Relating Lift and Drag to Stress Distributions http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
11.1 Relating Lift and Drag to Stress Distributions
This section explains how lift and drag forces are related to stress distributions. This section also introduces the
concepts of form and friction drag. These ideas are fundamental to understanding of lift and drag.
Integrating a Stress Distribution to Yield Force
Lift and drag forces are related to the stress distribution on a body through integration. For example, consider
the stress acting on the airfoil shown in Fig. 11.2. As shown, there is a pressure distribution and a shear-stress
distribution. To relate stress to force, select a differential area as shown in Fig. 11.3. The magnitude of the
pressure force is dFp = pdA and the magnitude of the viscous force is dFv = ÄdA.* The differential lift force is
normal to the free-stream direction
and the differential drag is parallel to the free-stream direction
Integration over the surface of the airfoil gives lift force (FL) and drag force (FD):
(11.1)
(11.2)
Equations (11.1) and (11.2) show that the lift and drag forces are related to the stress distributions through
integration.
Figure 11.2 Pressure and shear stress acting on an airfoil.
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Relating Lift and Drag to Stress Distributions http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
Figure 11.3 Pressure and viscous forces acting on a differential element of area.
Form Drag and Friction drag
Notice that Eq.(11.2) can be written as the sum of two integrals.
(11.3)
Form drag is the portion of the total drag force that is associated with the pressure distribution. Friction drag is
the portion of the total drag force that is associated with the viscous shear-stress distribution. The drag force on
any body is the sum of form drag and friction drag. In words, Eq. (11.3) can be written as
(11.4)
Copyright © 2009 John Wiley & Sons, Inc. All rights reserved.
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