Barometric altimeter data during high vertical g-forces?

Question

I’m contemplating that that under high vertical acceleration (such as the maximum limit of 2.5g for commercial airplanes), that hydrostatic atmospheric pressure wouldn’t be a complete model. Wikipedia states for atmospheric pressure:

In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point.

The derivation of the Barometric formula presumes hydrostatic pressure:

And assuming that all pressure is hydrostatic:

  dP=-ρgdz

It appears to me that without correction for the g-forces, a vertically accelerating barometric altimeter could potentially indicate uncorrected altitudes which are lower or higher (depending on the design of the altimeter) than true altitude even if all other factors had been corrected.

Is this a correct understanding and do Air Data Computers (ADC) described below make these corrections? If yes, can anyone provide an approximate formula or mathematical model for altitudes near ground level?

Another Aviation Stackexchange answer states:

^{_{However, altitude is also used for the purpose of traffic separation, and for this purpose, neither QNH or QNE is corrected. This might sound counter-intuitive, but as long as your altimeter is showing the same error as any conflicting traffic, you can be safely separated, therefore: The altitude shown on the altimeter is not corrected at all (except by calibration for possible aerodynamic interference, such as compressibility, venturi-effects etc).}}

In technically sophisticated aircraft, barometric altitude input is used for vertical navigation. Since vertical navigation is concerned with the true altitude of the aircraft, the aircrafts Air Data Computer (ADC) will calculated a true altitude based on information available to it (either through sensors, or through pilot input). The true altitude is however, as stated, not shown on the pilots primary flight instruments.

Answer 1

In the formula $dP = -\rho gdz$, $g$ is the local gravitational field that is pulling on the fluid (the atmosphere). The apparent value of $g$ within the airplane is not relevant.

So other than making sure the sensor itself isn't affected by changes in apparent weight, there's no need to correct for accelerations of the barometer.

And yes I am intending to ask whether the sensors are designed such that their “apparent weight” (or more generally their mass acted on by any directed force) is not an appreciable factor in their reported measurements?

My understanding is that no, it's not. Altimeters already have a measurement error at level flight, and they have a lag when altitude is changing. Additional errors due to apparent weight would have to exceed those to be worrisome.

"vertical acceleration" is rather small for almost everything that's not a military fighter. But a plane could easily pull 3g's in a level turn, and you would want your altimeter to remain accurate.

Obviously it's possible to design an instrument that is more susceptible to such inaccuracy (such as have the pressure vessel balance against a weight to indicate the altitude), but that shouldn't be a problem for a normal instrument.

The aneroids in a diaphragm barometer can be oriented so that downward forces have no effect on the reading. Also, the smaller and lighter the disks, the less that any acceleration will affect the reading.

I found lots of articles on various corrections for barometric altimeter readings based on temperature and different atmospheric profiles, but none on g-load corrections. That suggests to me that no correction is necessary for standard instruments. Perhaps someone can find published performance data for an installed instrument that calls it out explicitly. The lack of information I found appears reasonable, but not completely satisfying.