A-10 Warthog in detail & scale - D&S Vol. 19 by Dana Bell

By Dana Bell

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Extra info for A-10 Warthog in detail & scale - D&S Vol. 19

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The principle of dynamic similarity is the key. In the wing-design example in the previous subsection, it is clear that if we had known the flight Reynolds and Mach numbers for the prototype, we would be able to design a test matrix that held these quantities fixed; the number of required test conditions could be reduced drastically. It may not always be easy to match both the test Reynolds and Mach numbers to the prototype values. For instance, in testing a model of a hypersonic airplane, to fly at a Mach number of, for example, M = 11, configuring the test apparatus using a small model (no large wind tunnels can operate continuously in this Mach-number range) probably would lead to a Re that is too small to match that experienced on the full-sized prototype.

Students probably are already familiar with some or all of these ideas from their fundamental courses in mechanics or thermodynamics. Lagrangian versus Eulerian Mathematical Description In studying the motion of particles and rigid bodies in mechanics courses, students learned the Lagrangian approach in which each element of the system is represented by a detailed model of its absolute motion and its motion relative to other parts of the system. In aerodynamics (or fluid mechanics), two different mathematical viewpoints may be adopted.

Hundreds of these groups have been identified as important in engineering applications; they usually are assigned the name of the individual who first recognized its importance. For example, in the aerodynamic force expression derived in Eq. 16) Reynolds number Re = ρ Vd . 17) The first group was identified as a key parameter in describing the effects of compressibility in aerodynamic flows. It was introduced by the Austrian physicist Ernst Mach in the 1870s. The second is named for Osborne Reynolds, who showed in the 1880s that this group governs the role of viscous forces in the flow of liquids or gases.

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