Form Factor


The parasite drag associated with skin friction and pressure drag is determined by incrementing the flat plate results by a factor, k, to account for pressure drag and the higher-than-freestream surface velocities:

f = k cf Swet

The principal cause of increased drag is the increased surface velocity (supervelocity) due to thickness. For a given airfoil we can compute the maximum increase in velocity. This can also be done for a range of airfoil thickness ratios, wing sweeps, and Mach numbers to determine the form of variation with these parameters. After that one must still resort to experimental data to correlate the actual drag increment associated with skin friction and pressure drag. Such a variation is shown in the figure below at a Mach number of 0.5 for a family of airfoils similar to those used on commercial transports. Additional details on how this is computed are available here.

The fineness ratio of the fuselage affects the fuselage drag by increasing the local velocities and creating a pressure drag. The increase in skin friction due to higher-than-freestream velocities can be estimated by considering the symmetric flow around a body of revolution.

For bodies of revolution, the increase in surface velocity due to thickness is smaller than for 2-D shapes. The maximum velocity can be computed as a function of fineness ratio, assuming a family of fuselage shapes. The actual surface velocity distribution depends strongly on the shape of the body: paraboloids have about half again as much maximum perturbation velocity as ellipsoids, and fuselages with constant cross sections are quite different, but the idea here is to represent the correct trend theoretically, and then obtain empirical constants. The results are shown in the figure below with details available through this link.

When the body has a non-circular cross-section, the effective diameter may be computed from:

Deffective = (4 S / p )1/2

where S is the maximum cross-sectional area.

Nacelles may also be modeled as bodies of revolution, with an effective fineness ratio given by:

Here, Aexit = total exit area
Ainflow = effective inlet area based on mass flow, approximately = 0.8 Ainlet
Amax = maximum nacelle cross-section area

Typically Ainlet is approximately 0.7 Amax.