The accelerometers are microelectromechanical devices (MEMS devices) each consisting of a cantilever and a test mass. As the mass is accelerated, the cantilever bends, generating a signal proportional to the acceleration. Three orthogonal axes provide three channels of acceleration information for most experiments and an additional three channels of acceleration for high-g situations are also available. Acceleration measurements are used for the angle measurement.
The gyroscope is a microelectromechanical device that uses a vibrating structure to determine rate of rotation using the Coriolis force on the structure. Three orthogonal axes provide three different channels of rotation information.
The altimeter is a temperature-compensated, absolute air pressure sensor that can measure from 260 mBar up to 1260 mBar. We use the following equation to convert to altitude in meters:
assuming that p0, the pressure at sea level, is 1013.25 mBar. The resulting altitude range is from about –1800 m to 10000 m.
The absolute pressure accuracy is ±0.2 mBar which can give you an error of ±1.4 m to ±5 m depending on which end of the scale you are at (–1800 m or 10000 m respectively).
You will often want to study the change in altitude during an experiment. Examples would include roller coaster rides, sky dives, or bungee jumps. In these cases, the absolute altitude above sea level is not as important as relative altitude compared to the ground or to the starting point of data collection. Zero the sensor before collecting data to use relative altitude.
Additional Information about Acceleration
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.
Q: What does an accelerometer measure?
A: It meaures normal force per unit mass, otherwise known as proper acceleration.
Note that it’s not the net force per unit mass (which is 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 for one rounding 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.