Free fall
Encyclopedia
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, it also applies to objects initially moving upward. Since free fall in the absence of forces other than gravity produces weightlessness
Weightlessness
Weightlessness is the condition that exists for an object or person when they experience little or no acceleration except the acceleration that defines their inertial trajectory, or the trajectory of pure free-fall...

or "zero-g," sometimes any condition of weightlessness due to inertial motion is referred to as free-fall. This may also apply to weightlessness produced because the body is far from a gravitating body.

Although strict technical application of the definition excludes motion of an object subjected to other forces such as aerodynamic drag, in nontechnical usage, falling through an atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

without a deployed parachute
Parachute
A parachute is a device used to slow the motion of an object through an atmosphere by creating drag, or in the case of ram-air parachutes, aerodynamic lift. Parachutes are usually made out of light, strong cloth, originally silk, now most commonly nylon...

, or lifting device, is also often referred to as free fall. The drag forces in such situations prevent them from producing full weightlessness, and thus a skydiver's "free fall" after reaching terminal velocity
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....

produces the sensation of the body's weight being supported on a cushion of air.

## Examples

Examples of objects in free fall include:
• A spacecraft
Spacecraft
A spacecraft or spaceship is a craft or machine designed for spaceflight. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and transportation of humans and cargo....

(in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory going up for some minutes, and then down).
• An object dropped at the top of a drop tube.
• An object thrown upwards 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 .

Since all objects fall at the same rate in the absence of other forces, objects and people will experience weightlessness
Weightlessness
Weightlessness is the condition that exists for an object or person when they experience little or no acceleration except the acceleration that defines their inertial trajectory, or the trajectory of pure free-fall...

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
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

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 they experience a drag force which equals their weight once they have 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.
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 upon an object that has been dropped, the object will eventually reach a terminal velocity
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....

, around 56 m/s (200 km/h or 120 mph) for a human body. Terminal velocity depends on many factors including mass, drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...

, and relative surface area and will only be achieved if the fall is from sufficient altitude.

Free fall was demonstrated on the moon by astronaut David Scott
David Scott
David Randolph Scott is an American engineer, test pilot, retired U.S. Air Force officer, and former NASA astronaut and engineer, who was one of the third group of astronauts selected by NASA in October 1963...

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 much less than on Earth, approximately 1.6 m/s²).

### Uniform gravitational field without air resistance

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).

where is the initial velocity (m/s). is the vertical velocity with respect to time (m/s). is the initial altitude (m). is the altitude with respect to time (m). is time elapsed (s). is the acceleration due to gravity (9.81 m/s2 near the surface of the earth).

### Uniform gravitational field with air resistance

This case, which applies to skydivers, parachutists or any bodies with Reynolds number well above the critical Reynolds number, has an equation of motion:
where all the letters have a meaning.

Assuming an object falling from rest and no change in air density with altitude, the solution is:
,

where the terminal speed is given by

The object's speed versus time can be integrated over time to find the vertical position as a function of time:

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 Col. Joe Kittinger's record jump (see below) and the planned Le Grand Saut also belong in this category.

### Inverse-square law gravitational field

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
Gravitational two-body problem
For further relevant mathematical developments see also Two-body problem, also Kepler orbit, and Kepler problem, and Equation of the center – Analytical expansions...

being elliptic orbits obeying Kepler's laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

. This connection between falling objects close to the Earth and orbiting objects is best illustrated by the thought experiment Newton's cannonball
Newton's cannonball
Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion...

.

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
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

(radial elliptic trajectory). This allows one to compute the free-fall time
Free-fall time
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse...

for two point objects on a radial path. The solution of this equation of motion yields time as a function of separation:

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
is the standard gravitational parameter
Standard gravitational parameter
In astrodynamics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.\mu=GM \ The SI units of the standard gravitational parameter are m3s−2....

.

Substituting y=0 we get the free-fall time
Free-fall time
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse...

.

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:

Evaluating this yields:

For details of these solutions see "From Moon-fall to solutions under inverse square laws" by Foong, S. K., in European Journal of Physics, v29, 987-1003 (2008) and "Radial motion of Two
mutually attracting particles", by Mungan, C. E., in The Physics Teacher, v47, 502-507 (2009).

## Free fall in General Relativity

The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and confirmed to high accuracy by modern forms of the Eötvös experiment
Eötvös experiment
The Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with the same accuracy. The earliest experiments were...

, is the basis of the Equivalence Principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

, on which Einstein's theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

relies. An alternative statement of this law, as can be seen from Newton's 2nd law applied to free fall above, is that the gravitational and the inertial mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

of any object are the same.

## Record free fall parachute jumps

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 80,380 ft (24,500 m) from an altitude of 83,523 ft (25,460 m) near the city of Saratov, Russia on November 1, 1962. Though later jumpers would ascend higher, Andreev's record was set without the use of a drogue chute during the jump.

During the late 1950s, Captain Joseph Kittinger
Joseph Kittinger
Joseph William Kittinger II is a former Command Pilot and career military officer in the United States Air Force. He is most famous for his participation in Project Manhigh and Project Excelsior, holding the records for having the highest, fastest and longest skydive, from a height greater than...

of the United States was assigned to the Aerospace Medical Research Laboratories at Wright-Patterson AFB in Dayton, Ohio
Dayton, Ohio
Dayton is the 6th largest city in the U.S. state of Ohio and the county seat of Montgomery County, the fifth most populous county in the state. The population was 141,527 at the 2010 census. The Dayton Metropolitan Statistical Area had a population of 841,502 in the 2010 census...

. For Project Excelsior
Project Excelsior
Project Excelsior was a series of high-altitude parachute jumps made by Colonel Joseph Kittinger of the United States Air Force in 1959 and 1960 to test the Beaupre multi-stage parachute system...

(meaning "ever upward", a name given to the project by Colonel John Stapp
John Stapp
John Paul Stapp, M.D., Ph.D., Colonel, USAF was a career U.S. Air Force officer, USAF flight surgeon and pioneer in studying the effects of acceleration and deceleration forces on humans...

), 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
A. Leo Stevens Parachute Medal
The A. Leo Stevens Parachute Medal is named after Albert Leo Stevens. It was first awarded to Joe Crane of Mineola, New York on September 4, 1948 by Augustus Post at the Early Birds of Aviation banquet held in the Hotel Carter in Cleveland, Ohio, during the National Air Race.-Winners:*1948 Joe...

.

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) http://hypertextbook.com/facts/JianHuang.shtml 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. He set records for highest balloon ascent, highest parachute jump, longest drogue-fall (4 min), and fastest speed by a human through the atmosphere.

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-lb "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
Oak leaf cluster
An oak leaf cluster is a common device which is placed on U.S. Army and Air Force awards and decorations to denote those who have received more than one bestowal of a particular decoration. The number of oak leaf clusters typically indicates the number of subsequent awards of the decoration...

to his Distinguished Flying Cross
Distinguished Flying Cross (United States)
The Distinguished Flying Cross is a medal awarded to any officer or enlisted member of the United States armed forces who distinguishes himself or herself in support of operations by "heroism or extraordinary achievement while participating in an aerial flight, subsequent to November 11, 1918." The...

and awarded the Harmon Trophy
Harmon Trophy
The Harmon Trophy is a set of three international trophies, to be awarded annually to the world's outstanding aviator, aviatrix , and aeronaut...

by President Dwight Eisenhower.

## Surviving falls

The severity of injury increases with the height of a free fall, but also depends on body and surface features and the manner of body impacts on to the surface. The chance of surviving increases if landing on a surface of high deformity, such as snow or water.

Overall, the height at which 50% of children die from a fall is between four and five storey
Storey
A storey or story is any level part of a building that could be used by people...

heights above the ground.

JAT
Jat Airways
Jat Airways is the national airline of Serbia and the former national airline of Yugoslavia, and has its head office in the Jat Airways Business Center in Belgrade. It was established in 1927 as Aeroput, making it currently one of the world's oldest airlines still in operation...

stewardess Vesna Vulović
Vesna Vulovic
Vesna Vulović is a Serbian former flight attendant. She holds the world record, according to the Guinness Book of Records, for surviving the highest fall without a parachute: .-Plane explosion:...

survived a fall of 33000 feet (10,058.4 m) on January 26, 1972 when she was aboard JAT Flight 367. The plane was brought down by explosives over Srbská Kamenice
Srbská Kamenice
Srbská Kamenice is a village in the Czech Republic, Ústí nad Labem Region.It was founded in early 11th century by Sorbs, refugees from Germany after a military campaign of Henry II. In 2005, it had 206 inhabitants...

in the former Czechoslovakia
Czechoslovakia
Czechoslovakia or Czecho-Slovakia was a sovereign state in Central Europe which existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until 1992...

(now Czech Republic
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....

). The Serbia
Serbia
Serbia , officially the Republic of Serbia , is a landlocked country located at the crossroads of Central and Southeast Europe, covering the southern part of the Carpathian basin and the central part of the Balkans...

n 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."

In World War II there were several reports of military
Military
A military is an organization authorized by its greater society to use lethal force, usually including use of weapons, in defending its country by combating actual or perceived threats. The military may have additional functions of use to its greater society, such as advancing a political agenda e.g...

aircrew
Aircrew
Aircrew are the personnel who operate an aircraft while in flight. The composition of the crew depends on the type of aircraft as well as the purpose of the flight.-Civilian:*Aviator** Pilot-in-command** First officer** Second officer** Third officer...

Flight Sergeant Nicholas Stephen Alkemade was a tail gunner for a Royal Air Force Avro Lancaster bomber during World War II who survived a fall of 18,000 feet without a parachute after his plane was shot down over Germany....

, Alan Magee
Alan Magee
Alan Eugene Magee was an American airman during World War II who survived a 22,000-foot fall from his damaged B-17 Flying Fortress. He was featured in Smithsonian Magazine as one of the 10 most amazing survival stories of World War II.Alan Magee was born in Plainfield, New Jersey as the youngest...

, and Ivan Chisov all fell at least 5500 metres (18,044.6 ft) and survived.

Freefall is not to be confused with individuals who survive instances of various degrees of controlled flight into terrain
Controlled flight into terrain
Controlled flight into terrain describes an accident in which an airworthy aircraft, under pilot control, is unintentionally flown into the ground, a mountain, water, or an obstacle. The term was coined by engineers at Boeing in the late 1970s...

. Such impact forces affecting these instances of survival differ from the forces which are characterized by free fall.

It was reported that two of the victims of the Lockerbie bombing
Pan Am Flight 103
Pan Am Flight 103 was Pan American World Airways' third daily scheduled transatlantic flight from London Heathrow Airport to New York's John F. Kennedy International Airport...

survived for a brief period after hitting the ground (with the forward nose section fuselage
Fuselage
The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...

in freefall mode), but died from their injuries before help arrived.

Juliane Koepcke survived a long free fall resulting from the December 24, 1971, crash of LANSA Flight 508
LANSA Flight 508
LANSA Flight 508 was a Lockheed L-188A Electra turboprop, registered OB-R-941, operated as a scheduled domestic passenger flight by Lineas Aéreas Nacionales Sociedad Anonima , that crashed in a thunderstorm en route from Lima, Peru to Pucallpa, Peru, on December 24, 1971, killing 91 people –...

(a LANSA
Líneas Aéreas Nacionales S. A. (Peru)
Lineas Aéreas Nacionales S.A. was a Peruvian commercial airline headquartered in Peru. The airline had two major airline accidents, LANSA Flight 502 and LANSA Flight 508 ....

Lockheed Electra
Lockheed L-188 Electra
The Lockheed Model 188 Electra is an American turboprop airliner built by Lockheed. First flying in 1957, it was the first large turboprop airliner produced in the United States. Initial sales were good, but after two fatal crashes which prompted an expensive modification program to fix a design...

OB-R-941 commercial airliner) in the Peruvian rainforest. The airplane was struck by lightning
Lightning
Lightning is an atmospheric electrostatic discharge accompanied by thunder, which typically occurs during thunderstorms, and sometimes during volcanic eruptions or dust storms...

during a severe thunderstorm
Thunderstorm
A thunderstorm, also known as an electrical storm, a lightning storm, thundershower or simply a storm is a form of weather characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere known as thunder. The meteorologically assigned cloud type associated with the...

and exploded in mid air, disintegrating two miles up. Köpcke, who was 17 years old at the time, fell to earth still strapped into her seat. The German Peruvian
German Peruvian
A German Peruvian is a Peruvian citizen of German descent. In generally, the term is also applied to descents of other German speaking immigrants, such as Austrians or Swiss...

teenager survived the fall with only a broken collarbone, a gash to her right arm, and her right eye swollen shut.

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 he was supposed to have been given a signal by another skydiver to open his parachute, but it came two seconds too late. Mr Boole, who was filming the other skydiver for a television documentary, landed on snow-covered rocks and suffered a broken back and rib. 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 is much less severe than the 120 mph that might occur in normal freefall.

• Free-falling aircraft
Vomit Comet
A Reduced Gravity Aircraft is a type of fixed-wing aircraft that briefly provides a nearly weightless environment in which to train astronauts, conduct research and film motion pictures....

• Weightlessness
Weightlessness
Weightlessness is the condition that exists for an object or person when they experience little or no acceleration except the acceleration that defines their inertial trajectory, or the trajectory of pure free-fall...

• Terminal velocity
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....

• HALO jump
• g-force
G-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...

• Microgravity