# What does “inertial” refer to in “inertial reference”?

An ADIRU makes use of air data reference and inertial reference. Inertial reference calculates the heading, position, ground speed and attitude. I was wondering why is it called inertial. Is it related to the term inertia/mass?

• yes, based a/a few gyro(s) – user3528438 Apr 23 '18 at 16:30

It is called inertial, because it works by measuring—and integrating—inertial forces¹, that is forces due to acceleration of the reference frame (i.e. the aircraft). Gyroscopic effect used to measure rotation is also due to inertial forces.

The measured forces include gravity, which can't be easily separated, but this is done by observing that the speed is limited, so the average acceleration must be zero and therefore the long term average equals gravity.

¹ In general relativity the inertial forces are usually considered as real as any other, so the term “fictitious” is not really appropriate.

Inertial refers to any forces - Any forces acting on a body which produce an acceleration via Newton's second law of motion ( F = ma ).

In this respect, gravity, is not a force, as it does not produce an acceleration, it only causes a distortion in the geometry of space-time. By Mach's principal, The physics in an enclosed volume in outer space accelerating with one G of acceleration are identical to the physics we experience on the surface of the earth, just as the physics in a free-falling elevator, or an aircraft in a zero-G ballistic trajectory, are identical to the physics in an enclosed volume in free fall in outer space.

From this perspective, which is more accurate that traditional Newtonian perspective, the frame of reference we normally perform calculations in, the earth-bound 1-G frame of reference, is not an inertial frame of reference, as it is always experiencing 1 "G" of acceleration due to the "force" the earth itself exerts on the soles of our shoes.

... The frame of reference of a free-falling elevator, on the other hand, is an inertial frame of reference.

The word inertial does indeed come from Inertia, because the mass of af any body is a key property of all objects in the universe, but it participates in two physical relationships, which ostensibly seem to have no connection to one another. The first one is Newton's Second law, (F = ma ), which says that a body will accelerate when a force is exerted on it, proportional to it's mass. This is the law of inertia.

The second is Newton's law of gravitation, which stated that a body in a gravitational field of another body will experience a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

For many years scientists were perplexed by how incredibly identical the masses measured by these two physical processes were (Force and Gravitation).

It was only when Einstein proposed the General Theory (Gravitation), that this mystery was explained. These masses were the same because there is no force of gravitation. The "force" we think of is a fictitious force, which only exists because we are measuring things in an accelerated, not an inertial, frame of reference (the surface of the earth, which, in space-time, is continuously accelerating upwards at 32 ft/sec2). It is just as fictitious as the force we would think we see if we were in an enclosed spaceship accelerating at 1 "G" In outer space.

https://www.ion.org/publications/online-tutorial-intertial.cfm has my online tutorial for GPS/GNSS and inertial navigation, free to Institute of Navigation members. This basic material is also available at low cost to nonmembers. An inertial measuring unit "IMU" typically has a triad of gyros and a triad of accelerometers. These sensors DIRECTLY provide angular rate and "specific force" (defined shortly), and INDIRECTLY (by propagating the effects fo those direct measurements) provide velocity, position, and attitude. Gyros sense absolute (i.e., total) angular rate with respect to an inertial coordinate frame (i.e., one that doesn't rotate and doesn't accelerate). Specific force is the total NONgravitational force; if you dropped an accelerometer it would read close to zero (e.g., a drag effect), not 32 ft/sec/sec down -- and in a cruising aircraft a vertically aligned accelerometer would show the 1-g lift.