119
edits
Changes
From CUGC Wiki
new section
= Creation of lift: fake physics =
=== An incorrect explanation ===
The following argument is usually quoted in an attempt to explain the creation of lift:
“Air meets the wing and separates into two streams, but the particles must meet again at the trailing edge in the same time. Therefore, the airflow on the upper surface is faster because the route to be travelled in the same period is longer. According to Bernoulli’s Equation, fluid that travels faster has lower pressure. Therefore, there is a pressure difference between the two surfaces which integrates into the force 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. === What's wrong? === 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:
# 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).
= What does the lift force depend on =
== In two dimensions (aerofoils) ==
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.
Any symmetric aerofoil has a lift coefficient (lift force per unit chord and unit depth) of 2πα, where α is the angle of attack. A cambered aerofoil has an additional lift coefficient at zero angle of attack added to this value.
== In three dimensions (wings) ==
In 3D things are more complicated. Consider the tip of a wing: little pressure difference on the upper and lower surfaces can be sustained at the tip, otherwise the flow will accelerate to very high speeds because an escape from the lower to the upper surface is possible. Therefore, it is necessary that the flow around a 3D wing has a '''spanwise variation''', despite the wing might have the geometry of a uniform extrusion. As a result, it is expected that the '''aspect ratio''' of the wing (how slender or stubby it is) to have an effect on aerodynamic performance.
= Boundary layer and stall =
== Introduction ==
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.
== Boundary layer physics ==
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.
== Stalling in 2D ==
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.
== 3D stalling behaviour: planform and washout ==
=== Introduction ===
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.
Assume in this section that the aerofoil shape does not vary with span: it only scales larger or smaller.
A wing seldomly stall simultaneously (i.e. stalling at the same time for all spanwise locations). Instead, depending on the design of a wing (to be specific, the planform and twist), a stall firstly develops at a particular spanwise location. This location can be at the root, at the tip, or somewhere in the middle. These stalling behaviours are referred to as '''root stall''', '''tip stall''', and '''midspan stall''' respectively.
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'''.
=== Planform effects ===
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.
Rectangular wings or slightly tapered wings have the root stall characteristic. A root stall is the safe kind of stall: the leverage of the imbalanced forces is small, so the aeroplane will be slow to enter a wing drop. Furthermore, the aileron may still have some effectiveness even when the root of the wing is stalled, so the aeroplane is less tricky to handle (consider the exercise to maintain a glider in a straight stall using ailerons). This is the reason why trainer aeroplanes tend to have rectangular wings, e.g. the Cessna Skyhawk.
A special case is an elliptical wing, which will stall simultaneously. This is part of the reason why a Spitfire is difficult to handle.
=== Washout ===
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.
[[Category:Theory]]
