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

Froude — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The Kelvin wake, and the angle it comes out at. The wake behind something moving over deep water. Each curve joins everything radiated at one moment, wherever it has since travelled to. All of it stays inside a wedge whose half-angle is the inverse sine of one third, about nineteen and a half degrees, and that number does not depend on the speed, on gravity, or on the size of the vessel.

    The angle that does not care

    Every ship on deep water leaves a wake inside a wedge of the same angle. Not roughly the same — the same, for a rowing boat and a supertanker, at any speed either of them can manage, on any planet with any gravity.

    part 1 · regimes
  2. The one number that really is one. Three quantities against the Froude number. The upper line is the speed of a surface wave travelling downstream and the lower one the speed of the same wave travelling upstream, both in units of the wave speed itself; the second changes sign at Fr = 1 and not near it. That sign change is not a comparison of two term sizes going through unity — it is the moment a signal stops being able to reach upstream at all, so the equations change from elliptic to hyperbolic and the flow stops knowing what is ahead of it. The specific energy, drawn beneath, has its minimum at the same place, and for the same reason.

    The number that really is one

    Almost every threshold in this subject sits somewhere other than where its dimensionless group is one. The Froude number does not. At Fr = 1 a disturbance stops being able to travel upstream, the specific energy is least and the equations change type — three statements, one number, and no tolerance anywhere in it.

    part 2 · regimes

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