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This expression was inserted into the same sort of analysis as presented in Chapter
3, using a tip loss factor B = 0.97, γ = 15, and an arbitrary amount of linear twist. The
induced velocity was assumed to be constant.
As might be expected, the expressions for the force, torque, and flapping coefficients
were quite complicated, partly on account of the presence of the tip-loss factor B.
For performance estimation, Bailey and Gustafson5 calculated the induced, fuselage,
and tailrotor power contributions in a manner similar to that described in this chapter,
but for the profile power Bailey’s results were used by expressing them in chart form
for zero blade twist. However, in order to use the charts it was still necessary to find
the trim values of θ0 and λ and also to interpolate between charts. Although Bailey’s
analysis would appear to contain a more accurate representation of the blade drag, it
is doubtful if it justifies the extra complexity or even gives a more reliable value of
the profile power; for example, the inclusion of the tip loss factor leads to many terms
in B4 and B5 so that a bad choice of the value of B can clearly make a considerable
difference to the final result. In any case, the value of B normally assumed is based
on hovering flight theory and is not applicable to forward flight.
This illustrates the case against too great an expenditure of effort in estimating the
performance of the rotor, as can be seen also by referring to Fig. 4.20. The figure
shows the effective L /D ratio of the complete helicopter plotted against the L /D ratio
10
8
6
4
2
0
Total L/D
Rotor L/D
2 4 6 8 10 12 14 16
Clean helicopters
Aerodynamically unrefined
M = 20 000 kg
10 000
5000
2500
2500
5000
20 000
10 000
Fig. 4.20 Effect of L /D of rotor on L /D of complete helicopter
136 Bramwell’s Helicopter Dynamics
of the rotor alone. The effective drag has been calculated from the power expended,
P, by
D = P/V
giving
L /D = VW/P = VW/(Pp + Pi + Pt + Pf)
where Pp, Pi, Pt, and Pf are, respectively, the blade profile drag and the induced,
tailrotor, and fuselage power contributions.
At cruising speeds, i.e. for tip speed ratios of between, say, 0.25 and 0.35, it can
be calculated from the data of Fig. 4.14 that the L/D ratio for the rotor alone of our
example helicopter varies from about 7 to 10. Figure 4.20 shows that, at these values,
a comparatively large increase of the L/D ratio of the rotor would be needed to
produce a significant increase in the L/D ratio of the complete helicopter, especially
at low values of the gross weight.
Thus, there is a limit to the expenditure of effort that ought reasonably to be spent
in either making calculations of the rotor power or effecting real improvements in
rotor performance through aerodynamic refinement.
What has been said above applies strictly to the calculation of the performance of
the helicopter, by which we mean the estimation of the power for a given flight
condition or the flight range possible for a given installed power. The high speed
performance of modern helicopters, however, is far more likely to be restricted by the
vibration and increase of control loads due to blade stall and compressibility than
through lack of power. It is in this area that the aerodynamics of the rotor must be
considered in sufficient detail to be able to design a rotor in which these undesirable
effects are reduced to a minimum. The simple rotor force and flapping analysis of the
previous chapter is no longer adequate, and more advanced methods are necessary.
The complicated aerodynamics which need to be considered in these flight conditions
will be described in Chapter 6.
References
1. Price, H. L., ‘Rotor dynamics and helicopter stability’, Aircraft Engineering March to July
1963.
2. Bramwell, A. R. S., ‘Part I – the longitudinal stability and control of the tandem rotor helicopter.
Part II – the lateral stability and control of the tandem rotor helicopter,’ Aeronautical Research
Council R&M 3223, 1961.
3. Stroub, R. H., Young, L. A., Graham, D. R. and Louie, A. W., ‘Investigation of generic hub
fairing and pylon shapes to reduce hub drag, Paper No. 2.9, 13th European Rotorcraft Forum,
Arles, 8–11 Sept. 1987.
4. Bailey, F. J., jnr, ‘A simplified theoretical method of determining the characteristics of a lifting
rotor in forward flight’, NACA Rep. 716, 1941.
5. Bailey, F. J., jnr and Gustafson, F. B., ‘Charts for the estimation of the characteristics of a
helicopter rotor in forward flight. I – profile drag–lift ratio for untwisted rectangular blades’,
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