It is also interesting that Don Stackhouse says you need a bigger V-tail than projected area would indicate. I don't see why there is an advantage then as the total wetted area can't be much different.

No wonder the Germans mostly (2 out of 3) changed from V to horizontal tails on the Berlin Arianes.

From : Don Stackhouse

The advantages to a V-tail are for the most part more structural than aerodynamic. The whetted area is essentially the same, but they have less interference drag than a conventional tail (fewer corners, and usually wider angles in those corners).

In addition, dividing up the same total area into only two surfaces instead of three means that their span loading and/or Reynolds numbers will be better. This becomes increasingly significant the smaller you get, so it can be a very important factor for models. This is part of the reason why V-tails are more common on models than on full-scale aircraft. They also have some of the same aerodynamic benefits as T-tails, but without the T-tails' deep stall problems and horrendous structural penalties.

OTOH, there is some destructive interference between the panels of a V-tail for yaw stabilization and rudder authority, which is a disadvantage in full-scale. However, in my experience, the effects of the improved span loading and Reynolds numbers usually more than make up for this in most model aircraft applications.

Structurally, a V-tail keeps most of the structural weight low, close to the axis of the tail boom, like a conventional tail. This keeps the torsional loads on the tailboom small during groundloops and other landing mishaps (the Achilles' heel of the T-tail). It also minimizes bending loads on the tail boom due to decelleration forces, such as during the "lawn-dart" landings common in the spot landing tasks of thermal duration sailplane competitions.

Like the T-tail, the V-tail keeps the tail surfaces clear of the grass and other obstacles during landing. By comparison, the conventional tail tends to snag just about anything within the span of the stabilizer, which imposes HUGE bending moments on the tail boom. On lighter models, a V-tail also tends to lift up during a ground loop, keeping the tail clear of the ground entirely (a benefit that does not generally exist for the conventional or T-tail). It does tend to impose greater torsional loads on the tailboom than conventional or T-tails during a rudder input. This is a disadvantage for full-scale applications. However, for models, the determining factor for the tail boom strength is usually the landing loads (face it, we just don't land our models as gently as full scale!), and here (as I explained above) the V-tail has the advantage.

A cruciform (i.e.: stabilizer mounted part way up the fin) tail does help keep the stabilizer out of the grass, but it adds some more structural complexity, and it also has FOUR 90-degree corners making interference drag.

Don, it is a 110 degree V-tail. How much can I reduce the projected area if I go to a horizontal tail?

For a crude, but surprisingly accurate "rule of thumb", for essentially the same stability and control authority, a T, V or conventional tail should all have the same TOTAL area.

The V-tail angle determines how much of the tail's effectiveness is allocated to yaw stability vs. pitch stability. If you have a successful conventional tail and you want to convert it to a V-tail, add the (stab+elevator) and (fin+rudder) areas together, then divide by two. This is the area for each of your V-tail panels. Now divide the fin+rudder area by the stab+elevator area. This is the tangent of your V-tail's dihedral angle. Find the arctangent, and that's the dihedral, measured on each side from horizontal. Multiply by 2, then subtract the result from 180, and you get the angle between the panels of your V-tail.

Now let's work the same problem in the other direction, like in your situation. If you have a 110 degree V-tail that is working satisfactorally, then a conventional tail of the same total area should give you very similar results. The only question left is how to divide that area between the fin and stab. Since the effective fin area of your V-tail is equal to the effective stab area times the tangent of the dihedral angle, then the stab area you need is the total area divided by (1+ the tangent of the dihedral angle). The required fin area will then be the stab area times the tangent of the dihedral angle.

For example, let's say your present 110 degree included-angle V-tail has an area of 100 square inches. We first subtract 110 from 180, divide by two, and find that the dihedral angle of this tail measured from horizontal is 35 degrees. The tangent of 35 degrees is .700208 . Now we divide our 100 square inches by (1+.700208) and find that we need a stab area of 58.816 square inches. Multiply that by .700208 and we get our fin area of 41.184 square inches.

Just as a cross-check, let's now see if we can convert our conventional tail back into a V-tail. 41.184 plus 58.816 equals 100 square inches. OK so far. 41.184 divided by 58.816 is .700218 (note the round-off errors), and taking the arctangent we get a dihedral angle of 35.0004 degrees. Two times that, subtracted from 180 degrees gives us an included angle of 109.999 degrees. Sounds pretty close to me! Isn't trigonometry wonderful?

The one I saw was not a T-tail , just a regular slab on the bottom and vertical on top, and elevator control only. What Llyod did is projected the V-tail to a vertical and horizontal components. i.e. whatever of the vertical shadow of the V's is the size of the stabilizer and the side profile of the V's is the fin area.

This is the infamous "projected area method". From Brian's description, it sounds like Lloyd was using it in reverse (so he ended up with a conventional tail with more effect than the original V-tail), but the results are the same. This method's failure can be explained from a variety of approaches. From a stability standpoint, the effectiveness in pitch of a V-tail is proportional to the cosine squared of the dihedral angle, because the projected area is proportional to the cosine, but the angle of attack change it sees for a given pitch disturbance is ALSO proportional to the cosine of the tail's dihedral angle. Cosine times cosine is cosine squared, which (because cosine is always a fraction) is less than cosine alone. The projected area method gives you a stab equal to the cosine of the conventional tail area, but an effectiveness that is less than that.

Another way to look at it is from a control authority standpoint. This is the principle that the total area method I explained above is based on. A V-tail replaces both the fin/rudder function and the stab/elevator function. To do this it must be able to generate the same control forces about both the yaw axis and the pitch axis SIMULTANEOUSLY. (If you're not sure about this one, just try to recover from a fully developed spin with a V-tail designed by the projected area method!) The downfall of the projected area method is that it can generate the same pitch force, or the same yaw force, but NOT both at the same time! If you go through the numbers, you will find that to generate the same forces as the conventional tail about both control axes simultaneously, you have to have the same TOTAL area.

Just as I explained, and just as Brian reported from observation of such a tail design in actual flight tests, the projected area method results in a V-tail model with LESS stability than the conventional tail we are comparing it with. I rest my case.

ALAN RESPONDS with a VBG (Very Big Grin) " I rest my case. "

No NO !!!! that's Law school.....shouldn't this be ended with Q.E.D. ???

I thought about "Q.E.D.", it is more appropriate in this case, but I wasn't sure if all of the readers would be familiar with that expression. Since the subject has now been brought up, for those of you not familiar with it already, "Q.E.D." is a standard term in mathematics. It stands for the Latin "quod erat demonstrandum", which in English means that you have proven what you set out to prove. It's a customary "End" statement on geometrical proofs.

Only thing left...is the control authority side of the equation. Given that stable authority has been achieved, how can the area/shape/size of the moveable components with respect to the non-moveable ones be maximized so as to minimize forces on the control surface, yet not loosing any effectiveness.

.....and for that matter how do you size the "V"-avators with respect to the total area ?

Ruddervators are generally sized the same way you would size any other control surface. The key issue is where on the surface you can best put a kink in the camber line to get the biggest increase in Clmax (the maximum lift coefficient) and lift in general, for the least increase in drag. You also have to consider the stall characteristics involved; an abrupt stall of the tail can make things rather interesting in a hurry, to say the least!

It's different at different Reynolds numbers ("Re"). For full scale, the hinge is generally located in an area of turbulent flow, which means that the boundary layer is getting fresh infusions of energy, making it easy to negotiate a bump and still stay attached. In this case, it's generally a good idea to keep the hinge fairly well aft, where it will mess up the flow over as little of the airfoil as possible. Lots of aft camber (which is what you get from a well-aft hinge location) works fairly well at higher Re's. Also, on larger models and especially on full scale, a narrow chord control surface may be necessary to keep the forces required to move the control surfaces down to a reasonable level.

At very low Re, the boundary layer is laminar, which means that the only kinetic energy it has is what it started with, minus the energy it is constantly losing through skin friction. You'd better keep all discontinuities, bumps, etc., well forward on a low Re airfoil, at a point where the boundary layer airflow still has enough energy left to negotiate the bump and get itself composed again. If you put the hinge too far aft, the airflow doesn't have enough energy left to survive the bump, and so it simply separates at a very low amount of control surface deflection. A wider control surface in this case will allow you to get more camber change for a smaller angular deflection, and also keep the hinge line at a point where the airflow can better tolerate it. The result is more lift and less drag, which gives you a more effective and efficient control surface.

There are some guidelines for control surface hinge locations in Abbott & von Doenhoff's "Theory of Wing Sections". Unfortunately it is aimed entirely at full scale applications, so it doesn't work all that well for smaller, slower models. Altogether, this entire subject is a bit of a "black art", and if you don't have some really good airfoil analysis capabilities and the experience to interpret it (which is even more important than the quality of the analysis itself), you're pretty much out of luck.

Fortunately, the old "TLAR" (That Looks About Right") methods don't do too badly for most applications, at least for tail surfaces. Ailerons and especially flaps are another matter, but even there the TLAR method will usually be good enough for sport models. If you plan to design world-beater contest models, you need to do better than that, but that's what makes them world beaters. If anybody could easily draw a world-class design entirely by eyeball on the back of a napkin, with no analysis and no engineering training, then the entire business of designing better airplanes wouldn't be very fun or challenging at all!

Fun and success come to those who do their homework.

Don Stackhouse
DJ Aerotech