## Hovering–Stable or not?

February 27, 2009 by Tim McAdamsIn a recent blog (“Standing on a Basketball”) when discussing hovering, I stated that a helicopter is dynamically unstable. A reader commented, “Helicopters have neutral dynamic stability. They are not unstable.” This made me think that perhaps I should dig a little deeper into the subject. Sometimes a mathematical model or an engineer’s definition can be perceived differently when used in a practical application.

I’ll start with a basic definition of stability. An object is unstable if, displaced from its position, it continues to oscillate with increasing amplitude. It would be considered stable if it oscillated with decreasing amplitude, eventually returning to its original position. In the case of neutral stability, it does neither of these. That is, the amplitude does not increase nor does it decrease.

To get an engineering perspective on helicopter stability, I reviewed what Ray Prouty has written. Prouty has contributed to the helicopter industry for more than 50 years. He has done work ranging from preliminary design to performance and flight testing. He has also been honored for his contributions to the industry by the prestigious American Helicopter Society (a group that emphasizes engineering excellence in rotorcraft design www.vtol.org ), which named him an Honorary Fellow in 1983. He has written three books on helicopter aerodynamics and his writing is some of the best in terms of taking a complex engineering concept and explaining it in easy to understand language.

Chapter 8 of his book titled *Helicopter Aerodynamics* addresses dynamic stability. Here he provides a great explanation of what happens when a hovering helicopter is displaced by a gust of wind. He states, “A typical helicopter will go back and forth across its starting point with an ever increasing swinging motion until the pilot (or someone else) stops it.” According to Prouty, the rate of growth from one cycle to the next is a measure of the degree of instability. Finally he concludes that a hovering helicopter is unstable. Based on my experience teaching students to hover, I agree.

However, in a quest to produce a more stable helicopter, engineers designing early rotor systems developed devices that acted like gyros. While this made hovering much more stable, it reduced controllability. It was later determined that with practice a pilot could learn to hover without these stability enhancing devices. Today, systems like electronic forced trim and Stability Augmentation Systems (SAS) provide increased stability without sacrificing controllability. Helicopters equipped with these systems would behave more dynamically stable or neutral in a hover.

More information about SAS and other topics is available in Prouty’s books and I would recommend them to anyone who is interested in learning more about helicopter aerodynamics. He is a long time columnist for *Rotor & Wing* magazine and still writes for them occasionally. For more information on how to obtain his books or read his past columns, visit their website at www.aviationtoday.com/rw/