9.2 Introduction

9.1.1 What Is to Be Learned?

This chapter covers the following topics:

9.1.2 Coursework Content

The coursework task continues linearly. Readers will carry out aircraft component drag estimation and obtain the total aircraft drag.

9.2 Introduction

The drag of an aircraft depends on its shape and speed, which are design-dependent, as well as on the properties of air, which are nature-dependent. Drag is a complex phenomenon arising from several sources, such as the viscous effects that result in skin friction and pressure differences as well as the induced flow field of the lifting surfaces and compressibility effects (see Sections 3.12 and 3.16).

The aircraft drag estimate starts with the isolated aircraft components (e.g., wing and fuselage). Each component of the aircraft generates drag largely dictated by its shape. Total aircraft drag is obtained by summing the drag of all components plus their interference effects when the components are combined. The drag of two isolated bodies increases when they are brought together due to the interference of their flow fields.

The Re has a deciding role in determining the associated skin-friction coefficient, CF, over the affected surface and the type, extent, and steadiness of the boundary layer (which affects parasite drag) on it. Boundary-layer separation increases drag and is undesirable; separation should be minimized.

A major difficulty arises in assessing drag of small items attached to an aircraft surface such as instruments (e.g., pitot and vanes), ducts (e.g., cooling), blisters,

and necessary gaps to accommodate moving surfaces. In addition, there are the unavoidable discrete surface roughness from mismatches (at assembly joints) and imperfections, perceived as defects, that result from limitations in the manufacturing processes. Together, from both manufacturing and nonmanufacturing origins, they are collectively termed excrescence drag.

The review in Section 2.6 makes clear that accurate total aircraft drag estimation is not possible using analytical or CFD methods. Schmidt of Dornier in the AGARD 256 is categorical about the inability of CFD, analytical methods, or even windtunnel model-testing to estimate drag. CFD is steadily improving and can predict wing-wave drag (CDw ) accurately but not total aircraft drag – most of the errors are due to the smaller excrescence effects, interference effects, and other parasitic effects. Industrial practices employ semi-empirical relations (with CFD) validated against wind-tunnel and flight tests and are generally proprietary information. Most of the industrial drag data are not available in the public domain.

The methodology given in this chapter is a modified and somewhat simplified version of standard industrial practices ([1], [3], and [7]). The method is validated by comparing its results with the known drag of existing operational aircraft.

The design criterion for today’s commercial high-subsonic jet transport aircraft is that the effects of separation and local shocks are minimized (i.e., compressibility drag almost equal to zero) at the LRC (before the onset of wave drag) condition. At HSC, a twenty-count drag increase is allowed, reaching Mcrit, due to local shocks (i.e., transonic flow) covering small areas of the aircraft. Modern streamlined shapes maintain low separation at Mcrit; therefore, such effects are small at HSC. The difference in the Mach number at HSC and LRC for subsonic aircraft is small – on the order of Mach 0.05 to Mach 0.075. Typically, estimation of the drag coefficient at LRC is sufficient because it has a higher Cf, which gives conservative values at HSC when CDw is added. The LRC condition is by far the longest segment in the mission profile; the industry standard practice at the conceptual study phase uses the LRC drag polar for all parts of the mission profile (e.g., climb and descent). The Re at the LRC provides a conservative estimate of drag at the climb and descent segments. At takeoff and landing, the undercarriage and high-lift device drags must be added. In the next phase of the project, more detailed drag estimation is carried out.

Supersonic aircraft operate over a wider speed range: The difference between maximum aircraft speed and Mcrit is on the order of Mach 1.0 to Mach 1.2. Therefore, estimation of CDpmin is required at three speeds: (1) at a speed before the onset of wave drag, (2) at Mcrit, and (3) at maximum speed (e.g., Mach 2.0).

It is difficult for the industry to absorb drag-prediction errors of more than 5% (the goal is to ensure errors of <3%) for civil aircraft; overestimating is better than underestimating. Practitioners are advised to be generous in allocating drag – it is easy to miss a few of the many sources of drag, as shown in the workedout examples in this chapter. Underestimated drag causes considerable design and management problems; failure to meet customer specifications is expensive for any industry. Subsonic aircraft drag prediction has advanced to the extent that most aeronautical establishments are confident in predicting drag with adequate accuracy. Military aircraft shapes are more complex; therefore, it is possible that predictions will be less accurate.

9.3 Parasite Drag Definition

The components of drag due to viscosity do not contribute to lift. For this reason, it is considered “parasitic” in nature. For bookkeeping purposes, parasite drag is usually considered separately from other drag sources. The main components of parasite drag are as follows:

drag due to skin friction

drag due to the pressure difference between the front and the rear of an object

drag due to the lift-dependent viscous effect and therefore seen as parasitic (to some extent resulting from the nonelliptical nature of lift distribution over the wing); this is a small but significant percentage of total aircraft drag (at LRC, it is ≈2%)

All of these components vary (to a small extent) with changes in aircraft incidence (i.e., as CL changes). The minimum parasite drag, CDpmin, occurs when shock waves and boundary-layer separation are at a minimum, by design, around the LRC condition. Any change from the minimum condition (CDpmin) is expressed as CDp. In summary:

parasite drag (CDp) = (drag due to skin friction [viscosity]+drag due to

Oswald’s efficiency factor (see Section 3.12) is accounted for in the lift-dependent parasite drag. The nature of CDp is specific to a particular aircraft. Numerically, it is small and difficult to estimate.

Parasite drag of a body depends on its form (i.e., shape) and is also known as form drag. The form drag of a wing profile is known as profile drag. In the past, parasite drag in the FPS system was sometimes expressed as the drag force in pound force (lbf) at 100 ft/s speed, represented by D100. This practice was useful in its day as a good way to compare drag at a specified speed, but it is not used today. These two terms are not used in this book.

The current industrial practice using semi-empirical methods to estimate CDpmin is a time-consuming process. (If computerized, then faster estimation is possible, but the author recommends relying more on the manual method at this stage.) Parasite drag constitutes one-half to two-thirds of subsonic aircraft drag. Using the standard semi-empirical methods, the parasite drag units of an aircraft and its components are generally expressed as the drag of the “equivalent flat-plate area” (or “flat-plate drag”), placed normal to airflow as shown in Figure 9.1 (see Equation 9.7). These units are in square feet to correlate with literature in the public domain. This is not the same as air flowing parallel to the flat plate and encountering only the skin friction.

The inviscid idealization of flow is incapable of producing parasite drag because of the lack of skin friction and the presence of full pressure recovery.

Figure 9.1. Flat plate equivalent of drag

9.4 Aircraft Drag Breakdown (Subsonic)

There are many variations and definitions of the bookkeeping methods for components of aircraft drag; this book uses the typical U.S. practice [2]. The standard breakdown of aircraft drag is as follows (see Equation 9.1):

total aircraft drag = (drag due to skin friction + drag due to pressure difference)

+drag due to lift generation + drag due to compressibility

=parasite drag (CD p) + lift-dependent induced drag (CDi )

+wave drag (CDw )

=(minimum parasite drag[CDpmin]

+incremental parasite drag[ CD p])

+induced drag (CDi ) + wave drag (CDw )

Therefore, the total aircraft drag coefficient is:

The advantage of keeping pure induced drag separate is obvious because it is dependent only on the lifting-surface aspect ratio and is easy to compute. The total aircraft drag breakdown is shown in Chart 9.1.

It is apparent that the CD varies with the CL. When the CD and the CL relationship is shown in graphical form, it is known as a drag polar, shown in Figure 9.2 (all components of drag in Equation 9.2 are shown in the figure). The CD versus the CL2 characteristics of Equation 9.2 are rectilinear, except at high and low CL values (see

+ nonelliptical effect)

Chart 9.1. Total aircraft drag breakdown