# g force

Example: tripling the g- force in an airplane by flying in an upward curved path

g -forces are called loads that act on the human body, a commodity or a vehicle due to strong changes in size and / or direction of speed. The term load factor is alsousedfor loads on technical devices such as airplanes or when specifying load limits . The g -force is a “ force per mass ”, it therefore has the dimension of an acceleration and isspecifiedas a multiple of the gravitational acceleration g . High g ; forces occur, for example when driving with a roller coaster , with missile launches or collisions on objects.

## Physical basics

A racing driver feels a force that it at startup - pressed back into his seat - contrary to the direction of acceleration. This force arises from the fact that the racing car is accelerated forward. The driver's body would lag behind this acceleration because of its inertia if it were not dragged along by the seat. What the driver feels is not an actual external force that pushes him back into the seat, but his own inertia, which is noticeable here in the form of an inertial force . The driver is accelerated forward from the seat.

According to the basic equation of mechanics , the driver's body (mass ) experiences acceleration when a force acts on it . The physical term acceleration can also mean deceleration or change of direction depending on the direction of the force . The driver is at rest relative to his vehicle. In physics, one speaks of an accelerated reference system . For him there is a balance of forces between the accelerating force and the inertial force . The force of inertia is the opposite of the external force. Acceleration is therefore suitable for quantifying the inertial force related to the mass. The acceleration is then often given as a multiple of the acceleration due to gravity , because this is easy to compare with everyday experience: " " means that the acceleration experienced is the same as the acceleration due to gravity and that consequently the inertial force is the same as the weight force (on the Earth) is. ${\ displaystyle m}$${\ displaystyle a = F / m}$${\ displaystyle F}$${\ displaystyle F}$${\ displaystyle F ^ {*}}$${\ displaystyle a}$${\ displaystyle g \ approx 9 {,} 81 \; \ mathrm {m / s ^ {2}}}$${\ displaystyle 1g}$

### Special cases

#### Smooth straight acceleration

If a body is evenly accelerated from rest to speed on the route , then its acceleration is: ${\ displaystyle s}$${\ displaystyle v}$

${\ displaystyle a = {\ frac {v ^ {2}} {2s}}}$

This follows by converting the distance-time and speed-time laws of the uniformly accelerated movement :

${\ displaystyle s = {\ frac {1} {2}} at ^ {2}}$ or. ${\ displaystyle v = at}$

The same formula results for the amount of acceleration in the case of a body that brakes from speed to zero on the route (see also braking deceleration ). ${\ displaystyle s}$${\ displaystyle v}$

Examples
A car drives against a solid wall at 30 km / h, the crumple zone is compressed by 50 cm. The g force is 7 g . At 50 km / h and the same deformation path, the acceleration is almost 20 g .
A body falls to the ground from a height of 1 m. The more rigid the body and the ground, the higher the g force. If the floor does not give way and the body deforms by 0.1 mm and then remains in place, it was braked with an average of 10,000 g .

#### Cornering

When a body traverses a curve with the speed that has the radius , then it experiences the acceleration ${\ displaystyle v}$${\ displaystyle r}$

${\ displaystyle a = {\ frac {v ^ {2}} {r}}.}$
example
A racing car by running at a speed of 200 km / h, a curve having a radius of 160 m, then the centripetal acceleration is about what approximately corresponds.${\ displaystyle 19 {,} 3 \; \ mathrm {m / s ^ {2}},}$${\ displaystyle 2g}$

## Examples of g values ​​in nature, technology and everyday life

Machine or event g factor
Typical maximum value for a child's swing 1,0002.5
Maximum value for the Silver Star roller coaster 1,0004th
Maximum value for an Apollo capsule during re-entry into the earth's atmosphere after a flight to the moon 1,0007.19
Average maximum values ​​for aerobatic maneuvers (load duration between 1.5 and 3 seconds) 1,0008th
Maximum value for g- force that can be survived by people without serious injuries with a favorable direction of action of the acceleration and a short acceleration time (fractions of a second) 1.0100
According to the Guinness Book of Records, highest measured g- force survived by a human ( David Purley , 1977) 1.0180
IndyCar by Kenny Brack in a crash at the Texas Motor Speedway in 2003 (survived the driver) 1.0214
This is the magnitude of the impact of a ballpoint pen that falls from a height of 1 m onto hard ground and remains lying 01,000

## Effects of g forces on the human body

Coordinate system for determining the direction of the g force

### Influencing factors

The effect of g -forces on the human body strongly depends on the direction of the effect. Usually a coordinate system like the one in the picture on the right is used. An organism experiences positive g -forces in the z-direction, for example, when it is pressed into the seat during an inner loop on a roller coaster; negative if it is lifted out of the seat during an outside loop.

In addition to the strength and direction of the forces, how long they work is also of great importance. The human body can withstand relatively high loads for a short time (whereby “short” periods of time mean fractions of a second). If the force is sustained for a long time, there is a risk of circulatory disorders from a comparatively low strength .

### Directional dependence of the symptoms

With positive g -forces in the z-direction (exerted by the seat and floor, accelerating the seated person upwards) there is a risk that the blood will sink into the legs. This can lead to impaired vision or even loss of consciousness as a result of restricted cerebral blood flow (impaired consciousness ). This phenomenon is also known as g- LOC (“ Loss Of Consciousness ”). The so-called greyout and later blackout precede the unconsciousness , which is caused by the insufficient blood supply to the retina of the eye. In order to be able to better endure the stress that occurs in combat aircraft, their crews are fitted with anti-g suits , which are intended to limit the effects of the g forces by compressing the legs at high accelerations. As soon as the acceleration forces are no longer effective, blood flow to the brain and eyes is normal again and unconsciousness ends. The table below shows the reactions of the untrained human body to various positive g -forces in the z-direction (lasting several minutes) .

burden Symptoms
1-2 g unrestrictedly bearable
2-3 g beginning narrowing of the field of vision
3-4 g tubular field of view, greyout
4-5 g blackout
5-6 g unconsciousness

Negative g -forces in the z-direction (the harness pulls the person down) cause blood to flow towards the head. They are much more difficult to bear by humans. Just two to three g can lead to a redout .

In the x-direction (acceleration of the seated person forward due to the pressure of the armchair), g -forces are better tolerated by people, but lead to breathing problems from a strength of 20g . In the y-direction - across the body - on the other hand, if the head is not supported laterally, the main problem is often the overload of the neck muscles .

### Historical development

The effects of high g values ​​were first examined in detail in 1946–1948 by the American physician John Paul Stapp in the service of the US Army. As part of the project, he and other volunteers were accelerated to high speeds on rail-guided sleds using rocket drives and braked with special braking devices. The results of this research contributed greatly to the development of effective restraint and rescue systems.

## g -forces in aviation

Calculation of the load factor during a turn depending on the bank angle θ
g-factor (s) in turns as a function of bank angle${\ displaystyle \ beta}$

For g forces that act on aircraft in flight, a distinction is made between maneuver loads and gust loads. Gust loads are g -forces that arise from gusts, i.e. air movements that cause a brief change in the flow. Maneuver loads arise from flight maneuvers . The term “load multiple” is used to define the load limits of aircraft. The load multiple is defined as a dimensionless number by the ratio of buoyancy force to weight force : ${\ displaystyle n}$ ${\ displaystyle F _ {\ mathrm {A}}}$${\ displaystyle G}$

${\ displaystyle n = {\ frac {F _ {\ mathrm {A}}} {G}}}$

If one assumes that no additional forces act, for example by changing the engine power or speed change of the ambient air, then the load factor corresponds to n of g -Kraft acting on the people on board the aircraft. The load multiple is the factor by which the apparent weight force on objects in the aircraft increases due to additional inertial forces. In order to obtain the corresponding g force, the load multiple n must therefore be multiplied by the gravitational acceleration g . For a normal cruise, the load factor is equal to a g force of 1 g . In turning flight , the load multiple , wherein the transverse inclination is. ${\ displaystyle n = 1}$${\ displaystyle n = 1 / \ cos (\ beta)}$${\ displaystyle \ beta}$

The specification of maximum load multiples is used to determine the structural strength of an aircraft and thus permissible flight maneuvers. Example: A Beechcraft Bonanza A36 may be loaded with a g-factor of a maximum of 4.4 with its landing flaps retracted and maximum take-off weight . This load factor is achieved with a lateral inclination of 77 °.

## Shock resistance

The resistance of a commodity to short-term g -forces caused by shocks and vibrations (shocks) is known as shock resistance. Information on shock resistance can often be found in data sheets for hard drives , for example . The g -forces are usually only withstood for a very short time (order of magnitude 1  ms ), the specified limit values ​​often only apply to a certain form of load.

Commons : G-Kraft  - collection of images, videos and audio files

## Individual evidence

1. Diagrams showing the dependence of the load multiples and safe load multiples on the respective flight conditions
2. The centrifugal acceleration, which acts in addition to the gravitational acceleration, can be calculated for an initial deflection angle by .${\ displaystyle \ phi}$${\ displaystyle 2g \, (1- \ cos \ phi)}$
3. nanotribo course on acceleration (PDF; 260 kB) Archived from the original on July 21, 2016. Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Retrieved February 5, 2013.
4. amusement park information . Retrieved March 13, 2013.
5. Jeffrey R. Davis, Robert Johnson, Jan Stepanek: Fundamentals of Aerospace Medicine . Lippincott Williams & Wilkins, 2008, ISBN 0-7817-7466-7 , pp. 656 . googlebooks
6. Dennis F. Shanahan, MD, MPH: " 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 "
7. Craig Glenday: Guinness World Records 2008 . Random House Digital, Inc., 2008, ISBN 0-553-58995-4 , pp. 133 ( limited preview in Google Book search).
8. ^
9. Feel the G's: The Science of Gravity and G-Forces - by Suzanne Slade (page 37)
10. Average deceleration when the floor or pen gives 1mm on impact. The value can be calculated from the acceleration due to gravity · altitude / deceleration distance.
11. PDF ( memento from August 19, 2014 in the Internet Archive ) at csel.eng.ohio-state.edu
12. Eckhart Schröter: DHV paragliders and kites fly. Retrieved February 8, 2013 .
13. Joachim Scheiderer: Applied flight performance . Springer, 2008, ISBN 3-540-72722-1 , pp. 51 ( limited preview in Google Book search).
14. Niels Klußmann, Arnim Malik: Lexicon of aviation . Springer DE, 2012, ISBN 3-642-22500-4 , p. 158 ( limited preview in Google Book search).
15. Airplane Flight Manual of the Beechcraft Bonanza A36, pages 2–11 (accessed January 30, 2019)
16. E.g. in this data sheet ( Memento of the original from July 18, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 196 kB) only with half a sine wave. In the case of permanent exposure, only a fraction of it is withstood: 0.67 G "operating" instead of 400 G and 3.01 G "non-operating" instead of 2000 G.