9.7 Minimum Parasite Drag Estimation Methodology

Unfortunately, the complex 3D geometry of an entire aircraft in Equation 9.6 is not amenable to easy integration. CFD has discretized the flow field into small domains that are numerically integrated, resulting in some errors. Mathematicians have successfully managed the error level with sophisticated algorithms (see Chapter 14 for a discussion of CFD). The proven industrial-standard, semi-empirical methods are currently the prevailing practice and are backed up by theories and validated by flight tests. CFD assists in the search for improved aerodynamics.

9.6 Aircraft Drag Estimation Methodology (Subsonic)

The semi-empirical formulation of aircraft drag estimation used in this book is a credible method based on [1], [3], and [7]. It follows the findings from NACA/NASA, RAE, and other research-establishment documents. This chapter provides an outline of the method used. It is clear from Equation 9.2 that the following four components of aircraft drag are to be estimated:

1. Minimum parasite drag, CDpmin (see Section 9.7).

Parasite drag is composed of skin friction and pressure differences due to viscous effects that are dependent on the Re. To estimate the minimum parasite drag, CDpmin, the first task is to establish geometric parameters such as the characteristic lengths and wetted areas and the Res of the discrete aircraft components.

2. Incremental parasite drag, CDp (see Section 9.10).

CDp is characteristic of a particular aircraft design and includes the lift-dependent parasite drag variation, 3D effects, interference effects, and other spurious effects not easily accounted for. There is no theory to estimate CDp; it is best obtained from wind-tunnel tests or the CDp of similarly designed aircraft wings and bodies. CFD results are helpful in generating the CDp-versus-CL variation.

3. Induced drag, CDi (see Section 3.12).

The pure induced drag, CDi, is computed from the expression CDi = CL2/π AR.

4. Wave drag, CDw (see Section 9.11).

The last component of subsonic aircraft drag is the wave drag, CDw , which accounts for compressibility effects. It depends on the thickness parameter of the body: for lifting surfaces, it is the t/c ratio, and for bodies, it is the diameter-to-length ratio. CFD can predict wave drag accurately but must be substantiated using wind-tunnel test data. Transport aircraft are designed so that HSC at Mcrit (e.g., for the Airbus 320 type, ≈ 0.82 Mach) allows a twenty-count ( CDw = 0.002) drag increase. At LRC, wave-drag formation is kept at zero. Compressibility drag at supersonic speed is caused by shock waves.

9.7 Minimum Parasite Drag Estimation Methodology

The practiced method to compute CDpmin is first to dissect (i.e., isolate) the aircraft into discrete identifiable components, such as the fuselage, wing, V-tail, H-tail, nacelle, and other smaller geometries (e.g., winglets and ventral fins). The wetted

area and the Re of each component establishes skin friction associated with each component. The 2D flat-plate basic mean skin-friction coefficient, CF basic, corresponding to the Re of the component, is determined from Figure 9.19b for the flight Mach number. Sections 3.5.1 and 9.7.1 explain the worked-out examples carried out in this book for fully turbulent flow, as shown in Figure 9.19.

The various CF arising from the 3D effects (e.g., supervelocity) and wrapping effects of the components are added to the basic flat-plate CF basic. Supervelocity effects result from the 3D nature (i.e., curvature) of aircraft-body geometry where, in the critical areas, the local velocity exceeds the free-stream velocity (hence, the term supervelocity). The axi-symmetric curvature of a body (e.g., fuselage) is perceived as a wrapping effect when the increased adverse pressure gradient increases the drag. The interference in the flow field is caused by the presence of two bodies in proximity (e.g., the fuselage and wing). The flow field of one body interferes with the flow field of the other body, causing more drag. Interference drag must be accounted for when considering the drag of adjacent bodies or components – it must not be duplicated while estimating the drag of the other body.

The design of an aircraft should be streamlined so that there is little separation over the entire body, thereby minimizing parasite drag obtained by taking the total CF (by adding various CF, to CF basic). Hereafter, the total CF will be known as the CF. Parasite drag is converted to its flat-plate equivalent expressed in f square feet. Although it can be easily converted into the SI system, in this book, the FPS system is used for comparision with the significant existing data that uses the FPS system. The flat-plate equivalent f is defined as:

where Aw is the wetted area (unit in ft2).

The minimum parasite drag CDpmin of an aircraft is obtained by totaling the contributing fs of all aircraft components with other sundries. Therefore, the minimum

The stepwise approach to compute CDpmin is described in the following three subsections.

9.7.1 Geometric Parameters, Reynolds Number, and Basic CF Determination

The Re has the deciding role in determining the skin-friction coefficient, CF, of a component. First, the Re-per-unit-length speed and altitude is computed. Then, the characteristic lengths of each component [i.e., Re = (ρ∞ LcompV∞)/µ∞] are determined. The characteristic length L of each component is as follows: