Worked-Out Example: Configuring the Empennage in Civil Aircraft
Continuing with the fuselage and wing design example carried out in the previous sections, this section presents a worked-out example of empennage design. The aircraft specification used so far to configure the fuselage and wing is sufficient for empennage design. Figure 6.10b provides empennage statistics of the current Bizjet aircraft class. The empennage area size depends on tail arm length, which is not compared in the graphs. A coursework example would have a slightly smaller tail area than shown in Figure 6.10b for having a relatively larger tail arm (the high sweep of the V-tail is added to the tail arm – shown is an example of a designer’s choice for weight reduction). It is the tail volume coefficients that decide the tail areas.
Figure 6.12. Civil aircraft example of empennage sizing
To maintain component commonality, the empennage is the same for all three variants. The baseline-designed empennage area is made sufficient for smaller aircraft; larger aircraft have a longer tail arm to enhance the empennage effectiveness. So far, the civil aircraft design exercise provided the following data:
• Estimated aircraft weight = 9,500 kg (at this stage, not required for empennage sizing)
• Wing reference area = 30 m2 (low-wing design is popular and therefore chosen)
• Wing MAC = 2.2 m (computed from Equation 3.21)
• Fuselage length = 50 ft (aircraft length is different – see Figure 6.3)
To minimize the fuselage length, a T-tail configuration is chosen. The V-tail design arrangement is determined first to accommodate the position of the T-tail on top. Figure 6.12 illustrates the tail-arm lengths used to compute empennage areas.
Section 12.5 provides statistics for the V-tail volume coefficient, Cvt, within the range 0.05 < Cvt < 0.12. In the example, Cvt = 0.07 is appropriate for the smaller aircraft variant. The V-tail quarter-chord sweepback is 15 deg in line with the wing sweep, to increase the tail arm LVT = 7.16 m (23.5 ft) measured from the aircraft CG to the V-tail MAC. In general, SVT/SW ^ 0.12 to 0.2. The symmetrical aerofoil section is the NACA64-010. The V-tail height (semispan) = 7 ft (2.14 m) and the taper ratio = 0.6 to bear the load of a T-tail.
Equation 3.31 gives the V-tail reference area SVT = (CVT)(SW x wing span)/LVT. The V-tail is positioned on the fuselage end in consultation with structural engineers. Then, SVT = (0.07 x 30 x 15)/7.16 = 4.4 m2 (47.34 ft2). This would result in sensible geometric details of the V-tail, as follows:
• Note: Area, Sv = 12 (Cr + Ct) x b or 4.4 = 0.5 x 1.6 Cr x 2.14
• Root Chord = 8.43 ft (2.57 m)
• Tip Chord = 5.05 ft (1.54 m)
• Aspect Ratio = 2.08
• MAC = (2 x [(8.43 + 5.05) – (8.43 x 5.05)/(8.43 + 5.05] = 6.8 ft (2.07 m)
• The V-tail area must be shared by the rudder and the fin. Typically, the rudder encompasses 15 to 20% of the V-tail area – in this case, it is 17%. This gives a rudder area of 0.75 m2 (8 ft2).
To check the Cvt for the smaller variant, it should be more than 0.06. With one seat pitch plug removed from the aft fuselage, LVT_shon = 7.16 – 0.813 = 6.347 m (20.823 ft). This gives CyT_short = (4.4 x 6.347)/(30 x 15) = 0.062 (sufficient for the shorter variant).
Section 12.5 provides the statistics of the H-tail volume coefficient, CHT, within the range 0.5 < CHT < 1.2. In this example, CHT = 0.7 is appropriate for the smaller aircraft variant. The H-tail is placed as a T-tail (dominant for smaller aircraft to increase the tail arm). The H-tail sweepback is 15 deg, in line with the wing sweep, and slightly more to increase the tail arm LVT = 7.62 m (25 ft) measured from the aircraft CG to the H-tail MAC. In general, SHT/SW ^ 0.2 to 0.25. The aerofoil section is the NACA64-210 and the installation is inverted. The H-tail span equals 16.7 ft (5.1 m) and the taper ratio equals 0.5. Equation 3.30 gives the H-tail reference area, Sht = (Cht)(Sw x MAC)/Lht.
The H-tail is positioned to give SHT = (0.7 x 30 x 2.132)/7.62 = 5.88 m2 (63.3 ft2), which is about 20% of the wing area. This area must be shared by the elevator and the stabilizer. Typically, the elevator uses 18 to 25% of the H-tail area; in this case, it is 20%, which results in an elevator area of 1.21 m2 (13 ft2).
This would result in sensible geometric details of the H-tail, as follows:
• Note: Area, SH = % (CR + CT) x b or 5.88 = 0.5 x 1.5 CR x 5.1
• Root Chord = 5.04 ft (1.54 m)
• Tip Chord = 2.52 ft (0.77 m)
• Aspect Ratio = 4.42
• MAC = (3) x [(5.04 + 2.52) – (5.04 x 2.52)/(5.04 + 2.52)] = 3.9 ft (1.19 m)
To check the CHT for the smaller variant, it should be more than 0.6. With one seat pitch plug removed from the aft fuselage, LHT_shoii = 7.62 – 0.813 = 6.807 m (22.33 ft). This gives CuT_shon = (6.063 x 6.807)/(30 x 2.2) = 0.625 (sufficient for the shorter variant).