Question 3 of 7: Aerodynamic Definitions, Drag Mechanisms, High-Lift Devices and Longitudinal Stability

Question 3: Aerodynamic Definitions, Drag Mechanisms, High-Lift Devices and Longitudinal Stability (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Pressure altitude and density altitude

Pressure altitude is the altitude in the standard atmosphere at which the ambient pressure equals the pressure actually measured. It is what a barometric altimeter set to 1013.25 hPa displays, and because all aircraft in the same region use the same setting above the transition altitude, it is the basis of vertical separation in controlled airspace. Density altitude is the altitude in the standard atmosphere at which the ambient density equals the density actually present; it is the pressure altitude corrected for the departure of the real temperature from the ISA value. Aerodynamic and engine performance — lift at a given true airspeed, thrust, propeller efficiency, take-off run — scale with density, so density altitude, not pressure altitude, is the number that governs whether an aircraft will get off a given runway on a hot day. On a hot day the air is thinner than ISA at the same pressure, so the density altitude exceeds the pressure altitude, and the aeroplane performs as if the aerodrome were higher than it is.

(b) Induced drag and its reduction

Induced drag (drag due to lift, or vortex drag) is the price paid for generating lift with a wing of finite span. Because the pressure on the lower surface exceeds that on the upper surface, air spills round the tip from bottom to top, and the resulting trailing vortex sheet imparts a downward velocity — the downwash $w$ — to the air passing over the wing. The local flow at each section is therefore inclined downwards by an induced angle $\alpha_i = w/V$, and the section lift vector, which is by definition perpendicular to the local flow, is tilted rearwards by that same angle. Its component along the free-stream direction is the induced drag. For a wing with an elliptic lift distribution the classical result is

where $AR = b^2/S$ is the aspect ratio and $e$ the span efficiency factor. Three consequences follow directly, and they are the answer to "what can be done". First, increase the aspect ratio: a long, slender wing spreads the same lift over a longer span, weakening the downwash. This is why sailplanes have aspect ratios near 30 and why every generation of transport wing has been more slender than the last. Second, improve the span loading towards elliptical, raising $e$ towards unity, by choosing the twist and taper distribution appropriately. Third, treat the tip: winglets, raked tips and tip fences increase the effective span for a given structural span and can recover several per cent of cruise drag. Since induced drag varies as $C_L^2$ and therefore as $1/V^4$ at fixed weight, all of this matters most at low speed — at climb-out and at holding speeds — and hardly at all in high-speed cruise.

(c) Leading-edge slats and slotted flaps

Both devices exist to raise the maximum lift coefficient of the wing, and hence to reduce the stalling speed, without penalising the cruise configuration. They achieve it by different mechanisms.

A leading-edge slat is a small auxiliary aerofoil deployed ahead of and below the wing leading edge, forming a converging gap. It does not simply "blow the boundary layer with high-energy air", though that is the traditional shorthand; its dominant effect is a circulation effect. The slat's own circulation reduces the suction peak at the main wing's leading edge and hence the severity of the adverse pressure gradient behind it, so the boundary layer on the main element can negotiate a much higher angle of attack before separating. The stalling angle is typically increased by 6–10 degrees, and with it the maximum lift coefficient.

A slotted flap is a trailing-edge device that both increases camber and, through the slot between the main wing and the flap, allows air from the high-pressure lower surface to re-energise the boundary layer on the flap's upper surface. The camber increase raises the lift at every angle of attack; the slot prevents the flap from stalling under the very large pressure recovery it must sustain. Double- and triple-slotted arrangements repeat the trick, and a Fowler flap adds a rearward translation that also increases wing area. Used together, slats and slotted flaps take a typical transport wing from $C_{L\max} \approx 1.3$ clean to $2.3$ or more — exactly the values used in Question 2(b), where they cut the minimum speed by a quarter.

(d) Spoilers

A spoiler is a hinged panel on the upper surface of the wing, ahead of the flaps, which when raised deliberately separates ("spoils") the flow over the wing behind it. Raising it destroys lift locally and increases drag. Spoilers are fitted for three distinct purposes. As ground spoilers (or lift dumpers) they are deployed fully at touchdown, transferring the aircraft's weight from the wing to the undercarriage so the wheel brakes bite immediately and the wing does not continue to fly — this is the single most effective way to shorten the landing ground run, and it is why the ground-run lift coefficient in Question 6(b) is negative. As flight spoilers or speed brakes, symmetric partial deployment increases drag and steepens the descent path without increasing airspeed, which lets a transport lose height quickly when descent planning has left it high. As roll spoilers, asymmetric deployment kills lift on the down-going wing to augment or, on many modern aircraft, replace the ailerons at high speed, where aileron deflection would cause wing twist and aileron reversal.

(e) Skin-friction drag and pressure drag

Skin-friction drag is the streamwise resultant of the shear stresses that the viscous boundary layer exerts tangentially on the surface. It depends on the wetted area, on the Reynolds number, and above all on whether the boundary layer is laminar or turbulent — a turbulent layer produces several times the skin friction of a laminar one at the same Reynolds number, because turbulent mixing brings high-momentum fluid down to the wall and steepens the velocity gradient there.

Pressure drag (form drag) is the streamwise resultant of the pressure acting normal to the surface. In a perfect inviscid fluid it would be zero for any closed body — d'Alembert's paradox — because the pressure recovered on the rear of the body exactly balances that on the front. It is non-zero in a real flow because the boundary layer thickens and eventually separates, which prevents full pressure recovery over the aft surface and leaves a low-pressure wake behind the body. Pressure drag is therefore very sensitive to shape: a streamlined aerofoil delays separation to the trailing edge and has little of it, whereas a bluff body such as a landing-gear leg is almost entirely pressure drag.

The design tension between the two is the essence of practical aerodynamics. A laminar boundary layer minimises skin friction but separates readily, increasing pressure drag; a turbulent layer resists separation but costs friction. The best compromise is a body streamlined enough that separation is deferred to a very small aft region, so that the total — conventionally the sum called profile drag — is minimised.

(f) Laminar-flow aerofoils

A laminar-flow aerofoil is a section shaped so that the point of minimum pressure is moved well aft — typically to 40–60 % of chord instead of the 15–25 % usual on a conventional section. Because a boundary layer remains laminar only while the pressure gradient is favourable (pressure falling in the flow direction), moving the minimum-pressure point aft extends the favourable gradient and holds transition back over a much longer fraction of the chord. The characteristic shape is a section of maximum thickness well aft with a slowly converging forward contour, as in the NACA 6-series developed in the late 1930s.

They are used because skin-friction drag dominates the drag of a slender body at cruise, and laminar friction is a small fraction of turbulent friction: a genuine laminar run over half the chord can reduce section drag by 30–50 % within the design lift-coefficient range. The characteristic "drag bucket" — a narrow band of $C_L$ over which drag is markedly reduced — is the signature of the effect. Two heavy practical qualifications must accompany the answer. First, the benefit is confined to that bucket; outside it the drag is no better than a conventional section, and often slightly worse. Second, laminar flow is extraordinarily fragile: insect debris, rain erosion, paint roughness, manufacturing waviness or a rivet head will trip transition and remove the benefit entirely. That is why laminar sections are common on sailplanes and general-aviation aircraft, whose surfaces are smooth and whose Reynolds numbers are modest, but why transport aircraft use them chiefly as a starting point for supercritical design rather than for their laminar run.

(g) Achieving static longitudinal stability

An aircraft is statically stable in pitch if a disturbance that increases its angle of attack generates a nose-down pitching moment that tends to restore the original attitude — that is, if $dC_m/d\alpha < 0$, with $C_m$ measured about the centre of gravity. The methods used to secure it are all ways of ensuring that the aircraft's aerodynamic centre (the neutral point) lies behind the centre of gravity, with a positive static margin.

The conventional means are: (i) a horizontal tailplane on a moment arm behind the wing — when the aircraft pitches nose-up, the tail sees an increased angle of attack, generates additional download-relieving lift well aft of the centre of gravity, and produces the restoring nose-down moment; the tail volume coefficient $V_H = l_t S_t/(\bar{c}S)$ is the design parameter. (ii) Placing the centre of gravity ahead of the neutral point and controlling it in service by a loading schedule and, on transports, by fuel transfer between the wing and a trim tank; the certified forward and aft c.g. limits exist precisely to guarantee a positive static margin at all loadings. (iii) Wing sweep and washout, which on tailless aircraft move the wing's own aerodynamic centre aft and provide, with a reflexed trailing edge or negative tip incidence, the same restoring moment a tailplane would give. (iv) A canard layout, in which the forward surface is designed to stall first so that the nose drops before the main wing reaches its stalling angle. Modern combat aircraft deliberately abandon natural static stability — they are flown with the c.g. behind the neutral point to reduce trim drag and improve manoeuvrability — and rely on a full-authority fly-by-wire system to supply artificial stability many times a second.