Damping. Resistance of an oscillatory system to oscillate as the result of energy dissipating friction or resistance. In the case of line tension the term Mz = b/2 x Tsin(theta) where Mz = the moment around the vertical axis, b = wingspan, T = line tension and theta = the yaw angle with respect the the steady state neutral position. We could get completely wound up in the math but suffice it to say, I have a pretty good handle on what a harmonic oscillator is and aerodynamics. The line tension is a very significant damping element in the tethered airplane system. Case in point, the airplane travels in a circle as a result of the line tension. What I did not say is that the vertical stab plays no part, my statement is the tension has a larger influence on the stability of the system. Case in point, tailless combat plane. Combat planes don't do weird sit while flying squares. At least the Winders I built as a young man didn't and they do a fairly good rendition of the pattern in 14.5 seconds.
The squares and poor behavior is a very interesting topic and from my observation there are several aspects including some "hinging" kinds of things. I have watched what the only thing I can say is if the airplane weren't tethered it would do a snap roll but yet it doesn't and there are some resulting interesting "pulsations" in the lines. This is part of why I have tufted the airplane and am making video flights. Actually this is one of two reasons the other being how much flap deflection is causing separation and consequently drag.
I think I posted a video of a tufted wing test I did of the 4/4 scale Laser doing a snap roll. The way spins and snap rolls occur is that one wing stalls before the other creating a divergent condition where the forces generated cause the stalled wing to decelerate increasing the angle of attack and the less stalled wing to accelerate decreasing it's angle of attack. The result is the the wing decelerating wings lift decreases further while the drag increases causing and acceleration in yaw and roll rates. This condition is what is termed autorotation. Note, at no point is rudder required to drive the condition in fact I demonstrate this to my student pilots with the rudder nearly centered. The only thing necessary is a slight bit of yaw be present at the point when stall occurs.
During my initial flight testing the SV-11 had a similar "oddity" during the squares similar to Tim's partly because of the ham handed meat servo. I was working on adjusting tip weight and fix some hinging. During this I observed that not so hard pulls would fly cleanly while less than not so hard pulls would create some hinging and really hard pulls would create the "whifferdill" extremely violent motion. After a couple of repeats, my conclusion, given the build up tests, was that some of the hinging and definitely the violent case was the result of the wing stalling. My control set up had more elevator deflection that flap and reducing the elevator deflection, reducing AOA per control input, made strides to removing the arrant behavior. Moving the CG forward made a difference as well.
That increasing the size of the vertical would "fix" this condition isn't surprising, especially if the area balance of the airplane is biased forward of the CG causing the airplane to "skid" in it's flight path. Watch the tail cam video where I am flying in windy conditions of about 8 mph. In this video it can be seen that there is a definite wind element but the airplane has minimal yaw response. Without enough vertical surface the airplane would yaw adversely to gusts. In terms of maneuvering this is also important, especially with the asymmetric design of the airplanes being used. The flap areas being different will generate a large yaw moment which will in turn result in yawing of the aircraft. As stated above, stalling with yaw can result in autorotation.
Here's Tail Cam 1. The camera is mounted on the tail. There is another camera, Fuse Cam. It did not die but it did spend the evening in the field. It didn't fly nearly as far as I thought it did and I had to review the footage frame by frame to figure out it's initial trajectory which was pretty much straight down when it released and landed in the grass. I subsequently made a much better mount out of ABS as the Command tape wouldn't hold to the balsa.
Here's the video, I have more:
Added for your amusement, the departure of the fuse cam: