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Aerofoils and Wings

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You do not have to be an aeronautical engineer to fly gliders (though a considerable number of CUGC members actually are), but it generally helps the training and examinations if the pilot has a sound understanding of some of the fundamental physical concepts. This article aims to provide a correct understanding of how wings work, through a rather painless physical discussion.
== Definitions ==
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'''.
== What a wing actually does ==
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'''.
== How lift is created ==
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.
== Creation of lift: fake physics ==
The following argument is usually quoted in an attempt to explain the creation of lift:
This explanation is, disappointingly, being used by science textbooks in various countries, by flying instructors, and (so it is said) by the RAF. It cannot be stressed enough that this explanation is wrong, despite the fact that it invokes Bernoulli’s Equation which is of fundamental importance in the theory of potential flow. To be specific, this explanation contains two points of error:
1. # The Bernoulli’s Equations is a streamline equation. It can only be applied along a streamline and not otherwise, unless adequate treatment is given to the Bernoulli Constant to prove that it is the same for the two points of interest. This can, however, be done in this case. Furthermore, Bernoulli’s Equation is only strictly true for inviscid, incompressible fluids, and air is neither (but it is often assumed to be so). 2. # Air particles ''do not meet at the trailing edge in the same time'': this is easily demonstrated by using a pulse of smoke in a wind tunnel. In fact, the air over the upper surface flows faster and overtakes the same air used to be alongside it by a considerable amount by the time the trailing edge is reached. It can be proven that, if the air takes the same time to travel along the wing, no lift is generated.
For the same reason as in (1), blowing air over a sheet of paper is '''not''' a demonstration of the Bernoulli’s Equation (the paper will not bend sideways if held vertical). The sheet of paper works almost exactly as an aerofoil as explained before: it causes the streamlines to bend, thereby harvesting the reaction by the fluid.
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.
== What does the lift force depend on ==
In 2D, the lift force produced by an aerofoil depends only on two factors: the angle of attack, and the geometry of the aerofoil. To be specific, the only factor about an aerofoil that matters is the '''camber''' of the aerofoil, i.e. how bent it is (the mathematical definition will not be introduced in this elementary article). The thickness of the aerofoil has zero (in theory, and very little in practice) effect on lift, which is not easy to understand without working through the continuum mechanics. However, thickness is a useful design tool to modify the pressure distribution around the aerofoil, thereby improving the stalling characteristics.
This is the first reason why high aspect ratio (slender) wings are aerodynamically desirable.
== Boundary layer and stall ==
Glider pilots usually are introduced the phenomenon of '''stall''' within the first several flights. This section explains the fundamental physics of stall.