Compressibility Drag: Computing CDc
The increment in drag coefficient due to compressibility, CDc, from its first appearance to well beyond MDiv can be estimated from Figure 12 where CDc is normalized by dividing by cos3L and plotted against the ratio of freestream Mach number, M0 to Mcc. Actual aircraft may have slightly less drag rise than indicated by this method if very well designed. A poor design could easily have higher drag rise. The differences arise from early shocks on some portion of the wing or other parts of the airplane. Figure 12 is an empirical average of existing transport aircraft data.
Figure 12 Incremental Drag Coefficient Due To Compressibility
In summary, the method for estimating compressibility drag is as follows:
1. Determine the crest critical Mach number for the values of lift coefficient being studied from figure 7 for the appropriate values of the wing quarter chord sweep angle and the average thickness ratio for the exposed part of the wing.
2. Determine the incremental drag coefficient due to compressibility from figure 12 for the crest-critical Mach numbers from step 1.
When this method is used, the following limitations should be kept in mind:
1. The method assumes that the dominant factor in the airplane compressibility drag characteristics at cruising conditions is the wing. This means that the other components must have drag-divergence Mach numbers higher than that of the wing and that interference must be kept to a minimum in order for this method to be applicable.
2. The estimates for the crest critical Mach number in terms of the wing sweep angle, thickness ratio measured in the freestream direction, and lift coefficient are based on peaky airfoil sections. This method would not be reliable for significantly different types of airfoil sections.
One further note is in order. The expression "drag divergence Mach number" or MDiv is the Mach number at which the drag begins to rise abruptly. It is usually desirable to cruise close to MDiv.
Numerous definitions of 'rise abruptly' have been used including:
a. MDiv = M for CDc = .0014, or some other value varying from .0010 to .0025
b. MDiv = M for dCD/dM = .03 or .05 or 0.10
c. MDiv = M at constant lift coefficient for M CL/CD, a term in the range expression, equals 99% of the maximum M CL/CD
Method (c) is most meaningful and corresponds approximately to (dCD/dM) = .03 and usually to CDc = .0012 to .0016.
The MDiv for bodies can be related to the occurence of critical Mach number, or sonic velocity, at or behind the longitudinal station of maximum cross-sectional area. This is analogous to the crest theory of M for airfoils. Another factor is present on bodies, however, namely that the expanding forward portion of the body tends to thin the boundary layer and make it less likely to separate. Generally the MDiv of bodies can be assumed to be about 3% above the Mach number at which sonic velocity occurs at the maximum cross-sectional area.