What is G-force?

g-force (also g-load) is a measurement of an object's acceleration expressed in g's. It may also informally refer to the reaction force resulting from an acceleration, with the causing acceleration expressed in g's. The g (IPA pronunciation: [dʒiː]) is a non-SI unit equal to the nominal acceleration due to gravity on Earth at sea level, defined as 9.80665 m/s², or 32.174 ft/s². More precisely, g-force measures the net effect of the acceleration that an object actually experiences and the acceleration that gravity is trying to impart to it, as explained further below. The symbol g is properly written in lowercase and italic, to distinguish it from the symbol G, the gravitational constant, which is always written in uppercase; and from g, the symbol for gram, which is not italicised.

Connection with force

Although actually a measurement of acceleration, the term g-force is, as its name implies, popularly imagined to refer to the force that an accelerating object "feels". These so-called "g-forces" are experienced, for example, by fighter jet pilots or riders on a roller coaster, and are caused by changes in speed and direction. For example, on a roller coaster high positive g-forces are experienced on the car's path up the hills, where riders feel as if they weigh more than usual. This is reversed on the car's descent where lower g-forces occur, causing the riders to feel lighter or even weightless.

The relationship between force and acceleration stems from Newton's second law, F = ma, where F is force, m is mass and a is acceleration. This equation shows that the larger an object's mass, the larger the force it experiences under the same acceleration. Thus, objects with different masses experiencing numerically identical "g-forces" will in fact be subject to forces of quite different magnitude. For this reason, g-force cannot be considered to measure force in absolute terms. However, the interpretation of g-force as a force can be partially rescued by noting that its numerical value is the ratio of the force "felt" by an object under the given acceleration to the force that the same object "feels" when resting stationary on the Earth's surface. For example, a person experiencing a g-force of 3 g feels three times as heavy as normal.

Because of the potential for confusion about whether g-force measures acceleration or force, the term is considered by some to be a misnomer. Scientific usage prefers explicit reference to either acceleration or force, and use of the appropriate units (in the SI system, metres per second squared for acceleration, and newtons for force).

Calculating g-forces

Unlike simple acceleration, g-force is a measure of an object's acceleration relative to the local gravitational acceleration vector, rather than being compared to an inertial reference frame. In other words, it is the (vector) difference between an object's actual acceleration and the acceleration that it would experience if it were falling freely. It is this difference, rather than the actual acceleration of the object, that gives rise to the feeling of force ("apparent weight"), and hence to the feeling of heaviness and lightness in high and low g-force environments. For further details, including examples of conversion between acceleration and apparent weight force, see apparent weight.

In a simplified scenario, where accelerations are assumed to act only downwards (positive) or upwards (negative), calculating this difference simply amounts to subtracting the object's actual acceleration from the gravitational acceleration. For an object on or near the Earth's surface, gravitational acceleration is for practical purposes equal to 1 g. (For more precise measurements, the variation of Earth's gravity with location and altitude must be taken into account.) So, for example:

• A non-accelerating object experiences a g-force of 1 g − 0 g, or just 1 g ("normal weight").
• An object in free fall (accelerating downwards at 1 g) experiences a g-force of 1 g − 1 g = 0 g ("weightless")
• An object accelerating upwards at 1 g experiences a g-force of 1 g − (−1 g) = 2 g ("twice normal weight")
• An object accelerating downwards at 2 g experiences a g-force of 1 g − 2 g = −1 g ("negative g").

More generally, an object's acceleration may act in any direction (not just vertically), so in a fuller treatment it must be considered as a vector quantity. The "difference" in acceleration that g-force measures is found by vector addition of the opposite of the actual acceleration and the local gravitational acceleration vector (about 1  g downward on or near the Earth's surface).

In cases when the magnitude of the acceleration is relatively large compared to 1 g, and/or is more-or-less horizontal, the effect of the Earth's gravity is sometimes ignored in everyday treatments. For example, if a person in an car accident decelerates from 30 m/s to rest in 0.2 seconds, then their deceleration is 150 m/s², so one might say that they experience a g-force of about 150/9.8 g, or about 15.3 g. Strictly speaking, due to the vector addition of the gravitational acceleration, the true g-force has a slightly larger magnitude and is pointing slightly downwards (intuitively this is because the person is already experiencing 1 g just by sitting in the car).

The g-force experienced when cornering can be calculated from the radial acceleration formula, a = v²/r, where a is acceleration, v is speed and r is the corner's radius of curvature. For example, a racing car driver travelling at 50 m/s around a corner with radius of curvature 80 m undergoes an acceleration of 50²/80 m/s², or 31.25 m/s². This equates to a g-force of about 31.25/9.8 g, or about 3.19 g (again, for the purposes of this example, ignoring the additional g-force due to Earth's gravity).

Examples of usage

• The g is used in aerospace fields, where it is a convenient magnitude when specifying the maximum load factor which aircraft and spacecraft must be capable of withstanding. Light airplanes of the kind used in pilot training (utility category) must be capable of sustaining an upper load factor of 4.4 g (43 m/s², 141.5 ft/s²) with the undercarriage retracted^{FAR §23.337}. Airline airplanes and other airplanes in the transport category must be capable of an upper load factor of 2.5 g^{FAR §25.337}. Military aircraft and pilots with pressure suits can experience up to 9 g.
• The g is used in automotive engineering, mainly in relation to cornering forces and collision analysis.
• The g is used to express the amount of acceleration/shock force a device or component part of a device can withstand. For example, mechanical wrist-watches might withstand 7 g, aerospace rated relays might withstand 50 g, and GPS IMUs units for military howitzer shells might withstand 15,500 g.^[1]
• g-forces are an important factor in roller coasters and other theme park rides. They are often displayed in ride statistics.
• g-force is often used to describe a relatively long term acceleration: A short term acceleration is usually called a shock and is also measured in gs.

Human tolerance to g-force

Human tolerances depend on the magnitude of g-force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body.

The human body is flexible and deformable, particularly the softer tissues. A hard slap on the face may impose hundreds of g-s locally but not produce any real damage: a constant 15 g-s 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. Further some illnesses reduce g-tolerance, particularly cardiovascular problems.

Vertical axis g-force

Aircraft in particular exert g-force on 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.

In aircraft in particular, g-forces are often towards the feet, which forces blood away from the head; this causes problems with the eyes and brain in particular. As g-forces increase Brownout/greyout can occur, where the vision loses hue. If g-force is increased further tunnel vision will appear, and then at still higher g, loss of vision, while consciousness is maintained, this is termed "blacking out". Beyond this point losing consciousness will occur, also sometimes known as g-loc (loc stands for loss of consciousness). While tolerance varies, a typical person can handle about 5 g (50m/s²) before g-loc'ing, 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 (90 m/s²) sustained (for a period of time) or more.

Resistance to "negative" or upward gees, which drive blood to the head, is much less. This limit is typically in the -2 to -3 g (-20 m/s² to -30 m/s²) range. The vision goes red and is also referred to as a red out. This is probably due to capillaries in the eyes swelling or bursting under the increased blood pressure.

Humans can survive about 20 to 40 g instantaneously (for a very short period of time). Any exposure to around 100 g or more, even if momentary, is likely to be lethal, although the record is 179 g.^[1]

Horizontal axis g-force

The human body is considerably more able to survive g-forces that are perpendicular to the spine. In general when the g-force pushes the body backwards (colloquially known as 'eyeballs in'^[2]) a much higher tolerance is shown than when g-force is pushing the body forwards ('eyeballs out') since blood vessels in the retina appear more sensitive to that 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.^[3]

Human g-force experience

• Amusement park rides such as roller coasters typically do not expose the occupants to much more than about 3 g. Some notable exceptions are Oblivion in England, Speed at Oakwood Theme Park in Wales, Jetline at Gröna Lund in Stockholm and Titan in Texas, which all have a maximum of 4.5 g, and SheiKra in Tampa which pulls 4 g.^[4] The record for the most g forces on a roller coaster belongs to Mindbender at Galaxyland Amusement Park, Edmonton, Alberta, Canada, at 5.2 g. The highest g on a thrill ride can be experienced on Detonator at Thorpe Park, which reaches 5.5 g at the end of the drop by firing riders downwards pneumatically.
• A sky-diver in a stable free-fall experiences 1 g (full weight) after reaching terminal velocity.
• A scuba diver or swimmer experiences 1 g (full weight), but buoyancy largely cancels the weight of his body. However, density differences do create forces. The lungs are significantly buoyant.
• Astronauts in Earth orbit experience 0 g, or 'weightlessness'. They are still strongly attracted by the Earth's gravity. The value of gravity acceleration at the level of a 600 km (372 mi) high orbit is about 83% of the sea level gravity acceleration. However as they are in free fall they don't feel any acceleration.
• Passengers on planes on a parabolic trajectory experience 0 g (as in the Vomit Comet).
• Aerobatic and fighter pilots may sometimes experience a greyout between 6 and 9 g. This is not a total loss of consciousness but is characterized by temporary loss of colour vision, tunnel vision, or an inability to interpret verbal commands. They also experience a 'redout' at negative g. These effects are mostly caused by blood pressure differences between the heart and the brain.
• Pilots in the Red Bull Air Race commonly exceed 10 g for seconds during turns, occasionally surpassing 12 g.
• Formula One drivers usually experience 5 g while braking, 2 g while accelerating, and 4 to 6 g while cornering. Every Formula One car has an ADR (Accident Data Recovery) device installed, which records speed and g-force. According to the FIA Robert Kubica of BMW Sauber experienced 75 g during his 2007 Montreal GP crash. ^[5]

Everyday g-forces

• 3.5 g during a cough. ^[6][7]
  • 2.9 g during a sneeze. ^[6][7]

  Strongest g-forces survived by humans

  Voluntarily: Colonel John Stapp in 1954 sustained 46.2 g [1] in a rocket sled, while conducting research on the effects of human deceleration. See Martin Voshell (2004), 'High Acceleration and the Human Body'.
  
  Involuntarily: Formula One racing car driver David Purley survived an estimated 179.8 g in 1977 when he decelerated from 173 km/h (108 mph) to 0 in a distance of 66 cm (26 inches) after his throttle got stuck wide open and he hit a wall.^[1]

  See also

  • Cushioning
  • Earth's gravity
  • Load factor
  • Shock (mechanics)

  References

  1. ^ L-3 Communication's IEC Awarded Contract with Raytheon for Common Air Launched Navigation System.
  2. ^ NASA Physiological Acceleration Systems
  3. ^ 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
  4. ^ SheiKra webpage. Retrieved on 2007-01-21.
  5. ^ Kubica's crash data disclosed. Retrieved on 2007-06-20.
  6. ^

Elert, Glenn (1998-2006). Acceleration. The Physics Hypertextbook. Retrieved on 2007-01-21.
7. ^ (2003) "Are Amusement Park Thrill Rides Lethal?". Popular Mechanics (August 2003). Retrieved on 2007-01-21. 
8. ^
9. ^
10. ^ Anton Sukup (1977). David PURLEY Silverstone crash. Retrieved on July 31, 2006.