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Their airfoils are usually symmetrical, I'm wondering if t/c (thickness-to-chord ratio) is constant along the span, unlike wings where it is not constant.

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Is thickness-to-chord ratio constant along the span of horizontal and vertical stabilizers?

Generally, yes. The design of horizontal/vertical stabilisers is driven by maintaining control and stability in all circumstances, while main wing design has a major influence on operating costs (drag and weight).

For the main wings, the bending moment at the root is considerable. For aerodynamic reasons it makes sense to increase the aspect ratio as much as possible, creating a larger span for a given wing area. Increasing the wing thickness at the wing root creates a larger moment arm for counteracting the bending moment, allowing for lighter construction. Outside the wing root area, other considerations for flap/slat/aileron/stall behaviour may indeed induce a variable wing thickness after the design optimisation process.

In contrast, design of the stabiliser shapes is kept as simple as possible, to prevent unforeseen complications causing a fatal controllability issue. The major considerations in the design process are listed by Torenbeek section 9.5:

  • Stabiliser area, large enough for static and dynamic stability in all circumstances.
  • Aspect ratio, chosen such that the optimal lift-curve slope is used. Similar to main wing considerations, except sometimes in out-of-trim conditions.
  • Taper ratio. Moderate taper is usually chosen to save some structural weight.
  • Sweep angle. For high subsonic aeroplanes, the sweep angle and thickness ratio are chosen such that at design dive Mach number strong shock waves are not yet formed.
  • Airfoil shape. Must have a high $C_{Lmax}$ and large range of useful angles of attack, such as produced by symmetrical airfoils with thickness ratio between 9-12% and a large nose radius (NACA 0012).
  • Dihedral. To keep a large useable range outside the engine slipstream.

So design choices for the stabilisers are made such that the focus is on simplicity and functionality. A simple construction is less expensive, and less subject to manufacturing tolerances.

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