Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Transonic — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. The coefficient of the equation's second derivative, along a chord. The bracket multiplying the streamwise second derivative in the transonic small-disturbance equation, along a chord at Mach 0.85. Where it is positive the equation is elliptic and the flow is subsonic; where it is negative the equation is hyperbolic and the flow is supersonic. Which it is at a given point depends on the perturbation velocity there, which is the thing being solved for. Forty-two per cent of this chord is hyperbolic, and no amount of inspecting the problem beforehand could have said so.

    The equation that changes type inside its own answer

    Near Mach one the coefficient of the streamwise second derivative depends on the perturbation velocity, which is what is being solved for. Two solutions of the linear equation no longer add — the leftover is three times the term the linear theory keeps — and the critical Mach number approaches one as the two-thirds power of thickness.

    part 1 · compressible

All series