What is the formula for finding a angle for a vee tail?

I ahve seen a reference to it on your site, but can't find the acdtual formula.

From : Don Stackhouse

It's in several of the articles. However, some readers have a phobia about algebra, so I was always careful to write it out in words, not variables.

For most folks, the easiest approach is to first design a conventional tail, and then calculate the size and dihedral for an equivalent V-tail.

Design of a conventional tail is a subjective thing, and depends on the entire design specification for the airplane and on the details of the rest of the aircraft. Entire books could be written about this subject.

For example, the size of the fin on a twin-engined aircraft is often about three times bigger than a single-engine airplane would need, because of the requirement for enough rudder authority to counteract the yaw moment from an engine-out situation. Likewise, the horizontal tail area required for a model with flaps is often much greater than for one without flaps, because of the extra aerodynamic pitching moment the flaps cause and the extra elevator authority needed to counteract it. An airplane with a lot of mass in the extremities will need more horizontal and vertical tail area (or better yet, a longer tail moment arm) to get adequate dynamic stability (the ability to damp out oscillations after being disturbed by gusts, etc.).

The starting point for tail size is usually with something called tail volume coefficients. This is nothing more than a very crude way of measuring a given design's combination of tail authority and the major de-stabilizing forces its tail has to overcome. It gives you a number that represents the tail characteristics of your design, which you can then compare to other similar designs to see if your proposed tail size is in the ballpark. It's like distilling the collective experience of all the world's airplane designers throughout all of aviation history down to a simple list of numbers that you can then use to guide your own designs. Check the "Design" section of "Ask Joe and Don" on our website for articles on static and dynamic stability and on the use of tail volume coefficients.

Once you've arrived at a suitable conventional tail design, the next step is to calculate an equivalent V-tail design.

For the required tail area there is no controversy. Assuming there aren't some other major complications, such as substantial amounts of interference between panels, significant differences in Reynolds numbers, etc., the equivalent V-tail, T-tail, or conventional tail should all have the same TOTAL area.

There is also a theory out there that says that the equivalent V-tail should have the same area in the top view as the stabilizer+elevator of the supposedly equivalent conventional tail, and the same area in the side view as the fin+rudder of the conventional tail. Not surprisingly it's called the "projected area method", and I notice that someone else just posted to this thread today recommending this method (I won't mention any names, I'm not trying to embarrass anyone, just enlighten). It's also DEAD WRONG. If you design a V-tail by the projected area method, it WILL be too small, unless the conventional tail you're basing it on was way too big to begin with.

This theory just refuses to die, much like the debate about downwind turns. I've even seen it in college level aeronautical textbooks written by people who should have known better. The problem with the projected area method is that it can provide the same yaw authority, or the same pitch authority, but NOT BOTH AT THE SAME TIME. This can be an especially big problem in certain maneuvers, such as when trying to recover from a spin. Not a good time to discover that the designer used an erroneous theory in designing the tail!

As for tail dihedral, there are two schools of thought on V-tails that have good track records, the "constant stability" method and the "constant control authority" method.

The "constant stability" method says that for a conventional tail with (stab+elevator) area Ah and (fin+rudder) area Av, the tail dihedral (measured from horizontal on each side, just like you'd measure wing dihedral) should be equal to arctan((Av/Ah)^2).

The "constant control authority" method is a bit simpler; it says that for a conventional tail with (stab+elevator) area Ah and (fin+rudder) area Av, the tail dihedral should be equal to arctan((Av/Ah).

Note that in the first method the ratio of the vertical and horizontal tail areas is squared, but in the second method the ratio is linear. Mark Drela and I have had some enthusiastic debates about the relative merits of the two methods. Both methods yield acceptable results, although in my experience the "constant control authority" method seems to consistently work better for me. Either

is likely to get you close enough for a first try, and tail design is complex enough that you'd better expect to need some fine-tuning in flight tests regardless of which method you use.

Don Stackhouse
DJ Aerotech