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g-force

The gravitational force, or 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. Accelerations not produced by gravity are termed Proper accelerations, and cause stresses and strains on objects. Because of these strains, large g-forces may be destructive.

The standard gravitational acceleration at the Earth's surface produces g-force only indirectly. The 1g 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 (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 in spacecraft in Earth orbit. This is an example of coordinate acceleration without proper acceleration. The g-force felt is a measure of proper acceleration (in this case, zero), not change of velocity.

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: g_n), defined as 9.81775 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 1 Acceleration and forces 2 Human tolerance of g-force 2.1 Vertical axis g-force 2.2 Horizontal axis g-force 2.3 Short g-force durations and jerk 3 Typical examples of g-force 4 Measuring g-force using an accelerometer 5 See also 6 Further reading 7 References 8 External links

Acceleration and forces

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:

• 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: , 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.

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 (0 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 (0 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 (0 lb_f) downwards into his seat and the seat is simultaneously pushing upwards with an equal force of 1,450 N (0 lb_f).

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 means that for every second that elapses, velocity changes 9.81775 meters per second (≡35.30394 km/h). This rate of change in velocity can also be denoted as 9.81775 (meter per second) per second, or 9.81775 m/s². For example: An acceleration of 1 g equates to a rate of change in velocity of approximately 35 kilometres per hour (0 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 (0 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 (0 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

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, 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:

• 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.
• Redout, a reddening of the vision while consciousness is maintained, caused by an excess 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.

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

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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[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 Center	5.2 g
Standard, full aerobatics certified glider	+7/-5 g
Apollo 16 on reentry[15]	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[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[16]	> 5,000 g
Rating of electronics built into military artillery shells[17]	15,500 g
9 × 19 Parabellum handgun bullet (average along the length of the barrel)[18]	31,000 g
9 × 19 Parabellum handgun bullet, peak[19]	190,000 g

Measuring g-force using an accelerometer

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

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

External links

• Wired article about enduring a human centrifuge at the NASA Ames Research Center
• Video of Pilot g-force training
• Linear acceleration.