Definitions

# g-force

g-force (also G-force, g-load) is a measurement of an object's acceleration expressed in gs. It is proportional to the reaction force that an object experiences as a result of this acceleration—or, more correctly, as a result of the net effect of this acceleration and the acceleration imparted by natural gravity. G-force is not, however, an absolute measurement of force and the term is considered a misnomer by some; see "Connection with force", below.

The g is a non-SI unit equal to the nominal acceleration of gravity on Earth at sea level (standard gravity), which is defined as 9.80665 m/s2 (32.174 ft/s2). The symbol g is properly written both lowercase and italic to distinguish it from the symbol G, the gravitational constant and g, the symbol for gram, a unit of mass, which is not italicized.

The unit g is sometimes written as "gee", and g-forces are informally referred to as "gees" (as in expressions such as "pulling ten gees")" . .

## 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 inertial forces caused by changes in speed and direction. For example, on a roller coaster high positive g is experienced when the car's path curves upwards, where riders feel as if they weigh more than usual. This is often reversed when the car's path curves downwards, and lower than normal g is felt, 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

While accelerations are often calculated relative to the Earth, g-force measures an object's acceleration in an inertial reference frame. Thus, if one is given an object's acceleration relative to the Earth, one must subtract off the acceleration of the Earth's reference frame relative to free-fall. The latter amount is, for objects at or near the Earth's surface, approximately 1 g.

As acceleration is a vector quantity, this subtraction must be vector subtraction. However, if all the accelerations are in parallel directions, one can substitute scalar subtraction. Thus, in a simplified scenario where accelerations are assumed to act only upwards (positive) or downwards (negative), calculating g-force simply amounts to subtracting the acceleration (relative to the Earth) due to Earth's gravity (1 g in the downwards direction) from the object's acceleration relative to Earth. Since we are taking downward acceleration as negative, this is equivalent to adding 1 g. So, for example:

• An object at rest with respect to the Earth experiences a g-force of 0 g + 1 g, or just 1 g ("normal weight").
• An object in free fall (accelerating downwards at 1 g relative to the Earth) experiences a g-force of −1 g + 1 g = 0 g ("weightless")
• An object accelerating upwards at 1 g relative to the Earth experiences a g-force of 1 g + 1 g = 2 g ("twice normal weight")
• An object accelerating downwards at 2 g relative to the Earth experiences a g-force of −2 g + 1 g = −1 g ("negative g").

More generally, an object's acceleration may act in any direction (not just vertically), so in a fuller treatment the vector calculation must be used.

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 a 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 velocity 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 use

• In the aerospace industry the g is a convenient unit for specifying the maximum load factor which aircraft and spacecraft must be capable of withstanding. Light aircraft of the kind used in pilot training (utility category) must be capable of sustaining load factor of 4.4g (43 m/s², 141.5 ft/s²) with the undercarriage retracted.FAR §23.337 Airliners and other transport aircraft must be capable of 2.5g.FAR §25.337 Military aircraft and pilots (especially fighter pilots) with G-suits can withstand more than 9g.
• In the automotive industry the g is mainly used in relation to cornering forces and impact analysis.
• Roller coasters and other theme park rides often use g in the statistics of extreme rides.
• Very short-term accelerations, measured in milliseconds, are usually referred to as shocks and are often measured in g s. The shock that a device or component is required to withstand may be specified in g. For example, mechanical wrist-watches might withstand 7 g, aerospace rated relays might withstand 50 g, and GPS/IMU units for military artillery shells need to withstand 15,500g to survive the acceleration on firing.

## Human tolerance to 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.

The human body is flexible and deformable, particularly the softer tissues. A hard slap on the face may 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.

In aircraft, 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 loss of consciousness will occur, sometimes known as "g-loc" ("loc" stands for "loss of consciousness"). While tolerance varies, a typical person can handle about 5 g (49m/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 (88 m/s²) sustained (for a period of time) or more (see High-G training).

Resistance to "negative" or upward g's, which drive 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.

Humans can survive up to about 20 to 35 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 179.8 g. It has also been said that the height of a person can be shortened if high g-force is sustained for a continuous amount of time.

### Horizontal axis g-force

The human body is considerably better at surviving g-forces that are perpendicular to the spine. In general when the acceleration is forwards, so that the g-force pushes the body backwards (colloquially known as "eyeballs in) a much higher tolerance is shown than when the acceleration is backwards, and the g-force is pushing the body forwards ("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.

### NASA g-tolerance data

From NASA SP-3006:

Time (min) +Gx ("eyeballs in") -Gx ("eyeballs out") +Gz (blood towards feet) -Gz (blood towards head)
.01 (<1 sec) 35 28 18 8
.03 (2 sec) 28 22 14 7
.1 20 17 11 5
.3 15 12 9 4.5
1 11 9 7 3.3
3 9 8 6 2.5
10 6 5 4.5 2
30 4.5 4 3.5 1.8

## Human g-force experience

• Amusement park rides such as roller coasters typically do not expose the occupants to much more than about 3 g for more than around three seconds at the most. Some notable exceptions are G-Force at Drayton Manor Theme Park in England, Oblivion at Alton Towers in England, Speed at Oakwood Theme Park in Wales, Jetline at Gröna Lund in Stockholm, Titan in Texas, Dragon (Adventureland) at Adventureland (Iowa) in Altoona, Iowa which all have a maximum of 4.5 g for up to 1.3 seconds. The Superman Escape at Warner Bros. Movie World, Gold Coast, Queensland, Australia imparts 4.2 positive g and 1 negative g, traveling from 0–100 km/h (0–60 mph)) in two seconds. SheiKra in Tampa pulls 4 g. The record for the highest g-force 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, England, which reaches 5.5 g at the end of the drop by firing riders downwards pneumatically. Fuji-Q Highland, an amusement park in Fujiyoshida, Yamanashi, Japan, used to operate a shuttle coaster named Moonsault Scramble that subjected riders to 6.2 g in the track's high speed pretzel element. The current record for max g is Tower of Terror at Gold Reef City in Johannesburg, Gauteng South Africa, with a max of 6.3.
• A sky-diver in a stable free-fall experiences 1 g (full weight) after reaching terminal velocity.
• Paraglider pilots can experience 6 g or more in spiral dives.
• 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 ("weightlessness"). They are still strongly attracted by the Earth's gravity—acceleration due to gravity at an orbital height of 600 km (372 mi) is about 83% of that at sea level. However, as they are in free fall they do not feel any acceleration.
• Passengers on planes on a parabolic trajectory experience 0 g (as in the "Vomit Comet").
• Aerobatic and fighter pilots may experience a brownout/greyout between 6 and 9 g characterized by temporary loss of colour vision, tunnel vision, or an inability to interpret verbal commands. This may proceed to total loss of consciousness, known as g-LOC. They also experience a "red-out" at negative g. These effects are mostly caused by blood pressure differences between the heart and the brain.
• NASCAR Sprint Cup driver Jeff Gordon experienced the third-highest ranked g-force crash recorded by NASCAR at the 2006 Pennsylvania 500 race at Pocono Raceway, measuring an unprecedented 64 g. Gordon reported that at the time, it was the hardest hit he ever took in a car.
• Pilots in the Red Bull Air Race commonly exceed 10 g for seconds during turns, occasionally surpassing 12 g.
• In 2008, astronauts aboard a Soyuz capsule were subjected to 10 g when they returned to Earth on too steep a trajectory.
• 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 Canadian Grand Prix crash.

### Everyday g-forces

• 3.5 g during a cough.
• 2.9 g during a sneeze.

### Highest g-forces survived by humans

#### Voluntary

Colonel John Stapp in 1954 sustained 46.2 g in a rocket sled, while conducting research on the effects of human deceleration.

#### Involuntary

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 rest over a distance of 66 cm (26 inches) after his throttle got stuck wide open and he hit a wall.

Indy Car driver Kenny Bräck crashed on lap 188 of the 2003 race at Texas Motor Speedway. Bräck and Tomas Scheckter touched wheels, sending Bräck into the air at 200+ mph, hitting a steel support beam for the catch fencing. According to Bräck's site his car recorded 214 g.