Speed of a Skydiver (Terminal Velocity)

The terminal velocity of a falling body occurs during free fall when a falling body experiences zero acceleration. This is because of the retarding force known as air resistance. Air resistance exists because air molecules collide into a falling body creating an upward force opposite gravity. This upward force will eventually balance the falling body's weight. It will continue to fall at constant velocity known as the terminal velocity.

Source: Tom Henderson. Skydiving. Glenbrook South High School.
Reproduced with the permission of the author.

The magnitude of terminal velocity depends on the weight of the falling body. For a heavy object, the terminal velocity is generally greater than a light object. This is because air resistance is proportional to the falling body's velocity squared. For an object to experience terminal velocity, air resistance must balance weight. An example that shows this phenomenon was the classic illustration of a rock and a feather being dropped simultaneously. In a vacuum with zero air resistance, these two objects will experience the same acceleration. But on the earth this is not true. Air resistance will equal weight more quickly for the feather than it would for the rock. Thus the rock would accelerate longer and experience a terminal velocity greater than the feather.

Another factor that affects terminal velocity is the orientation at which a body falls. If an object falls with a larger surface area perpendicular to the direction of motion it will experience a greater force and a smaller terminal velocity. On the other hand, if the object fell with a smaller surface area perpendicular to the direction of motion, it will experience a smaller force and a greater terminal velocity.

The terminal velocity for a skydiver was found to be in a range from 53 m/s to 76 m/s. Four out of five sources stated a value between 53 m/s and 56 m/s. Principles of Physics stated a value of 76 m/s. This value differed significantly from the others. Then again, the value is variable since the weight and the orientation of the falling body play significant roles in determining terminal velocity.

Jian Huang -- 1998

Terminal velocity is often reported to be approximately 60 m/s for a typical skydiver in free fall. Exceptional skydivers are able to increase this value considerably by diving head first with their arms against the sides of their bodies, legs held firmly together, and toes pointed. This posture presents a minimal projected area perpendicular to the direction of motion thus reducing aerodynamic drag. Special helmets and slick body suits reduce drag even further.

Editor's Supplement -- 2019

On 16 August 1960, US Air Force Captain Joseph Kittinger entered the record books when he stepped from the gondola of a helium balloon floating at an altitude of 31,330 m (102,800 feet) and took the longest skydive in history. As of the writing of this supplement 39 years later, his record remains unbroken.

The air is so thin at this altitude that it would make for a moderate laboratory vacuum on the surface of the earth. With little atmosphere, the sky is essentially black and the sun's radiation is unusually intense despite polar temperatures.

Sitting in my gondola, which gently twisted with the balloon's slow turnings, I had begun to sweat lightly, though the temperature read 36 degrees below zero Fahrenheit. Sunlight burned in on me under the edge of an aluminized antiglare curtain and through the gondola's open door.

The density of air at 30 km is roughly 1.5 % that at sea level and thus drag is essentially negligible.

No wind whistles or billows my clothing. I have absolutely no sensation of the increasing speed with which I fall. [The clouds] rushed up so chillingly that I had to remind myself they were vapor and not solid.

This is not true for skydivers at ordinary altitudes, which is why they reach terminal velocity and cease to accelerate.

According to Captain Kittinger's 1960 report in National Geographic, he was in free fall from 102,800 to 96,000 feet and then experienced no noticeable change in acceleration for an additional 6,000 feet despite having deployed his stabilization chute. This gave him an unprecedented 3900 m (12,800 feet) over which to accelerate. At such extreme altitudes the acceleration due to gravity is not the standard 9.81 m/s², but the slightly lower value of 9.72 m/s². Using these numbers, it is possible to calculate the maximum theoretical velocity experienced during this record-setting jump. The result is amazingly close to the value recorded in National Geographic.

As one would expect the actual value is slightly less than the theoretical value. This agrees with the notion of a small, but still non-zero, amount of drag.

At nine-tenths the speed of sound, Captain Kittinger also holds the record for the greatest speed attained by a human without the use of an engine. The standard value of the speed of sound in air at 31,000 m is 300 m/s (670 mph).

Given this, why then do so many sources report that Kittinger exceeded the speed of sound? One possible answer comes from the relatively obvious similarity between Kittinger's self-reported value of 614 mph and the most frequently misreported value of 714 mph (319 m/s). Somebody must have heard 614 but entered 714 accidentally into some officious document (like an encyclopedia). Some other people read the error and then reported it as fact. Many more people read these "facts" and suddenly nearly everyone was remembering the day Captain Kittinger broke the sound barrier. Another factoid is born.

In the same way that science fiction humanoids appear human but are alien, real life factoids appear factual but are false. A factoid is a statement reported as truth that has, in fact, never been verified. Factoids are the scientific research of "they".

• "They say that cell phones cause brain cancer."
• "They say that margarine is better for you than butter."
• "They say that toilets spin the other way around in Australia."
• "They say that cows produce more milk when they listen to classical music than when they listen to rock and roll."

At least, that's the way I see it. In a fantastic irony, people have started using the word factoid to mean a fact that can be stated briefly. I would call that a "factette". In the same way that a cigarette is a small cigar, a factette is a small fact. The definition of factoid is itself becoming a factoid.

Captain Kittinger most likely did not exceed the speed of sound on 16 August 1960. To do so would have required an additional 1,300 m (4,200 feet) of free fall. That's a pretty large distance. I think he would have noticed it. This in no way detracts from his truly amazing accomplishment.

A variation of this analysis appears in the chapter on falling bodies in the companion textbook on this website. An uncredited, but obviously paraphrased version of this analysis appears at the end of this essay at aerospaceweb.com.

Editor's Supplement -- 1999, 2001, 2007

Two skydivers intend to break Joseph Kittinger's 1960 world record parachute jump: Cheryl Stearns of the United States and Rodd Millner of Australia. Stearns is scheduled to jump over New Mexico in October 2001. Millner is planning his jump over Alice Springs in March 2002. Both skydivers plan to jump from an altitude of 40 km (130,000 feet) -- 8 km (5 miles) higher than Captain Kittinger. With this additional distance, it is quite possible that one of these jumpers will exceed the speed of sound.

If we assume an average acceleration of 9.70 m/s², it is a simple matter to determine the altitude at which a skydiver starting at 40 km would break the sound barrier.

That's an altitude of about 116,000 feet. Keeping in mind that Captain Kittinger claimed not to sense any appreciable loss of acceleration until reaching 90,000 feet (27,430 m) it is now possible to project the next world record skydiving speed.

It is doubtful that Stearns or Millner would actually reach anything near this speed, which is nearly 200 m/s faster than the local speed of sound. At the incredible speeds we're dealing with, air resistance can not be ignored. Stearns' prediction of Mach 1.3 seems very reasonable compared to my prediction of Mach 1.6.

Editor's Supplement -- 2001

Add Michel Fournier, Steve Truglia, and Felix Baumgartner to the list of those going after Joseph Kittinger's record.

Editor's Supplement -- 2002, 2003, 2004, 2005, 2007, 2008, 2009, 2011

Images from the Red Bull Stratos live stream

Editor's Supplement -- 2012

Editor's Supplement -- 2015

Related pages in The Physics Factbook:

• Altitude of the Highest Manned Balloon Flight
• Altitude of the Highest Parachute Jump
• Altitude of the Highest Toy Balloon Flight
• Altitude of the Highest Unmanned Balloon Flight
• Speed of a Skydiver (Terminal Velocity)

External links to this page:

• An Investigation of Parachute Design, Teach the Teachers
• Ask Roger Ebert, Thursday, October 4, 2007, Universal Press Syndicate
• How Skydiving Works, Howstuffworks, Marshall Brain
• Modeling Falling and Skydiving, Angela B. Shiflet & George Shiflet, Wofford College
• Skydiving, Kaz Shimada's soaring and aerospace
• Sky diving from the edge of space Boiling ostrich eggs, WonderQuest, April Holladay, 9 May 2003
• Supersonic Jump. Andreas Müller. The Physics Teacher. Vol. 51 No. 14 (January 2013): 14–15.
• Slashdot
  • More on High Altitude Ballooning, Posted by michael on Friday July 11, 2003 @08:50AM
  • Skydiving from 25 Miles Up, Posted by michael on Sunday July 14, 2003 @04:17PM
• spiky-haired dragon, worthless knight
• Terminal Velocity, Wikipedia