What is G-Force?

Can you explain me what is the G-Force? I always thought it was the force caused by the gravitational acceleration.. But I just saw on myth busters that they calculated the g-force on a belt during a car crash by using accelerometers... and I just got confused and curious as well.

• When someone feel a G-force of $x$ it means it is subjected to an acceleration which is $x$ times the acceleration of gravity near the surface of the Earth, that is, $x\times 9.8\, m/s^2$. – Diracology Jan 24 '17 at 15:55
• It is, but it can apply in any direction, even upside down, in aircraft say. It's just a different unit of acceleration, for comparision purposes. – user140606 Jan 24 '17 at 15:56
• As mentioned, it's just multiples of the gravitational force at Earth's surface. Lie on your back and feel the pressure due to your weight. Now, accelerate in a car at 2 g. You will feel as if you weigh twice as much. – bpedit Jan 24 '17 at 16:02
• I've removed a comment discussion which was not constructive. – rob Jan 29 '17 at 20:09

A G-force is nothing more than a regular force but instead of expressing it in "normal" units (e.g., kg$~$m/s$^2$ or pounds), the magnitude of the force is expressed as a multiple of the force due to gravity on the specific object. So, if something is accelerating at 9.8 m/s$^2$, one would say it is accelerating at 1 G.

One advantage of expressing forces as G-forces is that it is more technically an expression of acceleration than of force, allowing for more direct comparisons between objects of different masses. Let me explain. In the example you use, forces from seatbelts on bodies, if a young child and I (an adult) were riding in a car and got in a crash then our seatbelts would be exerting very different forces on us (since I have a larger mass, the seatbelt will be exerting a larger force on me to keep me from flying out of the car) but would likely be exerting the same acceleration on us, assuming the seatbelts keep both of us in our seats. Thus, expressing the forces in terms of G-forces, in this situation both of our seatbelts would be exerting the same G-force, even if exerting different forces.

Another useful example is a roller coast. Going through a loop, the roller coaster exerts different forces on each rider depending on the rider's mass, but exerts the same acceleration (and thus G-force) on everybody. G-forces thus allow for a mass-independent comparison between different situations and their ability to generate forces. A 10-G turn in a jet aircraft will exert more force than a 5-G loop on a roller coaster.

G-force is acceleration minus the local gravitational field or $a-g$. Examples:

Standing on the ground

$a$=0, $g$=10 m/s $^2$ downwards, g-force = 10 m/s$^2$ upwards = 1 g.

Accelerating upwards in a rocket

$a$=30 m/s$^2$ upwards, $g$=10 m/s $^2$ downwards, g-force = 40 m/s$^2$ upwards = 4 g.

Free-fall on the Earth

$a$=10 m/s$^2$ downwards, $g$=10 m/s $^2$ downwards, g-force = 0.

Free-fall on the Moon

$a$=1.6 m/s$^2$ downwards, $g_{moon}$=1.6 m/s $^2$ downwards, g-force = 0.