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acceptabilty. Schmitz and Yu19 provided a comprehensive review of theoretical and
experimental studies as an aid to understanding the problems, and Lowson20 suggested
the way forward towards achieving quieter helicopters. From the point of view of the
observer on the ground, the most recognisable component of sound radiation is that
of ‘blade slap’, which tends to occur at slow to medium speeds with the helicopter in
descending flight. The interaction which normally provides the predominant effect is
number 4 in Fig. 6.29, for which the miss distance is small and the intersection angle
is highly oblique. For a four-bladed rotor, this occurs at an azimuth angle of about
60°, and leads to a directional preference for the radiated sound pressure level, as
described by Ehrenfried et al.21 in experimental tests and by Lowson22 from fundamental
considerations.
6.3 Aerofoil characteristics in forward flight
We saw in Chapter 3 that the blade encounters a wide range of conditions in forward
0.1
0
–0.1
–0.2
Lift coefficient CL
4 –2 0 2 4
Vortex position, xv (chords)
xv
Γ
Fig. 6.30 Lift coefficient time history (adapted from Leishman17)
222 Bramwell’s Helicopter Dynamics
flight. The incidence of the retreating blade increases with tip speed ratio so that the
stalling angle may be reached, particularly on the important outer section of the
blade, while on the advancing blade the Mach number may reach values at which the
compressibility drag rise begins. These varying conditions may be conveniently
shown in a ‘figure-of-eight’ diagram, as in Fig. 6.31, which shows the α–Mach
number relationship at the radial position x = 0.913 for a ‘Wessex’ rotor flying at
μ = 0.32. The hovering case would be represented by one point on the diagram.
As μ increases, the ‘figure-of-eight’ gradually expands, extending into regions of
higher CL and higher M. To test whether the aerofoil will encounter stall and
compressibility drag rise, one can plot on the same diagram the α–M boundaries for
these conditions. For the NACA 0012, which is the aerofoil on the ‘Wessex’, the
boundaries are shown in Fig. 6.32, together with the α–M variation of Fig. 6.31. It
can be seen that the α–M loop passes well into the stall region on the retreating blade
and well into the drag-rise region on the advancing blade. The effects on the pressure
distribution of the NACA 0012 aerofoil have been examined in detail by Pearcey et
al.23 and they show that the flow is supersonic over some part of the aerofoil for almost
the complete azimuth cycle of the blade. This is indicated in Fig. 6.32 by the fact that
the α–M loop lies entirely beyond the supercritical boundary. Pressure distributions
at the azimuth angles ψ = 112°, and ψ = 237° are shown in Fig. 6.33. Pearcey found
that the stall following ψ = 237° is precipitated by shock induced separation, the Mach
Fig. 6.32 Stall and compressibility boundary
16°
14°
12°
10°
8°
6°
4°
2°
0
0.2 0.4 0.6 0.8
M
α Boundary for
supercritical
flow
Onset of rapid
drag rise
CL max.
boundary
Fig. 6.31 ‘Figure-of-eight’ variation of incidence and Mach number
16°
14°
12°
10°
8°
6°
4°
2°
0
0.2 0.4 0.6 0.8
ψ = 303°
μ = 0.32
x = 0.913
M
340°
355°
10°
155°
112° 42°
199°
α
Rotor aerodynamics in forward flight 223
number near the leading edge being about 1.4 although the free stream Mach number
is only 0.4. There is then a collapse of the pressure distribution until reattachment
occurs when the blade reaches its most rearmost position (ψ = 360°).
The conditions described above relate to a section near to the blade tip, and
impose constraints on the performance of the helicopter. Improvements can be gained
through appropriate design of the tip to alleviate the adverse effects on both advancing
and retreating sides, and through design of the aerofoil shape itself in the tip region
and inboard of the tip. The NACA 0012 aerofoil was not designed with helicopter use
in mind and is not ideal for operating under the extreme conditions described above.
In pursuit of the alleviation of the most undesirable transonic effects on the advancing
side, tip shapes other than straight rectangular have been investigated and are currently
　
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