g-force

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

The g-force on something 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 per unit of the object's mass. Such accelerations, termed "proper accelerations," not produced by gravity itself, cause stresses and strains on objects which can make these sorts of forces significant. Because of these strains, sufficiently large g-forces may be highly destructive to objects and organisms.

The general exception of gravitational accelerations from "g-force" accelerations applies also to the case of standard gravitational acceleration at the Earth's surface, which does not produce g-force. The upward "1 g-force" which is "felt" by an object sitting on the Earth's surface is not due to gravity per se, but instead is caused by the stress of the mechanical force exerted in the upward direction by supporting materials (such as the ground) which must act to keep the object from going into free-fall. An object on the Earth's surface is accelerating relative to "free-fall," which is the path of an object falling freely toward the Earth's center. It is thus undergoing a proper acceleration, even if not undergoing a change in velocity (the more familiar "coordinate acceleration" of Newton's laws).

By contrast, objects allowed to free-fall, even under the influence of gravity, feel no "g-force," as demonstrated by the "zero-g" conditions in spacecraft in Earth orbit (or within a hypothetical elevator allowed to free-fall toward the center of the Earth, in vacuum). These objects serve as examples of things that undergo coordinate acceleration, but no proper acceleration. The g-force they feel (in this example, none) is always a measure of their proper acceleration (in this case, zero), not simply their velocity change.

The unit of measure of g-force in the International System of Units (SI) is m/s2. However, for easy comparison with the stationary situation on Earth, and to emphasize the distinction of this acceleration relative to free-fall from simple acceleration (rate of change of velocity), often the unit g is used - the acceleration due to gravity at the Earth's surface; it can be written g, g, or G. More accurately, it is the standard gravity (symbol: gn), defined as 9.80665 metres per second squared,[3] or equivalently 9.80665 newtons of force per kilogram of mass.[4] Sometimes the plural Gs is used. The unit g is not one of the SI units, which uses "g" for gram; also, "G" should not be confused with 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.

Contents

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 accelerations 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:

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 lbf). 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 lbf). 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 to suddenly 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 lbf) downwards into his seat and the seat is simultaneously pushing upwards with an equal force of 1,450 N (330 lbf).

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]

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, in particular, exert g-force 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 (49m/s²) before 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 9 g (88 m/s²) sustained (for a period of time) or more (see High-G training).

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 (−20 m/s² to −30 m/s²) range. The subject's vision turns red, referred to as a red out. This is probably because capillaries in the eyes swell or burst under the increased blood pressure.

In aircraft, 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 g-force is progressively increased the pilot may experience:

Horizontal axis g-force

The human body is better at surviving g-forces that are perpendicular to the spine. In general when the g-force/acceleration is forwards (subject essentially lying on their back, colloquially known as "eyeballs in"[10]) a much higher tolerance is shown than when the g-force/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.[11] 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.[12]

Short g-force durations and jerk

Toleration of g-force also depends on its duration and the rate of change in acceleration, known as jerk. In SI units, jerk or horizontal g force g is expressed as m/s3. In non-SI units, jerk can be expressed simply as gees per second (g/s). Very short durations or high jerk forces of 100g have been claimed. There is no jerk g without push F; g=F/m, where F is mechanical push force on mass m. Then horizontal acceleration is a=gt. Then velocity at acceleration time t=600 seconds and constant g=1 m/s3 is: v=gt2=360,000 metres/second. For constant g=5 m/s3 and t=6000 second, speed v=gt2=180 million metres/second.[13]

Typical examples of g-force

Example g-force
(or gravity)
The gyro rotors in Gravity Probe B and the free-floating
proof masses in the TRIAD I navigation satellite[14]		 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 1.18 g
Space Shuttle, maximum during launch and reentry 3 g
High-g roller coasters[15] 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 Center 5.2 g
Standard, full aerobatics certified glider +7/-5 g
Apollo 16 on reentry[16] 7.19 g
Typical max. turn in an aerobatic plane or fighter jet 9–12 g
Force encountered in the REDBULL Air Race 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[13] > 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[17] > 5,000 g
Rating of electronics built into military artillery shells[18] 15,500 g
9 × 19 Parabellum handgun bullet (average along the length of the barrel)[19] 31,000 g
9 × 19 Parabellum handgun bullet, peak[20] 190,000 g

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. But if the car driver brakes sharply, the accelerometer will read about −0.9 g, corresponding to a deceleration. Jerk due to a change in motion and gravity pull on ground on the accelerometer should not be considered as the same thing.

However, if the accelerometer is rotated by 90°, so that its axis points upwards, it will read +1 g upwards even though still 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. During free fall in an aurplane the accelerometer does not measure the force of gravity of the earth. The reading is the acceleration the instrument would have if it were exclusively subject to that force (accelerometers measure only the mechanical components of accelerations, and thus directly read "g-force" acceleration only).

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 notable 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 will double to 19.6 N/kg—the extra force being caused by the extra lift, and again transmitted though the seat.

See also

Further reading

Faller, James E.; 0.3 (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. 

References

  1. ↑ http://newton.dep.anl.gov/askasci/phy99/phy99491.htm
  2. ↑ [1]
  3. ↑ BIPM: Declaration on the unit of mass and on the definition of weight; conventional value of gn
  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

    Symbol g: MEMSIC: ACCELEROMETER PRIMER

  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. ↑ Beyond the Black Box: the Forensics of Airplane Crashes; George Bibel, John Hopkins University Press, 2008 (ISBN 0-8018-8631-7), p350
  9. ↑ Burton RR (January 1988). "G-induced loss of consciousness: definition, history, current status". Aviation, Space, and Environmental Medicine 59 (1): 2–5. PMID 3281645. 
  10. ↑ NASA Physiological Acceleration Systems
  11. ↑ 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
  12. ↑ http://www.ejectionsite.com/stapp.htm
  13. ↑ 13.0 13.1 “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
  14. ↑ 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.
  15. ↑ Beyond the Black Box: the Forensics of Airplane Crashes; George Bibel, John Hopkins University Press, 2008 (ISBN 0-8018-8631-7), p340
  16. ↑ NASA: Table 2: Apollo Manned Space Flight Reentry G Levels
  17. ↑ Omega FAQ, Ball Watch Technology
  18. ↑ "L-3 Communication's IEC Awarded Contract with Raytheon for Common Air Launched Navigation System". http://www.iechome.com/news/032003.htm. 
  19. ↑ Assuming a 8.04 gram bullet, a muzzle velocity of 350 metres per second (1,100 ft/s), and a 102 mm barrel.
  20. ↑ Assuming a 8.04 gram bullet, a peak pressure of 240 MPa (35,000 psi) and 440 N of friction.

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