Lesson 6: Flow Effects and Flight
Section 2 - Subsonic Flow Effects
THE SHAPE OF AN AIRFOIL
An important aspect of airplane design is in determining the shape of an airfoil.
By taking a slice out of an airplane wing and viewing it from the side, you have the shape of the airfoil called the airfoil cross section or more simply airfoil section. The question arises as to how this shape is determined.
The ultimate objective of an airfoil is to obtain the lift necessary to keep an airplane in the air. A flat plate at an angle of attack, for example, could be used to create the lift but the drag is excessive. Sir George Cayley and Otto Lilienthal in the 1800's demonstrated that curved surfaces produced more lift and less drag than flat surfaces.
In the early days of canvas and wood wings, and the time of the Wright Brothers, few air foil shapes evolved from theory. The usual procedure at that time was the "cut and try" method. Improvements came from experimentation. If the modification helped performance, it was adopted. Early tests showed, in addition to a curved surface, the desirability of a rounded leading edge and a sharp trailing edge. The hit and miss methods of these early days were replaced by much better, systematic methods used at Gottingen, by the Royal Air Force, and finally by the National Advisory Committee for Aeronautics (NACA). The purpose here was to determine as much information as possible about "families" of airfoil shapes. During World War II, NACA investigations produced results that are still in use or influence the design of most of today's airplanes. What follows is based heavily on NACA results.
DETERMINING AIRFOIL SHAPE
The following six terms are essential in determining the shape of a typical airfoil:
- The leading edge
- The trailing edge
- The chord line
- The camber line (or mean line)
- The upper surface
- The lower surface
The step-by-step geometric construction of an airfoil section requires:
(1) the desired length of the airfoil section is determined by placing the leading and trailing edges at their desired distance apart,
(2) the amount of curvature is determined by the camber line. This curvature greatly aids an airfoil section's lifting abilities,
(3) a thickness function is "wrapped" about the camber line, that is, one adds the same amount of thickness above and below the camber line; this thickness determines the upper and lower surfaces,
(4) the last step shows the final result- a typical airfoil shape. It has a specific set of aerodynamic characteristics all its own which may be determined from wind-tunnel testing.
In a two-dimensional wing, there is no variation of aerodynamic characteristics in a spanwise direction.
(a) the airfoil section at station A is the same as at station B or anywhere along the span, and the wing is limitless in span.
The point of this is to prevent air from flowing around the wing tips and causing three-dimensional effects (to be discussed later). It is necessary to separate the airfoil's aerodynamic characteristics from the wing's three-dimensional effects.
Bear in mind that no wing is infinite in length but a close simulation may be obtained by insuring that the model of the airfoil section, when placed in the wind tunnel for measurements, spans the wind tunnel from one wall to the other.
In this case (except for minor tunnel-wall effects that can be corrected accordingly), the wing behaves two dimensionally, that is, there is no spanwise variation of the airfoil section aerodynamic characteristics.
TWO-DIMENSIONAL WING
Concerning the circulation about a two-dimensional wing: the fluid flow about an airfoil may be viewed as consisting of two superimposed patterns - one is the free-stream motion of the fluid about the airfoil, and the other is a circulatory flow, or circulation, around the airfoil. These two flows coexist to give the total flow pattern.
Consider this question, if the free-stream flow is prescribed, can the circulation, represented by ѓ [Greek letter capital Gamma] be of any value? A physical condition provides the answer. The flow about the pointed trailing, edge cannot turn a sharp corner without the velocity becoming infinite.
As this is not possible with a real fluid, the flow instead leaves the trailing edge tangentially and smoothly. This is the Kutta condition and it sets the required value of ѓ such that the rear stagnation point moves to the trailing edge. The Kutta-Joukowsky theorem relates the circulation to the section lift by
l = ρ∞ V∞ ѓ where:
l = lift/unit span of two-dimensional wing
ρ∞ = free-stream air density [Greek letter rho]
V∞ = free-stream velocity
Ѓ = circulation strength [Greek letter Capital Gamma]
Therefore, the circulation strength Ѓ is set by a necessary physical condition, and the lift l is uniquely determined.
For a perfect fluid, the drag per unit length is zero. However, in a viscous fluid flow one must include a skin-friction drag and a pressure drag along with a resulting loss of lift.
TWO DIMENSIONAL COEFFICIENTS
In two dimensional coefficients, the point of intersection of the chord line and the line of action of this resultant force is the center of pressure. The resultant aerodynamic force may be resolved into lift and drag components. The lift, drag, and center of pressure are for the cambered airfoil shown to vary as the angle of attack is changed. No aerodynamic moments are present at the center of pressure because the line of action of the aerodynamic force passes through this point.
If the airfoil mounted at some fixed point along the chord, for example, is a quarter of a chord length behind the leading edge, the moment is not zero unless the resultant aerodynamic force is zero or the point corresponds to the center of pressure.
The moment about the quarter-chord point is generally a function of angle of attack.
There is a point, the aerodynamic center, where the moment is independent of the angle of attack.
