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The thread: Lift is circulation — page 10

Page 10 of 10, continuing through the 84 essays this motif runs through.

84 essays carry this thread — page 10 of 10.

Inside the layer the upper parcel's lead grows with depth. The transit lag, lower parcel minus upper, of parcels held at a quarter, a half and three-quarters of the boundary layer's thickness and just outside it, timed from either side of the attachment point to each chordwise station, on a thin cambered section at zero incidence, up to the upper layer's laminar separation at 62% chord. At mid-chord the lag outside the layer is 0.183 chord-over-speed units; at three-quarters of the thickness 0.195, at half 0.281 and at a quarter 0.695.

Inside the layer the upper parcel leads by more

Two parcels parting at a wing's attachment point arrive at different times, and outside the boundary layer the difference is the circulation over the speed squared. Inside the layer one might expect the slow, sticky fluid to wash the difference out. It does the opposite: deep in the layer the upper parcel's lead is several times the inviscid one, because the suction side's layer is fuller than the pressure side's. Only the layer's outer quarter reads the inviscid lead, and on the suction side the laminar layer gives out before the trailing edge.

A trainer's sortie wants the washout of its cruise, not of its average. The span efficiency of a rectangular wing of aspect ratio 8 averaged over a training sortie — eight minutes' climb, thirty of cruise, ten of slow flight and twelve of circuits — against its linear washout. Untwisted it is 0.9367. The best washout for the sortie is 3.43°, reaching 0.9774: the optimum for a lift coefficient of 0.436, the distance-weighted harmonic mean of the sortie's. The cruise alone would want 2.6°; the time-averaged lift coefficient, 0.671, would want 5.28° and lose 1.2% of the efficiency.

Circulation and lift

One twist is chosen for the speed flown per metre

A twisted wing is best at one lift coefficient and an aeroplane flies at many. Average its induced drag over a flight the way fuel and height are actually spent, per metre, and the twist that wins is the one for the root-mean-square speed of the flight — so the cruise outvotes the slow flight, a glider's circling barely counts, and a trainer's usual three or four degrees of washout turn out to be right for reasons nobody fitted them for.

Circulation and lift

A bending moment never chooses a span

Hold a wing's lift and its bending moment and ask for the least induced drag, and the answer does not stop: the span grows for ever and the tips push down. Both celebrated answers — Prandtl's bell at √(3/2) of the span for 8/9 of the drag, and the root-moment wing at 4/3 for 27/32 — are the span at which the least-drag loading's tips stop lifting. The structure sets how much is saved; a condition nobody states sets where the saving ends.

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