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behaviour of the NACA4412 aerofoil is shown in Figure A3.20 for angles of attack below and just above the stall. Positive lift occurs at zero angle of attack. Zero lift occurs at a small negative angle of attack of approximately −4°.

The centre of pressure (i.e. the point at which the lift acts), which is at the quarter‐chord position on symmetrical aerofoils, lies aft of the quarter‐chord position on cambered aerofoils and moves towards the leading edge with increasing angle of attack until the stall. After the stall the centre of pressure on all aerofoils moves rearward towards the midchord. However, if forces are evaluated with reference to a fixed chordwise position, then the resultant force through this point is accompanied by a pitching moment about this point (nose‐up positive, by convention). The reference point is usually the quarter‐chord point (c/4 back from the leading edge), but sometimes it is the midchord and sometimes the torsion axis of the section. If a pitching moment coefficient is defined as

      (A3.8)

Figure A3.19 Classification of the NACAXXXX aerofoil range.

Figure A3.20 The characteristics of the NACA4412 aerofoil for Re = 1.5·10⁶.

      then there will be a position, called the aerodynamic centre, for which . Theoretically, the aerodynamic centre lies at the quarter‐chord position and is close to this point for most practical aerofoils.

      The value of C_m depends upon the degree of camber, but for the NACA4412 the value is −0.1. Note that pitching moments are always negative in practice (nose down) despite the sign convention.

      Above the stall the pre‐stall position of the aerodynamic centre usually continues to be used, although no longer satisfying the above definition.

Note

      1 1 There is not complete agreement on the appropriate name for this limit because Lanchester (1915), Betz (1919, 1920), and Joukowski (1920) all published relevant papers. Betz limit is the most commonly used name. See also comment in Chapter 1.

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