as shown in Table 9.5, based on the wing reference area (interpolation is used for the between sizes).

Aerials

Navigational and communication systems require aerials that extend from an aircraft body, generating parasite drag on the order 0.06 to 0.1 ft2, depending on the size and number of aerials installed. For midsized transport aircraft, 0.075 ft2 is typically used. Therefore:

9.9 Notes on Excrescence Drag Resulting from Surface Imperfections

This section may be omitted because there is no coursework exercise involved. Semi-empirical relations discussed in Sections 9.8.4 and 9.8.5 are sufficient for the purpose. Excrescence drag due to surface imperfections is difficult to estimate; therefore, this section provides background on the nature of the difficulty encountered. Capturing all the excrescence effects over the full aircraft in CFD is yet to be accomplished with guaranteed accuracy.

A major difficulty arises in assessing the drag of small items attached to the aircraft surface, such as instruments (e.g., pitot and vanes), ducts (e.g., cooling), and necessary gaps to accommodate moving surfaces. In addition, there is the unavoidable discrete surface roughness from mismatches and imperfections – aerodynamic defects – resulting from limitations in the manufacturing processes. Together, all of these drags, from both manufacturing and nonmanufacturing origins, are collectively termed excrescence drag, which is parasitic in nature. Of particular interest is the excrescence drag resulting from the discrete roughness, within the manufacturing tolerance allocation, in compliance with the surface-smoothness requirements specified by aerodynamicists to minimize drag.

Mismatches at the assembly joints are seen as discrete roughness (i.e., aerodynamic defects) – for example, steps, gaps, fastener flushness, and contour deviation – placed normal, parallel, or at any angle to the free-stream air flow. These defects generate excrescence drag. In consultation with production engineers, aerodynamicists specify tolerances to minimize the excrescence drag – on the order of 1 to 3% of the CDpmin.

The “defects” are neither at the maximum limits throughout nor uniformly distributed. The excrescence dimension is on the order of less than 0.1 inch; for comparison, the physical dimension of a fuselage is nearly 5,000 to 10,000 times larger. It poses a special problem for estimating excrescence drag; that is, capturing the resulting complex problem in the boundary layer downstream of the mismatch.

The methodology involves first computing excrescence drag on a 2D flat surface without any pressure gradient. On a 3D curved surface with a pressure gradient, the excrescence drag is magnified. The location of a joint of a subassembly on the 3D body is important for determining the magnification factor that will be applied on the 2D flat-plate excrescence drag obtained by semi-empirical methods. The body is divided into two zones (see Figure 16.5): Zone 1 (the front side) is in an adverse pressure gradient, and Zone 2 is in a favorable pressure gradient. Excrescences in Zone 1 are more critical to magnification than in Zone 2. At a LRC flight speed (i.e., below Mcrit for civil aircraft), shocks are local, and subassembly joints should not be placed in this area (Zone 1).

Estimation of aircraft drag uses an average skin-friction coefficient CF (see Figure 9.19b), whereas excrescence-drag estimation uses the local skin-friction coefficient Cf (see Figure 9.19a), appropriate to the location of the mismatch. These fundamental differences in drag estimation methods make the estimation of aircraft drag and excrescence drag quite different.

After World War II, efforts continued for the next two decades – especially at the RAE by Gaudet, Winters, Johnson, Pallister, and Tillman et al. – using windtunnel tests to understand and estimate excrescence drag. Their experiments led to semi-empirical methods subsquently compiled by ESDU as the most authoritative information on the subject. Aircraft and excrescence drag estimation methods still remain state of the art, and efforts to understand the drag phenomena continue.

Surface imperfections inside the nacelle – that is, at the inlet diffuser surface and at the exhaust nozzle – could affect engine performance as loss of thrust. Care must be taken so that the “defects” do not perturb the engine flow field. The internal nacelle drag is accounted for as an engine-installation effect.

9.10 Minimum Parasite Drag

The aircraft CDpmin can now be obtained from faircraft. The minimum parasite drag

of the entire aircraft is CDpmin = (1/Sw ) fi, where fi is the sum of the total fs of the entire aircraft:

9.11 CDp Estimation

Equation 9.2 shows that CDp is not easy to estimate. CDp contains the liftdependent variation of parasite drags due to a change in the pressure distribution with changes in the angle of attack. Although it is a small percentage of the total aircraft drag (it varies from 0 to 10%, depending on the aircraft CL), it is the most difficult to estimate. There is no proper method available to estimate the CDp-versus- CL relationship; it is design-specific and depends on wing geometry (i.e., planform, sweep, taper ratio, aspect ratio, and wing–body incidence) and aerofoil characteristics (i.e., camber and t/c). The values are obtained through wind-tunnel tests and, currently, by CFD.

During cruise, the lift coefficient varies with changes in aircraft weight and/or flight speed. The design-lift coefficient, CLD, is around the mid-cruise weight of the

Figure 9.8. Typical CDp and CDw

LRC. Let CLP be the lift coefficient when CDp = 0. The wing should offer CLP at the three-fourths value of the designed CLD. This would permit an aircraft to operate at HSC (at Mcrit; i.e., at the lower CL) with almost zero CDp. Figure 9.8a shows a typical CDp-versus-CL variation. This graph can be used only for coursework in Sections 9.18 and 9.19.

For any other type of aircraft, a separate graph must be generated from windtunnel tests and/or CFD analysis. The industry has a large databank to generate such graphs during the conceptual design phase. In general, the semi-empirical method takes a tested wing (with sufficiently close geometrical similarity) CDp- versus-CL relationship and then corrects it for the differences in wing sweep (↓), aspect ratio (↓), t/c ratio (↑), camber, and any other specific geometrical differences (Figure 9.8a).

9.12 Subsonic Wave Drag

Wave drag is caused by compressibility effects of air as an aircraft approaches high subsonic speed because local shock (i.e., supervelocity) appears on a curved surface as aircraft speed increases. This is in a transonic-flow regime, in which a small part of the flow over the body is supersonic while the remainder is subsonic. In some cases, a shock interacting with the boundary layer can cause premature flow separation, thus increasing pressure drag. Initially, it is gradual and then shows a rapid rise as it approaches the speed of sound. The industry practice is to tolerate a twenty-count (i.e., CD = 0.002) increase due to compressibility at a speed identified as Mcrit (Figure 9.8b). At higher speeds, higher wave-drag penalties are incurred.

A typical wave drag (CDw ) graph is shown in Figure 9.8b, which can be used for coursework (civil aircraft) described in Section 9.19. Wave-drag characteristics are design-specific; each aircraft has its own CDw , which depends on wing geometry (i.e., planform shape, quarter-chord sweep, taper ratio, and aspect ratio) and aerofoil characteristics (i.e., camber and t/c). Wind-tunnel testing and CFD can predict wave drag accurately but must be verified by flight tests. The industry has a large