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(without decreasing the actual blade thickness), thereby avoiding the shock on the
upper side and consequent pitching moment change when the blade is advancing.
When the blade is retreating, a tip vortex is initiated from the outermost part of the
tip at low angles of incidence, but when at high angles of incidence, the vortex starts
at the point where the chord changes, i.e. at the the start of the parabolic leading edge.
It acts rather in the same manner as the bound vortex on a narrow delta wing aircraft,
e.g. Concorde, maintaining a flow on the upper surface of the aerofoil at a high
incidence and delaying stall (see Fig. 6.38).
The forward extension of the leading edge at the start of the parabolic sweepback
allows the pitching moment caused by a normal geometric sweep of the tip to be minimised.
6.4 Aerofoil characteristics when oscillating at conditions of
high incidence
So far the discussion of rotor characteristics and the calculations made have assumed
226 Bramwell’s Helicopter Dynamics
Fig. 6.37 The BERP blade
that the characteristics of the aerofoil sections of the blade are the same as those
measured in two-dimensional steady flow. Provided the theoretical values of incidence
do not exceed about 12° anywhere over the rotor disc, theoretical and experimental
values of rotor forces and flapping motion are generally in good agreement. However,
it was observed in, for example, the wind tunnel tests of Squire et al.26 that, for a
given collective pitch angle, the slope of the curve of the thrust coefficient with shaft
incidence decreased when the shaft angle exceeded a certain value. It was assumed
that, in this region, stall was occurring on the retreating blade and that the stall area
Rotor aerodynamics in forward flight 227
Fig. 6.40 Thrust coefficient as a function of shaft angle (Boeing-Vertol tests)
Fig. 6.38 Tip vortex at high incidence on BERP tip
20°
12°
0.16
0.12
0.08
0.04
–16° –8° 0° 8°
tc
‘Linear’
aerodynamics CH-47C
8ft model rotor
‘Nonlinear’ steady
2-D aerodynamics
αnf
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
–20° –18°–16°–14°–12°–10°–8° –6°
12ft rotor tests
Linear aerodynamics
Nonlinear aerodynamics
Shaft angle, αnf
Thrust coefficient, tc
Fig. 6.39 Thrust coefficient as a function of shaft angle (RAE tests)
was increasing with increase of shaft incidence. At that time the introduction of
aerodynamic data which included the stall was not possible, as it required computer
facilities which were not available until the 1960s. When such data was included in
rotor theory, it was rather suprising to find that the slope of the thrust coefficient in
the stalled region was much less than that given by experiment27, Fig. 6.39. The
phenomenon had also been reported by Harris et al.28, Fig. 6.40.
228 Bramwell’s Helicopter Dynamics
120°
90°
60°
30°
ψ = 0°
330°
240°
0.2
0.3
0.2
0.3
0.5
0.7
1.1
1.3
180°
150°
300°
270°
210°
0.5
μ = 0.3
θ0 = 8°
αnf = –5°
Reversed
flow
Fig. 6.41 CL contours derived from wind tunnel tests (Meyer and Falabella)
150°
120°
90°
60°
30°
ψ = 0°
330°
300°
270°
240°
210°
180°
0.95
0.9
0.85
0.85
0.85
0.85
0.9
0.95
0.95
μ = 0.3
θ0 = 12°
αnf = –10°
Reversed
flow
Fig. 6.42 Computed CL contours using two-dimensional steady aerofoil data
0.7
0.9
1.3 1.1
0.9
0.95
It was also found that the calculated torque was considerably higher than the
experimental values. It was therefore concluded that the rotor blade did not stall in
the same manner as when under two-dimensional steady conditions. This notion was
reinforced by analysis of the wind tunnel tests of Meyer and Falabella29 and the
flight-test data of Scheiman30 which indicated values of lift coefficient far in excess
of the maximum steady values, as in Fig. 6.41, which shows the results from the tests
of Meyer and Falabella. The CL contours for calculations made with the steady twodimensional
data and uniform induced velocity distribution are shown in Fig. 6.42
　
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