where Sref is the reference area. The reference area is not so clear when the wing is not a simple tapered planform, but for the purposes of this class, it is taken to be the projected area of the equivalent trapezoidal wing planform.
Drag may be divided into components in several ways:
To highlight the change in drag with lift:
Drag = Zero-Lift Drag + Lift-Dependent Drag + Compressibility Drag
To emphasize the physical origins of the drag components:
Drag = Skin Friction Drag + Viscous Pressure Drag + Inviscid (Vortex) Drag + Wave Drag
The latter decomposition is stressed in these notes. There is sometimes some confusion in the terminology since several effects contribute to each of these terms. The definitions used here are as follows:
Compressibility drag is the increment in drag associated with increases in Mach number from some reference condition. Generally, the reference condition is taken to be M = 0.5 since the effects of compressibility are known to be small here at typical conditions. Thus, compressibility drag contains a component at zero-lift and a lift-dependent component but includes only the increments due to Mach number (CL and Re are assumed to be constant.)
Zero-lift drag is the drag at M=0.5 and CL = 0. It consists of several components, discussed on the following pages. These include viscous skin friction, vortex drag due to twist, added drag due to fuselage upsweep, control surface gaps, nacelle base drag, and miscellaneous items.
The Lift-Dependent drag, sometimes called induced drag, includes the usual lift- dependent vortex drag together with lift-dependent components of skin friction and pressure drag.
For the second method:
Skin Friction drag arises from the shearing stresses at the surface of a body due to viscosity. It accounts for most of the drag of a transport aircraft in cruise.
Viscous pressure drag also is produced by viscous effects, but not so directly. The pressure distribution is modified by the presence of a boundary layer. Although in 2-D inviscid flow the pressures on forward and aft surfaces balance so that no drag is produced, the effect of the boundary layer leads to an imperfect canceling of these pressures so some additional drag is created.
Inviscid or vortex drag is produced by the trailing vortex wake of a three-dimensional lifting system.
Wave drag is produced by the presence of shock waves at transonic and supersonic speeds. It is the result of both direct shock losses and the influence of shock waves on the boundary layer. The wave drag is often decomposed into a portion related to lift and a portion related to thickness or volume.
In these notes, a somewhat more detailed drag breakdown is used. The total drag is expressed as the sum of the following components:
Drag =
Non-lifting skin friction and pressure drag
+ Fuselage Upsweep Drag
+ Control Surface Gap Drag
+ Nacelle Base Drag
+ Miscellaneous Items
+ Vortex Drag
+ Lift-Dependent Viscous Drag
+ Wave Drag (Lift-Dependent and Volume-Dependent)
The first five of these items do not change as the lift changes and are taken together as the parasite drag. This is not quite the same as the drag at zero lift because the zero lift drag may include vortex drag when the wing is twisted. Another drag item that is sometimes considered separately is trim drag, the drag increment associated with the required tail load to trim the aircraft in pitch. Here we consider trim drag in the discussion of vortex drag of the lifting system.
The drag is often expressed in dimensionless form:
where Sref is the reference area. The reference area is not so clear when the wing is not a simple tapered planform, but for the purposes of this class, it is taken to be the projected area of the equivalent trapezoidal wing planform.
The parasite drag is often written in terms of the equivalent flat plate drag area, f:
Subsequent sections deal in some detail with each of the components of the aircraft drag. The drag associated with compressibility is treated in the following chapter.
The parasite drag components include:
The lift-dependent drag contributions include:
The wave drag contributions may include: