Airplanes normally have a download on the horizontal tail. Many of the Old Timer free flight models have horizontal stabilizers with a wing-like airfoil section, intended to give an up load on the tail.

How is pitch stability maintained? Finally, would it be OK to substitute a flat airfoil for the curved one in the horizontal?

From : Don Stackhouse

Now, on to Bob's question about how an upward-lifting tail can be stable.

Stability depends not on which direction the wing and tail are lifting, but rather on how much the lift of each changes relative to each other when the angle of attack or airspeed of the aircraft changes. For example, let's assume we're flying in trimmed level flight, and something (a gust, perhaps) bumps the nose up. Both the wing and tail now see a higher (i.e.: more nose-up) angle of attack. If the upward lift of the wing increases proportionately less than the lift of the tail (regardless of whether the lift of the tail becomes more positive, or just less negative), then the tail will tend to come back up and the nose back down, returning the aircraft's pitch attitude back to where it was before the disturbance.

Note that it's not the absolute value of the lift of each flying surface that matters, but the way that lift changes relative to the other flying surfaces. There are many factors involved in this relationship, but the C/G location is probably the biggest one. As I alluded to before, for any airplane there is a particular C/G location called the "neutral point". If the C/G is ahead of this point, the airplane will be statically stable in pitch (i.e.: if it is disturbed in pitch, it will try to return to the original pitch attitude), and aft of this point it will be statically unstable (if disturbed, it will try to depart from the original pitch attitude even further. If the C/G is exactly at the neutral point, it will keep its pitch attitude wherever you point it.

The neutral point of the airplane is usually pretty close to its aerodynamic center. The aerodynamic center depends in turn on the locations of the aerodynamic centers of the individual flying surfaces and their relative areas.

What exactly constitutes a flying surface is subject to some interpretation; for example, if you were building a model of a "Super Guppy" (those enormously fat transports that are used for shipping ailrliner fuselages and rocket booster sections), the fuselage generates lift and other aerodynamic forces that are a significant percentage of the total aircraft's, and therefore the fuselage would have to be considered a "flying surface". The same is true for blimps. However, for most models the fuselage and most other components can be ignored, and the aircraft's aerodynamic center is essentially determined by the wing and the tail.

First find the Mean Aerodynamic Chord ("MAC") of the wing and of the tail by themselves. For a straight-tapered flying surface, the MAC is the chord at which the area outboard of that point is the same as the area inboard of that point.

Let's assume we have a model with a trapezoidal (straight-tapered) wing of 800 square inches, and a 200 sq. in. trapezoidal stabilizer. To find their individual MAC's, draw a line the length of their root chord forward from the leading edge of their tip chord, and a line equal to the length of their tip chord aft from the trailing edge at the root. Draw a diagonal line between the far ends of these two lines.

Now draw a line from the middle (the 50% point) of the root chord to the middle of the tip chord. The point where this line crosses the diagonal line is the spanwise location of the MAC for that trapezoid. Draw in the MAC, then measure its length and mark a point on it that is 25% of the way back along the MAC from its leading edge. This point is the Aerodynamic Center ("AC") of that trapezoid.

If your wing has a double taper (two trapezoidal sections), just find the AC of each trapezoid, draw a line between those AC's, and find the location along that line of the AC for the two panels together, based on the ratio of their areas. For example, if the area of one trapezoid is 300 square inches and the other is 100 square inches (that's 400 square inches for the two of them together), the AC for the pair of panels is 1/4 (that's 100/400) of the way along the line betwen the individual panel AC's, starta pair of combined panels will be closer to the AC of the larger of the two.

If you have something even weirder than a double taper, just break it down into a series of trapezoids that approximate its shape. Divide those up into pairs of trapezoids, find the AC of each pair, then take the pairs two at a time and find their combined AC's, then the AC's of pairs of the pairs, etc., until you have the AC location for the entire wing. BTW, you can also use this method to find the AC of a biplane, the other wing is simply another trapezoid or two, added to the combination.

Now that you've found the AC's of the wing and tail, you can use this same method again to find the AC of the entire aircraft. In the case of our example, there's 1000 square inches total in the combination of the wing and tail (800 + 200 square inches). The AC of the entire airplane will be 1/5 (that's 200/1000) of the way from the wing's AC to the tail's AC, starting at the wing's AC. Once again, the ratio to use is the area of one of the panels divided by the area of the total, and the AC of the combination will be closer to the larger of the two panels. Note, this method will work for ANYTHING, whether it's a monoplane, canard, biplane, triplane three-surface, or even a flying wing.

Right about now you're thinking "My brain hurts. So why did we bother going through all of this calculation?" OK, fair question. There can be some exceptions and extenuating factors (as always!), but in general, THE NEUTRAL POINT C/G LOCATION WILL BE AT, OR AT LEAST CLOSE TO, THE AERODYNAMIC CENTER OF THE AIRCRAFT THAT WE JUST CALCULATED. That's right, as long as your C/G is forward of the point we just (so laboriously) calculated, the airplane will be statically stable in pitch! And remember, this method works for almost ANY aircraft, regardless of layout.

The further ahead of the neutral point ("NP") you put the C/G, the more statically stable in pitch the airplane becomes. This distance, expressed as a percent of the wing's MAC, is called the "static margin". For example, if your plane had a wing MAC with a chord of 10", and a C/G that was 1.5" ahead of the neutral point, it would have a static margin of 15% (that's 1.5/10 x 100%). If you calculate the static margin for an airplane you like (preferably reasonably similar to the one you're designing) and make your new airplane's static margin equal to that, its static pitch stability should be reasonably similar to the first airplane's.

One limit on static margin is elevator authority. The more static margin, the harder the elevator has to work to lift the nose on rotation during takeoff, and to flare at touchdown on landing. If you have too much static margin and not enough elevator authority, you might not be able to rotate for takeoff, or you might stall the elevator during the landing flare (early Cessna Cardinals had this problem, which was fixed by adding slots to their stabilators). Tends to be VERY hard on nosewheels!

Note, there is also a neutral point for yaw, although if you have adequate pitch stability, the yaw stability is usually OK as well. The exception is usually flying wings and canards. These tend to have truly AWFUL moment arms for the vertical fins (if they have vertical fins at all!), and often have plenty of side area ahead of the C/G as well.

We recently ran into this problem on a standoff-scale profile canard pusher model we're working on for our Roadkill Series profile indoor models. When we set the static margin similar to a conventional-tailed model that flew OK, we couldn't get it to rotate for takeoff, the canard stalled before it could lift the nose. With the C/G moved aft enough to allow rotation, the yaw stability was unacceptable (moving the C/G aft also reduced the effective moment arm for the fins, degrading the yaw stability). By enlarging the canard and by adding camber to it, we moved the neutral point forward (which helped the yaw stability by increasing the moment arm for the fins) and also increased the elevator authority, allowing more static margin (which helped both the pitch and the yaw stability). The airplane now seems to be behaving itself, in both pitch and yaw.

Like I've said before, when you change one thing on an airplane, there are usually ripple effects throughout much of the rest of the design.

Don Stackhouse
DJ Aerotech