A {\displaystyle A} , with Reynolds number well above the critical Reynolds number, so that the air resistance is proportional to the square of the fall velocity, v {\displaystyle v} , has an equation of motion
m d v d t = m g − 1 2 ρ C D A v 2 , {\displaystyle m{\frac {dv}{dt}}=mg-{\frac {1}{2}}\rho C_{\mathrm {D} }Av^{2}\,,}
where ρ {\displaystyle \rho } is the air density and C D {\displaystyle C_{\mathrm {D} }} is the drag coefficient, assumed to be constant although in general it will depend on the Reynolds number.
Assuming an object falling from rest and no change in air density with altitude, the solution is:
v ( t ) = v ∞ tanh  ( g t v ∞ ) , {\displaystyle v(t)=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right),}
where the terminal speed is given by
v ∞ = 2 m g ρ C D A . {\displaystyle v_{\infty }={\sqrt {\frac {2mg}{\rho C_{D}A}}}\,.}
The object's speed versus time can be integrated over time to find the vertical position as a function of time:
y = y 0 − v ∞ 2 g ln  cosh  ( g t v ∞ ) . {\displaystyle y=y_{0}-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right).}
Using the figure of 56 m/s for the terminal velocity of a human, one finds that after 10 seconds he will have fallen 348 metres and attained 94% of terminal velocity, and after 12 seconds he will have fallen 455 metres and will have attained 97% of terminal velocity. However, when the air density cannot be assumed to be constant, such as for objects or skydivers falling from high altitude, the equation of motion becomes much more difficult to solve analytically and a numerical simulation of the motion is usually necessary. The figure shows the forces acting on meteoroids falling through the Earth's upper atmosphere. HALO jumps, including Joe Kittinger's and Felix Baumgartner's record jumps (see below), and the planned Le Grand Saut, also belong in this category.[2]
Inverse-square law gravitational field[edit]
It can be said that two objects in space orbiting each other in the absence of other forces are in free fall around each other, e.g. that the Moon or an artificial satellite "falls around" the Earth, or a planet "falls around" the Sun. Assuming spherical objects means that the equation of motion is governed by Newton's Law of Universal Gravitation, with solutions to the gravitational two-body problem being elliptic orbits obeying Kepler's laws of planetary motion. This connection between falling objects close to the Earth and orbiting objects is best illustrated by the thought experiment, Newton's cannonball.
The motion of two objects moving radially towards each other with no angular momentum can be considered a special case of an elliptical orbit of eccentricity e = 1 (radial elliptic trajectory). This allows one to compute the free-fall time for two point objects on a radial path. The solution of this equation of motion yields time as a function of separation:
t ( y ) = y 0 3 2 μ ( y y 0 ( 1 − y y 0 ) + arccos  y y 0 ) {\displaystyle t(y)={\sqrt {\frac {{y_{0}}^{3}}{2\mu }}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)}
where
t is the time after the start of the fall
y is the distance between the centers of the bodies
y0 is the initial value of y
μ = G(m1 + m2) is the standard gravitational parameter.
Substituting y = 0 we get the free-fall time.
The separation as a function of time is given by the inverse of the equation. The inverse is represented exactly by the analytic power series:
y ( t ) = ∑ n = 1 ∞ [ lim r → 0 ( x n n ! d n − 1 d r n − 1 [ r n ( 7 2 ( arcsin  ( r ) − r − r 2 ) ) − 2 3 n ] ) ] {\displaystyle y(t)=\sum _{n=1}^{\infty }\left[\lim _{r\to 0}\left({\frac {x^{n}}{n!}}{\frac {\mathrm {d} ^{\,n-1}}{\mathrm {d} r^{\,n-1}}}\left[r^{n}\left({\frac {7}{2}}(\arcsin({\sqrt {r}})-{\sqrt {r-r^{2}}})\right)^{-{\frac {2}{3}}n}\right]\right)\right]}
Evaluating this yields:[3][4]
y ( t ) = y 0 ( x − 1 5 x 2 − 3 175 x 3 − 23 7875 x 4 − 1894 3931875 x 5 − 3293 21896875 x 6 − 2418092 62077640625 x 7 − ⋯ ) {\displaystyle y(t)=y_{0}\left(x-{\frac {1}{5}}x^{2}-{\frac {3}{175}}x^{3}-{\frac {23}{7875}}x^{4}-{\frac {1894}{3931875}}x^{5}-{\frac {3293}{21896875}}x^{6}-{\frac {2418092}{62077640625}}x^{7}-\cdots \right)\ }
where
x = [ 3 2 ( π 2 − t 2 μ y 0 3 ) ] 2 / 3 {\displaystyle x=\left[{\frac {3}{2}}\left({\frac {\pi }{2}}-t{\sqrt {\frac {2\mu }{{y_{0}}^{3}}}}\right)\right]^{2/3}}
Free fall in general relativity[edit]
Main article: General relativity
In general relativity, an object in free fall is subject to no force and is an inertial body moving along a geodesic. Far away from any sources of space-time curvature, where spacetime is flat, the Newtonian theory of free fall agrees with general relativity but otherwise the two disagree.[how?]
The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.
Record free fall parachute jumps[edit]
Joseph Kittinger starting his record-breaking skydive in 1960. His record was broken only in 2012.
In 1914, while doing demonstrations for the U.S. Army, a parachute pioneer named Tiny Broadwick deployed her chute manually, thus becoming the first person to jump free-fall.
According to the Guinness Book of Records, Eugene Andreev (USSR) holds the official FAI record for the longest free-fall parachute jump after falling for 24,500 metres (80,400 ft) from an altitude of 25,458 metres (83,524 ft) near the city of Saratov, Russia on November 1, 1962. Although later on jumpers would ascend higher altitudes, Andreev's record was set without the use of a drogue chute during the jump and therefore remains the longest genuine free fall record.[5]
During the late 1950s, Captain Joseph Kittinger of the United States was assigned to the Aerospace Medical Research Laboratories at Wright-Patterson AFB in Dayton, Ohio. For Project Excelsior (meaning "ever upward", a name given to the project by Colonel John Stapp), as part of research into high altitude bailout, he made a series of three parachute jumps wearing a pressurized suit, from a helium balloon with an open gondola.
The first, from 76,400 feet (23,290 m) in November 1959 was a near tragedy when an equipment malfunction caused him to lose consciousness, but the automatic parachute saved him (he went into a flat spin at a rotational velocity of 120 rpm; the g-force at his extremities was calculated to be over 22 times that of gravity, setting another record). Three weeks later he jumped again from 74,700 feet (22,770 m). For that return jump Kittinger was awarded the A. Leo Stevens parachute medal.
On August 16, 1960 he made the final jump from the Excelsior III at 102,800 feet (31,330 m). Towing a small drogue chute for stabilization, he fell for 4 minutes and 36 seconds reaching a maximum speed of 614 mph (988 km/h)[6] before opening his parachute at 14,000 feet (4,270 m). Pressurization for his right glove malfunctioned during the ascent, and his right hand swelled to twice its normal size.[7] He set records for highest balloon ascent, highest parachute jump, longest drogue-fall (4 min), and fastest speed by a human through the atmosphere.[8]
The jumps were made in a "rocking-chair" position, descending on his back, rather than the usual arch familiar to skydivers, because he was wearing a 60-pound (27 kg) "kit" on his behind and his pressure suit naturally formed that shape when inflated, a shape appropriate for sitting in an airplane cockpit.
For the series of jumps, Kittinger was decorated with an oak leaf cluster to his Distinguished Flying Cross and awarded the Harmon Trophy by President Dwight Eisenhower.
In 2012, the Red Bull Stratos mission took place. On October 14, 2012, Felix Baumgartner broke the records previously set by Kittinger for the highest free fall, the highest manned helium balloon flight, and the fastest free fall; he jumped from 128,100 feet (39,045 m), reaching 833.9 mph (1342 km/h) - Mach 1.24. Kittinger was a member of the mission control and helped design the capsule and suit that Baumgartner ascended and jumped in.
On October 24, 2014, Alan Eustace broke the record previously set by Baumgartner for the highest free fall. He jumped from a height of 135,908 feet (41,425 m).[9]
Surviving falls[edit]
A falling person at low altitude will reach terminal velocity after about 12 seconds, falling some 450 m (1,500 ft) in that time. The person will then maintain this speed without falling any faster.[10] Terminal velocity at higher altitudes is greater due to the thinner atmosphere and consequent lower air resistance; free-fallers from high altitudes, including Kittinger, Baumgartner and Eustace discussed in this article, fell faster at higher altitudes.
The severity of injury increases with the height of a free fall, but also depends on body and surface features and the manner that the body impacts on to the surface.[11] The chance of surviving increases if landing on a soft surface, such as snow.[11]
Overall, the height at which 50% of children die from a fall is between four and five storey heights above the ground.[12]
JAT stewardess Vesna Vulović survived a fall of 10,000 metres (33,000 ft)[13] on January 26, 1972 when she was aboard JAT Flight 367. The plane was brought down by explosives over Srbská Kamenice in the former Czechoslovakia (now the Czech Republic). The Serbian stewardess suffered a broken skull, three broken vertebrae (one crushed completely), and was in a coma for 27 days. In an interview, she commented that, according to the man who found her, "…I was in the middle part of the plane. I was found with my head down and my colleague on top of me. One part of my body with my leg was in the plane and my head was out of the plane. A catering trolley was pinned against my spine and kept me in the plane. The man who found me, says I was very lucky. He was in the German Army as a medic during World War Two. He knew how to treat me at the site of the accident."[14]
In World War II there were several reports of military aircrew surviving long falls from severely damaged aircraft: Flight Sergeant Nicholas Alkemade jumped at 18,000 feet (5,500 m) without a parachute and survived as he hit pine trees and soft snow. He suffered a sprained leg. Staff Sergeant Alan Magee exited his aircraft at 22,000 feet (6,700 m) without a parachute and survived as he landed on the glass roof of a train station. Lieutenant Ivan Chisov bailed out at 23,000 feet (7,000 m). While he had a parachute his plan was to delay opening it as he had been in the midst of an air-battle and was concerned about getting shot while hanging below the parachute. He lost consciousness due to lack of oxygen and hit a snow-covered slope while still unconscious. While he suffered severe injuries he was able to fly again in three months.
It was reported that two of the victims of the Lockerbie bombing survived for a brief period after hitting the ground (with the forward nose section fuselage in freefall mode), but died from their injuries before help arrived.[15]
Juliane Koepcke survived a long free fall resulting from the December 24, 1971, crash of LANSA Flight 508 (a LANSA Lockheed Electra OB-R-941 commercial airliner) in the Peruvian rainforest. The airplane was struck by lightning during a severe thunderstorm and exploded in mid air, disintegrating two miles (3.2 km) up. Köpcke, who was 17 years old at the time, fell to earth still strapped into her seat. The German Peruvian teenager survived the fall with only a broken collarbone, a gash to her right arm, and her right eye swollen shut.[16]
As an example of "freefall survival" that was not as extreme as sometimes reported in the press, a skydiver from Staffordshire was said to have plunged 6,000 metres without a parachute in Russia and survived. James Boole said that he was supposed to have been given a signal by another skydiver to open his parachute, but it came two seconds too late. Boole, who was filming the other skydiver for a television documentary, landed on snow-covered rocks and suffered a broken back and rib.[17] While he was lucky to survive, this was not a case of true freefall survival, because he was flying a wingsuit, greatly decreasing his vertical speed. This was over descending terrain with deep snow cover, and he impacted while his parachute was beginning to deploy. Over the years, other skydivers have survived accidents where the press has reported that no parachute was open, yet they were actually being slowed by a small area of tangled parachute. They might still be very lucky to survive, but an impact at 80 mph (129 km/h) is much less severe than the 120 mph (193 km/h) that might occur in normal freefall.[original research?]
Parachute jumper and stuntman Luke Aikins successfully jumped without a parachute from about 25,000 feet (7,600 m) into a 10,000-square-foot (930 m2) net in California, US, on 30 July 2016.[18]
See also[edit]
Equations for a falling body
Reduced-gravity aircraft
Weightlessness
Terminal velocity
High-altitude military parachuting
G-force
Micro-g environment
References[edit]
^ Jump up to: a b "Free fall graph" (PDF). Green Harbor Publications. 2010. Retrieved 14 March 2016.
Jump up ^ An analysis of his and similar jumps is given in Mohazzabi, P.; Shea, J. (1996). "High altitude free fall" (PDF). American Journal of Physics. 64 (10): 1242. Bibcode:1996AmJPh..64.1242M. doi:10.1119/1.18386.
Jump up ^ Foong, S K (2008). "From Moon-fall to motions under inverse square laws". European Journal of Physics. 29 (5): 987. Bibcode:2008EJPh...29..987F. doi:10.1088/0143-0807/29/5/012.
Jump up ^ Mungan, Carl E. (2009). "Radial Motion of Two Mutually Attracting Particles". The Physics Teacher. 47 (8): 502. Bibcode:2009PhTea..47..502M. doi:10.1119/1.3246467.
Jump up ^ Data of the stratospheric balloon launched on 8/16/1960 For EXCELSIOR III. Stratocat.com.ar. Retrieved on 2016-07-31.
Jump up ^ "Speed of a Skydiver (Terminal Velocity)". Hyper Text Book.
Jump up ^ Higgins, Matt (May 24, 2008). "20-Year Journey for 15-Minute Fall". The New York Times. Retrieved May 2, 2010.
Jump up ^ Joseph W. Kittinger – USAF Museum Gathering of Eagles. Web.archive.org. Retrieved on 2016-07-31.
Jump up ^ Markoff, John (24 October 2014). "Parachutist's Record Fall: Over 25 Miles in 15 Minutes". The New York Times. Retrieved 25 October 2014.
Jump up ^ Notes and figures on free fall. Greenharbor.com. Retrieved on 2016-07-31.
^ Jump up to: a b Atanasijević, T; Nikolić, S; Djokić, V (2004). "Level of total injury severity as a possible parameter for evaluation of height in fatal falls". Srpski arhiv za celokupno lekarstvo. 132 (3–4): 96–8. doi:10.2298/sarh0404096a. PMID 15307311.
Jump up ^ Barlow, B.; Niemirska, M.; Gandhi, R. P.; Leblanc, W. (1983). "Ten years of experience with falls from a height in children". Journal of Pediatric Surgery. 18 (4): 509–511. doi:10.1016/S0022-3468(83)80210-3. PMID 6620098.
Jump up ^ Free Fall. greenharbor.com
Jump up ^ Interviewed by Philip Baum, Green Light Aviation Security Training & Consultancy, in Belgrade, December 2001. "Vesna Vulovic: how to survive a bombing at 33,000 feet". Archived from the original on 2008-01-08. CS1 maint: Multiple names: authors list (link)
Jump up ^ Cox, Matthew, and Foster, Tom. (1992) Their Darkest Day: The Tragedy of Pan Am 103, ISBN 0-8021-1382-6
Jump up ^ "Survivor still haunted by 1971 air crash". CNN.com. July 2, 2009. Retrieved 2009-07-02.
Jump up ^ "Jumper survives 6,000ft free fall". BBC News. May 18, 2009. Retrieved January 4, 2010.
Jump up ^ "US skydiver jumps without parachute into net from 25,000ft". BBC News. 31 July 2016. Retrieved 31 July 2016.
External links[edit]
Unplanned Freefall? A slightly tongue-in-cheek look at surviving free-fall without a parachute.
Free fall accidents, mathematics of free fall – detailed research on the topic
Freefall formula calculator
Chuteless jump survivors
"Joseph W. Kittinger and the Highest Step in the World". Greg Kennedy. March 17, 2010. detailed account of origins and development of EXCELSIOR project
The Way Things Fall an educational website
H.S. Free fall lesson with videos and interactive flash animations.
Wikimedia Commons has media related to Free fall.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Free_fall&oldid=863949995"
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