"Instantly" as in "before the airspeed has had time to change at all?" Related: can we tell what RPM the prop will spin at, at a given airspeed, by testing the motor, prop, and fuselage in a wind tunnel, or do we have to know the aircraft's pitch attitude as well? I think this answer may have room for improvement.

@quietflyer There ya go.

I'm pretty sure that's not how it works but unfortunately don't have access to an airplane to go jump into to test it at the moment! But thanks for clarifying what you meant, that's an important point of distinction.

I'd suggest a car w/ automatic transmission rolling along at a fixed throttle setting only varies rpm in relation to speed, not pitch attitude. The influence of road grade (pitch attitude) on rpm is only via speed. Of course that's different from a driver varying the throttle as needed to go up and down hills at a constant speed, or to hold a car stationary on a hill. In this case we could indeed see a rpm variation that we could attribute to "slippage". Food for thought. So there's something to what you are saying but I don't think it really is the correct answer to the exact question asked.

"Slippage" is happening in the constant-throttle case too-- whether we mean a car or a plane-- but not in a way that changes rpm for any given particular combination of throttle setting and instantaneous speed. Regardless of pitch attitude-- as I see it.

On the other hand if the original question had specified that airspeed was held constant and throttle position was not, then your answer would be close to perfect.

"then your answer would be close to perfect"-- at least assuming the throttle changes were automatically applied INSTANTLY, to prevent any acceleration/ deceleration from happening at all, after a change in pitch attitude.

Too good an answer to waste-- someone should ask another question so it can be put to good use there.

"I'd suggest a car w/ automatic transmission rolling along at a fixed throttle setting only varies rpm in relation to speed, not pitch attitude. The influence of road grade (pitch attitude) on rpm is only via speed" -- That would be true a) on a rack railway, or b) in a stick-shift car which substantially emulates a rack railway, or c) a lockup torque converter in lockup, which emulates a stickshift car. The fluid coupling changes specific things about that. Think about what it changes. This is hard.

@quietflyer And what I'm saying is the amount of slippage changes depending on load; it's not a flat percentage of RPM always. So RPM, throttle position and airspeed are not in a rigid relationship. You have to account for load, and changing pitch changes load.

So, it comes down to "what is the fundamental cause of load on an airplane motor". Isn't it the air drag on the prop? Will vary with airspeed and prop rpm. I still say for a given fixed throttle setting, then all variation in prop rpm can be attributed to variation in airspeed. There is no additional component of variation in rpm that needs to be attributed to pitch attitude. But I've said too much already; signing off on this

Chrysler made an automatic transmission in the 60's with a second oil pump powered by the output shaft... so that if the car was rolling but the engine off, the transmission could be shifted into gear. It was, and I believe still is, the only automatic transmission vehicle that could be push started.

How does the hydrostatic load change? How does changing AoA relative to propeller plane instantly increase propeller drag?

@Koyovis hydrostatic load changes when you pitch up or down. For any given pitch angle and throttle position, there is a balance airspeed and RPM that it will eventually settle out to. You can change pitch angle almost instantly, but the airplane has mass and it’s airspeed takes longer to change.

One might say that the glider equivalent of your idea is that if you were somehow to fly a constant angle-of-attack loop (which would be a somewhat ungraceful and un-round maneuver, with G-load varying according to airspeed squared), the drag coefficient would be lower whenever the nose is pointing steeply down, because that's when the glider wants to gain airspeed. I'm still not buying it. And what do you see in actual practice when you watch the tach immediately after an abrupt nose-down pitch change?

@quietflyer have you read the question? OP reports immediate RPM increase.

I don't see "immediate" or "instant". I see the same phrasing I would use to describe the airspeed change resulting from a pitch change, whether in a glider or a powered airplane.

Sorry - why dies hydrostatic load change immediately when pitching up or down?

@Koyovis because the force@airspeed needed to climb is considerably more than the force@airspeed needed to descend. Same reason your car crests a hill, and transitions from the engine pushing the road to the road pushing the engine. On a stickshift car that has no effect on RPM because road speed and RPM are locked; that is not true on a non-lockup torque converter because it is not hard-geared.

It works that way with vehicles which use the earth as a reaction mass, not for aircraft which use air. The propeller does not care whether the air flows in horizontally or vertically.