g-force

This article is about a type of acceleration. For other uses, see G force (disambiguation).

This top-fuel dragster can accelerate from zero to 160 kilometres per hour (100 mph) in 0.86 seconds. This is a horizontal acceleration of 5.3 g. Combined with the vertical g-force in the stationary case the Pythagorean theorem yields a g-force of 5.4 g.

The g-force (with g from gravitational) associated with an object is its acceleration relative to free-fall.^[1][2] 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 it is only these that are measured in g-force units. They cause stresses and strains on objects, which are felt as weight (any g-force can thus be simply described, and measured, as a "weight per unit mass"). Because of these strains (weight forces), large proper accelerations (large g-forces), may be destructive.

The standard gravitational acceleration at the Earth's surface produces g-force only indirectly. The 1 g force on an object sitting on the Earth's surface is caused by mechanical force exerted in the upward direction by the ground, keeping the object from going into free-fall. An object on the Earth's surface is accelerating relative to the free-fall condition, which is the path an object would follow falling freely toward the Earth's center. It is thus experiencing proper acceleration, even without a change in velocity (which is dv/dt, the familiar "coordinate acceleration" of Newton's laws).

Objects allowed to free-fall under the influence of gravity feel no g-force, as demonstrated by the "zero-g" conditions inside a freely-falling elevator falling toward the Earth's center (in vacuum), or (to good approximation) conditions inside a spacecraft in Earth orbit. These are examples of coordinate acceleration (a change in velocity) without proper acceleration. Since the g-force felt is always a measure of proper acceleration (which, in these cases, is zero, even though the objects are freely changing velocity due to gravity) all of these conditions of free-fall produce no g-force. The experience of no g-force (zero-g), however it is produced, is synonymous with weightlessness.

In the absence of gravitational fields, or in directions at right angles to them, proper and coordinate accelerations are the same, and any coordinate acceleration must be produced by a corresponding g-force acceleration. An example here is a rocket in free space, in which simple changes in velocity are produced by the engines, and produce g-forces on the rocket and passengers. The same happens in a dragster (see illustration) when it is changing velocity in a direction at right angles to the acceleration of gravity: such changes must be produced by accelerations that are appropriately measured in g-force units in the horizontal direction, since they produce g-force effects in that direction.

Unit and measurement

The unit of measure of acceleration in the International System of Units (SI) is m/s². However, to distinguish acceleration relative to free-fall from simple acceleration (rate of change of velocity), the unit g (or g) is often used. One g is the acceleration due to gravity at the Earth's surface and is the standard gravity (symbol: g_n), defined as 9.80665 metres per second squared,^[3] or equivalently 9.80665 newtons of force per kilogram of mass.^[4]

The unit g is not one of the SI units, which uses "g" for gram. Also "g" should not be confused with "G", which is the standard symbol for the gravitational constant.^[5]

Measurement of g-force is typically achieved using an accelerometer (see discussion below in Measuring g-force using an accelerometer). In certain cases, g-forces may be measured using suitably calibrated scales. Specific force is another name that has been used for g-force.

Acceleration and forces

Newton’s third law: law of reciprocal actions

The term g-force is technically incorrect as it is a measure of acceleration, not force. While acceleration is a vector quantity, g-forces are often expressed as a scalar, with positive g-forces working towards the bottom of a vehicle and negative forces towards the top. However, g-force can also be expressed as a vector acceleration.

G-forces, when multiplied by a mass upon which they act, are associated with a certain type of mechanical force in the correct sense of the term force, and this force produces compressive stress and tensile stress. If for example a g-force is vertically upward and applied by the ground or the floor of an elevator to a standing person, most of the body experiences compressive stress which at any height, if multiplied by the area, is the related mechanical force, which is the product of the g-force and the supported mass (the mass above the level of support, including arms hanging down from above that level). At the same time, the arms themselves experience a tensile stress, which at any height, if multiplied by the area, is again the related mechanical force, which is the product of the g-force and the mass hanging below the point of mechanical support. The mechanical resistive force spreads from points of contact with the floor or supporting structure, and gradually decreases toward zero at the unsupported ends (the top in the case of support from below, such as a seat or the floor, the bottom for a hanging part of the body or object). With compressive force counted as negative tensile force, the rate of change of the tensile force in the direction of the g-force, per unit mass (the change between parts of the object such that the slice of the object between them has unit mass), is equal to the g-force plus the non-gravitational external forces on the slice, if any (counted positive in the direction opposite to the g-force).

For a given g-force the stresses are the same, regardless of whether this g-force is caused by gravity, by acceleration, or a combination. Hence, for people it feels exactly the same, and both for people and objects the question whether they can withstand the g-force is the same. For example, upward acceleration (e.g. increase of speed when going up or decrease of speed when going down) on Earth feels the same as being stationary on a celestial body with a higher surface gravity.

Examples of important situations involving g-forces include:

• The g-force acting on a stationary object resting on the Earth's surface is 1 g (upwards) and results from the resisting reaction of the Earth's surface bearing upwards equal to an acceleration of 1 g, and is equal and opposite to gravity. The number 1 is approximate, depending on location.
• The g-force acting on an object in any weightless environment such as free-fall in a vacuum is 0 g.
• The g-force acting on an object under acceleration can be much greater than 1 g, for example, the dragster pictured right can exert a horizontal g-force of 5.3 when accelerating.
• The g-force acting on an object under acceleration may be downwards, for example when cresting a sharp hill on a roller coaster.
• If there are no other external forces than gravity, the g-force in a rocket is the thrust per unit mass. Its magnitude is equal to the thrust-to-weight ratio times g, and to the consumption of delta-v per unit time.
• In the case of a shock, e.g. a collision, the g-force can be very large during a short time.

A classic example of negative g-force is in a fully inverted roller coaster which is accelerating (changing velocity) toward the ground. In this case, the roller coaster riders are accelerated toward the ground faster than gravity would accelerate them, and are thus pinned upside down in their seats. In this case, the mechanical force exerted by the seat causes the g-force by altering the path of the passenger downward in a way that differs from gravitational acceleration. The difference in downward motion, now faster than gravity would provide, is caused by the push of the seat, and it results in a g-force toward the ground.

All "coordinate accelerations" (or lack of them), are described by Newton's laws of motion as follows:

The Second Law of Motion, the law of acceleration states that: F = ma., meaning that a force F acting on a body is equal to the mass m of the body times its acceleration a.

The Third Law of Motion, the law of reciprocal actions states that: all forces occur in pairs, and these two forces are equal in magnitude and opposite in direction. Newton's third law of motion means that not only does gravity behave as a force acting downwards on, say, a rock held in your hand but also that the rock exerts a force on the Earth, equal in magnitude and opposite in direction.

This acrobatic airplane is pulling up in a +g maneuver; the pilot is experiencing several gees of inertial acceleration in addition to the force of gravity. The cumulative vertical axis forces acting upon his body make him momentarily 'weigh' many times more than normal.

In an airplane, the pilot’s seat can be thought of as the hand holding the rock, the pilot as the rock. When flying straight and level at 1 g, the pilot is acted upon by the force of gravity. His weight (a downward force) is 725 newtons (163 lb_f). In accordance with Newton’s third law, the plane and the seat underneath the pilot provides an equal and opposite force pushing upwards with a force of 725 N (163 lb_f). This mechanical force provides the 1.0 g-force upward proper acceleration on the pilot, even though this velocity in the upward direction does not change (this is similar to the situation of a person standing on the ground, where the ground provides this force and this g-force).

If the pilot were suddenly to pull back on the stick and make his plane accelerate upwards at 9.8 m/s², the total g‑force on his body is 2 g, half of which comes from the seat pushing the pilot to resist gravity, and half from the seat pushing the pilot to cause his upward acceleration—a change in velocity which also is a proper acceleration because it also differs from a free fall trajectory. Considered in the frame of reference of the plane his body is now generating a force of 1,450 N (330 lb_f) downwards into his seat and the seat is simultaneously pushing upwards with an equal force of 1,450 N (330 lb_f).

An automobile and its driver undergoing lateral acceleration

Unopposed acceleration due to mechanical forces, and consequentially g-force, is experienced whenever anyone rides in a vehicle because it always causes a proper acceleration, and (in the absence of gravity) also always a coordinate acceleration (where velocity changes). Whenever the vehicle changes either direction or speed, the occupants feel lateral (side to side) or longitudinal (forward and backwards) forces produced by the mechanical push of their seats.

The expression "1 g = 9.80665 m/s²" means that for every second that elapses, velocity changes 9.80665 meters per second (≡35.30394 km/h). This rate of change in velocity can also be denoted as 9.80665 (meter per second) per second, or 9.80665 m/s². For example: An acceleration of 1 g equates to a rate of change in velocity of approximately 35 kilometres per hour (22 mph) for each second that elapses. Therefore, if an automobile is capable of braking at 1 g and is traveling at 35 kilometres per hour (22 mph) it can brake to a standstill in one second and the driver will experience a deceleration of 1 g. The automobile traveling at three times this speed, 105 km/h (65 mph), can brake to a standstill in three seconds.

In the case of an increase in speed from 0 to v with constant acceleration within a distance of s this acceleration is v²/(2s).

Preparing an object for g-tolerance (not getting damaged when subjected to a high g-force) is called g-hardening. This may e.g. apply to instruments in a projectile shot by a gun.

Human tolerance of g-force

John Stapp was subjected to 15 g for 0.6 second and a peak of 22 g during a 19 March 1954 rocket sled test. He would eventually survive a peak of more than 46 g, with more than 25 g for 1.1 sec.^[6]

Human tolerances depend on the magnitude of the g-force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body.^[7][8]:350

The human body is flexible and deformable, particularly the softer tissues. A hard slap on the face may briefly impose hundreds of g locally but not produce any real damage; a constant 16 g for a minute, however, may be deadly. When vibration is experienced, relatively low peak g levels can be severely damaging if they are at the resonance frequency of organs and connective tissues.

To some degree, g-tolerance can be trainable, and there is also considerable variation in innate ability between individuals. In addition, some illnesses, particularly cardiovascular problems, reduce g-tolerance.

Vertical axis g-force

Aircraft pilots (in particular) exert g-forces along the axis aligned with the spine. This causes significant variation in blood pressure along the length of the subject's body, which limits the maximum g-forces that can be tolerated.

Positive, or "upward" g, drives blood downward to the feet of a seated or standing person (more naturally, the feet and body may be seen as being driven by the upward force of the floor and seat, upward around the blood). Resistance to positive g varies. A typical person can handle about 5 g (49 m/s²) before losing consciousness ("G-LOC"), but through the combination of special g-suits and efforts to strain muscles—both of which act to force blood back into the brain—modern pilots can typically handle a sustained 9 g (88 m/s²) (see High-G training)^{[citation needed]}.

In aircraft particularly, vertical g-forces are often positive (force blood towards the feet and away from the head); this causes problems with the eyes and brain in particular. As positive vertical g-force is progressively increased (such as in a centrifuge) the following symptoms may be experienced:

• Grey-out, where the vision loses hue, easily reversible on levelling out.
• Tunnel vision, where peripheral vision is progressively lost.
• Blackout, a loss of vision while consciousness is maintained, caused by a lack of blood to the head.
• G-LOC a loss of consciousness ("LOC" stands for "Loss Of Consciousness").^[9]
• Death, if g-forces are not quickly reduced, death can occur.^[10]

Resistance to "negative" or "downward" g, which drives blood to the head, is much lower. This limit is typically in the −2 to −3 g (about −20 m/s² to −30 m/s²) range. This condition is sometimes referred to as red out where vision is literally reddened^[11] due to expansion of the capillaries in the eye.^[12] Negative g is generally unpleasant and can cause damage. Blood vessels in the eyes or brain may swell or burst under the increased blood pressure.

Horizontal axis g-force

The human body is better at surviving g-forces that are perpendicular to the spine. In general when the acceleration is forwards (subject essentially lying on their back, colloquially known as "eyeballs in"^[13]) a much higher tolerance is shown than when the acceleration is backwards (lying on their front, "eyeballs out") since blood vessels in the retina appear more sensitive in the latter direction.

Early experiments showed that untrained humans were able to tolerate 17 g eyeballs-in (compared to 12 g eyeballs-out) for several minutes without loss of consciousness or apparent long-term harm.^[14] The record for peak experimental horizontal g-force tolerance is held by acceleration pioneer John Stapp, in a series of rocket sled deceleration experiments culminating in a late 1954 test in which he was stopped in a little over a second from a land speed of Mach 0.9. He survived a peak "eyeballs-out" force of 46.2 times the force of gravity, and more than 25 g for 1.1 sec, proving that the human body is capable of this. Stapp lived another 45 years to age 89, but suffered lifelong damage to his vision from this last test.^[15]

Short g-force durations and jerk

Main article: Shock (mechanics)

Main article: Jerk (physics)

Toleration of g-force also depends on its duration. Shock is a short-term transient exitiation and is often measured as an acceleration. Very short duration shocks of 100 g have been survivable in racing car crashes.^[16]

Jerk is the rate of change of acceleration. In SI units, jerk is expressed as m/s³. In non-SI units, jerk can be expressed simply as gees per second (g/s).^{[citation needed]}

Other biological responses to g-force

Recent research carried out on extremophiles in Japan involved a variety of bacteria including E. coli and Paracoccus denitrificans being subject to conditions of extreme gravity. The bacteria were cultivated while being rotated in an ultracentrifuge at high speeds corresponding to 403,627 g. Paracoccus denitrificans was one of the bacteria which displayed not only survival but also robust cellular growth under these conditions of hyperacceleration which are usually only to be found in cosmic environments, such as on very massive stars or in the shock waves of supernovas. Analysis showed that the small size of prokaryotic cells is essential for successful growth under hypergravity. The research has implications on the feasibility of panspermia.^[17][18]

Typical examples of g-force

Main article: Orders of magnitude (acceleration)

Example	g-force*
The gyro rotors in Gravity Probe B and the free-floating proof masses in the TRIAD I navigation satellite[19]	0 g
A ride in the Vomit Comet	≈ 0 g
Standing on the Moon at its equator	0.1654 g
Standing on the Earth at sea level–standard	1 g
Saturn V moon rocket just after launch	1.14 g
Bugatti Veyron from 0 to 100 km/h in 2.4 s	1.55 g†
Space Shuttle, maximum during launch and reentry	3 g
High-g roller coasters[8]:340	3.5–6.3 g
Top Fuel drag racing world record of 4.4 s over 1/4 mile	4.2 g
Formula One car, maximum under heavy braking	5+ g
Luge, maximum expected at the Whistler Sliding Centre	5.2 g
Formula One car, peak lateral in turns [20]	5–6 g
Standard, full aerobatics certified glider	+7/-5 g
Apollo 16 on reentry[21]	7.19 g
Typical max. turn in an aerobatic plane or fighter jet	9–12 g
Maximum for human on a rocket sled	46.2 g
Death or serious injury likely	> 50 g
Sprint missile	100 g
Brief human exposure survived in crash[16]	> 100 g
Space gun with a barrel length of 1 km and a muzzle velocity of 6 km/s, as proposed by Quicklaunch (assuming constant acceleration)	1,800 g
Shock capability of mechanical wrist watches[22]	> 5,000 g
Current formula one engines, maximum piston acceleration [23]	8,600 g
Rating of electronics built into military artillery shells[24]	15,500 g
9 × 19 Parabellum handgun bullet (average along the length of the barrel)[25]	31,000 g
9 × 19 Parabellum handgun bullet, peak[26]	190,000 g
Mean acceleration of a proton in the Large Hadron Collider[27]	190,000,000 g
Acceleration from a Wakefield plasma accelerator[28]	8.9×1020 g

* Including contribution from resistance to gravity. † Directed 40 degrees from horizontal.

Measuring g-force using an accelerometer

Six Flags' "Superman: The Escape" amusement ride provides 6.5 seconds of ballistic weightlessness.

An accelerometer, in its simplest form, is a damped mass on the end of a spring, with some way of measuring how far the mass has moved on the spring in a particular direction, called an 'axis'.

Accelerometers are often calibrated to measure g-force along one or more axes. If a stationary, single-axis accelerometer is oriented so that its measuring axis is horizontal, its output will be 0 g, and it will continue to be 0 g if mounted in an automobile traveling at a constant velocity on a level road. When the driver presses on the brake or gas pedal, the accelerometer will register positive or negative acceleration.

If the accelerometer is rotated by 90° so that it is vertical, it will read +1 g upwards even though stationary. In that situation, the accelerometer is subject to two forces: the gravitational force and the ground reaction force of the surface it is resting on. Only the latter force can be measured by the accelerometer, due to mechanical interaction between the accelerometer and the ground. The reading is the acceleration the instrument would have if it were exclusively subject to that force.

A three-axis accelerometer will output zero‑g on all three axes if it is dropped or otherwise put into a ballistic trajectory (also known as an inertial trajectory), so that it experiences "free fall," as do astronauts in orbit (astronauts experience small tidal accelerations called microgravity, which are neglected for the sake of discussion here). Some amusement park rides can provide several seconds at near-zero g. Riding NASA's "Vomit Comet" provides near-zero g for about 25 seconds at a time.

A single-axis accelerometer mounted in an airplane with its measurement axis oriented vertically reads +1 g when the plane is parked. This is the g-force exerted by the ground. When flying at a stable altitude (or at a constant rate of climb or descent), the accelerometer will continue to indicate 1 g, as the g-force is provided by the aerodynamic lift, which now acts in place of the ground to keep the plane from free-falling. Under such conditions, the upward force acting upon the pilot's body (which keeps him from falling) is the normal value of about 9.8 newtons per kilogram (N/kg), and it is provided by his seat, which in turn is supported by the lift of the wings. If the pilot pulls back on the stick until the accelerometer indicates 2 g, the g-force acting upwards on him through the seat doubles to 19.6 N/kg.

See also

• Earth's gravity
• Artificial gravity
• Centrifuge
• Metre per second squared
• Impact (mechanics)
• Shock (mechanics)
• Jerk (physics)
• Load factor (aeronautics)
• Thrust-to-weight ratio
• Relation between g-force and apparent weight
• Peak ground acceleration – g-force of earthquakes
• Euthanasia Coaster

References

1. ^ G Force. Newton.dep.anl.gov. Retrieved on 2011-10-14.
2. ^ Sircar, Sabyasachi (2007-12-12). Principles of Medical Physiology. ISBN 9781588905727. http://books.google.com/?id=zFl7y5xqHj4C&lpg=PA6&dq=%22apparent%20acceleration%22%20%22g-force%22&pg=PA6#v=onepage&q=%22apparent%20acceleration%22%20%22g-force%22&f=true. 
3. ^ BIPM: Declaration on the unit of mass and on the definition of weight; conventional value of g_n
4. ^ Note that the unit does not vary with location- the g-force when standing on the moon is about 0.18g
5. ^ Symbol g: ESA: GOCE, Basic Measurement Units, NASA: Multiple G, Astronautix: Stapp, Honeywell: Accelerometers, Sensr LLC: GP1 Programmable Accelerometer, Farnell: accelometers, Delphi: Accident Data Recorder 3 (ADR3) MS0148, NASA: Constants and Equations for Calculations, Jet Propulsion Laboratory: A Discussion of Various Measures of Altitude, Vehicle Safety Research Centre Loughborough: Use of smart technologies to collect and retain crash information, National Highway Traffic Safety Administration: Recording Automotive Crash Event Data

   Symbol G: Lyndon B. Johnson Space Center: ENVIRONMENTAL FACTORS: BIOMEDICAL RESULTS OF APOLLO, Section II, Chapter 5, Honywell: Model JTF, General Purpose Accelerometer

6. ^ The Ejection Site: The Story of John Paul Stapp
7. ^ Balldin, Ulf I (2002). "33". Acceleration effects on fighter pilots. In: Medical conditions of Harsh Environments. 2. Washington, DC. http://www.bordeninstitute.army.mil/published_volumes/harshEnv2/harshEnv2.html. Retrieved 2009-04-06. 
8. ^ ^{a b} George Bibel. Beyond the Black Box: the Forensics of Airplane Crashes. Johns Hopkins University Press, 2008. ISBN 0-8018-8631-7.
9. ^ Burton RR (1988). "G-induced loss of consciousness: definition, history, current status". Aviation, Space, and Environmental Medicine 59 (1): 2–5. PMID 3281645. 
10. ^ The Science of G Force- Joshua Davis
11. ^ Brown, Robert G (1999). On the edge: Personal flying experiences during the Second World War. ISBN 9781896182872. http://books.google.com/books?id=hw_0x_pBP3AC&lpg=PA60. 
12. ^ redout. Free Dictionary. Retrieved on 2011-10-14.
13. ^ NASA Physiological Acceleration Systems
14. ^ NASA Technical note D-337, Centrifuge Study of Pilot Tolerance to Acceleration and the Effects of Acceleration on Pilot Performance, by Brent Y. Creer, Captain Harald A. Smedal, USN (MC), and Rodney C. Vtlfngrove
15. ^ Fastest Man on Earth- John Paul Stapp. Ejection Site. Retrieved on 2011-10-14.
16. ^ ^{a b} "Several Indy car drivers have withstood impacts in excess of 100 G without serious injuries." Dennis F. Shanahan, M.D., M.P.H.: "Human Tolerance and Crash Survivability, citing Society of Automotive Engineers. Indy racecar crash analysis. Automotive Engineering International, June 1999, 87–90. And National Highway Traffic Safety Administration: Recording Automotive Crash Event Data
17. ^ Than, Ker (25 April 2011). "Bacteria Grow Under 400,000 Times Earth's Gravity". National Geographic- Daily News. National Geographic Society. http://news.nationalgeographic.com/news/2011/04/110425-gravity-extreme-bacteria-e-coli-alien-life-space-science/. Retrieved 28 April 2011. 
18. ^ Deguchi, Shigeru; Hirokazu Shimoshige, Mikiko Tsudome, Sada-atsu Mukai, Robert W. Corkery, Susumu Ito, and Koki Horikoshi (2011). "Microbial growth at hyperaccelerations up to 403,627 xg". Proceedings of the National Academy of Sciences 108 (19): 7997. Bibcode 2011PNAS..108.7997D. doi:10.1073/pnas.1018027108. http://www.pnas.org/content/early/2011/04/20/1018027108.abstract. Retrieved 28 April 2011. 
19. ^ Stanford University: Gravity Probe B, Payload & Spacecraft, and NASA: Investigation of Drag-Free Control Technology for Earth Science Constellation Missions. The TRIAD 1 satellite was a later, more advanced navigation satellite that was part of the U.S. Navy’s Transit, or NAVSAT system.
20. ^ 6 g has been recorded in the 130R turn at Suzuka circuit, Japan. [1] Many turns have 5 g peak values, like turn 8 at Istanbul or Eau Rouge at Spa
21. ^ NASA: Table 2: Apollo Manned Space Flight Reentry G Levels
22. ^ Omega [2], Ball Watch Technology
23. ^ Cosworth V8 engine ; Up to 10,000 g before rev limits
24. ^ "L-3 Communication's IEC Awarded Contract with Raytheon for Common Air Launched Navigation System". http://www.iechome.com/news/032003.htm. 
25. ^ Assuming a 8.04 gram bullet, a muzzle velocity of 350 metres per second (1,100 ft/s), and a 102 mm barrel.
26. ^ Assuming a 8.04 gram bullet, a peak pressure of 240 MPa (35,000 psi) and 440 N of friction.
27. ^ (7 TeV / (20 minutes * c))/proton mass
28. ^ (42 GeV / 85 cm)/electron mass

External links

Faller, James E. (November–December 2005). "The Measurement of Little g: A Fertile Ground for Precision Measurement Science". Journal of Research of the National Institutes of Standards and Technology 110 (6): 559–581. http://nvl-i.nist.gov/pub/nistpubs/jres/110/6/j110-6fal.pdf. 

• "How Many Gs Can a Flyer Take?", October 1944, Popular Science one of the first detailed public articles explaining this subject
• Wired article about enduring a human centrifuge at the NASA Ames Research Center
• Video of Pilot g-force training
• Linear acceleration.