Theg-force orgravitational force equivalent is amass-specific force (force per unit mass), expressed inunits ofstandard gravity (symbolg org0, not to be confused with "g", the symbol forgrams).It is used for sustainedaccelerations that cause a perception ofweight. For example, an object at rest on Earth's surface is subject to 1 g, equaling the conventional value ofgravitational acceleration on Earth, about9.8 m/s2.[1]More transient acceleration, accompanied with significantjerk, is calledshock.
When the g-force is produced by the surface of one object being pushed by the surface of another object, the reaction force to this push produces an equal and opposite force for every unit of each object's mass. The types of forces involved are transmitted through objects by interiormechanical stresses.Gravitational acceleration is one cause of an object'sacceleration in relation tofree fall.[2][3]
The g-force experienced by an object is due to the vector sum of all gravitational and non-gravitational forces acting on an object's freedom to move. In practice, as noted, these are surface-contact forces between objects. Such forces causestresses andstrains on objects, since they must be transmitted from an object surface. Because of these strains, large g-forces may be destructive.
For example, a force of 1 g on an object sitting on the Earth's surface is caused by the mechanical force exerted in theupward direction by the ground, keeping the object from going into free fall. The upward contact force from the ground ensures that an object at rest on the Earth's surface is accelerating relative to the free-fall condition. (Free fall is the path that the object would follow when falling freely toward the Earth's center). Stress inside the object is ensured from the fact that the ground contact forces are transmitted only from the point of contact with the ground.
Objects allowed to free-fall in aninertial trajectory, under the influence of gravitation only, feel no g-force – a condition known asweightlessness. Being in free fall in an inertial trajectory is colloquially called "zero-g", which is short for "zero g-force". Zero g-force conditions would occur inside an elevator falling freely toward the Earth's center (in vacuum), or(to good approximation) inside a spacecraft in Earth orbit. These are examples of coordinate acceleration (a change in velocity) without a sensation of weight.
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 of this is a rocket in free space: when the engines produce simple changes in velocity, those changes cause g-forces on the rocket and the passengers.
Theunit of measure ofacceleration in theInternational System of Units (SI) is m/s2.[4] However, to distinguish acceleration relative to free fall from simple acceleration (rate of change of velocity), the unitg is often used. Oneg is the force per unit mass due to gravity at the Earth's surface and is thestandard gravity (symbol:gn), defined as9.80665 metres per second squared,[5] or equivalently9.80665 newtons of force per kilogram of mass. Theunit definition does not vary with location—the g-force when standing on theMoon is almost exactly1⁄6 that on Earth.The unitg 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 thegravitational constant.[6] This notation is commonly used in aviation, especially in aerobatic or combat military aviation, to describe the increased forces that must be overcome by pilots in order to remain conscious and notg-LOC (g-induced loss of consciousness).[7]
Measurement of g-force is typically achieved using anaccelerometer (see discussion below in section#Measurement using an accelerometer). In certain cases, g-forces may be measured using suitably calibrated scales.
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The term g-"force" is technically incorrect as it is a measure ofacceleration, not force. While acceleration is avector quantity, g-force accelerations ("g-forces" for short) are often expressed as ascalar, based on the vector magnitude, with positive g-forces pointing downward (indicating upward acceleration), and negative g-forces pointing upward. Thus, a g-force is a vector of acceleration. It is an acceleration that must be produced by a mechanical force, and cannot be produced by simple gravitation. Objects acted upononly by gravitation experience (or "feel") no g-force, and are weightless.g-forces, when multiplied by a mass upon which they act, are associated with a certain type of mechanicalforce in the correct sense of the term "force", and this force producescompressive stress andtensile stress. Such forces result in the operational sensation of weight, but the equation carries a sign change due to the definition of positive weight in the direction downward, so the direction of weight-force is opposite to the direction of g-force acceleration:
The reason for the minus sign is that the actualforce (i.e., measured weight) on an object produced by a g-force is in the opposite direction to the sign of the g-force, since in physics, weight is not the force that produces the acceleration, but rather the equal-and-opposite reaction force to it. If the direction upward is taken as positive (the normal cartesian convention) thenpositive g-force (an acceleration vector that points upward) produces a force/weight on any mass, that actsdownward (an example is positive-g acceleration of a rocket launch, producing downward weight). In the same way, anegative-g force is an acceleration vectordownward (the negative direction on the y axis), and this acceleration downward produces a weight-force in a directionupward (thus pulling a pilot upward out of the seat, and forcing blood toward the head of a normally oriented pilot).
If a g-force (acceleration) is vertically upward and is applied by the ground (which is accelerating through space-time) or applied by 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 mechanical resistance to gravity, or by a coordinate-acceleration (change in velocity) caused by a mechanical force, or by a combination of these. Hence, for people all mechanical forces feels exactly the same whether they cause coordinate acceleration or not. For objects likewise, the question of whether they can withstand the mechanical g-force without damage is the same for any type of g-force. 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 highersurface gravity. Gravitation acting alone does not produce any g-force; g-force is only produced from mechanical pushes and pulls. For a free body (one that is free to move in space) such g-forces only arise as the "inertial" path that is the natural effect of gravitation, or the natural effect of the inertia of mass, is modified. Such modification may only arise from influences other than gravitation.
Examples of important situations involving g-forces include:
A classic example of negative g-force is in a fully invertedroller 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 byNewton's laws of motion as follows:
Thesecond law of motion, the law of acceleration, states thatF =ma, meaning that a forceF acting on a body is equal to themassm of the body times its accelerationa.
Thethird 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.
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 725newtons (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. This mechanical force provides the 1.0 g upwardproper 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 aproper 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 1450 N.
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"1g =9.80665 m/s2" means thatfor every second that elapses, velocity changes9.80665 metres per second (35.30394 km/h). This rate of change in velocity can also be denoted as9.80665 (metres per second) per second, or9.80665 m/s2. For example: An acceleration of 1 g equates to a rate of change in velocity of approximately 35 km/h (22 mph) for each second that elapses. Therefore, if an automobile is capable of braking at 1 g and is traveling at 35 km/h, 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 tov with constant acceleration within a distance ofs this acceleration isv2/(2s).
Preparing an object for g-tolerance (not getting damaged when subjected to a high g-force) is called g-hardening.[citation needed] This may apply to, e.g., instruments in aprojectile shot by a gun.
Human tolerances depend on the magnitude of the gravitational force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body.[9][10]: 350
The human body is flexible and deformable, particularly the softer tissues. A hard slap on the face may briefly impose hundreds ofg locally but not produce any real damage; a constant 16 g for a minute, however, may be deadly. Whenvibration is experienced, relatively low peak g-force levels can be severely damaging if they are at theresonant frequency of organs or connective tissues.[citation needed]
To some degree, g-tolerance can be trainable, and there is also considerable variation in innate ability between individuals. In addition, some illnesses, particularlycardiovascular problems, reduce g-tolerance.
Aircraft pilots (in particular) sustain 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-force, 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-force varies. A typical person can handle about 5 g0 (49 m/s2) (meaning some people might pass out when riding a higher-g roller coaster, which in some cases exceeds this point) beforelosing consciousness, but through the combination of specialg-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 g0 (88 m/s2) (seeHigh-G training).
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 acentrifuge) the following symptoms may be experienced:[citation needed]
Resistance to "negative" or "downward" g, which drives blood to the head, is much lower. This limit is typically in the −2 to −3 g0 (−20 to −29 m/s2) range. This condition is sometimes referred to asred out where vision is literally reddened[12] due to the blood-laden lower eyelid being pulled into the field of vision.[13] Negative g-force is generally unpleasant and can cause damage. Blood vessels in the eyes or brain may swell or burst under the increased blood pressure, resulting in degraded sight or even blindness.
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"),[14] 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.[citation needed]
Early experiments showed that untrained humans were able to tolerate a range of accelerations depending on the time of exposure. This ranged from as much as20 g0 for less than 10 seconds, to10 g0 for 1 minute, and6 g0 for 10 minutes for both eyeballs in and out.[15] These forces were endured with cognitive facilities intact, as subjects were able to perform simple physical and communication tasks. The tests were determined not to cause long- or short-term harm although tolerance was quite subjective, with only the most motivated non-pilots capable of completing tests.[16] The record for peak experimental horizontal g-force tolerance is held by acceleration pioneerJohn Stapp, in a series of rocket sled deceleration experiments culminating in a late 1954 test in which he was clocked in a little over a second from a land speed of Mach 0.9. He survived a peak "eyeballs-out" acceleration of 46.2 times the acceleration of gravity, and more than25 g0 for 1.1 seconds, proving that the human body is capable of this. Stapp lived another 45 years to age 89[17] without any ill effects.[18]
The highest recorded g-force experienced by a human who survived was during the2003 IndyCar Series finale at Texas Motor Speedway on 12 October 2003, in the 2003 Chevy 500 when the car driven byKenny Bräck made wheel-to-wheel contact withTomas Scheckter's car. This immediately resulted in Bräck's car impacting the catch fence that would record a peak of214 g0.[19][20]
Impact andmechanical shock are usually used to describe a high-kinetic-energy, short-term excitation. A shock pulse is often measured by its peak acceleration inɡ0·s and the pulse duration.Vibration is a periodicoscillation which can also be measured inɡ0·s as well as frequency. The dynamics of these phenomena are what distinguish them from the g-forces caused by a relatively longer-term accelerations.[citation needed]
After a free fall from a height followed by deceleration over a distance during an impact, the shock on an object is· ɡ0. For example, a stiff and compact object dropped from 1 m that impacts over a distance of 1 mm is subjected to a 1000ɡ0 deceleration.[citation needed]
Jerk is the rate of change of acceleration. In SI units, jerk is expressed as m/s3; it can also be expressed instandard gravity per second (ɡ0/s; 1ɡ0/s ≈ 9.81 m/s3).[citation needed]
Recent research carried out onextremophiles in Japan involved a variety of bacteria (includingE. coli as a non-extremophile control) being subject to conditions of extreme gravity. The bacteria were cultivated while being rotated in anultracentrifuge at high speeds corresponding to 403,627 g.Paracoccus denitrificans was one of the bacteria that 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 ofsupernovas. Analysis showed that the small size of prokaryotic cells is essential for successful growth underhypergravity. Notably, two multicellular species, thenematodesPanagrolaimus superbus[21] andCaenorhabditis elegans were shown to be able to tolerate 400,000 ×g for 1 hour.[22]The research has implications on the feasibility ofpanspermia.[23][24]
| Example | g-force[a] |
|---|---|
| The gyro rotors inGravity Probe B and the free-floating proof masses in the TRIAD I navigation satellite[25] | 0 g |
| A ride in theVomit Comet (parabolic flight) | ≈ 0 g |
| Standing onMimas, the smallest and least massive known bodyrounded by its own gravity | 0.006 g |
| Standing onCeres, the smallest and least massive known bodycurrently inhydrostatic equilibrium | 0.029 g |
| Standing onPluto at average ground level | 0.063 g |
| Standing onEris at average ground level | 0.084 g |
| Standing onTitan at average ground level | 0.138 g |
| Standing onGanymede at average surface level | 0.146 g |
| Standing on theMoon at surface level | 0.1657 g |
| 2000Toyota Sienna from 0 to 100 km/h in 9.2 s[26] | 0.3075–0.314 g |
| Standing onMercury | 0.377 g |
| Standing onMars at its equator at mean ground level | 0.378 g |
| Standing onVenus at average ground level | 0.905 g |
| Standing on Earth at sea level–standard | 1 g |
| Saturn V Moon rocket just after launch and the gravity ofNeptune where atmospheric pressure is about Earth's | 1.14 g |
| Bugatti Veyron from 0 to 100 km/h in 2.4 s | 1.55 g[b] |
| Gravitron amusement ride | 2.5–3 g |
| Gravity ofJupiter at its mid-latitudes and where atmospheric pressure is about Earth's | 2.528 g |
| Uninhibited sneeze after sniffing ground pepper[27] | 2.9g |
| Space Shuttle, maximum during launch and reentry | 3 g |
| High-groller coasters[10]: 340 | 3.5–12 g |
| Hearty greeting slap on upper back[27] | 4.1g |
| Top Fueldrag racing world record of 4.4 s over 1/4 mile | 4.2 g |
| First world war aircraft (ex:Sopwith Camel,Fokker Dr.1,SPAD S.XIII,Nieuport 17,Albatros D.III) in dogfight maneuvering. | 4.5–7 g |
| Luge, maximum expected at the Whistler Sliding Centre | 5.2 g |
| Shock Wave, current highest g-force rollercoaster in operation | 5.9 g |
| Formula One car, maximum under heavy braking[28] | 6.3 g |
| Tower Of Terror, highest g-force steel rollercoaster | 6.3 g |
| Formula One car, peak lateral in turns[29] | 6–6.5 g |
| Standard, full aerobatics certifiedglider | +7/−5 g |
| Apollo 16 on reentry[30] | 7.19 g |
| Maximum permitted g-force inSukhoi Su-27 plane | 9 g |
| Maximum permitted g-force inMikoyan MiG-35 plane and maximum permitted g-force turn inRed Bull Air Race planes | 10 g |
| Flip Flap Railway, highest g-force wooden rollercoaster | 12 g |
| Jet Fighter pilot duringejection seat activation | 15–25 g |
| Gravitational acceleration at the surface of theSun | 28 g |
| Maximum g-force inTor missile system[31] | 30 g |
| Maximum for human on a rocket sled | 46.2 g |
| Formula One2021 British Grand PrixMax Verstappen Crash withLewis Hamilton | 51 g |
| Formula One2020 Bahrain Grand PrixRomain Grosjean Crash[32] | 67 g |
| Sprint missile | 100 g |
| Brief human exposure survived in crash[33] | > 100 g |
| IndyCar2003 TexasKenny Bräck Crash | 214 g |
| Formula One2014 Japanese Grand PrixJules Bianchi Crash | 254g |
| Formula One1994 Monaco Grand PrixKarl Wendlinger[34] Crash | ≈360 g |
| Coronal mass ejection (Sun)[35] | 480g |
| Formula One1994 San Marino Grand PrixRoland Ratzenberger Qualifying Crash | 500g |
| Space gun with a barrel length of 1 km and amuzzle velocity of 6 km/s, as proposed byQuicklaunch (assuming constant acceleration) | 1,800g |
| Shock capability of mechanical wrist watches[36] | > 5,000g |
| V8Formula One engine, maximum piston acceleration[37] | 8,600g |
| Mantis Shrimp, acceleration of claw during predatory strike[38] | 10,400g |
| Rating of electronics built into military artillery shells[39] | 15,500g |
| Analytical ultracentrifuge spinning at 60,000 rpm, at the bottom of the analysis cell (7.2 cm)[40] | 300,000 g |
| Calculated acceleration of the mandibles of the ant speciesMystrium camillae[41] | 607,805 g |
| Acceleration of anematocyst: the fastest recorded acceleration from any biological entity.[42] | 5,410,000 g |
| Mean acceleration of a proton in theLarge Hadron Collider[43] | 190,000,000 g |
| Gravitational acceleration at the surface of a typicalneutron star[44] | 2.0×1011 g |
| Acceleration from awakefield plasma accelerator[45] | 8.9×1020 g |
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Anaccelerometer, in its simplest form, is adamped 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 oftencalibrated 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: thegravitational force and theground 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 aballistic trajectory (also known as aninertial 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-force for about 25 seconds at a time.
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