Every so often an article appears in the popular press pointing to the apparent confusion surrounding the topic of aerodynamic lift and alleging that even the “experts” don’t fully understand it. This makes attention-grabbing copy, but it overstates the case. Actually, the science of lift is not in dispute. It is well understood in terms of a quantitative mathematical theory that is based on established laws of physics, produces accurate predictions, and has been agreed on by the science and engineering communities since the early 20th century. Confusion arises only in connection with explaining lift in qualitative terms.
References
1.
See, for example,
K.
Chang
, “What does keep them up there?
” New York Times
, Dec.
9, 2003
, http://www.nytimes.com/2003/12/09/news/staying-aloft-what-does-keep-them-up-there.html, accessed Dec. 12, 2015.2.
Doug
McLean
, “Aerodynamic lift, part 2: A comprehensive physical explanation
,” Phys. Teach.
56
, 521
–524
(Nov.
2018
).3.
For an overview, see
D.
McLean
, Understanding Aerodynamics - Arguing from the Real Physics
(Wiley
, 2012
), Sec. 10.2.4.
A fluid parcel (or fluid element) is defined as containing the same material fluid particles for all time (ignoring molecular diffusion), and thus the requirement that parcel boundaries move with the flow. Parcels can have sizes and shapes chosen arbitrarily at any instant, but at all other times they must move and deform as dictated by the flow. For more discussion, see
G. K.
Batchelor
, An Introduction to Fluid Dynamics
(Cambridge University Press
, 1967
), Sec. 2.1, or Ref. 3, Sec. 3.4.5.
M.
Drela
, “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,” in Low Reynolds Number Aerodynamics
, (Lecture Notes in Engineering), Vol. 54
, edited by T. J.
Mueller
(Springer-Verlag
, 1989
). Also http://web.mit.edu/drela/Public/papers/xfoil_sv.pdf, accessed Sept. 19, 2017.6.
F. M.
White
, Viscous Fluid Flow
, 2nd ed. (McGraw-Hill
, 1991
). The no-slip condition is discussed in Sec. 1-4.1, and the formation of a thin boundary layer is discussed in Sec. 4-1. Turbulence is discussed in Sec. 6-1.1, with a very nice illustration in Fig. 6-1.7.
J. S.
Huebner
and S.
Jagannathan
, “Explaining airfoil lift in introductory physics
,” Am. J. Phys.
56
, 855
–866
(Sept.
1988
).8.
F. M.
White
, Fluid Mechanics
, 7th ed. (McGraw-Hill
, 2011
). For the compressible-flow counterpart to Bernoulli’s equation see Sec. 9.3, Eq.. 9.28a.9.
G. D.
Freier
, “Lift and flow
,” Phys. Teach.
28
, 518
(Nov.
1990
).10.
D.
Anderson
and S.
Eberhardt
, “A Physical Description of Flight; Revisited
,” https://www.udocz.com/read/a-physical-description-of-flight--revisited--pdf-, accessed September, 2018.11.
N. F.
Smith
, “Bernoulli and Newton and fluid mechanics
,” Phys. Teach.
10
, 451
–455
(Nov.
1972
).12.
C.
Waltham
, “Flight without Bernoulli
,” Phys. Teach.
36
, 457
(Nov.
1998
).13.
Physics Textbook Review Committee
, “Quibbles, misunderstandings, and egregious mistakes: Survey of high-school physics texts
,” Phys. Teach.
37
, 297
–305
(May
1999
).14.
See Ref. 8. The control-volume concept is developed in detail in Chap. 3.
15.
P. B. S.
Lissaman
, “The facts of lift
,” AIAA, 34th Aerospace Sciences Meeting and Exhibit
, Reno, NV
, Jan. 15-18, 1996
. Read more at https://arc.aiaa.org/doi/abs/10.2514/6.1996-161.16.
See Ref. 3. Vertical momentum imparted by a lifting wing is discussed in Sec. 8.5.
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