krujje,
"...how do you change your AoA without adjusting your climb angle?"
You're confusing climb angle and pitch attitude!
The climb angle is 90°.
For a "steady-state" vertical climb, lift has to be zero or the climb wouldn't stay vertical, so you have to fly at zero lift AoA.
On most aircraft, that corresponds to a slightly nose-down pitch attitude.
So while your flight path is vertical, the nose of your aircraft is not pointing exactly to the zenith....
Oh, and that leads to a nice one....
In our theoretical perfect steady vertical climb..... the thrust line is unlikely to be perfectly aligned with the flight path. So there will be a small but noticeable component normal to the flight path.... which you then have to compensate for with a small but measurable amount of "lift".
fullyspooled, re accelerometers, I fully concur.
But you said...
You do however correctly point out (in my lesson of the day) that the accelerometer will indicate temporary accelerations caused by pitching moments.
Negative. If the accelerometer is installed in the right location, pitching moments accelerations become second-order.
Of course.... if you install it under the pilot's bottom... that's a different story.
ft, re zero lift... so sorry to contradict you slightly, above, because your reasoning is basically correct!
CJ