By Holt Ashley
This glorious, leading edge reference bargains a wealth of precious details and a pretty good historical past within the basics of aerodynamics. Fluid mechanics, consistent density inviscid movement, singular perturbation difficulties, viscosity, thin-wing and slim physique theories, drag minimalization, and different necessities are addressed in a full of life, literate demeanour and observed through diagrams.
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Extra resources for Aerodynamics of Wings and Bodies
Until quite lately it was believed that, to render constant-density fluid motion unique in a multiply connected region, a number of circulations must be prescribed which is one less than the degree of connectivity. A forthcoming book by Hayes shows, however, that more refined topological concepts must be employed to settle this question. He finds that the indeterminacy is associated with a topological property of the region known as the Betti number. Since the mathematical level of these ideas exceeds what is being required of our readers, we confine ourselves to citing the reference and asserting that it confirms the correctness of the simple examples discussed here and in the following section.
2-41 SOLID MOVING THROUGH CONSTANT-DENSITY FLUID 33 Since the foregoing constitute a result of rigid-body mechanics, we attempt to see how these ideas can be extended to the surface S moving through an infinite mass of constant-density fluid. For this purpose, we associate with 5 and X the impulsive force and impulsive torque which would have to be exerted over the surface of the solid to produce the motion instantaneously from rest. ”) I n view of the relationship between impulsive pressure and velocity potential, the force and torque can be written 4 == #p-dS, #r x (p@n)dS.
Du -. (2-72) dt For instance, if the acceleration occurs entirely parallel to the x-axis, the force is still found to have components in all three coordinate directions: Fbody= -iA du - - jC‘-du dt at - kB’du -. dt (2-73) It is clear from these results why the quantities A , B, . . , are referred t o as virtual masses or apparent masses. In view of the facts that the _- 2-61 TWO- AND THREE-DIMENSIONAL FLOWS-NO CIRCULATION 37 virtual masses for translation in different directions are not equal, and that there are also crossed-virtual masses relating velocity components in different directions, the similarity with linear acceleration of a rigid body is only qualitative.