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

Wave drag — where it appears

The drag a body has in steady inviscid supersonic flow, which d'Alembert's theorem forbids below Mach one. It is the work done against the pressure field of the waves the body radiates, and for a slender body it depends only on the cross-sectional area distribution.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Lift and wave drag on a flat plate at Mach 2, exactly and to first order. The lift and wave-drag coefficients of a supersonic section against incidence, computed face by face from shocks and fans, with Ackeret's linear result dashed over them. The two agree to three decimal places at small angles and part company slowly — which is what a first-order theory is supposed to do, and evidence rather than tautology, since the two routes share no algebra.

Drag with nothing to rub

d'Alembert's paradox says a closed body in a steady, inviscid flow has no drag, and four essays on this site argue it and none of them is wrong. Above Mach one it is false — the flow is still inviscid, still steady, and the drag is real, finite and quadratic in incidence.

compressible · Wave drag Four bodies of identical length and volume, and their wave drags. Each body has the same length and the same volume; only the distribution of area along it differs. The Sears–Haack body — the spindle whose area goes as the three-halves power of x(L−x) — has the least wave drag of the four, and every other shape pays between thirty-seven per cent and a hundred and seventy-five per cent more for carrying the same volume the same distance. Nothing about the cross-sections' shape enters: only the area distribution does.

The least drag a volume can have

A body's supersonic wave drag depends on nothing about it except how its cross-sectional area is distributed along its length. Minimising that for a given volume gives one shape — and the answer goes as the volume squared over the fourth power of the length.

compressible · Wave drag

Named alongside it

The objects these essays reach for when they reach for this one.

Ackeret's linear theoryArea ruleConstraintd'Alembert's paradoxDragEntropyInviscidLiftMinimum-drag speedModel limitOptimisationSears haack

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