Empennage

Because it is the same procedure as for the wing, it is not repeated. The same percentage increment as for the wing is used for the coursework exercise. In the industry, engineers must compute systematically as shown for the wing.

V-tail:

wetted area, AwVT = 235.33 ft2

basic CF V−tail = 0.00277

fVT = 1.12 × 0.00277 × 235.33 = 0.73 ft2

H-tail:

wetted area, AwHT = 388.72 ft2

basic CF H−tail = 0.002705

fHT = 1.12 × 0.002705 × 388.72 = 1.18 ft2

9.19.4 Summary of Parasite Drag

The wing reference area Sw = 700 ft2, CDpmin = f/Sw . Table 9.20 summarizes the Vigilante parasite drag. As indicated in Section 9.16, [3] provides a correlated factor of 1.284 to include all the so-called other effects. Therefore, the final flat-plate equivalent drag is faircraft = 1.284 × 8.87 = 11.39 ft2, 28.4% = 11.62 ft2, to include military aircraft excrescence. This gives CDpmin at Mach 0.6 = 11.39/700 = 0.01627 ([3] uses 0.1645). This is the CDpmin at the flight Mach number before compressibility effects begin to appear; that is, it is seen as the CDpmin at incompressible flow. At higher speeds, there is a CF shift to a lower value. The CDpmin estimation must be repeated with a lower CF at Mach 0.9 and Mach 2.0. To avoid repetition in accounting for compressibility, a factor of 0.97 is used (i.e., a ratio of values at Mach 0.9 and Mach 0 in Figure 9.20b – a reduction of 3%) is taken at 0.9 Mach. A factor of 0.8 (i.e., a reduction of 20%) is taken at Mach 2.0, as shown in Table 9.16. At

Table 9.20. Vigilante parasite drag summary

the compressible flow, the wave drag is added. At supersonic speed, shock waves contribute to it.

To correlate with the methodology presented herein, the following values ofCDp were extracted from [3].

9.19.5 CDp Estimation

The data for CDp given in Table 9.21 were extracted from [3] and are approximate.

9.19.6 Induced Drag

The formula for induced drag used is:

CDi = CL2/(3.14 × 3.73) = CL2 /11.71 (Table 9.22)

9.19.7 Supersonic Drag Estimation

Supersonic flight would have a bow shock wave that is a form of compressibility drag, which is evaluated at zero CL. Drag increases with a change of the angle of attack. The difficulty arises in understanding the physics involved with an increase in the CL. Clearly, the increase – although lift-dependent – has little to do with viscosity unless the shock interacts with the boundary layer to increase pressure drag. Because the very purpose of design is to avoid such interaction up to a certain CL, this book addresses the compressibility drag at a supersonic speed composed of compressibility drag at a zero CL (i.e., CD shock) plus compressibility drag at a higher CL (i.e., CDw ).

To compute compressibility drag at a zero CL, the following empirical procedure is adopted from [3]. The compressibility drag of an object depends on its thickness parameter; for the fuselage, it is the fineness ratio and for the wing it is the t/c ratio. The fuselage (including the empennage) and wing compressibility drags are computed separately and then added in with the interference effects. Graphs are used extensively for the empirical methodology (Figures 9.19 through 9.26). Compressibility drag at both Mach 0.9 and Mach 2.0 is estimated.

Drag estimation at Mach 0.9 follows the same method as worked out in the civil aircraft example and is tabulated in Section 9.19.8. For the fuselage compressibility drag (including the empennage contribution) at Mach 2.0, the thickness parameter is the fuselage fineness ratio.

Table 9.22. Vigilante induced drag

Step 1: Plot the fuselage cross-section along the fuselage length as shown in Figure 9.17 and obtain the maximum cross-section Sπ = 45.25 ft2 and the fuselage base Sb = 12 ft2. Find the ratios (1 + Sb/Sπ ) = 1 + 12/45.25 = 1.27 and Sπ /Sw = 45.25/700 = 0.065.

Step 2: Obtain the fuselage fineness ratio l/d = 73.3/7.788 = 9.66 (d is minus the intake width). Obtain (l/d)2 = (9.66)2 = 93.3.

Step 3: Use Figure 9.21 to obtain CDπ (l/d)2 = 18.25 at M∞ = 2.0 for (1 + SD/Sπ ) = 1.27. This gives CDπ = 18.25/93.3 = 0.1956. Convert it to the fuselage contribution of compressibility drag expressed in terms of the wing reference area: CDw f = CDπ × (Sπ /Sw ) = 0.1956 × 0.065 = 0.01271.

For the wing compressibility drag at Mach 2.0, use the following steps:

Step 1: Obtain the design CL DES from Figure 9.22 for the supersonic aerofoil for the AR × (t/c)1/3 = 3.73 × (0.05)1/3 = 1.374. This gives CL DES = 0.352. Test data of CL DES from [3] gives 0.365, which is close enough and used here.

Step 2: Obtain from Figure 9.23 the two-dimensional design Mach number, MDES 2D = 0.784. Using Figure 9.24, obtain MAR = 0.038 for 1/AR =

0.268. Using Figure 9.24, obtain MD 1/ = 0.067 for 1/ = 37.5 deg.

4 4

Figure 9.17. Vigilante RA-C5 fuselage cross-section area distribution

CDw versus CL is to be taken from CFD/test data.

Figure 9.18. Vigilante RA-C5 drag polar

(a) Local skin friction

Finally, the interference drag at supersonic speed must be added to the fuselage and wing compressibility drag. Following is the procedure for estimating the wing– fuselage interference drag:

Step 1: Compute (fuselage diameter at maximum area/wing span) = 7.785/53.14 = 0.1465.