THEORIES OF DEVELOPMENT OF AERODYNAMIC FORCES
- Total Reaction (TR). The resultant of all the aerodynamic forces acting on the wing or aerofoil section.
- That component of the TR, which is perpendicular to the flight path or Relative Air Flow (RAF).
- That component of TR which is tangential to the flight path i.e. parallel to the RAF.
- Chord Line. A straight line joining the centers of curvature of the leading and trailing edges of an aerofoil.
- Chord (c). The distance between the leading and trailing edge measured along the chord line. Mean chord is often used as a datum linear dimension in the same way that the wing area (S) is used as a datum area e.g. for the LCA the chord is about 4.5 m and it is about 5.6 m for the MiG 29 etc.
- Span (b). Span of a wing is the distance between the two wing tips and is usually denoted as b, the examples are. 50.5 m for the IL 76, 11.36 m for the MiG 29 etc.
- Wing Area (S). Area of the wing projected on a plane perpendicular to the normal axis e.g. about 40 m2 for the Mirage 2000 and 23 m2 for the MiG 21 etc.
- Mean Line or Camber Line. A line joining the leading and trailing edges of an aerofoil equidistant from the upper and lower surfaces. Maximum camber is usually expressed as a ratio of the maximum distance between the camber line and the chord line to chord length. Where the camber line lies above the chord line, the aerofoil is said to have positive camber.
- Angle of Attack (α). Angle between the chord line and the flight path or RAF. In many old textbooks this was referred to as Incidence.
- (Rigger’s) Angle of Incidence. Angle at which an aerofoil is attached to the It is the angle between the mean chord line and the longitudinal fuselage datum. The term is often used erroneously instead of Angle of Attack.
- Thickness / Chord Ratio (t/c). Maximum thickness or depth of an aerofoil section expressed as a percentage of chord length e.g. 5.5% for the SU 30 and 10% for the Hawk aircraft.
- Centre of Pressure (CP). A point, usually on the chord line, through which the TR may be considered to act.
- Streamline. It is the path traced by a particle in a steady fluid flow. It can also be defined as an imaginary line drawn in the field of flow such that the velocity vector at any point on the line is always tangential to the line. It follows from this definition that through every point in the field there passes one, and only one, streamline. In general, no two streamlines can intersect each other, since this would imply that at the point of intersection the velocity vector points in two directions at once, and this is clearly inconsistent. There is one exceptional case where a streamline may intersect itself i.e. at a point in the flow where the local velocity is zero. Here there is no velocity vector, and so no inconsistency. Such a point is called ‘stagnation point’.
- Aspect Ratio. Span/ Chord = Span²/ Wing Area
- Wing Loading. Weight per unit are of the wing. Weight/ wing area.
- Load Factor ( g or n). Total Lift/ Total Weight. L/W.
- Steady Streamlined Flow. In a steady streamline flow the flow parameters (e.g. speed, direction, pressure etc.) may vary from point to point in the flow but, at any point, are constant with respect to time. This flow can be represented by streamlines and is the type of flow, which it is hoped, will be found over the various components of an aircraft. Steady streamline flow may be divided into two types:
- Classical Linear Flow.
(b) Controlled Separated Flow or Leading Edge Vortex Flow. This is a halfway stage between steady streamline flow and unsteady flow described later. Due to boundary layer effects, generally at a sharp leading edge, the flow separates from the surface, not breaking down into a turbulent chaotic condition but instead, forming a strong vortex, which because of its stability and predictability, can be controlled and made to give a useful lift force.
- Unsteady Flow. In this type of flow the flow parameters vary with time and the flow cannot be represented by streamlines.
- Two-dimensional Flow. If a wing is of infinite span, or, if it completely spans a wind tunnel from wall to wall, then each section of the wing will have exactly the same flow pattern round it except near the tunnel walls. This type of flow is called two-dimensional flow since the motion is confined to a plane parallel to the free stream direction.
- Three-dimensional Flow. The wing on an aircraft has a finite length and, therefore, whenever it is producing lift the pressure differential tries to equalize around the wing tip. This induces a span-wise drift of the air flowing over the wing, inwards on the upper surface and outwards on the lower surface, producing a three-dimensional flow.
- Vortices. Because the effect of the spilling at the wing tip is progressively less pronounced from tip to root, the amount of transverse flow reduces towards the fuselage. As the upper and lower airflows meet at the trailing edge they form vortices, small at the wing root and larger towards the tip. These form one large vortex in the vicinity of the wing tip, rotating clockwise on the port wing and anti-clockwise on the starboard wing, as viewed from the rear. Tip spillage means that an aircraft wing can never produce the same amount of lift as an infinite span wing. If the wing has a constant section and riggers angle of incidence from root to tip then the lift per unit span of the wing may be considered be virtually constant until about 1.2 chord distance of the wing tip.
- Vortex Influences. The overall size of the vortex at the trailing edge will depend on the amount of the transverse flow. Therefore, the greater the force (pressure difference), the larger it will be. The familiar pictures of wing-tip vortices showing them as thin white streaks , only show the low pressure central core and it should be appreciated that the influence on the airflow behind the trailing edge is considerable. The number of accidents following loss of control by flying into wake vortex turbulence testifies to this. The vortex upsets the balance between the upwash and downwash of two-dimensional flow, reinforcing the downwash and reducing the effective angle of attack, also inclining the lift vector slightly backwards, as the effective relative airflow is now inclined downwards. The component of TR, parallel to the line of flight is increased. This increase is termed as the induced drag. The resolved lift vector perpendicular to the flight direction is reduced.
The pattern of the airflow round an aircraft at low speeds depends mainly on the shape of the aircraft and its attitude relative to the free stream flow. Other factors are the size of the aircraft, density & viscosity of air and speed of the airflow. These factors are usually combined to form a parameter known as Reynolds Number “RN” and the airflow pattern is then dependent only on the shape, attitude and Reynolds Number.
Reynolds Number (i.e. size, density, viscosity and speed) and condition of surface determines the characteristics of the boundary layer. This, in turn, modifies the pattern of the airflow and distribution of pressure around the aircraft. The effect of boundary layer on the lift produced by the wings may be considered insignificant throughout the normal operating range of angles of attack. In later chapters it will be shown that the behavior of boundary layer has a profound effect on the lift produced at high angles of attack.
When considering the velocity of the airflow it does not make any difference to the pattern whether the aircraft is moving through the air or the air is flowing past the aircraft. It is the relative velocity which is the important factor.