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

Load factor — where it appears

The lift an aircraft carries divided by its weight, which is one in level flight and larger in a turn or a gust. The structure is designed to a stated maximum, and a gust's contribution to it is what the manoeuvring envelope's sloping lines represent.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The left wall is not a speed, it is an angle drawn in speed coordinates. The V–n diagram: every combination of speed and load factor the aircraft can reach. The curved left boundary is the wing at its stalling angle — n = ½ρV²S C_Lmax /W, a parabola — and it is the same limit at every point along it. The flat top and bottom are the structure. Where the two meet is the corner speed, 56.6 metres per second here: the slowest speed at which the aircraft can reach its limit load factor, and therefore the speed at which it turns hardest. Above it the wing can pull more than the structure allows — at the never-exceed speed it could reach 9.6g before stalling — and the pilot's limit stops being the air.

An angle, not a speed

The number is printed in the handbook, marked in white on the airspeed indicator and used in every briefing, and the wing has no way of knowing it. A wing stalls at an angle. The speed at which an aeroplane reaches that angle is an answer with four other variables in it, and every one of them moves.

misconceptions · Stall speed The mean lift is not the lift at the mean angle. A finite wing's lift curve, with a gust distribution of standard deviation 3° about a mean angle of 10° drawn along the foot. The wing spends its time spread across that distribution, so what it averages is the average of the curve: 0.7951 against the 0.8368 the mean angle promises, a deficit of 5.0 per cent. Nothing has stalled, and no gust has taken the wing past the stall angle: the deficit comes entirely from the curve bending over, and it is there at every angle where the curve is not straight.

The lift at the mean angle

A wing in rough air flies at every angle in turn, so what it averages is the average of its lift curve rather than the lift at its average angle. Where the curve bends over near the stall the two differ by five per cent at three degrees of gust and by fourteen at five, and the drag goes the other way.

circulation · Gust Wagner's function and Küssner's, from one solver and two inputs. Lift as a fraction of its steady value, against distance travelled in semichords. The step in incidence and the sharp-edged gust are the same unsteady problem with two different right-hand sides, and Jones's exponential fits to both are drawn over the solve. From four semichords on they are nearly the same curve — which is why they get interchanged.

Two answers to one question

Unsteady aerofoil theory collapses a wing's whole history onto one function of one variable, and every quasi-steady gust calculation convolves something with it. There are two such functions, not one: a wing that is pitched changes its boundary condition everywhere at once, and a wing flying into a gust has not met most of the gust yet.

circulation · Unsteady lift A gust, the aeroplane's response, and the load it is left with. A one-minus-cosine gust twenty-five chords long, as an angle of attack, against distance flown, and the lift it produces on two aeroplanes free to rise — a light single with a mass parameter of 16 and an airliner at eleven kilometres with 149. Both loads lag the gust, because lift takes several chords to build. The light aeroplane's also peaks lower and falls away early: it has started to rise with the gust, which lowers its own angle of attack.

The aeroplane rises out of its own gust

A gust pushes a wing up, and the wing, being attached to an aeroplane that is free to move, starts rising — which lowers its angle of attack and takes away part of the load the gust was delivering. How much depends on one number, and the formula every airworthiness code used for forty years is a fit to the calculation this essay does again.

circulation · Gust A gust spectrum at a point, across a span, and as a load. The spectrum of vertical gust velocity at a single point — von Kármán's, falling as the minus five-thirds power — and the same gust averaged across a wing whose span is a tenth of the turbulence scale and across one as wide as the scale. Averaging removes the wavenumbers shorter than the span, one power steeper. Through Sears' filter for a chord of a five-hundredth of the scale, the tenth-span load falls as the minus eleven-thirds power, steep enough to converge.

The span takes away the infinity, not the gust

A two-dimensional wing in turbulence reverses its load infinitely often, because the gust spectrum never falls fast enough. A real wing averages the gust across its span, and the average keeps ninety-five per cent of the gust's strength and removes the infinity. The load's crossing rate settles at about two per turbulence scale flown and stops depending on where anyone cut the spectrum off.

circulation · Gust

Named alongside it

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

GustModel limitFlight envelopeUnsteady liftAveragingDynamic pressureMeasurementStallStatisticsAdded massAirspeed indicatorAngle of attack

All concepts