Editing Lift (force) (section)

===Reynolds-averaged Navier–Stokes (RANS) equations===

These are the NS equations with the turbulence motions averaged over time, and the effects of the turbulence on the time-averaged flow represented by [[turbulence modeling]] (an additional set of equations based on a combination of [[dimensional analysis]] and empirical information on how turbulence affects a boundary layer in a time-averaged average sense).<ref>White (1991), Section 6-2</ref><ref>Schlichting(1979), Chapter XVIII</ref> A RANS solution consists of the time-averaged velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil.

The amount of computation required is a minuscule fraction (billionths)<ref name=Spalart /> of what would be required to resolve all of the turbulence motions in a raw NS calculation, and with large computers available it is now practical to carry out RANS calculations for complete airplanes in three dimensions. Because turbulence models are not perfect, the accuracy of RANS calculations is imperfect, but it is adequate for practical aircraft design. Lift predicted by RANS is usually within a few percent of the actual lift.