On decrease/increase resolution: The further out on the servo horn you place the link ball the less resolution your controlled surface will have. On the other hand, the closer to the servo shaft you mount the link ball, the more resolution in control you will have for the controlled surface. Also, the closer in to the servo axle the more torque per increment of servo movement that will be brought to bear on that surface. With a shorter lever arm at the servo horn, the greater the force that can be transmitted to the linkage.
However, as Tony said, there is a trade off. With increased resolution comes less range of motion on the controlled surface. Having 2048 points of resolution is great, but if each point is only .003 degrees at the controlled surface (if you had the ball mounted very close to the servo axle, like 1mm) then you only get +/-3 degrees of movement of the surface. It is very precise within that range of movement, but not practical for a control surface on a plane or heli. Conversely, if you move the ball out further, say to 10mm, you still have 2048 points of resolution (this is determined by the capabilities of your servo, Rx/FBL, and Tx) but now each point is equal to .03 degrees of movement of the control surface, so now you have +/- 30 degrees of movement. Much more useful, although less precise (.01 degree is plenty for our purposes, though).
If you aren't bored to tears yet:
My numbers up there were off, but done that way for the sake of simplicity. Consider that a servo may have a sweep range of 240 degrees, over which that 2048 points of resolution are spread. So each point is equivalent to .117 degrees of movement at the axle. In a normal use case, though, you only use maybe a total of 140 degrees of that sweep and that has to translate into maybe 80 degrees of total control surface movement. 140/80 is a 1.75:1 mechanical advantage. Which means our .117 deg per point of resolution at the servo is becoming .067 degrees per point of resolution at the controlled surface. That mechanical advantage ratio is determined by the lengths of the ball from pivot point at the servo (ball to axle center) and at the tail control arm (actually two lengths there, ball to pivot center, and pivot center to slider interface point). If we assume the two lengths on the tail control arm are the same, and they equal 20mm, that means we want the ball to axle distance on the servo horn to be 20mm / 1.75, or 11.42mm. 11.42mm isn't a common hole position on a horn, so if we go to 10 or 11mm then we reduce the range of motion on the tail blades a bit, but gain a bit of precision. If we go out to 12 or 13 mm then we lose some precision but gain a little more range of motion.
One last trade off in all this: time to move a given control surface amount. In the case of a low resolution, large sweep of motion setup, it may take .1s to move the surface 40 degrees. In a high resolution, low sweep of motion setup, that same 40 degree move may take .2s, because the servo is having to move the axle a lot more to achieve the same controlled surface motion amount.
Hope you aren't in a coma. Good day!
