What is the relative efficiency of a V-tail compared to various conventional tails?

...I'm curious about the relative efficiency of a V-tail compared to the various conventional tails. A high-mounted horizontal stabiliser (eg on a T-tail) can be smaller (in area) than that of a low mounted one because it is out of the wake of the wing. A V-tail is partly in, partly out of the wing wake and I would have thought that some adjustment to its area would be required to take this into account. In other words, a straight area-for-area conversion would result in a V-tail that was slightly oversize (undersize) compared to a low-mounted conventional tail (T-tail). I guess some adjustment should also to be made because the equivalent of the fin/rudder is less efficient now that it is partly in the wing wake!

From : Don Stackhouse

Richard, first of all I have to point out that unless the differences are very large, it's EXTREMELY difficult to see any significant differences between different tail design concepts. The problem is that tail sizing is largely subjective. Small changes in tail size generally don't make very noticeable changes in aircraft behavior in most cases. Since it's nearly impossible to quantitatively measure with enough precision to determine if two different tail concepts are exactly "equal" in their effectiveness, and because there are a variety of ways and methods on which to base the analysis, it's also nearly impossible to tell with any precision whether a T-tail of a slightly different size is more or less effective than a given size conventional tail. Virtually any analysis we attempt will come down to uncertain conclusions at best of what inevitably turns out to be an "apples and oranges" comparison.

With that caveat I will attempt to toss a few apples and oranges of my own at the problem.

This theory about the effects of the wing wake on tail size is widespread "common knowledge", but I think we would be very hard pressed indeed to find a successful significant application of it in actual practice, even in smaller full-scale airplanes. Yes, T-tails work, but the possible reduction in area due to this "wing wake" factor is ridiculously small if it even exists at all, at least in the world of model aviation.

The theory is based on the idea that the wake is directly behind the wing, that it is significantly strong in terms of its reduction in airspeed below the "freestream" velocity, and that it is fairly well defined in the vertical sense. If any of these assumptions are invalid for the case in question, then the idea of a reduced tail size for equivalent tail effectiveness is less valid.

There are several things happening in the wake. First of all is the downwash. The wing makes lift by accelerating air downward. It's Newton's law about action and reaction, if you shove air downward, the air shoves you up. The air coming off the back of the wing is going downhill at a small "downwash angle", whose magnitude is related to the induced drag of the wing. The more downhill the downwash is angled, the more induced drag there is. This field extends quite some distance above and below the wing, so that just about any sort of tail will be immersed in this flowfield, although it is most intense in the center of this wake.

If you increase the angle of attack of the wing (assuming it doesn't stall), you increase the lift, and therefore the downwash. This tends to push the tail down, which is a de-stabilizing effect. In normal situations this change in the angle of the downwash is less than the angle of attack change of the wing and tail, so overall you still get a change in the lift of the tail that tries to bring the wing's angle of attack back to its original position, despite the effects of the downwash.

At first it would seem that the T-tail might have an advantage here, since it is supposedly above the center of this wake, and therefore in a less severe area of downwash. In actual practice it doesn't exactly work out this way. Remember how the angle of attack changes more than the downwash angle? This means that if you start out with the tail near the center of this wake (like a conventional tail), the change in the angle of attack will lower the tail to an area below the center of the wake (a less severe area of downwash), which will help change the force on the tail to bring the aircraft back to the trimmed position.

In the case of a V-tail, there is part of the tail immersed in the strongest part of the downwash most of the time, and although the particular region of the tail involved may change, the total percentage of the tail area involved stays about the same.

In the case of a T-tail however, the tail starts out in a less severe downwash zone and moves closer to the center of the wake, into a more severe downwash zone. This increases the de-stabilizing effects on the T-tail. In extreme cases such as deep stalls, this can result in an un-recoverable conditions. There are a number of cases on record of T-tails that refused to recover from this situation. I know of specific cases of aircraft and test pilots that were lost during deep-stall tests of certain T-tailed airliners and business jets this way, among others.

The wing also has a boundary layer. This is a layer of air at the surface of the wing where the air is transitioning from the speed of the skin to the speed of the freestream. Skin friction drags this layer along with the wing, so that the velocity of the air in this thin layer after it slides off the trailing edge of the wing is less than the surrounding air in the downwash field. The fuselage also has a boundary layer, typically a bit thicker than the wing's because of its longer length. If a tail is immersed in this layer of "sluggish" boundary layer air, its ability to make lift will be reduced. This would seem to be the real case in favor of a T-tail; to get the stabilizer out of this old, stale layer of leftover boundary layer air behind the wing.

So just how thick is this boundary layer? Well, it depends on the relative size of the aircraft (in other words, Reynolds number). You can see about how thick this is from observing certain features on various aircraft. Air inlets are a good example. Ever notice how big the gap is between the bottom of the nacelle for the tail mounted engine on a DC-10 (or MD-11) and the top of the fuselage? That gap is there to keep the inlet clear of the fuselage's boundary layer. The gap is several feet across, so the boundary layer thickness is a bit less than that.

Now consider the P-51 Mustang's belly scoop for the radiator. It also has a gap to keep the inlet out of the boundary layer under the wing (the original prototype didn't have this gap, and had cooling problems because it was feeding the radiator with stagnant boundary layer air). It's a much smaller and slower airplane than the DC-10, and sure enough, the gap (and the boundary layer) is smaller, about 2.5 inches.

On a model it's even thinner. To get an idea, check "Soartech 8", Michael Selig's doctoral thesis on low Reynolds number airfoils. One of the techniques he uses to improve low Reynolds number performance is called a bubble ramp. This is an area on the airfoil where the surface is relieved slightly to allow room for the "laminar separation bubble" where the boundary layer is momentarily separating and re-attaching during its transition from laminar to turbulent flow. By relieving the surface by the thickness of this bubble, the shape the air outside the boundary layer sees is much smoother. The key here is that the amount of change in the shape of the surface is incredibly small, typically a tiny fraction of an inch. That's about how thick the boundary layer is on a model in most cases. In addition, after it leaves the trailing edge of the wing, friction with the surrounding airflow quickly brings its speed back up to nearly that of the rest of the flow. By the time it reaches the stabilizer you will have difficulty measuring it.

On a big airliner you might have a sluggish wake of boundary layer air big enough to swallow a stabilizer, but that's highly unlikely to be a significant factor on a model. The T-tail doesn't have a significant advantage in this case because that sort of wake simply doesn't exist on a well designed model. If you have a model with a very thick wing (generally very bad for efficiency at our Reynolds numbers), and if you have a very short tail moment (very bad for dynamic stability), you might see some differences from trying to get the tail clear of the boundary layer wake of the wing. Please note however, that the reason you MIGHT see a small improvement in this case is only because the basic design of the aircraft is lousy to begin with!

One final nail in the coffin of the "smaller T-tail stabilizer" theory is the effects of Reynolds number and span on the stabilizer itself. In the case of both the T-tail and the conventional tail the total tail area is already divided into separate vertical and horizontal segments. For a given area, this reduces either their span or their chord (and Reynolds number) or both. This significantly reduces their effectiveness. If you then try to reduce the size of the T-tail's stabilizer even further, these effects become even worse. For smaller models like R/C hand-launched sailplanes, the tail can be very sensitive to this effect. The V-tail concentrates its area into only two surfaces instead of three, which significantly improves their span and/or Reynolds number.

On powered aircraft there is one sort of "wake" that a high-mounted or T-tail style stabilizer does get reasonably clear of (at least most of the time), the slipstream of the propeller. This does tend to reduce the amount of elevator trim change due to power setting changes, but it can also reduce elevator effectiveness in certain flight modes, especially rotation on takeoff. As a result, T-tailed aircraft often require longer takeoffs. It's quite common for a T-tailed aircraft to need a substantially higher liftoff speed (and therefore much more runway) than normal in order to get enough air blowing across its high-mounted elevator to get the nosewheel off the ground. This also tends to cause quirky handling during rotation, because as the nose finally starts to come up and the tail starts to come down, the slipstream is held pretty much horizontal by the ground. As the stabilizer descends into the slipstream there is a sudden increase in elevator effectiveness, which tends to cause over-rotation.

Regarding structural issues, a T-tail has a lot of weight, in the form of its entire stabilizer and attachment structure, mounted on the end of a long lever, the vertical fin. This also means additional weight in the fin and tail boom to provide sufficient stiffness and strength, particularly in the torsional sense. This means that the aircraft now has a lot of extra weight in the farthest extremities of the aircraft. Not only does this create problems with getting the C/G correct, it also adds substantially to the rotational inertia of the model in the pitch and yaw axes, which hurts stability for both. It also degrades roll response if rudder is used to provide roll control, like on a typical 2-channel polyhedral sailplane. Of course to counteract this we have to make the fin and stabilizer bigger (and even heavier!). So much for the myth of the T-tail's smaller stabilizer.

In actual practice, what I've discussed above are usually not major factors for most models, but I haven't seen any convincing evidence that a T-tail or high-mounted stabilizer can be significantly smaller.

The V-tail does better in the structural issues. It does about as good a job as the T-tail of keeping the tail clear of rocks and grass clumps, so both of them don't have to deal with the high bending loads the conventional tail sees when the stabilizer snags on something during landing. Stabilizers mounted part way up the fin are also good in this regard, which is one of the reasons they are fairly common on model sailplanes. The structural weight of the V-tail is lower (in the vertical sense), and also typically lighter and simpler than the T-tail's, so it doesn't see the high torsional loads that a T-tail can impose on the tailboom during a groundloop. As a result, a well designed V-tail is typically the lightest of the three major possibilities. It usually does generate higher torsional loads on the tailboom during rudder deflections than conventional or T-tails, but this is usually less important than the typically much larger loads on the tailboom from landing forces.

There are other factors that play against the V-tail in some situations, so overall the net effect is that none of the three main types of tail show a clear aerodynamic advantage over the others. The same total area seems to consistently work well for all three in most applications. In general I prefer the V-tail because although it is usually not measurably better or worse in the aerodynamic issues, it usually comes out noticeably better in the structural considerations.

I'm currently working on a new tail concept (not a T, V or conventional) that should improve on the shortcomings of all three different tail types while keeping their benefits, but I'll have to wait till we finish flight testing it to see if it works out that way in practice. No, I won't tell you what it looks like, you'll just have to wait till we get it done.

While we're still on the subject, with all these disadvantages, why do they use T-tails on full scale aircraft? In some cases it's mostly for looks, like when Piper switched to T-tails for some of their products a while back. Please note that they have since switched those same aircraft back to conventional tails! In other cases, it's typically for logistical reasons, such as making room for tail-mounted engines, or to keep the stabilizer up out of the way of baggage carts and other vehicles.

Also how do you decide on the size of the movable surfaces?

Simple eye-balling of 3-views in any of the magazines shows that rudders frequently approach 50% (some are clearly more) of the total area of the vertical stabiliser whereas the elevator is far less. Simply adding together the rudder and elevator areas to get a total area for the control surfaces seems an unlikely answer (wouldn't work with an AMT). Just use the equivalent of the rudder area on each side of the V?

There's some data in "Theory of Wing Sections" which is often used. It looks primarily at hinge moments (the determining factor in the control forces the pilot feels) vs. control effectiveness. For ailerons it comes to the conclusion that the point of diminishing returns is at about 20-25% of chord. With tail surfaces larger percentages are more typical, somewhere around 30-50%. While this data is often used by model designers, I personally find it to be of limited usefulness without some modifications. First of all, the data in the book is looking at a manned aircraft situation, and assuming human pilot actuated controls. Models don't have this constraint. Our modern servos have enough torque that usually the control forces aren't a significant problem for them, at least for smaller models. Wider surfaces do have more potential problems with flutter, etc., but those issues are usually manageable as well. The other problem with the "Theory of Wing Sections" data is that it's for full scale aircraft at much higher Reynolds numbers than what we see in models. This is another case where it's not enough to know what their conclusions were, you must also understand WHY they reached those conclusions, and also what assumptions were inherent in the analysis. The conclusions may not be valid for your situation.

I personally prefer a different approach, I look at it as an issue of airfoil design. The key question is, assuming structural issues can be adequately addressed, where is the best place on the airfoil to add an abrupt change in camber in order to get the most change in lift with the least increase in drag? In most cases at very low Reynolds numbers the best place is closer to the high point of the airfoil, although other issues (such as structure) may dictate a somewhat further aft location. On larger models the airfoil characteristics (such as the location of a laminar-to-turbulent boundary layer transition) and servo loads may indicate that a more aft location is best. It really needs to be on a case-by-case basis.

Somewhere some time ago I read that a V-tail adds to the effective dihedral. Is this right, as I would have thought the opposite was generally true given that tailplanes typically "lift" downwards. Or is the yaw-induced change in the angle of attack, as seen by the V-tail, an effective decrease rather than the increase as seen by the wing?

The direction the tail is lifting doesn't matter here. What matters is the change in the amount of lift on each side. In this sense a V-tail does tend to add a dihedral effect, helping to roll the aircraft away from the direction of a sideslip as it simultaneously tries to yaw it towards the sideslip.

Pitch and yaw controls appear "backwards" from the point of view of an R/C pilot on the ground when the model is inverted. Roll does not show this reversal. Picture yourself standing behind your model as it flies away from you. Add some right aileron. The model starts to roll clockwise in your field of view.

Now picture the model trimmed in level inverted flight, still flying away from you. Now add that same amount of right stick. The model still rolls clockwise in your field of view, even though the wing lift is now "downwards" relative to the model's point of view. This is still true even if you're using rudder and yaw to create the roll command.

The only time roll shows a reversal is if the airplane is flying backwards!

This same phenomenon is acting on the V-tail in a sideslip, regardless of whether the tail is lifting up or down.

Now the catch: this doesn't really "add" much to the effective dihedral of the model compared to a conventional or T-tail, because they both have a "dihedral" effect too! The sideward force generated by the fin in a sideslip is above the roll axis in most normal tail designs, so it also tends to roll the aircraft away from a sideslip.

Just like normal dihedral on a wing, all of these effects are destabilizing with respect to roll in inverted flight.

You would have an opposite ("anhedral") effect from an under-slung tail, or from an inverted V-tail. A fin centered on the roll axis in the vertical sense would not have a dihedral effect.

None of these effects are significant for most aircraft. The tail is typically so small in span compared to the wing that its contributions to roll are negligible. If the span of the tail was large compared to the wing, you might start to see some of these effects.

One other comment sometimes made against the upright V-tail (usually by proponents of inverted V-tails) is that a rudder input also causes a rolling moment away from the intended roll direction; i.e.: right ruddder also acts like a small left aileron input in the tail. Once again, unless you have an extremely large span tail, this effect is negligible. Also, just like the dihedral effect discussed above, this effect also occurs on conventional and T-tails, although usually to a somewhat lesser extent. The extra weight incurred by an inverted V-tail to allow it to survive being dragged through the grass, plus its destabilizing effects regarding dihedral generally destroy any advantages it might have in this roll control issue.

As I said at the beginning, although there are differences in enough areas to make a direct comparison between the different tail types virtually impossible, aerodynamically any differences amount to little more than "splitting hairs". The final selection of tail configuration ultimately comes down to one of structural and logistical considerations in most cases.

Don Stackhouse @ DJ Aerotech
djarotec@bright.net