49
2.1 Aerofoils
tations the trailing side (B) mostly has no thickness (a practical aerofoil is obtained
by truncating). The leading edge is the final point of the camber line at the leading
side and the trailing edge is the final point at the trailing side. The chord is the line
segment between the leading and the trailing edges (AB).
The camber line is described by the distance to the chord ( y) as a function of
a coordinate ( x) along the chord beginning at the leading edge and running to the
trailing edge. The local thickness is commonly given as a function of the same coordinate. The angle between the chord and the oncoming flow is termed chord angle
or angle of attack. Generally, chord angle means the angle between the chord and a
geometric reference line while angle of attack means the angle between the chord
and the oncoming flow direction. The concepts coincide with a free-standing aerofoil, but become different for an aerofoil in a machine setting. Most aerofoils have
camber. As a consequence, lift is already generated with a zero value of the angle
of attack. The angle of attack must then be negative in order to obtain zero lift. The
position of the zero-lift defines a direction termed zero-lift line. The angle of attack
may also be defined as the angle between the zero-lift line and the oncoming flow.
The latter definition has the advantage of a zero lift with a zero value of the angle
of attack. However, the zero-lift line cannot be indicated on the aerofoil a priori.
From fluid mechanics it follows that this line is found with a good approximation
by connecting the trailing edge to the point of maximum camber on the camber line.
2.1.2 Performance Parameters
Figure 2.3 sketches, as an illustration, the lift coefficient as a function of the angle
of attack for a NACA 4412 aerofoil [1]. This aerofoil was formerly (before the
contemporary common use of computational fluid dynamics techniques) typically
applied in axial pumps and axial hydraulic turbines. The aerofoil shape is sketched
in the figure as well. The NACA denomination refers to the classification by the
National Advisory Committee for Aeronautics, the forerunner of the NASA, National Aeronautics and Space Administration. Also shown in Fig. 2.3 is the drag
coefficient as a function of the lift coefficient. The tangent from the origin to the
curve determines the angle of attack with maximum L/D ratio. Use of the aerofoil
with this angle of attack realises maximum efficiency in most applications. The
corresponding lift coefficient is about 1.00, the drag coefficient about 0.01. The lift
Fig. 2.2 Camber line, chord, thickness and angle of attack of an aerofoil
2.1 Aerofoils
tations the trailing side (B) mostly has no thickness (a practical aerofoil is obtained
by truncating). The leading edge is the final point of the camber line at the leading
side and the trailing edge is the final point at the trailing side. The chord is the line
segment between the leading and the trailing edges (AB).
The camber line is described by the distance to the chord ( y) as a function of
a coordinate ( x) along the chord beginning at the leading edge and running to the
trailing edge. The local thickness is commonly given as a function of the same coordinate. The angle between the chord and the oncoming flow is termed chord angle
or angle of attack. Generally, chord angle means the angle between the chord and a
geometric reference line while angle of attack means the angle between the chord
and the oncoming flow direction. The concepts coincide with a free-standing aerofoil, but become different for an aerofoil in a machine setting. Most aerofoils have
camber. As a consequence, lift is already generated with a zero value of the angle
of attack. The angle of attack must then be negative in order to obtain zero lift. The
position of the zero-lift defines a direction termed zero-lift line. The angle of attack
may also be defined as the angle between the zero-lift line and the oncoming flow.
The latter definition has the advantage of a zero lift with a zero value of the angle
of attack. However, the zero-lift line cannot be indicated on the aerofoil a priori.
From fluid mechanics it follows that this line is found with a good approximation
by connecting the trailing edge to the point of maximum camber on the camber line.
2.1.2 Performance Parameters
Figure 2.3 sketches, as an illustration, the lift coefficient as a function of the angle
of attack for a NACA 4412 aerofoil [1]. This aerofoil was formerly (before the
contemporary common use of computational fluid dynamics techniques) typically
applied in axial pumps and axial hydraulic turbines. The aerofoil shape is sketched
in the figure as well. The NACA denomination refers to the classification by the
National Advisory Committee for Aeronautics, the forerunner of the NASA, National Aeronautics and Space Administration. Also shown in Fig. 2.3 is the drag
coefficient as a function of the lift coefficient. The tangent from the origin to the
curve determines the angle of attack with maximum L/D ratio. Use of the aerofoil
with this angle of attack realises maximum efficiency in most applications. The
corresponding lift coefficient is about 1.00, the drag coefficient about 0.01. The lift
Fig. 2.2 Camber line, chord, thickness and angle of attack of an aerofoil