Reflections of a Paleoaerodynamicist

PERSPECTIVES IN BIOLOGY AND MEDICINE Volume 29 ¦ Number 3, Part 1 ¦ Spring 1986 REFLECTIONS OF A PALEOAERODYNAMICIST JOHN H. McMASTERS* Nomenclature1 I. ToVariables a = speed of sound (speed at which a pressure disturbance is propagated) AR= aspect ratio, O2IS b = wingspan c = wing or airfoil chord c = average wing chord, SIb Cd,Cl = three-dimensional-configuration drag and lift coefficients, Îovce/qS D = drag (fluid-resistance) force£ = energy consumption F = force g = acceleration due to gravity L = lift force L,1 = characteristic length M,m= mass M = Mach number (Via) P = power q = dynamic pressure (pV2/2) The author owes a large debt to many individuals and organizations for providing inspiration and assistance in preparing this manuscript. The following must be identified for special thanks: G. W. Brune, B. Dillner, R. C. Stoner, I. H. Rettie, M. D. Mack, G. S. Schairer, H. W. Rush, L. H. Schick, L. W. Langston, Jr., and K. Padian. This article is based on American Institute of Aeronautics and Astronautics paper 842167 , presented at the second AIAA Applied Aerodynamics Conference, Seattle, Washington , August 1984. *Aerodynamics Staff, Boeing Commercial Airplane Company, Seattle, Washington 98124. 'Editor's Note.—This fascinating interdisciplinary paper employs some aerodynamic terms whose meanings may not be familiar to some of our readers. We have accordingly asked Mr. McMasters to provide us with brief definitions and explanations of those more likely to be foreign to biologists. They are listed in the appendix to this article. 1984 by the author and The Boeing Company. Perspectives in Biology and Medicine, 29, 3, Part 1 ¦ Spring 1986 \ 33 1 R = range (distance traveled) Re= Reynolds number (VcIv) S = wing area T = thrust t = time U = payload weight V = speed W = weight xji,z= Longitudinal, lateral, and vertical coordinates ? = vertical velocity (sink rate) a = angle of attack ? = kinematic viscosity ? = air density F = objective function or index of performance II.Subscripts ! = PIWV F2 = EIWR(1) F3 = UIW Having performed this little exercise, one asks, so what? A little thought and a review of the literature show that several investigators have had a good time with these parameter groups, that they have interesting physical meanings, and that one even has a name. The first group (PlWV) is usually referred to as the "transport-economy index." To clarify its meaning, consider the following further manipulations: Assume that in the transportation process the motion is steady—that is, that V is constant. In this case the "tractive force" (T) producing the motion is equal to the sum of the forces (F) resisting the motion. For flying devices the tractive force, T, is the thrust (T) and the resisting force, F, is the drag (D). Now we observe that R = Vt, and P = EIt = E VlR = TV = FV.(2) Thus we find that F! = PIWV = EVIWRV = EIWR = F2,(3) and that the transport-economy index (PIWV) is the energy consumed per unit weight per unit distance traveled in the transportation process. Furthermore, if one confines one's attention to flying devices (and assumes either that the power required is that delivered directly to the air or that there is no aeromechanical loss in the system), then F? = PlWV = TVIWV = TIW = (LID)' \ (4) where L = lift = W, and we find that the transport-economy index is merely the reciprocal of the flight vehicle's lift-to-drag ratio. For subsonic flying devices it can further be shown (using relations from the following section on variations in vehicle size with weight) that O1 = PIWV ~ V2IWV3,(5) Perspectives in Biology and Medicine, 29, 3, Part 1 ¦ Spring 1986 \ 337 since P = TV = DV, D- V2S, and 5 ~ W2/3, and (F, decreasing^ good). But again, so what? What new clarifications of the overall transportation problem—and of its "optimization"—does this bit of arithmetic provide? Two examples, one due to engineers and the other due to a biologist, are of interest. The first example is from a classic paper entitled "What Price Speed," written in 1950 by Cabrielli and von Karman [I]. Having discovered the transport-economy index, the authors set about collecting , from standard references, power, weight, and speed data for a wide variety of transportation devices. An immediate difficulty in such a...