Speed of a Skydiver (Terminal Velocity)

The Physics Factbook
Edited by Glenn Elert -- Written by his students
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Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
Tipler, Paul A. College Physics. New York: Worth, 1987: 105. "For a skydiver with parachute closed, the terminal velocity is about 200 km/h." 56 m/s
Ardley, Neil. Dictionary of Science: 2000 Key Words Arranged Thematically. London: Dorling Kindersley, 1994: 57. "The terminal velocity of this skydiver is about 124 mph (200 kph)." 55.6 m/s
Relating to Velocities. Cockpit Physics. United States Air Force Academy Physics Department. "Skydiver 54 m/s" 54 m/s
Bueche, Fredrick. Principles of Physics. New York: McGraw Hill, 1977: 64. "The more compact and dense the object, the higher its terminal velocity will be. Typical examples are the following: raindrop, 25 ft/s, human being, 250 ft/s." 76 m/s
Falling Feather. Science Snacks. Exploratorium. "The terminal velocity of a falling human being with arms and legs outstretched is about 120 miles per hour (192 km per hour) — slower than a lead balloon, but a good deal faster than a feather!" 53 m/s

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.

animation
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

Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
rec.skydiving FAQ "However, by diving or "standing up"in free fall, any experienced skydiver can learn to reach speeds of over 160-180MPH. Speeds of over 200MPH require significant practice to achieve. The record free fall speed, done without any special equipment, is 321MPH. Obviously, it is desirable to slow back down to 110MPH before parachute opening." 143 m/s
(max.)

49 m/s
(safe)
Bloomfield, Louis A. "What is Terminal Velocity?"How Things Work. University of Virginia. 23 December 1999. "A person has a terminal velocity of about 200 mph when balled up and about 125 mph with arms and feet fully extended to catch the wind." 56–89 m/s

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 -- 1999

Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
Kittinger, Joseph W, Jr. "The Long, Lonely Leap." National Geographic. December 1960: 854-873. "An hour and thirty-one minutes after launch, my pressure altimeter halts at 103,300 feet. At ground control the radar altimeters also have stopped-on readings of 102,800 feet, the figure that we later agree upon as the more reliable. It is 7 o'clock in the morning, and I have reached float altitude …. Though my stabilization chute opens at 96,000 feet, I accelerate for 6,000 feet more before hitting a peak of 614 miles an hour, nine-tenths the speed of sound at my altitude." 274 m/s
(most reliable)
"Ballooning: A History." National Geographic. September 1999: 48. "Rocketing downward for 13 minutes, he falls at more than 600 miles per hour, almost breaking the sound barrier with his body." > 268 m/s
Friend, Tim. "Captain's jump put NASA on the map." USA Today. 12 February 1999. "Kittinger fell for four minutes before his main chute opened. In the vacuum of the upper stratosphere, his body accelerated to 714 mph, breaking the sound barrier." 319 m/s
(unreliable)
Frisbee, John L. "The Longest Leap." Air Force Magazine, vol 68 no. 6, June 1985. "With that and other hazards in mind, he stepped out of the gondola and plunged through the stratosphere, reaching supersonic speed in the rarefied atmosphere. Between 90,000 and 70,000 feet, he experienced great difficulty in breathing. At about 50,000 feet, his free-fall speed had dropped to 250 miles an hour in the denser atmosphere." > 300 m/s
(unreliable)
Hamilton, Tom. "Balloonmeister - Joe Kittinger." Balloon Life. October 1995: 41. "On the descent Kittinger became the first man to exceed the Speed of Sound without an aircraft or space vehicle." > 300 m/s
(unreliable)
Ejection Seat Trivia. Kevin Coyne. "His later jumps were much more stable, and with a functioning 6 foot drogue, he achieved a terminal velocity of 702 MPH!" 314 m/s
(unreliable)
Kittinger, Joseph William. National Aviation Hall of Fame. "During his decent he reached speeds of up to 714 miles per hour, exceeding the speed of sound without an aircraft or space vehicle (another world record)." 319 m/s
(unreliable)
Joseph W. Kittinger - USAF Museum Gathering of Eagles. United States Air Force Museum, Wright-Patterson Air Force Base. "In freefall for 4.5 minutes at speeds up to 714 mph and temperatures as low as -94 degrees Fahrenheit, Kittinger opened his parachute at 18,000 feet. In addition to the altitude record, he set records for longest freefall and fastest speed by a man (without an aircraft!)" 319 m/s
(unreliable)

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.

equation

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".

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

Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
Australian to Jump from 130,000 ft. Dropzone (11 March 2001). "An Australian parachutist is planning to jump out of a balloon floating nearly 40 kilometres above the Earth's surface. Rodd Millner expects to reach speeds of between 1,600 and 1,800 kilometres (994-1,118 miles) per hour during his descent. If he pulls it off, he will become only the second man to break the sound barrier by merely falling through the air." 444–500 m/s
(projected)
Kenneally, Christine. The Man Who Fell to Earth. Feed. 9 March 2001. "[Rodd] Millner believes that he will reach a speed of between 700 and 900 miles per hour within one minute of leaping from the balloon. If he is successful, he will be the first human to break the sound barrier sans vehicle." 300–400 m/s
(projected)
Australian plans skydive from edge of space. CNN. 6 March 2001. "[Rodd] Millner expects to fall at speeds up to 1,800 km/h (1,118 mph). It will take Millner two and half hours to reach 130,000 feet, but only 10 minutes to parachute to earth." 500 m/s
(projected)
Frequently Asked Questions. stratoquest.com "Q: How fast will Cheryl [Stearns] go in freefall?
A: Max. Speed is estimated @ 885 (1.3 mach) dependant [sic] on temp. density and weight."

"Q: Will Cheryl [Stearns] break the sound barrier?
A: There is currently no information on this subject and no human has ever broke the barrier without an external vehicle. The speed that Cheryl will be traveling (1.3 mach) infers that she will break the barrier, although we are not sure that she will have the mass to actually make this happen."
396 m/s
(projected)
Cheryl Stearns, Breaking Barriers. cherylstearns.com

"Mission: A record-setting, high-altitude skydive from 130,000 feet dedicated to scientific research, education and space exploration."

"Records: First human to exceed the speed of sound without a vehicle. Break the 1960 world skydive record of 102,800 feet."

> 300 m/s
(projected)

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.

equation

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.

equation

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.

Access
Date
Cheryl Stearns
StratoQuest
Michel Fournier
Le Grand Saut
Steve Truglia
Project Space Jump
Felix Baumgartner
Red Bull Stratos
November
2002
"Our current window and location for project launch ... is September 2003, Fort McConnell Air Force Base, Wichita Kansas -- 'Centennial of Flight Airshow'." "After 12 years of efforts, Michel Fournier and his partners have still to be a little bit patient, and wait until beginning of May 2003 to see the Super Jump finally happen [over Saskatchewan]."    
June
2003
  "An unforeseen development forces the postponement of Michel Fournier's scheduled second attempt to carry out his stratospheric jump [over Saskatchewan].... until the end of August [2003]."    
September
2003
"UPDATE: Three intense training sessions will take place prior to the StratoQuest Launch in October 2004." "5th of August 2003 09:00. At 7 am, the balloon, still fixed to the truck, slowly filled with helium. During the release process, the balloon ripped at the top.... The 2003 Big Jump attempt failed."    
October
2004
"130,000ft StratoQuest Launch: September 2005"      
June
2005
"The attempt will likely be made in October ofnext year [2006], probably somewhere in Arizona or Texas...." fortbraggnc.com
2005-04-21
     
Access
Date
Cheryl Stearns
StratoQuest
Michel Fournier
Le Grand Saut
Steve Truglia
Project Space Jump
Felix Baumgartner
Red Bull Stratos
September
2005
"I have determined that it is not feasible for me to safely jump from that high an altitude at this time." "Michel Fournier was a victim of a financial swindle by a pseudo sponsor who carried out a false credit transfer on the bank of the Great Jump."    
August
2007
  "In August 2007 … Michel Fournier will drop out of the stratosphere from an altitude from about 130,000 feet (40 kilometers, nearly 25 miles) above the plains of Saskatchewan, Canada"    
May
2008
  "Using a narrow weather window starting May 25, [2008] Michel will ascend in a pressurized capsule, harnessed to a 161-metre helium balloon, rising to the edge of space." WebWire "Steve Truglia will attempt to set a new World High Altitude Parachute Record this Summer by parachuting from the edge of space, 120,000 feet (or over 23 miles high)."  
September
2009
  "We are still in progress in testing the equipment and the budget is not yet finalized. As a result, we are postponing the jump for the spring of 2010." "Space Jump project is in the final stages of preparation. Sponsors are required to complete this exciting project."  
December
2009
  "The jump will take place within the next MTO window if I complete my budget."    
Access
Date
Cheryl Stearns
StratoQuest
Michel Fournier
Le Grand Saut
Steve Truglia
Project Space Jump
Felix Baumgartner
Red Bull Stratos
December
2011
"Cheryl is working on sponsorship for StratoQuest. Updates to her project will be posted on this web site." "Unfortunately, the Big Jump will not take place in August for two reasons : - My budget is not complete and, - I will not be able to have my balloon in Canada before September 15th, there for the MTO window will be closed"   "The legal action filed by Daniel Hogan and PerDan, LLC … has been mutually resolved by the parties out of court and the lawsuit has been dismissed."

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

Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
Live Broadcast | Red Bull Stratos. 20:40 GMT 14, October 2012. Exit altitude: 128,100 feet, 39,045 m; Freefall: 4 minutes 20 seconds, 19,846 feet, 36,529 m; Maximum vertical velocity: 373 m/s, 1342.8 km/h, 833.9 mph, mach 1.24 (all results unofficial) 373 m/s
     
Images from the Red Bull Stratos live stream
 
The balloon near its highest altitude Inside the gondola Outside the gondola
     
Felix Baumgartner takes his own long, lonely, leap An infrared image of Baumgartner near his greatest vertical velocity Colonel Joe Kittinger and Felix Baumgartner at their first press conference after the historic jump

Editor's Supplement -- 2012

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