# Sluggish response to transients in very high L/D ratio airfoils

A sailplane has very high aspect-ratio wings and can have a glide ratio up to 70:1 (the wing L/D ratio is even higher since the fuselage adds drag).

The flow at such high L/D ratios for such long, thin wings approximates 2D potential flow.

Potential flow is how an idealized zero-viscosity incompressible fluid flows. There is no energy dissipation and zero drag. The flow-field has no curl (shear stress is needed to rotate a fluid parcel, which requires viscous shearing on said parcel) and no divergence. This greatly simplifies fluid dynamics calculations and is useful as a conceptual first approximation.

In 2D potential flow lift is proportional to the circulation around the object and the airspeed of the object. Circulation can be thought of as the total amount of curl in a region: the curl in some sense is "concentrated" at boundary of the air foil. Since the vector field is curl-free everywhere else, any curve drawn that goes around the airfoil will have the same circulation.

Any value of circulation can be plugged into the potential flow equations; it is a free parameter. In real life however, viscosity is used to generate circulation. The most obvious way is to drag air around a spinning cylinder. Since potential flow ignores viscosity, it cannot differentiate between a non-spinning cylinder and a spinning one. But real fluids can.

Airfoils also generate circulation. Trailing edges of airfoils generally point downward with respect to the air-stream, even at zero angle of attack (due to camber). Suppose a glider with very long wings is in still air and is suddenly launched. The flow around the wings initially has zero circulation. But (I think) this is (very roughly!) what will happen: drag from the airfoil will tend to slow down fluid parcels that pass near it. But the trailing edge is tilted downwards, which means that it is initially sheltered somewhat from the airflow and generates less drag. This asymmetry in drag will induce a circulation that speeds up air passing over the top (and slows down air passing over the bottom). Eventually an equilibrium is reached; the Kutta condition gives a simple way to estimate this equilibrium circulation.

This is my valiant attempt to unify three explanations of lift: Newton's "deflect air down", Bernouli's "moving faster = lower pressure" and "potential circulation but with a little viscosity". But there is little drag to get this process going. Naively, I assume that wing with an L/D ratio of 100 must travel 100 times the it's chord before the lift is "fully" built up. Is this intuition (backed up with crude experiments dragging a flat plate through water at an angle) correct?

A symmetric airfoil at zero angle of attack generates no lift. If my reasoning is correct, coating the top with shark skin to reduce drag should cause such an airfoil to have a positive lift.

• Where is the question? This comes across as a ramble. SA posts are supposed to contain one clear question. You may want to Google the 'impulsive start' of an airfoil. Commented Jul 19, 2023 at 17:20

Just a couple of clarification from my side, sorry for being pedantic 😉

Since potential flow ignores viscosity, it cannot differentiate between a non-spinning cylinder and a spinning one.

Potential theory only models the flow around a shape; if you know how the flow around a spinning and a non-spinning cylinder looks like then the potential theory can perfectly differentiate between the two (obviously if viscous effects are negligible). Potential theory doesn't even know the concept of lift and it cannot differentiate between a lifting and a not lifting airfoil, that's why the Kutta condition has to be imposed by adding the condition that just above the trailing edge and just beneath it the speed is the same.

This is my valiant attempt to unify three explanations of lift

There are no three "explanations" of lift rather only one mathematical modelling obtained by applying the conservation of mass, energy and momentum i.e. the Navier-Stokes equations. Conservation of momentum is also known as Newton's second plus third law. Bernoulli equation and potential flow are what you get from the Navier-Stokes equations after the simplification of inviscid and irrotational fluid, so all three explanations really are just the same thing (with increasingly degree of simplifications).

I assume that wing with an L/D ratio of 100 must travel 100 times the it's chord before the lift is "fully" built up

The lift starts immediately to be generated, it doesn't need time or space to develop.

A symmetric airfoil at zero angle of attack generates no lift. If my reasoning is correct, coating the top with shark skin to reduce drag should cause such an airfoil to have a positive lift

Coating only the top with shark skin (or anything interfering with the boundary layer) would for sure energize and thicken the boundary layer, virtually making the shape of the airfoil no more symmetric; this will or will not improve the aerodynamic characteristics according to how exactly the boundary layer is modified: for example at low Reynolds number (where the viscous effect of the boundary layer are predominant) I'd expect a $$C_l$$ no more symmetrical (i.e. not passing through the 0), a smoother stall at an higher AoA, possibly a lower $$C_{l_{max}}$$ and a drag reduction at high AoA. This is nothing new and this trick is actually broadly used in model airplanes.