Monday, January 10, 2011

Book Review: "Monocopters" by Francis G. Graham

"Monocopters", by Francis G. Graham, provides a brief history of "single-winged, powered vehicles". It is 70 pages long, including the index. Graham, for you rocket history types, was one of the founding members of what is now the Tripoli Rocketry Association (circa 1964). He is now a physics professor at Kent State. This book is available from Apogee.  In case there is a revision, note this review describes the 1st Edition.

Update: This review provides info regarding the corrected set of equations.

Follow the tags to find all my posts on monocopters, including the ones I've built.


The book is informally published in a 5.5" x 8.5" format (height x width). It is bound with cloth tape. The quality of the printing is poor with the most of the photos being largely unintelligible, and several pages were printed out of sequence.

So, what is a monocopter?

Monocopters are basically single-bladed helicopters. The engine, whether an airplane engine or rocket motor, both drives and counteracts the lift forces produced by the single blade. This delicate balancing act, if orchestrated properly, causes the monocopter to rise into the air, usually with a satisfying, "whump, whump, whump...". They are fascinating contraptions and are usually one of the highlights of any launch. I have been fortunate enough to witness a high-power monocopter launch - it was one of the coolest flights I've ever seen.

In chapter one, "A Cue from Nature", Graham provides a very brief history of flight, starting, as the title implies, with dinosaurs, birds, plants, etc., and leading to the concept of the monocopter. I'm sure many of you have seen a single bladed seed spinning in the wind. The author then presents the history of monocopters. The first documented monocopter was built in 1953, and was powered by a model airplane engine. He concludes this section with some contacts for commercially available propeller-driven models. In the next brief chapter, he talks about the monocopter's role in sci-fi. Anyone remember them in the Gerry Anderson series "Stingray"?

From there, he moves on to describe the development of the rocket-powered monocopter, whose history starts in the early 70's with rocket-powered "helicopter" models. According to Graham, the first rocket-powered monocopter was built in 1982-83 by Korey Kline. These started in mid-power, but soon staged and high power versions emerged. For a short time, they were even produced commercially by ACE rockets - now that's an OOP kit I'd like! This chapter includes over twenty diagrams and photos, including diagrams of two of the author's designs. Earlier, I complained about the photos. Luckily, however, the diagrams are much better.

The next chapter covers the physics of the monocopter, and presents a set of design equations. For a monocopter to fly properly, you have to balance the forces on the rocket in all three axes. The derivation of some of these equations is OK, but the author makes some large jumps. I personally haven't been able to convince myself that there aren't errors in this section. However, there are so many variables to deal with that it is possible that a general understanding of the forces involved, and the rules of thumb the author provides, is all one can expect out of these equations anyway. Despite my criticisms, I still found section interesting.

Update: Yahoo groups user krambo63 had the same misgivings about the equations but actually followed through.  He worked with Francis to update them and has posted the corrections.  You can find images of the corrected pages in the Yahoo Monocopters Group (membership required, see 'files' section).

The following chapter discusses the stability of monocopters. Amid some more fuzzy math (not to be confused with fuzzy logic), he presents several techniques to stabilize your monocopter, the most common of which seems to be a double-weighted balance beam perpendicular to the wing's axis (e.g. the thin rods seen in my photo).

The remaining material includes a description of Graham's personal experiments, musings about the feasibility of manned monocopters, a detailed bibliography, and the index.


In summary, I thoroughly enjoyed this book. It was fun and interesting reading, even though the photos are poor, and is well worth the $10 price tag. The material included some technical stuff (equations, math, etc.) but the presentation was not rigorous or thorough. Yet, enough design tips were provided for me to build my first model. My suggestions for the next edition include better print quality and some examples of how to utilize the equations.

Side note:  Since this book was published, several groups (at least 3) have built guided monocopters (see the 'monocopters' tag below).  This accomplishment required that the equations of motion be known with certainty.  If you are a member of the right technical societies, you might even be able to find them.