Perhaps someone can shed some light on this: I've got 2 v-tailed slopers that have radically different rudder effectiveness. I'm wondering what the various effects of v-tail size, shape, and the cg have on yaw authority...

From : Don Stackhouse

As you ask further down in your post, aspect ratio of the tail can be an issue, although it usually isn't the main one. Increasing the aspect ratio of a flying surface increases its "lift curve slope", or in engineering jargon the "dCl/d-alpha". For those of you with a phobia about Calculus, that simply means the amount that Cl, the lift coefficient, changes in response to small changes in "alpha", the angle of attack. For example. if we had two flying surfaces of different aspect ratios, both with the same area, and we changed their angle of attack by one degree each, the higher aspect ratio surface would have a bigger change in its lift than the lower aspect ratio surface. This is true regardless of whether it's a wing, a fin, a stabilizer, or the panel of a V-tail.

However, the biggest factors in the effectiveness of any tail, regardless of whether it's a V-tail or a conventional tail, are tail moment arm and tail area. In the case of V-tails there's a particular tendency for some designers to make the tail too small, because of an old myth call the "Projected Area Method". This idea proposes that if you have an airplane with a "correctly" sized conventional tail, then the equivalent V-tail will have the same projected area in the top view and the same projected area in the side view. This idea is dead wrong, and will result in a seriously undersized V-tail. This approach is probably the single biggest reason for all the unfair and unwarranted bad press heaped on V-tails. The planes don't have sluggish controls because of using V-tails, their controls are sluggish because the tail is simply just too small.

A properly sized V-tail should have the same TOTAL area as the equivalent conventional tail.

The other big factor is the tail's dihedral angle. This is analogous to the conventional tail's ratio of vertical surface area to horizontal surface area. If you increase the tail dihedral, it's just like making a conventional tail's fin+rudder bigger and its stab+elevator smaller.

That's the basics in a nutshell, but there are quite a few more in-depth articles on the subject of V-tails and tails in general in the "Ask Joe and Don" section of our website:

Don Stackhouse
DJ Aerotech