Subscribe to WIRED Magazine

What is a G Force?

Perhaps John Burk covered this well enough, but a good question is almost always worth answering again.

Why Worry About G Force?

You see? I added some extra questions.

Suppose you have an app on your phone that measures acceleration. Here is a screen shot from the iPhone AccelMeter App.

I Photo 1

It’s a pretty cool app. It shows a 3-D representation of the g-force vector in real time. Here you can see that I am just holding the phone to produce a vector with a magnitude of 1.00 g. Why doesn’t the phone give the acceleration vector instead? Because the phone can’t tell the difference between the gravitational field and an acceleration.

Recall how an accelerometer works. I actually wrote about this a long time ago – but here is a more recent (and popular) video describing modern accelerometers. At the basic level, an accelerometer is just a spring and the measurement of a g-force is based on the amount the spring is stretched. Consider two springs that can only move in one dimension. The first spring is vertical and at rest. The other spring is horizontal and accelerating.

Drawings Summer 12.key 1

For the vertical hanging spring on the left, it is in equilibrium. This means that for the forces in the vertical direction, the following would be true:

La te xi t 1

For most springs, the force exerted by the spring is proportional to the amount the spring is stretched. This is known as Hooke’s Law and can be written as:

La te xi t 1 2

Here k is the spring constant – essentially a measure of the ‘stiffness’ of the spring and s is the amount the spring is either compressed or stretched from it’s natural length. Yes, I know that many times you will see a negative sign in this equation to indicate that the spring force is in the opposite direction that the spring is stretched. I didn’t include that since I am just show the magnitude. But getting back to the vertical spring, I can find the amount the spring is stretched if I know the spring constant and the mass. Oh, g is the gravitational field. It has a magnitude of 9.8 Newtons per kilogram.

La te xi t 1 3

Ok. Now to look at the horizontal spring (I have only included the horizontal forces in case you couldn’t tell). For this object, there is only the spring force on it. The force equation in the x-direction would be:

La te xi t 1 4

And here is the cool part. What if the mass is accelerating with a magnitude of 9.8 m/s2? Well, since the acceleration has the same value as the gravitational field (and same units since 1 N/kg = 1 m/s2), the spring would have the same stretch. In an accelerometer, the stretch (or compression) of the spring is really the only thing that is measured. So, the accelerometer can’t tell the difference between accelerations and gravitational forces.

Neither can you. In short, this is why you feel “weightless” in orbit. If you want the longer version, here is a more detailed post about apparent weight and weightlessness.

What is the G Force?

First, it isn’t really a measure of force. If two objects are sitting on the table, they will both be at 1 g even if they are different masses. The gravitational forces will be different and the force of the table pushing up will be different.

I am not sure everyone completely agrees on the definition of g-force, but I like this definition.

La te xi t 1 6

If an object is at rest, then the net force on that object would be zero (zero vector). Subtracting the gravitational force would leave a g-force of 9.8 m/s2 or 1 g. If an object is accelerating UP at 9.8 m/s2, the net force would also be a vector pointing up. Subtracting a vectoring pointing down (gravitational force) would result in a larger g-force of 2 g’s. If the object was accelerating down at 9.8 m/s2, the net force would be the same as the gravitational force. Subtracting them would give the zero vector and a g-force of 0 g’s.

Human Tolerance of G-Force

One of the best ways to look at human body damage is to consider the acceleration. Acceleration is the killer, well usually. Consider this model of a human body colliding with the ground.

Drawings Summer 12.key 2

In this model, there are two balls connected by a spring. If the body falls and collides with the ground, it must accelerate in the upward direction. Let me just look at the top ball. Since it has to accelerate up, it must have a net force pointing upwards. This means that the force the inner spring exerts on the top ball must be greater than the gravitational force. The greater the acceleration, the greater this spring force must be and the more compressed the inner spring will be. If this spring is compressed too much, it could break. Breaking springs would be bad. This is where the damage comes into play.

So, large accelerations can cause damage. Always? No. What if there was some long range force to accelerate this two-ball model of a body? If this same force was on both balls in the model, you could get a super high acceleration without having to compress the inner spring. No inner spring compression means no body damage. But how would this work? I don’t know. The only force that pulls on all parts of a body would be the gravitational force (since all the parts have mass). But wouldn’t that be cool? If there was some force field that could stop you (or shoot you off like a bullet) without causing damage? Yes. That would be cool.

Then what kind of accelerations can a human body withstand? In a previous episode of Mythbusters – the jumping from a building with bubble wrap one, they state that stunt men aim for a maximum acceleration of 10 g’s. A good goal to aim for. Wikipedia’s g-force tolerance page lists 50 g’s as “likely death”. However, it also says that some people may have survived accelerations up to 100 g’s. It seems that the duration of the acceleration is quite important. An acceleration of just 16 g’s for an extended time period can be deadly also.