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

Sears haack — where it appears

The body of least supersonic wave drag for a given length and volume, whose area distribution is a pure second harmonic. Its radius goes as the three-quarter power of the distance from each end, and its drag goes as the volume squared over the fourth power of the length.

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

One signature, aged four times. The pressure signature of a slender body at four distances, computed by the exact Lax formula for the nonlinear propagation. Each point of the waveform moves forward in proportion to its own overpressure, so the compression at the front catches the undisturbed air and a shock forms there, while the expansion at the rear falls behind and forms a second one. What is left is an N-wave: two discontinuities and a straight line between them, spreading and weakening.

The signature that forgets the shape

The pressure field near a supersonic aeroplane depends on every part of it. What reaches the ground has two parameters. Two bodies whose near-field signatures differ by fifty-five per cent in peak and by their whole shape age into the same N-wave, to two and a half per cent.

compressible · Sonic boom 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.

Area ruleModel limitSlender bodySonic boomAeroacousticsBlast waveConstraintDiscontinuityDragFar fieldMeasurementMinimum-drag speed

All concepts