I hope this idea did not come up from the idea that phase shift 90 degrees is not the same as 90 degrees geometry
Hell no.
when you say two motors that makes me think of two directions being required, but adding a phase shifted wave superimposes on the piezo input
No.
The two motor analog is only an analog, attempting to illustrate the basic idea. Let me explain in detail, and compare it to the described drive.
Both have a mechanism to oscillate their center of mass. In the drive, this is the primary frequency of the piezo stack. In the analog, this is the vibration motor that has its axis perpendicular to the surface the analog is sitting on.
The drive paper claims that a second harmonic imposed on the piezo stack causes a mass oscillation effect, explaining this vaguely by invoking
Mach's principle. (You can argue they talk about
inertia and not mass, but existing experiments have proven that inertial mass equals heavy mass to within our measurement precision (high), and the fundamental mechanism they claim is basically the oscillation in mass of a closed system, anyway. You see, the "range" of Mach's effect described is limited to the system containing the drive, and the mass moving at its center in a specific way is the cause of the oscillation in inertial mass of the rest of the system. This is why small components are needed for this experiment, too: fast speeds, short ranges.)
In other words, that by synchronizing the mass (or inertial) oscillation with the oscillation of the center of the mass, they can produce thrust.
In my analog, the second vibration motor has its axis parallel to the surface, and causes the mechanism to bounce off the surface. When the two motors are in sync, with a correct phase difference, the bounces caused by the second motor occur with the first motor in the same phase, thus bouncing off the surface with the same inertial vector, generating thrust. Of course, here the thrust is generated by bouncing off the surface, while the drive claims an exotic inertial mass oscillation effect in a piezo stack, but as an analog, it's the closest one I could come up with.
My analog is the actually working one. I do not think their piezo stack actually generates thrust, and what they measured was due to interaction of the piezo stack with their measurement setup.
In my analog, you can replace one of the vibration motors with angled "hairs" (springs) at the bottom surface, and it'll move even better. But it is no longer analogous to the drive here. (The second motor, by jumping the analog off the surface, is the sort-of-analog of the inertial mass oscillation effect in the drive paper.)
The paper states that without the second harmonic frequency, they don't see any thrust. They also say that when the phase shift between the primary frequency and the second harmonic is zero, they see no effect; and somehow, because of that, it cannot be an interaction with the experiment setup. That "somehow" is the bullshit part: of course the phase shift between the primary frequency and the second harmonic can make the difference,
because it affects the overall waveform of the piezo stack and therefore the center of mass; and when coupled to a measurement system with a (torsion) spring, the exact shape of the waveform (especially phases of the harmonics) can obviously affect the strength of the coupling, depending on the properties of the (torsion) spring –– this is damn easy to experimentally verify, too. Even metal fatique could be involved. Basic stuff.
The correct experiment setup would have had a separate oscillator, preferably mechanic (and not piezoelectric) – a spring type would be optimal, in a perpendicular direction, with a careful measurement of position along this axis. When oscillating along this axis, one would compare the oscillation to when the piezo stack is unpowered, and when the piezo stack is powered with various waveforms, including the primary plus second harmonic with a 90 degree phase difference. There is no need to try to measure thrust in this case, because the point is to verify whether there is indeed a mass/inertial oscillation. If there is, the position (frequency/phase) along the separate axis will differ if there is inertial mass oscillation: if inertial mass oscillation frequency is higher, it will be imposed in the perpendicular position; if lower, it will show up as modulation in the perpendicular position.
I admit, I'm pretty familiar with the claims by Podkletnov, Ning, et. al., because I'm the personality type who does not feel threatened by standing on the precipice of their understanding, and gazing into the abyss filled with foil hatted nutjobs, because sometimes there is a truth somewhere under there. In this case, I think this is more about the authors
choosing an unconventional explanation for an effect, one they could have trivially ruled out, just so they could write an intriguing paper on it.
This happens way more than you'd think; even in physics, more than one paper in ten is like this. (I don't know much about other subjects, as I mostly read physics and computing articles myself.)