Looking for a "KindaSorta" ballpark formula that works to Size a Stab and Fuse length for a Set of Wings I have laying around ....

Think I remember hearing Stab Area ~23% of Wing area, but I've never read about the length of the fuse behind the wing to the tail as a percentage of ?? wing area ??

From : Don Stackhouse

As several others have mentioned, the formula you're looking for is called "tail volume coefficient", and you can read about it in Martin Simon's book, or in John Roncz's articles in "Sport Aviation" in 1990, or any number of good aero engineering texts. You can also read about it in the "Design" section of the "Ask Joe and Don" department of our website:

http://www.bright.net/~djwerks/

For those of you who can't visit our website right now, I give you...

"Volume coefficients in a nutshell:"

Imagine that you were the world's most experienced airplane designer, with thousands of aircraft designs "under your belt". With your experienced eye, you could probably get the tail size and proportions pretty close just by eye, right?

Now imagine that you could take all the experience of all the airplane designers in the history of flight (including nature), and attach a number to each design that would roughly describe the effectiveness of its tail. With that tool, you would be able to take advantage of much of the experience of all of those designers! Just by reviewing what numbers corresponded in general to what kind of aircraft behavior, you could predict with reasonably good accuracy what sort of behavior to expect from a new design. A very powerful tool indeed!

This is exactly what tail volume coefficients are. We simply take all the major factors that improve stability and multiply them together, then divide by all the factors that tend to make stability worse. The result is called the "volume coefficient". It doesn't correspond to any real volume of course, it's just that if you figure out the units that result from the equation, they come out as cubic units, like a volume, hence the name "volume coefficient".

For the horizontal tail, more tail area and more moment arm make the plane more stable, so those go in the numerator. More wing area or more wing chord make the plane less stable, so those go in the denominator. The resulting formula is:

Vht = (hor. tail area/wing area) x (hor. tail moment/MAC of the wing)

MAC is the Mean Aerodynamic Chord of the wing (sort of an "aerodynamic average" chord), and for a typical single-tapered wing it's slightly inboard of the middle of the panel, at the point where the area inboard of there equals the area outboard of there. Tail moment is the distance parallel to the fuselage from the 25% point on the MAC of the wing to the 25% point on the MAC of the tail. BTW, vertical tail moment is measured by the same method.

The chord of the wing is what pivots about the pitch axis for pitch stability, which is why we use wing chord for the Vht ("Horizontal Tail Volume Coefficient") calculation. For the vertical tail, half the wingspan is what pivots about the yaw axis, so the volume coefficient formula for the fin and rudder is:

Vvt =(vert.tail area/wing area) x (vert.tail moment/semispan of the wing)

Now, just find some models that are generally similar (similar no. of engines, similar kind of construction, similar types of controls and flaps, etc. - the more similar your model to the ones you're comparing it to, the better this method works), and calculate their volume coefficients. You can even set up a spreadsheet on your computer and make yourself a whole list of different models to compare to. A brief look at the list plus a little knowledge of how those airplanes behaved should give you a fairly good idea of what sort of Vht and Vvt to use for your model.

The really nice thing about this method is that PROPERLY APPLIED (ah, yes, the "Achilles' heel" of all "rules of thumb"), it will work for a wide variety of aircraft types, not just sailplanes, or racers, or scale twins, or whatever.

When I design a tail I have a number of other factors I look at as well, including some other coefficients I've invented that relate to dynamic stability. I won't go into those details here (after all, I make my living as a model designer, and I can't afford to give away ALL my secrets!), but you can get some general guidance on some of these other factors by reading the articles in "Ask Joe and Don". In any case, a good choice of volume coefficients will usually get your tail size reasonably close.

Don Stackhouse
DJ Aerotech