When practicing steep turns, I'm running into an unusual phenomenon.
If the airplane is losing altitude in coordinated flight and I apply
aft stick pressure to pitch up and correct, I notice that the ball
swings to the outside of the turn indicating a skidding condition.
Conversely if the airplane is gaining altitude and I release back
pressure to the stick to descent, the ball always swings to the inside
of the turn, indicating a slip.
This question surprised me. Your observations are in fact consistent with a statement by Wolfgang Langewiesche in his aviation classic "Stick and Rudder". He claimed that while turning1, a sideslip is often caused by "insufficient lift" and should often be fixed by increasing elevator back pressure rather than adding inside rudder. But I've never found his claim to be consistently true and I've long believed that it is one of the few significant errors in his otherwise excellent book.2
I have found that very pronounced elevator inputs while turning that create very significant changes in G-loading do produce brief, small excursions of the slip-skid ball in the direction predicted by Langewiesche's idea. I believe these are produced by complex three-dimensional changes in the flight path that are beyond the scope of simple analyses. Or to take a somewhat related situation, in a wingover involving a full 90 degrees of bank, if the aircraft is allowed to "float" over the top at a rather low G-loading (involving little or no aft pressure on the control stick), with no bottom rudder applied, the slip/skid ball and or yaw string will indeed show quite a pronounced slip as the aircraft "falls" earthward.3
But in simple turning maneuvers involving only moderate changes in the direction of the flight path in the vertical plane (i.e. only moderate changes in climb or descent rate), I've not found elevator inputs to play a role in turn coordination (in the sense of avoiding slips and skids) in any consistent manner. (In single-engine prop planes, there definitely can be an effect due to p-factor, but the direction of the effect will depend on the direction of turn.) I've done rather extensive tests to look at this in several single-engine airplanes and ultralights (including some with a high-mounted pusher engine), and several different sailplanes.
The topic has long been of special interest to me, because in the hang gliding community, at least in the US, there's long been an idea that the "correct" pitch inputs while entering a turn will keep the flight path "coordinated", while inadequate pitch inputs will cause the glider to "sideslip". Along the same lines, an intentional nose-down pitch input while the glider is entering a turn, or is turning, is thought to produce a very pronounced "sideslip". (If true, this would be compatible with Langewiesche's idea as noted above.) Many pages have been devoted in training manuals and magazine articles to "explanations" of these supposed phenomena. While it makes some sense to use the word "coordinated" to describe the harmonized use of all available flight controls to produce the desired results-- and the only available control inputs in hang gliding are weight-shift pitch and roll inputs-- I've found the idea that pitch inputs have something to do with causing or preventing sideslip in hang gliders to be a complete "red herring". Some hang glider pilots appear to be mistaking the sensations of a diving, accelerating turn for the sensations of a true "slipping" turn. Extensive experiments with yaw strings and slip-skid balls on hang gliders suggest that sideslip in hang gliders is related almost entirely to roll rate, with a slight residual sideslip remaining when the bank angle is constant-- and this slight slip seen in a constant-banked turn tends to be greater when the airspeed (and sink rate) are low than when the airspeed (and sink rate) are high-- exactly opposite to what the community "conventional wisdom" (and Langewiesche's idea) would predict. Part of the confusion may be due to the fact that in some hang gliders, especially those with pronounced anhedral, "pulling in" the control bar while rolling from wings-level into a turn can produced a marked increase in roll rate, thus indeed producing a rather pronounced sideslip, which ends very soon after the roll rate is brought back to zero. Anyway, the long and short of it is that sideslip in hang gliders is produced primarily by adverse yaw while rolling, and for a given roll rate, this slip due to adverse yaw is not reduced by moving the control bar forward to "coordinate" the turn and reduce the gain in airspeed and loss of altitude. Pulling the bar aft while holding the glider in a constant bank doesn't make the glider sideslip as it dives and accelerates. (End of tangent-- but may help the reader understand why I've spent quite a bit of time exploring these relationships in more "conventional" aircraft as well. And the basic results were the same in all the aircraft tested.)
I'm assuming you are flying a single-engine prop plane with a nose-mounted engine turning in the "conventional" direction (clockwise as seen by pilot). Is this true? Have you demonstrated the phenomena to be consistently true while turning in both directions?
At the risk of contradicting both the original OP of the question and the esteemed Wolfgang Langewiesche, I'd suggest that this is not an effect that can be consistently replicated in both directions in a wide variety of aircraft. Would be most interested to be directed to video footage or other verification that suggests otherwise-- ideally with pilots feet clearly visible off the rudder pedals!
Can anyone else confirm this?
I'm not sure whether the OP meant (by "this") his theory was to what was happening, or simply the observed phenomena, but I'd sure like to see answers posted (or chat replies) by other ASE members who are able (or unable) to confirm the observed phenomena-- with specifics as to bank angle, and whether the effect is transitory (connected to changes elevator back pressure and airspeed) or lasting (enduring as long as aircraft is climbing or descending, even with pitch attitude constant), and confirmation that the effect was observed in both directions of turn, etc-- regardless of what the underlying mechanism is believed to be.4
Langewiesche didn't specify that the turn must be steep in order for this phenomena to be observed. OP mentions "steep" turns. It's possible that my own experiments described in this answer were mainly focused around turns of 45 degrees bank or less-- need to check notes for more details to refresh memory.
Similar content-- perhaps inspired by the content in "Stick and Rudder"?-- appeared in some (circa 1969?) editions of a book called "Modern Airmanship", edited by Neil D. Van Sickle. In later editions, such as the 1999 8th edition edited by John F. Welch, Lewis Bjork, and Linda Bjork, this content has been removed.
We can think of slips as fundamentally being caused by either of two phenomena: (one), an aerodynamic asymmetry creating a yaw torque that is only brought into balance when the aircraft is flying in a slipping condition, with the nose yawed to point to the "outside" or "high side" of the actual direction of the flight path, or (two) a sudden demand for an increased yaw rotation rate (if the nose is to remain aligned with the flight path), which the aircraft's yaw rotational inertia tends to resist, until a large enough slip angle is achieved to create a significant yaw torque to overcome the yaw rotational inertia and increase the yaw rotation rate. As the airspeed reaches a minimum at the top of a wingover, and aerodynamic forces thus are low, while the rate of earthward curvature of the flight path (due to gravity) reaches a maximum, the latter effect probably best describes the reason for the sideslip seen at this point. The steeper the bank angle, the more the earthward curvature of the flight path demands a yaw rotation rather than a pitch rotation, if the nose is to remain aligned with the flight path.
A few more words about the possible "underlying mechanism", or lack thereof, for increased back pressure to tend to cause a skid, and decreased back pressure to tend to cause a slip, as OP has reported -- the immediate effect of increased back pressure on the stick or yoke would seem to be an increased aerodynamic force that acts "straight up" in the reference frame of the inclinometer (slip-skid ball) tube, and so should not influence the deflection of the slip-skid ball. (Keep in mind that the slip-skid ball does not respond to some sort of "balance" between aerodynamic forces and gravity-- rather it responds to aerodynamic forces alone.) The longer term effect of increased back pressure on the stick or yoke is a lower airspeed, and thus (for same bank angle) a lower turn radius, a higher turn rate, and a higher required yaw rotation rate. It would seem that when extra back pressure is applied on the stick or yoke and the airspeed drops and the radius of curvature of the flight path decreases, and the turn rate increases, and the required yaw rotation rate also increases, the aircraft's yaw rotational inertia would have some tendency to keep the nose yawed too far toward the "outside" or "high side" of the flight path (basically a "lagging" effect) which should produce some temporary sideslip (not skid). Yet OP's observation is that increased back pressure tends to cause a skid. I'm at a loss to reconcile this discrepancy. Of course, the steeper the bank angle, the less changes in turn rate involve changes in yaw rotation rotation rate at all-- at steep bank angles the dynamics at play mainly involve the pitch axis.