I'm still feeling that one of the core problems in the original question is that the op seems to feel that a discrepancy between turn rate (rate of curvature of flight path) (or more correctly, yaw component of rate of curvature of flight path), and yaw rotation rate, is the cause of sideslip. When actually this is the driver of a change in sideslip angle. Though some discrepancy must have existed at some point, for the sideslip angle to ever become non-zero.

Likewise the dynamics that the op wants to describe as a "vertical sideslip" seem more related to a change in angle-of-attack, not a non-zero angle-of-attack. I.e., a mismatch between pitch rotation rate, and the actual rate of curvature of the flight path in the pitch dimension. As in the "cobra" maneuver.

But at the end of the day, the same answer still applies - for normal maneuvering, if you make pitch control (stick) inputs as needed to obtain the desired angle-of-attack or g-load or pitch rate, all the other relevant variables must automatically "follow along for the ride".

Becausr

And what exactly distinguishes "normal" maneuvering from Cobra etc? I dunno, I guess that angle-of-attack never gets too extreme, and changes in pitch attitude aren't wildly different from changes in direction of flight path? Have to think about it some more later...

Is it as simple as staying "on the front side of the drag curve" - or the L/D curve - or the power curve- ?

@RobertDiGiovanni -- re " In any circle, G's are determined by radius and speed, therefore your second "actuator" is throttle or thrust" -- as a glider pilot, I'd say the throttle is irrelevant to the most basic dynamics of turning flight, assuming we aren't imposing the constraint of maintaing a constant altitude (relative to airmass) -- so I think you are on the wrong track here--

Might apply to radical maneuvers like "cobra" though...

One thing's clear enough -- attempting to give a complete explanation of the dynamics of maneuvering in the pitch plane-- what is the elevator really most directly controlling, etc -- is not simple. Even setting aside the complication of the "sideslip" analogy, the question provides good food for thought--

@quietflyer yes, the "skid/slip" discussion really was an unnecessary distraction to the original question of pitch controlling centripetal acceleration. Even a glider burns "fuel" to manuver. OP was stating that elevator could not control pitch and centripetal acceleration at the same time. Lacking thrust, the glider would have to lose speed (and tighten the spiral) or use gravity (descending flight), to maintain centripetal .

acceleration. So, the OP was correct, it can't be just the elevator. I could change "throttle/thrust" to energy.

So, ha, we now have our emergency descent spiral, no?

@CharlesBretana the issue may be we lump gravity and acceleration into one term: "G". So, in your spaceship, 1 G is from acceleration. And it's counterforce (just like earth) is the floor resisting the F of ma (on earth: mg).

Nothing "ficticious" there. In turning flight force vectors the centripetal vector is NOT matched by drag (a real force). That's how we can say a constant velocity turn is accelerating (in a new direction).

But drag is greater in the "old" direction. That may be how we get forces to balance for constant velocity.

@Robert, a great diagram from the authoritative text on Gravitation, displays the trajectories of a baseball, a bullet and a photon in space time in a gravity field. Look at it. It can be seen on page 33. Look at xdel.ru/downloads/lgbooks/…

If you graph the three trajectories in our theoretical space ship (or on the earth) in a zero-Gravity frame of reference, Like a free falling elevator), they will all be absolutely straight lines.

The point being, that what you think is acceleration is actually only a perceptual illusion due to the fact that you are measuring and displaying things in an accelerated frame of reference.

In space-time, if you do the analysis (and display the trajectory) in an unaccelerated frame of reference (Free-Fall), anything that does not have a REAL force acting on it (and is therefore in free fall) will be traveling in a straight line.

And to your point about the earth's "counterforce". I posited this thought experiment far away from the earth so that it would be clear that the "Gravity Force" is NOT the same as the acceleration. The force of gravity decreases with the inverse of distance squared, so 300,000 km from earth it is a miniscule fraction of 1 G. And, think about the same thing way far away - in interstellar space where we can assume that the strength of the gravitation field is indeed infinitesimal. What then?

On a completely unrelated topic, Help me out... How do I get the reference to your login to show in color as you are doing with mine?

Ok, but in relation to aviation, surely it's often practical and useful (even if slightly incorrect) to treat gravity as a real force, and to treat the earth as an unaccelerated reference frame -- from this perspective one can still sort forces into "real" and "apparent" or "fictitious" -- with the "apparent" or "fictitious" forces only being relevant if we shift our reference frame to the moving aircraft or pilot--

-- with the "apparent" or "fictitious" forces only being relevant if we shift our reference frame to the moving aircraft -- e.g. to "explain" the pilot's (or slip-skid ball's) tendency to shift left or right relative to the aircraft itself--

Quiet Flyer, Yes, absolutely agree. And to stress the point, This is totally unnecessary, and indeed, would be confusing to a new pilot, in early training. But I think it is important that we not teach the opposite. ... and, (quibbling here).. it's not slightly incorrect. Although it is equivilent, to a remarkable degree of accuracy, in it's predictions, it is completely wrong.

Understanding how the choice of the frame of reference we use affects our understanding of the principles of flight is not as important when we talk about gravity, but it is critical when we talk about the movement of the atmosphere (the wind), and when we discuss aircraft in steady-state turns, and/or slips and skids. In those scenarios, too often, the explanation completely ignores the fact that the frame of reference attached to the aircraft is an accelerated frame of reference.

And this, because it requires the addition of additional fictitious forces to balance everything out, confuses and delays the understanding that needs to be conveyed to a student.

And, on another quibble, "Drag" is not a singular, direct force acting on the airframe. it is the result of a complex aggregation process of a almost uncountable number of forces from collisions of air molecules with the surface of the airframe, and then mathematically taking the component of that aggregation that lies parallel to the true airspeed velocity vector.

Re " In those scenarios, too often, the explanation completely ignores the fact that the frame of reference attached to the aircraft is an accelerated frame of reference." -- yes, and FAA flight training materials have included some real "clunker" diagrams where the pseudoforces are mismatched to the real forces (when they should by definition be equal in magnitude but opposite in direction... )

As an aside, the original motivatation behind my interest in some of these dynamics is that I encountered some hang gliding training materials (no rudder!) that claimed a strong correlation between a pilot's pitch control inputs while entering a turn, and the glider's tendency (or lack thereof) to sideslip. Hands-on explorations showed nothing to it, sideslip was actually almost entirely driven by roll rate.

Basically an accellerating dive during the turn entry was being misidentified as an increased tendency to sideslip.

All sorts of diagrams and "explanations" were included in the training materials to "support" the incorrect theory, containing some of the same errors we've mentioned here --

The incorrect claim was that failing to give forward pressure on the control bar to increase the angle-of-attack while turning or while rolling in to a turn would promote sideslip -- in reality accelerating dive during the turn entry was being misidentified as an increased tendency to sideslip --

Andif you page through "Stick and Rudder" you'll actually find a page with a similar fallacy, suggesting that sideslip can often be eliminated by increasing back pressure on the elevator-- I've not found this to be the case generally speaking--

@CharlesBretana interesting that once a "free falling" object reaches terminal velocity, G=1. (the elevator ride). Sorry, I don't know how these captions are highlighted, but thanks for the reference anyways.

@Robert, Yes, at terminal velocity there is indeed only one real force, the drag of the falling body. In the earth's 1G accelerating frame of reference, you need the fictitious force of Gravity to balance that.

@quietFlyer, Yes, the many many incorrect and/or misleading diagrams depicted in numerous "authoritative" texts and manuals are part of the reason I am so consistently annoying on this topic in these forums!

And oh yes, one other point. Sometimes it is really important to gain clarity as to exactly what someone means by the terms they are using. I suspect that when the op uses the term Yaw, and yaw rate, he is confusing this with turn rate. Yaw angle is not the heading, it is the lateral angle between the fuselage and the relative wind. An aircraft in a coordinated turn has zero yaw angle and zero yaw rate. Misunderstanding this would create all sorts of erroneous ideas in one's head.