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Empennage airfoils are usually symmetric. What is the process behind choosing the airfoil used in the tail of the airplane? Is it related to the stability? And then how would the angle of attack of the tail be determined?

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Selection of the profile is only a small portion of the design procedure of the empennage:

  • Aerodynamic centre of the aircraft minus tail is determined first.
  • Aft Centre of Gravity is determined.
  • Static longitudinal stability criteria determine the area of the empennage - upon a disturbance in Angle of Attack, the total aircraft must generate a moment that counteracts the disturbance. Usually, wings and fuselage contribute negative stability, and the tailplane must be sized such that the stabilising moment compensates for this in all circumstances.
  • Once the area is determined, the aspect ratio, taper ratio, sweep angle and profile thickness are chosen considering a host of factors, including the lift-curve slope, stall behaviour, out-of-trim conditions, structural weight, design diving Mach number.
  • And then the airfoil shape is chosen. From Torenbeek section 5.5.1.d:

    The basic requirements are that the airfoil section should have a high $C_{L_\alpha}$ and a large range of usable angles of attack. Frequent use is made of approximately symmetrical airfoils with a thickness ratio of 9 to 12 percent and a large nose radius, e.g. NACA 0012. Tailplane stalling - at the lower surface - can be postponed by adopting negative camber (e.g. NACA 23012 upside down), upward nose droop, an increase in the nose radius or by means of a fixed slot.

Table 9-2 from the same book contains (dated) horizontal tailplane design data and lists some profiles used:

  • Cessna 177: NACA 0012/009
  • Fokker F27: NACA 63A-014 mod.
  • Lockheed C-130B: NACA 23012 inv.
  • Cessna Citation 500: NACA 0010/0008
  • B737/100: 12%/9%
  • Boeing 707/320: BAC-317
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To answer your three questions one by one:

What is the process behind choosing the airfoil used in the tail of the airplane?

Initially, some generic airfoil is chosen during development and the size is determined from the tail volume of comparable designs. Next, all load cases are determined and checked against the preliminary tail. Its size is adjusted until all requirements can be covered. Normally, the required lift coefficients are not spread out symmetrically, so the camber and incidence are adjusted such that drag in cruise is minimal. This in combination with the powerful flaps explains why most airliners have a negatively cambered tail. In a last step, the tail airfoil can be optimized such that the same tail load can be generated with a smaller tail surface. Or the designers stick with what they know.

Is it related to the stability?

Yes, but stability drives tail size, not the choice of airfoil. More stability means a more forward c.g. location and more variation in the load at the tail between slow and fast flight.

And then how would the angle of attack of the tail be determined?

This can be done by a simple potential flow analysis. This answer explains step by step which effects add up to determine tail angle of attack. And then some aircraft prefer to set the incidence of the tail in flight, so the angle of attack (more precisely, the combination of angle of attack and elevator angle) can be adjusted.

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