Non-Dimensionalization and Parameterization

6.3.1 Dimensionless variables

Aerodynamic characteristics are almost invariably defined, described, or provided in terms of the following dimensionless force coefficients, moment coefficients, and rotation rates. The latter two are commonly used in either the body or the stability axes.

(6.9)

All the reference quantities are arbitrary. The traditional choice for the reference area Sref is the projected wing area S. This typically includes any hidden “carry-through” wing area inside a fuselage, but may exclude root fairings or fillets. The choice for bref is the actual projected wingspan, which may or may not include tip devices such as winglets. The traditional choice for cref is the wing’s mean aerodynamic chord,

1 Ґ2 2

Cref — cmac = — / C(y) d у (6.10)

S – b/2

which is in effect a root-mean-square chord. Workable alternatives are the average chord cref = S/b, or simply the root chord cref = c(0).

Theoretically, additional important parameters are the dimensionless flow-angle rates.

This antifies the strength and influence of the wing’s shed vorticity, which is present in unsteady airfoil flows and is discussed in more detail in Section 7.4.2. In brief, a determines the time delay in the wing’s downwash seen by the horizontal tail, and therefore during pitching maneuvers it influences the time evolu­tion of the overall Cm, and to a lesser extent of the Cl also. In most aircraft в has relatively little influence and is usually ignored, although it may be significant for unusual aircraft configurations.