Helicopter Theory

In the introduction to the book, the author defines a helicopter as an aircraft that uses rotating wings to provide lift, propulsion, and control. He then discusses briefly the basic physical principles that a helicopter needs in order to sustain vertical lift, as well as to move translationally. The design engineer must then weigh the factors that enable the helicopter to move against the maintenance and human factors involved in the use of the helicopter for transportation. The rest of the book is then an extremely detailed and fascinating account of the engineering analysis that goes into the design of a succesful helicopter. The author also overviews the history behind the helicopter, beginning with the Chinese rotor, circa 400 B.C. and with the first succesful flight with one passenger, and one meter above the ground, for about one minute, by Breguet-Richet of France in 1907. The author remarks that helicopter engineering currently emphasizes research and development than with invention. This is especially true in the military environment, with the Apache helicopter being a superb example of just how sophisticated a helicopter can be. It will be interesting to see how the technology and design of helicopters will change in the decades ahead. The trend might be towards pilotless flight for delivering military supplies or manufactured goods from one point to another, or perhaps helicopters that can morph into completely vertical or horizontal aircraft as the need arises.

The physics behind vertical flight is described by the author as 'momentum theory', which was developed for marine propellors in the late nineteenth century. As the name implies, this is just an application of the principle of conservation of momentum. The rotor disk of the helicopter feels a thrust created by the action of the air on the helicopter blades. It must therefore exert an equal and opposite force on the air. This forces the velocity of the air in the rotor wake to be opposite in direction to the direction of the thrust. Momentum conservation, energy conservation, and mass conservation then give a relation between the induced power loss and the rotor thrust. The author also gives details on the 'vortex theory', which is based more on fluid dynamical laws of the flow field of the rotor wake. Emphasizing the local aspects, it reduces to momentum theory in appropriate limits. The author also shows how momentum theory applies to the forward flight of the helicopter.

The author also treats helicopter performance analysis, which boils down to determining the power required and available for a range of flight conditions. The rotor forces and power must be calculated, and the author details two methods to do this: the 'force balance method' and the 'energy balance method'. The use of the computer has made this analysis considerably easier for the design engineer of course. The author gives a very interesting overview of helicopter speed limitations and how the helicopter could be landed safely after an engine failure, all of this being analyzed from a physics perspective.

The mathematics of rotating systems is included in the book, along with the differential equations of motion for the rotor blade. The motion of the blade is expanded into a normal mode representation and analyzed using Sturm-Liouville theory. The author though outlines other approaches to the blade dynamics, such as the Lagrangian formulation and the Galerkin method. And also, in spite of the ability of computers to solve for the aeroelastic equations of motion, the author considers their analytical solution for the cases where such solutions can be obtained. One very interesting part of this discussion was that of 'ground resonance', which is a dynamic instability involving the the coupling of the blade lag motion with the in-plane motion of the rotor hub. There is then a resonance between the frequency of the rotor lag motion and the natural frequency of the structure supporting the rotor.