What is measured with g-forces?

Question

When sitting at rest, a typical "g-meter" shows a value of one, however the meter is not accelerating. In orbit, it shows zero, but is under constant acceleration. The actual force of gravity in both situations is almost identical, so what exactly is being measured?

Answer 1

Technically, an accelerometer does not measure acceleration, it measures the difference in acceleration between the "sensing body" inside the sensor and the sensor's exterior casing. That means that if you have an accelerometer sitting still on a desk, it will measure somewhere around $9.81 \frac{\text{m}}{\text{s}^2}$ or 1G pointing downwards because while gravity is pulling on the "sensing body", the desk below is pushing upwards and preventing the casing from moving (see Newton's laws).

If you then flip the sensor on it's side, it will measure the same magnitude of acceleration, but pointing sideways instead, and someone who is just watching the numerical output change on the computer wouldn't be able to tell if the sensor had just been rotated on its side or if the direction of gravity had changed.

This also means that if the casing of the sensor is experiencing the same acceleration as the actual measuring tool inside, the sensor will read "zero gravity" because the difference is zero. You can test this by downloading an app that logs acceleration data on a smartphone and then (gently and carefully!) throwing it into the air. Afterwards you will see that the moment the phone leaves your hands, the acceleration jumps to zero along all three directions (XYZ typically) because the phone, which is connected to the sensor's casing, is itself accelerating downwards at 1G and thus the difference becomes zero despite the fact that seen from an external reference frame, it is accelerating downwards.

This is why your g-sensor will read zero and you will feel an apparent "zero-g" in orbit, because you are effectively in a free-fall all the time. You are constantly accelerating but because the internals of the sensor are too, the difference reading is zero.

Answer 2

There's at least one other answer here that is correct in all its details, but it gives a lot of details. Here's the simple version:

An accelerometer measures the force that's needed to keep a "test mass" stationary with respect to its supporting structure, and then it divides that number by the nominal weight of the test mass to give a reading in "g" units.

As @Barmar said in a comment on another answer, the mechanism of an accelerometer is the same as the mechanism of a bathroom scale. The only difference is in how the measurement is interpreted. With the scale, the mass is unknown, and the acceleration is assumed to be 1G ($9.8\frac{m}{s^2}$ at sea level on Earth). With the accelerometer, the mass is the known quantity, and the acceleration is the unknown.

Answer 3

What is measured with g-forces?

In Newtonian mechanics, it's acceleration (scaled by $9.80665\,\text{m/s}^2$) due to real forces, except for gravitation. Accelerometers do not measure accelerations due to fictitious forces such as the fictitious centrifugal and Coriolis effects as those are not real forces. In general relativity, it's acceleration due to real forces (also scaled by $9.80665\,\text{m/s}^2$) as gravitation is a fictitious force rather than a real force in general relativity.

The general relativity explanation is perhaps easier, at least conceptually. (The mathematics of general relativity is a rather difficult.) That gravitation is a fictitious force in general relativity is a consequence of the equivalence principle. No local experiment (an accelerometer is close to being a local experiment) can detect acceleration due to gravitation.

From a Newtonian mechanics perspective, accelerometers do not detect acceleration due to gravitation because every accelerometer has a test mass inside it. That test mass is somewhat free to move with respect to the accelerometer case. The accelerometer uses some device such as a spring to keep the test mass inside the accelerometer case. In the case of a spring, the accelerometer reading is the extension or compression of the spring.

Consider an accelerometer orbiting the Earth. The gravitational acceleration of the case is the same as the gravitational acceleration of the test mass. The accelerometer reads nothing.

Next consider an accelerometer at rest on the top of a table which in turn is at rest with respect to the Earth's surface. The accelerometer is subject to gravitation plus the normal force exerted by the tabletop. The test mass is subject to gravitation plus the spring force (or whatever other mechanism is used to keep the test mass inside the case) -- but not the normal force. The acceleration of the test mass due to the spring force (spring force divided of the test mass's mass) has to be equal to the acceleration of the case due to the normal force. The accelerometer registers 1 g up.

Answer 4

It is the amount of acceleration relative to the conditions of free-fall -- that is what an accelerometer measures. Acceleration defined as relative to the conditions of free-fall is referred to as "proper acceleration". Here is how the relevant Wikipedia article introduces us to this concept:

[...] proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero.

In your question, you are correct to notice that an accelerometer sitting at rest on the surface of the Earth shows $1\ g$ despite not accelerating. However, let's consider a different frame of reference, where we agree to set the accelerometer's scale in a way that $0\ g$ means "the conditions the accelerometer would be experiencing during free-fall". Then, we arbitrarily assign "zero acceleration" to that state -- in other words, we define an "accelerational standstill" to be the state of any object experiencing free-fall. From the viewpoint of an object being in the state of free-fall, an accelerometer sitting at rest on the Earth's surface does indeed accelerate; in specific, it experiences $1\ g$.

Meanwhile, being in an orbit IS being in freefall. The experiences are equivalent^† and an accelerometer reads $0\ g$ in those cases.

An analogous example would be to consider a hypothetical scenario where we agreed that, in a certain context, we will be using a specifically modified measuring tape. The modification is such that the tape does not start at the point where it reads $0\ cm$; instead, it extends another $10\ cm$ in the opposite direction, and that "duplicated" $10\ cm$ mark is where it starts. Going from the start, the numbers go down until they reach zero, then start increasing again as they would do in a normal tape:

Going along with that, one could ask a perfectly valid hypothetical question similar to yours: if I am measuring something of zero length, why does the tape read "$10\ cm$" instead? If I am measuring the tree log illustrated above, which clearly has non-zero length, why does the measurement read "$0\ cm$"? Answering those, hopefully trivial, questions and applying analogous thought process to your initial question could help the concept of accelerometer's spirit truly click in for you.

---

^{† g-forces could be really small, but are never exactly zero; the small-but-not-zero values could differ a little. For all intents and purposes, however, the experiences are equivalent, and the value of zero could be used as if it was exact.}

Answer 5

An accelerometer may be built from a small mass held by a spring. The force on the mass is measured by the deformation of the spring.

According to Einstein's very famous thought experiment with the elevator you can't decide with measurements made only inside the closed elevator box what is the reason of the measured acceleration. It may be a gravitational field only or an accelerated movement or a combination of both.

Zero gravity may be measured when the elevator is very far away from any star or planet. But a free falling elevator may cause zero gravity, too. You can't measure with the accelerometer if it is a circular or elliptical orbit around Earth or a linear, parabolic, or hyperbolic trajectory.

A Lagrange point is another possibility for zero gravity.

Answer 6

G-force is acceleration (its magnitude). Yes it is that simple! A spinning object or a non-rigid object will have different acceleration at different points, so the g-force across the object varies. Thus the crash earpieces in F1 cars.

Objects at rest on Earth's surface have zero coordinate acceleration. Meaning that they are not changing the numerical values of their coordinates (such as altitude). But they are constantly accelerating upward at $9.8 \frac{\text{m}}{\text{s}^2}$ (and towards Earth's axis at a smaller number due to Earth's rotation). We are more interested in coordinate acceleration if we want to know where we are in space so many meters subtract out the $9.8$. Since gravity varies slightly, some meters have a "sit still" calibration procedure to measure the precise gravity.

With all this acceleration, why are these objects not getting anywhere? Spacetime is curved around massive planets such that geodesics tend to converge as do "parallel" lines on the sphere. Thus you have to keep accelerating to fight this divergence and stand still.

Answer 7

There is no physical difference at all between being supported in a gravity field and being accelerated, or between free-falling in a gravity field and floating in (a hypothetical) gravity-free space. Spacetime, as seen by the accelerometer, is curved — or not curved — in exactly the same way, and this curvature exerts forces on masses, and these forces are measured by it.

There is a little paradox here, if you want: In a gravity field, the accelerometer actually measures the absence of acceleration as observed by a third party: After all, we are sitting still relative to our gravity well. Therefore, accelerometer is something of a misnomer because it shows acceleration where a third party observer does not see any. (I mention the "third party" because only relative to the third party an accelerometer sitting on a table in a black box is un-accelerated. The accelerometer itself, as mentioned, perceives being accelerated.)

What the accelerometer measures is the force (if any) keeping it from following a geodesic, the shortest path between two points in spacetime.

Paradoxical consequence: Since there is no gravity-free point in spacetime, all accelerometers showing zero acceleration — because they are in free-fall — are actually accelerating according to third party observers at rest relative to the source of gravity. And conversely, all accelerometers at rest relative to a near-by gravity well — like the one on your desk — actually show acceleration.