LarryC,
As you said, the Altimeter Two is going to register 1G when sitting on the table pointing straight up. Let us call that the Z axis and the Z axis accelerometer is providing the 1G data. Now your cat comes along and knocks the rocket over onto its side so the X axis acceleromter is pointing up. The altimeter output is still 1G. Your cat thinks this is a fun toy and flips the rocket over 90 degrees so that the Y axis is now pointing up and down. Still a 1G output on the altimeter. Now your cat knocks the rocket off the table and the rocket lands on its nose, but is leaning against hat which the cat knocked off the table earlier. The rocket is leaning at a 45 degree angle. Now at least two of the accelerometers are registering something, possibly all three. The combined output is still 1G.
OK! Deep breath!
Consider a rocket sitting on a table. The rocket has a three-axis accelerometer inside it. We get the resultant acceleration and the instrument reads 1g. This is an absolute value of acceleration, and tells us nothing about the orientation of the rocket. We can knock this rocket over and it still registers 1g. The instrument is obviously registering gravity, and the world is obviously flat. (Actually, I have many rocket-oriented computer programs based on the flat world model. :blush
In fact, the accelerometer is not registering gravity *directly*.
The true total acceleration of the rocket, in all instances, is 0. This total acceleration of the rocket is the resultant acceleration of gravity and the force of the table underneath the rocket. The instrument is not registering 0, though; it is registering 1g. It must be failing to measure either the component of acceleration from gravity or from the table.
(Aside: Note that in the case of a single-axis accelerometer, one can tell right off that gravity is not sensed, because the reading there is 1g, the component from the table, and not -1g, the component from gravity. The three-axes obscure things, because we compute the absolute magnitude of the acceleration, which isnt signed.)
Suppose we substitute a rocket motor for the table, and we arrange the motor to always thrust vertically with a force equal to the weight of the assembly. The rocket hangs in space with thrust equal to weight. We have an equivalent situation to the table scenario. The reading stays the same and the rocket remains (at least theoretically) motionless. I claim the accelerometer is not registering gravity; it is registering the thrust of the motor. Heres the proof:
Suppose we cut the all thrust. The rocket is now in freefall and the accelerometer (before drag kicks in) registers 0g. Gravitational acceleration still pertains You can see it! The rocket is actually accelerating at -1g before your very eyes! If the accelerometer registers gravity, it should be registering that acceleration, -1g (or 1g in absolute value). Its registering 0g!
Still not convinced? Suppose we turn the thrust back on but adjust it to 1/4 the earthly weight of the assembly. The rocket now falls at the rate of 3/4g, and the accelerometer registers 1/4g! Gravity is still pulling at -1g, but the accelerometer doesnt register it; it registers (before drag kicks in) the amount of acceleration from the thrust of the motor (1/4g) and not the acceleration from gravity (1g in absolute value).
If you take the same rocket motor and orient it in any direction, the accelerometer reading remains the same. The acceleration of the rocket differs according to is orientation, though.
Conclusion: When the rocket was on the table, it was registering the component of acceleration from the force of the table. That component was 1g. That reading registered gravity because of a property of tables (they push back as hard as you push down on them), and not because of a property of accelerometers.
If you apply the same force (the earthly weight of the rocket) in free space, the rocket actually accelerates at 1g there. The accelerometer in free space measures that acceleration and reads exactly what it read on earth under the same conditions with the same force applied. If you cut the motor in free space, the rocket stops accelerating (it still has velocity) immediately, and the accelerometer registers zero just as it did in free fall (no table, no thrust) on earth.
The accelerometer reading is unaffected by gravity, but the rockets motion is affected.
In a rocket flight, the accelerometer registers the resultant of thrust, drag, lift, wind, and other aerodynamic forces. It doesnt register gravity. That is why, in a vertical flight, you subtract 1g from the resultant you are, in effect SIMULATING the effect of gravity, which is missing from the data. That simulation is based on the assumption of verticality.
If the flight is off-vertical, you have to subtract 1g *from the vertical component* of the resultant and not from the entire resultant to get the correct acceleration. But since the flight is off-vertical, you dont know the orientation of the acceleration vector without gyros.
An accelerometer analysis program, whether it be for a 1 or 3-axis instrument, is not entirely empirical. It's only a partially informed simulation combining empirical accelerations with the simulated effect of gravity. If you have an independent reference for the orientation of gravity like gyros or an altimeter, you can get more empirical estimates. You need independent references, though. A 3-axis instrument by itself doesnt do it.
I sure that helps
.
For further discussion, please see:
https://www.lunar.org/docs/LUNARclips/v5/v5n1/Accelerometers.html
https://www.rocketryplanet.com/images/pdf/Analysis-of-Flight-Computer-Data.pdf
and
https://www.rocketryplanet.com/images/pdf/Barometric-Adjustment-of-Inertial-Flight-Data.pdf