Definitions

# Free-fall

Free fall is motion with no acceleration other than that provided by gravity. Since this definition does not specify velocity, it also applies to objects initially moving upward. Although the definition specifically excludes all other forces such as aerodynamic drag, in nontechnical usage falling through an atmosphere is also referred to as free fall.

## Examples

Examples of objects in free fall include:

Examples of objects not in free fall:

• Standing on the ground: the gravitational acceleration is counteracted by the normal force from the ground.
• Flying horizontally in an airplane: the wings' lift is also providing an acceleration.
• Jumping from an airplane: there is a resistance force provided by the atmosphere.

### On Earth

Near sea level, an object in free fall in a vacuum will accelerate at approximately 9.81 m/s$^2$, regardless of its mass. With air resistance acting upon an object that has been dropped, the object will eventually reach a terminal velocity, around 56 m/s (200 km/h or 120 mph) for a human body. 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.

## Free fall in Newtonian mechanics

### Without air resistance

$v\left(t\right)=-gt+v_\left\{0\right\},$

$y\left(t\right)=-frac\left\{1\right\}\left\{2\right\}gt^2+v_\left\{0\right\}t+y_0$

where

$v_\left\{0\right\},$ is the initial velocity (m/s).
$v\left(t\right),$is the vertical velocity with respect to time (m/s).
$y_0,$ is the initial altitude (m).
$y\left(t\right),$ is the altitude with respect to time (m).
$t,$ is time elapsed (s).
$g,$ is the acceleration due to gravity (9.81 m/s2 near the surface of the earth).

### With Stokes friction

$ma=-kv-mg,$

where

$m,$ is the mass of the object
$k,$ is the friction coefficient
$v_\left\{yinfty\right\},$ is the terminal velocity,
please note that the positive direction in the coordinate system is upwards (just as in the picture to the right)

$frac\left\{dv\right\}\left\{dt\right\}=-g\left(1+frac\left\{k\right\}\left\{mg\right\}v\right)$

$int frac\left\{1\right\}\left\{1+frac\left\{k\right\}\left\{mg\right\}v\right\},dv=-gint,dt+C$

$frac\left\{mg\right\}\left\{k\right\}ln\left\{\left(1+frac\left\{kv\right\}\left\{mg\right\}\right)\right\}=-gt +C$

$v=frac\left\{mg\right\}\left\{k\right\}\left[exp\left(-frac\left\{kt\right\}\left\{m\right\}+frac\left\{kC\right\}\left\{mg\right\}\right)-1\right]$

$v_\left\{infty\right\}=lim_\left\{t to infty\right\}v = - frac\left\{m\right\}\left\{k\right\}g$
$t=0$, then $v=v_\left\{0\right\}$

$y=-frac\left\{m\right\}\left\{k\right\}\left\{\left(v_\left\{o\right\}+frac\left\{m\right\}\left\{z\right\}g\right)\left(e^\left\{frac\left\{-k\right\}\left\{m\right\}t\right\}-1\right)+gt\right\}+y_0.$

### With turbulent drag

$mfrac\left\{dv\right\}\left\{dt\right\}=-frac\left\{1\right\}\left\{2\right\} rho C_D A v^2 - mg,$

where

$m,$ is the mass of the object,
$g,$ is the gravitational acceleration,
$C_D,$ is the drag coefficient,
$A,$ is the cross-sectional area of the object, perpendicular to air flow,
$v_y,$ is the fall (vertical) velocity,
and $rho,$ is the air density.

This case, which applies to skydivers, parachutists, or any bodies with Reynolds number well above the critical Reynolds number, has a solution

$v\left(t\right) = -v_\left\{infty\right\} tanh\left(frac\left\{gt\right\}\left\{v_infty\right\}\right),$

where the terminal speed is given by

$v_\left\{infty\right\}=sqrt\left\{frac\left\{2mg\right\}\left\{rho C_D A\right\}\right\},$.

## Surviving falls

JAT stewardess Vesna Vulović survived a fall of 33,000 feet (over 10,000 meters) on January 26, 1972 when she was thrown from JAT Flight 364. The plane was brought down by explosives planted by Croatian (Ustashe) terrorists, over Srbská Kamenice in the former Czechoslovakia (now 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 with Hitler's troops as a medic during the War. He was German. He knew how to treat me at the site of the accident."

In World War II there were several reports of military aircrew surviving long falls: Nick Alkemade, Alan Magee, and I.M.Chisov all fell at least 5,500 meters and survived.

Freefall is not to be confused with individuals who survive instances of various degrees of controlled flight into terrain. 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 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.

## Record 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 80,380 ft (24,500 m) from an altitude of 83,523 ft (25,457 m) near the city of Saratov, Russia on November 1, 1962. Andreev did not use a drogue chute during his jump.

Captain Kittinger was then 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 (23,287 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 (22,769 m). For that return jump Kittinger was awarded the Leo Stevens parachute medal.

On August 16, 1960 he made the final jump from the Excelsior III at 102,800 feet (31 333.44 meters). Towing a small drogue chute for stabilization, he fell for 14 minutes and 36 seconds reaching a maximum speed of 614 mph (988 km/h) before opening his parachute at 14,000 feet. Pressurization for his right glove malfunctioned during the ascent, and his right hand swelled to twice its normal size.[1] He set records for highest balloon ascent, highest parachute jump, longest drogue-fall (14 min), and fastest speed by a human through the atmosphere[2].

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 to his D.F.C. and awarded the Harmon Trophy by President Dwight Eisenhower.