by

Stan Hall

Technical Advisor, Engineering, EAA Chapter 62

In design, sizing the tail is a very subjective process, one which involves often conflicting requirements of c.g. range, stability, control and desired aircraft handling properties. Small tails tend to limit the permissible c.g.travel and thus yield low static stability, but on the plus side, yield low stick (or pedal) forces and low drag. Conversely, low-stability airplanes are harder to fly on instruments than higher-stability aircraft. For single-seat airplanes, however, the pluses of small tails sometimes outweigh the minuses. This is, however, the exception, not the rule.

On the other hand, airplanes carrying large tails provide a wider permissible c.g. range and tend to be more stable and thus easier to fly on instruments - but are often heavier on the controls, (depending on where the c.g. is). Large tails also produce more drag.

How, then, does a designer decide how big to make the tail on his new project? Unless he is a good
mathematician and simply loves complicated arithmetic he will find what is known as the *Tail
Volume Coefficient* much simpler to use, yet very effective.

The Tail Volume Coefficient is denoted by the letter V and is determined by one equation for the horizontal tail and another, quite similar one, for the vertical tail. The Tail Volume Coefficients relate the area of the surface, the distance that area is from the aircraft's c.g., the wing area, the mean aerodynamic wing chord and the wing span. Aircraft having the same Volume Coefficients tend to have similar static stability characteristics. Knowing this eases the design process.

In equation form Horizontal Tail Volume Coefficient (V_{H}) looks like this.

For the Vertical Tail Volume Coefficient (V_{V}) the equation looks like this.

The table below excerpts some Tail Volume data lifted from L. Pazmany's excellent book, "Light
Airplane Design" (which I highly recommend). The table lists the dimensions of 3 of several well
known aircraft in Pazmany's book and their Volume Coefficients. Note the wide range of coefficients
among them. One can expect the low-V_{H} Piper J-3 to have a small permissible c.g travel and the
high- VH Navion to have a large one. In the J-3 the passenger sits essentially on the c.g and so,
little c.g. travel needs be designed in. The Navion, on the other hand, is a 4-seater, which involves
greater c.g. travel because it carries a wider range of loads, and they're spread out more in the
fore and aft direction. Go with the Tail Volume of the airplane you "like" and solve for the tail area
and/or distance to the c.g. that will yield that same Tail Volume Coefficient in your airplane.

Airplane | S_{W} | m.a.c. | S_{H} | S_{H} / S_{W} (%) | L_{H} | V_{H} | S_{V} | S_{V}/ S_{W}(%) | L_{V} | b | V_{V} |

Piper J-3 | 178.5 | 5.33 | 24.5 | 13.7 | 13.2 | .340 | 10.2 | 5.7 | 13.4 | 35.2 | .022 |

Luscombe Silvaire | 140.0 | 4. 17 | 21.7 | 15.5 | 11.8 | .442 | 10.6 | 7.6 | 11.9 | 35.0 | .026 |

Ryan Navion | 184.0 | 5.22 | 42.8 | 23.3 | 15.5 | .692 | 14.6 | 7.9 | 14.6 | 33.4 | .040 |

Once you've settled on a V_{H} or V_{V} you can solve for the other needed dimensions from:
For the horizontal tail: S_{H} = V_{H} x S_{W} x m.a.c. /L_{H}; L_{H} = V_{H} x S_{W} x m.a.c./S_{H}
For the vertical tail: S_{V} = V_{V} x S_{W} X b / L_{V}; L_{V} = V_{V} x S_{W} x b/ S_{V}

Shown below is a sketch of how to determine the mean aerodynamic chord (m.a.c.) and the position of the aerodynamic center (a.c.) by graphical means. While the results are approximate they are considered accurate enough for the purposes discussed here.

Let me close by reciting a couple of old engineering bromides. (1) It is easy to design a tail that is too small. It is difficult to design one that is too large. (2) Big tails are more user friendly than small ones. Hint: Tailheaviness can often be cured simply by the addition of horizontal tail area. Adding it by increasing the tail span is more effective than adding it elsewhere because the tail aspect ratio is then increased, making it more efficient.

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