Since the accelerometer is sensitive to both acceleration and the Earth’s gravitational field, interpreting accelerometer measurements is complex. A useful model for understanding accelerometer measurements is a spring-based scale with a reference mass (or object) attached to the scale. If the scale is pointing upward (the usual orientation for such a device) the weight of the mass causes the spring to compress, and you get a non-zero reading. If you were to turn the scale upside down, the spring will be extended, instead of compressed, and we get a reading of the opposite sign. If you turn the scale so it points sideways, and keep it motionless, then the spring will just be at its relaxed length, and the reading will be zero. If you accelerated the scale toward the mass, then the spring would compress. If you accelerate the scale away from the mass the spring would stretch. In each case the scale is reading a value corresponding to the normal force on the mass. This reading can be made relative by dividing out the mass, giving units of N/kg, which is the same as m/s2. The accelerometer measurements can be interpreted in exactly this way.
Q: What does an accelerometer measure?
A: Normal force per unit mass.
Note that it’s not the net force per unit mass (which would be acceleration), but it is the normal force per unit mass. This somewhat unusual quantity corresponds with what a rider on a roller coaster feels during the turns. This interpretation is useful even for the scalar total acceleration value, which is
9.8 N/kg for a 3-axis accelerometer at rest, zero for one in free fall, and greater than 9.8 N/kg for one making a corner.
This normal force interpretation works even for a one-axis accelerometer being accelerated in a horizontal direction. The reading is non-zero as the test mass inside the device has to have a force applied to accelerate it. That’s just a normal force that happens to be horizontal.
When discussing the accelerometer reading, we can call it the Normal Force per Unit Mass, with units of N/kg.
Q: I thought the accelerometer measured acceleration!
A: Here we are being very careful to not call something an acceleration when it is not a kinematic acceleration. For example, an “acceleration” of 9.8 m/s2 for an object that remains at rest is clearly a problematic interpretation, yet that’s what the accelerometer reads.
You can correct the accelerometer reading to get a true acceleration by adding the component of the gravitational acceleration field along the direction of the sensor arrow. For example, if the axis of the accelerometer is pointing upward, then the gravitational component is –9.8 m/s2. The accelerometer reads
9.8 m/s2 when the arrow is upward and the device is at rest. By adding
–9.8 m/s2, we get zero, which is the correct acceleration. If the arrow is horizontal, then the reading is zero, but the gravitational component is zero, and we still have zero for the true acceleration.
Q: What about g-force measurements?
A: We avoid the term g-force because the quantity doesn’t have units of force. Instead, g-factor can be used as a simplified label for Normal Force per Unit Mass in axis labels and discussions.
You can see that the g-factor is then 1 for an object sitting at rest on a table, zero in free fall, etc. The g-factor is dimensionless. If the Normal Force is a vector, then so is the g-factor. g-factor is completely optional–it is just a shortcut to avoid a long name.