Rotorcraft is a class of aircraft that uses large-diameter rotating wings to accomplish efficient vertical takeoff and landing. The class thus encompasses helicopters of numerous configurations, tilting proprotor aircraft, compound helicopters, and many other innovative concepts.

Defining “aeromechanics” is more difficult. Today's dictionaries do not capture what the term means for the rotorcraft community. The definitions are not broad enough, and they do not reflect the multidisciplinary facet of the word as applied to rotorcraft. In my 2010 Nikolsky Lecture for the American Helicopter Society, I proposed the following definition:

Aeromechanics covers much of what ther otorcraft engineer needs: performance, loads, vibration, stability, flight dynamics, and noise. These topics cover many of the key performance attributes and many of the often encountered problems in rotorcraft designs.

As with my previous book Helicopter Theory (written in 1976, published in 1980 by Princeton University Press, republished in 1994 by Dover Publications), this text is focused on analysis, with only occasional reference to test data to develop arguments or support results, and with nothing at all regarding the techniques of testing in wind tunnels or flight. Calculated results are presented to illustrate analysis characteristics and rotor behavior.

This chapter summarizes the principal nomenclature to be used in the text. The intention is to provide a reference for the later chapters and also to introduce the basic elements of the rotor and its analysis. Only the most fundamental parameters are included here; the definitions of the other quantities required are presented as the analysis is developed. A number of the basic dimensionless parameters of helicopter analysis are also introduced. An alphabetical listing of symbols is provided at the end of the chapter.

Dimensions

Generally the analyses in this text use dimensionless quantities. The natural reference length scale for the rotor is the blade radius R, and the natural reference time scale is the rotor rotational speed Ω(rad/sec). For a reference mass the air density ρ is chosen.

For typographical simplicity, no distinction is made between the symbols for the dimensional and dimensionless forms of a quantity when the latter are based on ρ, Ω, and R. New symbols are introduced for t hose dimensionless parameters normalized using other quantities.

Nomenclature

Physical Description of the Blade

R = the rotor radius; the length of the blade, measured from center of rotation to tip.

Ω = the rotor rotational speed or angular velocity (rad/sec).

ρ = air density.

Rotary-wing flow fields are as complex as any in aeronautics. The helicopter rotor in forward flight encounters three-dimensional, unsteady, transonic, viscous aerodynamic phenomena. Rotary-wing problems provide a stimulus for development and opportunities for application of the most advanced computational techniques.

Inviscid, potential aerodynamics is the starting point for many computational methods for rotors, allowing practical solutions of compressible and unsteady problems. Lifting-surface theory solves the linearized problem by using the result for a moving singularity, often of the acceleration potential. Panel methods use surface singularity distributions to solve problems with arbitrary geometry. Transonic rotor analyses use finite-difference techniques to solve the nonlinear flow equation.

The rotor wake is a factor in almost all helicopter problems. A major issue in advanced aerodynamic methods is how the wake can be included. Wake formation must at some level be considered a viscous phenomenon, and the helical geometry of the helicopter wake means that the detailed structure is important even at scales on the order of the rotor size. A useful rotor aerodynamic theory must account for the effects of viscosity, such as wake formation and blade stall, which are important for most operating conditions. Solution of Navier-Stokes equations for rotor flows is now common. Hybrid methods can be used for efficiency, typically using Navier-Stokes solutions near the blade and some vortex method for the rest of the flow field.

Sources for the derivations of the equations are Lamb (1932), Morse and Feshback (1953), Garrick (1957), A shley and Landahl (1965), and Batchelor (1967).

Helicopter Rotor Noise

The helicopter is the quietest VTOL aircraft, but its noise level can still be high enough to compromise its utility unless specific attention is given to designing for low noise. As the restrictions on aircraft noise increase, the rotor noise becomes an increasingly important factor in helicopter design. The complex aerodynamics of rotors lead to a number of significant noise mechanisms. Helicopter rotor noise tends to be concentrated at harmonics of the blade passage frequency NΩ, because of the periodic nature of the rotor as seen in the non-rotating frame. There is sound radiated because the mean thrust and drag forces rotate with the blades and because of the higher harmonic loading as well. The spectral lines are broadened at the higher harmonics because of the random character of the rotor flow, particularly variations in the wake-induced loads. The acoustic pressure signal is basically periodic in time (the period is 2π/NΩ), with sharp impulses due to localized aerodynamic phenomena such as compressibility effects and vortex-induced loads. Figure 14.1 illustrates the spectrum of rotor-generated sound. The contributions to helicopter rotor noise can be classified as vortex or broadband noise, rotational noise, and impulsive noise or blade slap. Although the distinction between these types of rotor noise is not as sharp as was once thought, the classification remains useful for purposes of exposition. Cox (1973), Burton, Schlinker, and Shenoy (1985), and Brentner and Farassat (1994, 2003) have presented summaries of helicopter rotor noise mechanisms and analysis.

The Helicopter Rotor in Forward Flight

Efficient hover capability is the fundamental characteristic of the helicopter, but without good forward flight performance the ability to hover has little value. During translational flight of the helicopter, the rotor disk is moving edgewise through the air, remaining nearly horizontal, generally with a small forward tilt to provide the propulsive force for the aircraft. A tiltrotor cruises with the rotors tilted to operate as propellers. A compound helicopter reduces the lift and propulsive force required of the rotor. Yet all rotorcraft configurations execute low-speed forward flight with the flapping rotor in edgewise flow, which is the subject of this chapter.

Thus in forward flight the rotor blade sees both a component of the helicopter forward velocity and the velocity due to its own rotation. On the advancing side of the disk the velocity of the blade is increased by the forward speed, whereas on the retreating side the velocity is decreased. For a constant angle-of-attack of the blade, the varying dynamic pressure of the rotor aerodynamic environment in forward flight would tend to produce more lift on the advancing side than on the retreating side; that is, a rolling moment on the rotor. If nothing were done to counter this moment, the helicopter would respond by rolling toward the retreating side of the rotor until equilibrium was achieved, with the rotor moment balanced by the gravitational force acting at the helicopter center-of-gravity. The rotor moment could possibly be so large that an equilibrium roll angle would not be achieved.

The aeroelastic equations of motion for the rotor were derived in Chapter 16. The present chapter examines the solutions of these equations for a number of fundamental stability problems in rotor dynamics. To obtain analytical solutions, each problem must be restricted to a small number of degrees of freedom and to only the fundamental blade motion. Rotorcraft engineering currently has the capability to routinely calculate the dynamic behavior for much more detailed and complex models of the rotor and airframe. Thus elementary analyses are less necessary for actual numerical solutions, but are even more important as the basis for understanding the rotor dynamics.

Pitch-Flap Flutter

Traditionally, the term “flutter” refers to an aeroelastic instability involving the coupled bending and torsion motion of a wing. For the rotary wing, flutter refers to the pitch-flap motion of the blade. Often the term is generalized to include any aeroelastic instability of the rotor or aircraft, but the subject of this section is the blade pitch-flap stability. The classical problem considers two degrees of freedom: the rigid flap and rigid pitch motion of an articulated rotor blade. Since the control system is usually the softest element in the torsion motion, the rigid pitch degree of freedom is a good representation of the blade dynamics. A general fundamental flap mode with natural frequency υβ is considered. A thorough analysis of the flutter of a hingeless rotor blade usually requires that the in-plane motion be modeled as well.

So far, we have concentrated on developing a method for modeling fluids. We established the idea of the continuum to allow us to describe flows with continuous functions, and we introduced the use of the control volume (CV) to free us from having to follow individual fluid particles (see Chapter 3). We described a method of accounting for stresses in fluids (see Chapter 4) and showed how stress and motion are related through the constitutive equation (see Chapter 5). We developed a solution methodology that led to the microscopic balance equations and, finally, to solutions of simple flow problems (see Chapter 6). We have all of the tools necessary to solve flow problems, and we now turn to the task of modeling and understanding the flow behaviors described in Chapter 2.

In this chapter, we concentrate on internal flows, which are flows through closed conduits. Chapter 8 discusses both external flows, in which fluid moves over or around obstacles, and an important class of flows called boundary-layer flows.

In this chapter and in Chapter 8, we address complex, realistic, and practical flow problems with our modeling methods. We begin the analysis of complex problems with a microscopic analysis on an idealized system.

Our task is to learn to model flows. To set up the models, we draw on our intuition of how fluids behave; for example, we often can guess the direction that a flow takes under the influence of particular forces. Intuition also may enable us to identify symmetries in a flow field. Intuition comes from experience, however, and for introductory students, experience may be in short supply.

One solution to a lack of experience is to experiment with fluids. Unfortunately, not all of us have access to pumps, flow meters, and piping systems; therefore, it is worthwhile to take a laboratory course in fluid mechanics, if possible. Another way to build experience with fluid behavior is to view flow-visualization videos. Between 1961 and 1969, a group of experts in fluid mechanics (the National Committee for Fluid Mechanics Films [NCFMF]) produced a series of flow- demonstration films [112] that introduce fluid behavior; the films and film notes are now available on the Internet. There also are books [170] and other media [65] that catalog fluid behavior, as well as Web sites on which researchers have posted flow-visualization videos, including the Gallery of Fluid Motion [133], and elsewhere [182]. These sites bring to life all types of fluid behavior, from the mundane to the esoteric.