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For simplicity, this article only considers flight at gliding speed (Mach ~0.1), so any compressible flow effect is ignored.

A cross section of a wing has the geometry of an '''aerofoil'''.

In the aeroplane frame of reference, the angle between the chord line and the incident flow is the '''angle of attack'''.

=== Force and moment ===

The '''aspect ratio''' of something is (roughly) the ratio between the length and the width. It describes how slender or stubby something is. A square has the aspect ratio of 1 because its width is the same as its length. A (new) pencil has a larger aspect ratio than a piece of rubber.

The fundamental purpose of having wings is to produce '''lift''', which balances the gravitational force on the aeroplane so that it can stay airborne.

Wherever forces are involved, a resultant moment can be defined. By definition, an aerofoil produces a constant moment irrespective of angle of attack around its '''aerodynamic centre'''.

Consider an object moving along a curved path. Elementary Newtonian physics dictates that force (at least a component of it) must be exerted on the object in the direction normal to its path pointing into the concave side of the path, i.e. the '''centripetal force'''.

Note that the energy approach is generally not applicable to the explanation of lift: no work is being done nor is any energy being transferred between the aeroplane and the air in the process.

=== An incorrect explanation ===

People with some qualitative aerodynamic knowledge often argues that it is the “Kutta condition” that the air meets at the trailing edge in the same time. However, the Kutta condition, despite a lack of precise mathematical formulation, requires nothing more than the trailing edge being a stagnation point (in 2D). In other words, it requires that the streamlines meet, just like two carriage ways merge into one, but the vehicles on the carriage ways can travel at very different speeds before reaching the junction.

=== In two dimensions (aerofoils) ===

This is the first reason why high aspect ratio (slender) wings are aerodynamically desirable.

Glider pilots usually are introduced the phenomenon of '''stall''' within the first several flights. This section explains the fundamental physics of stall.

Review how lift is created: it is necessary that the streamlines follow the shape of the aerofoil and bends accordingly. If the streamlines cease to follow the aerofoil, i.e. the flow detaches from the aerofoil, lift will be reduced very significantly. This is fundamentally what a stall is. It is observed that wings stall once a critical angle of attack is reached. To understand the physics of stall, the concept of '''boundary layers''' must first be introduced.

Consider pouring honey out of a jar: can you empty the jar completely? This is not possible because the honey sticks on the inside wall of the jar and it will not come off completely no matter how long you allow the jar to drain. This is the '''no-slip condition''' of viscous flow: honey is a viscous fluid, and whenever it contacts a wall, it will not slip on it but stick onto it.

Things are, unfortunately, further complicated by the fact that, while the wing can remove energy from the boundary layer, the outer flow can help the boundary layer by “dragging it along”. The interacting factors become such a mess that a mathematical description of the precise point of separation is not yet possible. However, it is generally observed that, there are two methods to make a boundary layer separate, namely a very steep adverse pressure gradient, or a less steep adverse pressure gradient over a prolonged distance.

Here it is necessary to quote without proof that the pressure gradients over the upper surface of an aerofoil is generally proportional to the angle of attack.

A '''trailing edge stall''' happens when the boundary layer separation point near the trailing edge moves forward because the adverse pressure gradient is increased due to an increased angle of attack. This type of stall is more gentle with plenty of warning signs and a gradual loss of lift. This is the stall behaviour observed on training gliders, e.g. K21s.

The stalling of wings in 3D is slightly more complicated than the 2D case. As discussed before, we would expect the spanwise variation of the flow field to have an effect.

In addition, the stall of an aeroplane is almost never symmetric, i.e. the two wings almost always stall differently, this can be a difference of how deep the stall is, or one stalls but the other one does not. The reader probably has been told by an instructor that this is the fundamental cause of a '''wing drop''' and a '''spin'''.

Tip stalling is a characteristic of strongly tapered wings. A tip stall is unpleasant and difficult to handle. This is because the imbalanced force from the stalling sites (which are at the wing tips) can create a large moment around the roll axis of the aeroplane, because the leverage is large. This means the aeroplane can enter a wing drop very quickly and a spin will readily develop. In addition, because the ailerons are typically located at the wing tip rather than the root, a tip stall means the ailerons will be completely ineffective.

A special case is an elliptical wing, which will stall simultaneously. This is part of the reason why a Spitfire is difficult to handle.

An aeroplane designer will usually aim to give the aeroplane the root stall characteristic. When a rectangular wing is not suitable for use, there is another method to move the stall site inboard, which is to add a twist along the spanwise direction, referred to as “'''washout'''”. This makes the tip installation incidence less than the root, so when the aeroplane increases its angle of attack, the critical value is firstly reached at the root instead of the tip. A K-21 has this feature.

Washout can also be used to modify the lift distribution and reduce the induced drag: this is not the primary consideration of this article.

A classic problem in hydrodynamics is called the “d'Alembert’s Paradox”. It describes the very bizarre result that, despite every care being taken and a wide range of cases and methods considered, theoretically anything moving in a fluid will have precisely, absolutely, identically zero drag. Any child who has waved a tennis bat will be able to tell that this is complete rubbish, but for hundreds of years fluid dynamists could not tell what had gone wrong.

An aeroplane experiences three kinds of drag, namely '''skin-friction drag''', '''form drag''', and '''induced drag'''.

Unfortunately, before the discussion of drag creation, it is necessary to introduce the concept of laminar and turbulent boundary layers. In short, a flow can be either '''laminar''' or '''turbulent''', and going from laminar to turbulent is called the “'''transition'''”. This is most easily visualised by observing a burning cigarette in still air: the smoke initially goes straight up nicely (laminar), but after some distance the column suddenly goes unstable (transition) and the smoke wraps up into some unpredictable shape (turbulent flow).

A laminar boundary layer can naturally transit into a turbulent one due to inherent instability, typically when the flow speed is sufficiently high. If natural transition does not occur, it is possible to use a “tripping device” to force premature transition at lower speeds.

Form drag, also known as '''pressure drag''', is the drag caused by the pressure in front of the body being higher than the rear pressure. This is most obvious for a “bluff body”, i.e. a body that does not have a streamlined shape. It is difficult to cycle or walk into strong head wind, because a human body is a bluff body with a lot of form drag. The pressure in front of you is greater than the pressure on your back, and this pressure difference tries to push you backwards. Going forward and you have to continuously fight against this form drag.

A wake is created by boundary layer separation. Recall that a turbulent boundary layer is more reluctant to separate compared with a laminar one, so somehow making the boundary layer turbulent can reduce the form drag considerably. This is the reason why golf balls have dimples: the dimples can trip the boundary layer so that it is turbulent.

Pulling a teaspoon out of a cup of tea can be effortless, but pulling it out of a jar of honey can be more difficult. This is because the teaspoon moving in honey experiences a significant skin-friction drag. Skin-friction drag is created by the viscous fluid sticking onto the solid object, and it largely depends on the '''surface area''' submerged (or in case of an aeroplane, indeed almost all the surface area). Unfortunately, streamlining a body to reduce form drag usually means creating a large surface area, so there is a subtle balance between form drag and skin-friction drag for the aeroplane designer to get right.

Most of the skin-friction drag on a glider comes from the wings. Recall that a laminar boundary layer causes less skin-friction than a turbulent boundary layer, so a lot of gliders use what is called “'''laminar flow aerofoils'''” which are aerofoils designed to keep the boundary layer laminar for as long as possible. The problem being laminar boundary layers separate easily, so the post hoc fix is to add a turbulent trip on the surface of the wing, just before the point where it would otherwise separate. Such a device can be found on the lower surface of the wing of DM (a CGC single seater).

Induced drag only exists in 3D: there is no 2D equivalent. When a lifting wing flies through the air, it is well known that a pair of '''tip vortices''' will be created behind the aeroplane. This is generally explained by considering the air escaping from the under side to the upper side around the tip: a more precise explanation is very involved and shall not be discussed here. However, by creating these vortices, extra kinetic energy is transferred to the air, which now has an additional swirl motion. This energy must come from the wing, and the result to the aeroplane is known as induced drag.

The magnitude of the induced drag coefficient is proportional to the lift coefficient to the second power, and '''inversely proportional to the aspect ratio of the wing'''. When the aspect ratio tends to infinity, the induced drag is zero. This is the second reason that, for aeroplanes whose drag is critical, high aspect ratio wings are desirable. Almost all gliders have large aspect ratio wings: the most extreme example being the ETA, which has a record-breaking glide ratio of 70:1.

It can be shown that, for a glider, the aeroplane lift-to-drag ratio is identical to the glide ratio. It just needs to be noted that the aeroplane lift-to-drag ratio is not the same as the wing L/D, because the fuselage contributes only to drag but not lift.