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angle to trim in a pull-up gives a direct indication of the normal acceleration response.
Again, as with the static stability, the c.g. position has little influence on the slope of
the control angle with acceleration, but we note that C1′ is not confounded by the
presence of forward velocity derivatives and its value can be directly affected by a
tailplane. Thus, with a large enough tailplane, one can always ensure that C1′ is
positive, although the tailplane may have to be inconveniently large to suppress the
inherent instability of the hingeless rotor at high speeds. However we should note
that a large tailplane (negative mw) with a positive zu may lead to static instability, as
indicated in the discussion relating to E1.
References
1. Hohenemser, K., ‘Dynamic stability of a helicopter with hinged rotor blades’, NACA Tech.
Memo. 907, 1939.
2. Sissingh, G. J., ‘Contributions to the dynamic stability of rotary wing aircraft with articulated
blades’, Air Material Command Trans. F–TS–690–RE, August 1946.
3. Padfield, G. D., Helicopter flight dynamics, Blackwell Science, 1996.
4. Bryant, L. W. and Gates, S. B., ‘Nomenclature for stability coefficients’, Aeronautical Research
Council R&M 1801, 1937.
5. Johnson, W., Helicopter theory, Princeton Univ. Press, Princeton NJ, 1980.
6. Pitt, D. M. and Peters, D. A., ‘Rotor dynamic inflow derivatives and time constants from
various inflow models’, Paper No. 55, 9th European Rotorcraft Forum, Stresa, Italy, 13–15
Sept. 1983.
7. Peters, D. A. and HaQuang, N., ‘Dynamic inflow for practical applications’, J. Amer. Helicopter
Soc., 33(4), pp. 64–68, Oct. 1988.
8. Amer, K. B., ‘Theory of helicopter damping in pitch or roll and a comparison with flight
measurements’, NACA Tech. Note 2136, 1950.
9. Bramwell, A. R. S., ‘Longitudinal stability and control of the single rotor helicopter’, Aeronautical
Research Council R&M 3104, 1959.
10. Zbrozek, J. K., ‘Introduction to the dynamic longitudinal stability of the single rotor helicopter’,
RAE Rep. Aero. 2248, 1948.
11. Bramwell, A. R. S., ‘The lateral stability and control of the tandem-rotor helicopter’, Part II
Aeronautical Research Council R&M 3223, 1961.
12. McLean, D., Automatic flight control systems, Prentice-Hall, 1990.
13. Pallett, E. H. J. and Coyle, S., Automatic flight control, Blackwell Science, 1993 (4th edition).
6
Rotor aerodynamics in forward
flight
6.1 Introduction
In Chapter 3 we gave some methods for calculating the induced velocity in forward
flight on the assumption that the rotor could be regarded as a lifting surface. These
methods give simple expressions for the induced velocity which can be incorporated
into the equations for calculating the rotor forces and blade flapping and which
eventually lead to fairly simple formulae for these forces and moments. We have so
far used only ‘linear’ aerofoil characteristics, e.g. a linear lift slope without stall and
a constant drag coefficient.
We now consider the fact that, as in hovering flight dealt with in Chapter 2, vortex
wakes spring from the individual blades and form a complicated downwash pattern
as the vortex elements spiral downwards below the rotor plane. We also consider the
aerofoil characteristics under conditions of high Mach number and changing incidence.
6.2 The vortex wake
Consider the blade in steady forward flight. As in hovering flight the circulation, in
general, varies along the span and, in consequence, vortex lines leave the trailing
edge and spiral downwards beneath the rotor. In addition, however, and as we saw in
Chapter 3, both the incidence and chordwise velocity vary over wide ranges in
forward flight causing timewise changes of incidence at a given radial position. In
accordance with Kelvin’s theorem each change of circulation at the blade must result
in a counter vortex being shed in the wake. Thus, in forward flight the vortex wake
also includes vortex lines which lie in the spanwise direction. These are referred to
as ‘shed’ vortices, to distinguish them from the ‘trailing’ vortex lines arising from the
spanwise circulation variation. The trailing vortices themselves are of varying strength
due to the timewise variation in the bound circulation in forward flight. The vortex
wake from a blade can be represented as in Fig. 6.1.
Rotor aerodynamics in forward flight 197
Shed vortex
Trailing vortex
Let us look at a small portion of the wake in more detail. Consider an element of
the blade of span dr. The local circulation is Γ, and trailing vortices of this strength
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