1b) Karnopp, D. (2004). Vehicle Stability, Marcel Dekker.

Karnopp presents material on a basic bicycle model in chapter 7 that can be used to understand counter-steering. He also develops a basic controller for his model and discusses rear wheel steering. Chapter 8 discusses casters.

2b) Patterson, W. B. (2004). The Lords of the Chainring. Santa Maria.

So far this is the only attempt at developing design guidelines for handling qualities of a bicycle that I have come across. This is the text for a class taught at California Polytechnic State University, San Luis Obispo by the author. Visit [11o] to find out how to purchase a copy of the text.

Patterson develops a model which is based on the simple models presented in [1b], [2p], and [4b]. He begins by adding a relationship that relates steering input at the handlebars to the effective steering angle. The relationship includes the effects of head tube angle and roll angle but neglects frame pitch.

He then calculates the velocity of the center of mass of the bike which leads to a relationship between the yaw rate and the roll rate of the bicycle. With a little linearization and manipulation, this leads to two relationships. The first is a relationship between the roll rate and the steering input angle that Patterson calls this 'Roll Control Authority' and the second is the relationship between yaw rate and steering angle input, 'Yaw Control Authority', which are both linear with respect to velocity. He shows how the roll and yaw control authority can be calculated for a bicycle with known handling qualities and an unconventional bike's geometry can then be adjusted to have similar values for roll and yaw control authority. These relationships are his first two important design guidelines.

Patterson expands his model to include forces and focuses on determining the moment about the steering axis due to the normal and friction forces from the ground onto the wheel contact point. His formulation is more akin to a modified static analysis than true dynamic and may be similar to the one presented in [1p] on page 30. He uses this force balance of a bicycle in a constant rate turn (with no roll) to formulate the forces acting on the front wheel contact patch when the effective steering angle is small. This leads to a relationship between the moment about the steer axis and the input steering angle. This relationship includes several important parameters but most importantly trail is added into the model. Patterson calls this second design guideline the 'control spring' and it shows what the rider feels when a certain steering angle is applied.

Thirdly, Patterson includes the moment about the steering axis due to normal force on the front wheel contact patch when the bike is rolled. This is once again a static analysis and he uses it to develop a relationship between the moment about the steering axis and the roll angle. He calls this 'fork flop' and says that most riders desire fork flop because it provides sensory feedback through the handlebars.

Patterson and his students have used these three design guidelines to design hundreds of unconventional bicycles and has had good success in designing good handling vehicles at the drawing board. His equations carry many assumptions and neglections (most of which he fails to mention in his book) but seem to be somewhat sound guidelines that a novice bike builder with basic algebra knowledge can use to design a bike that handles well. It would be nice if he cleaned up the formatting of the book, expanded some the writing and published the book in an easy to follow version. The book currently is difficult to read and he pieces together dynamic principles to with very little clarity. The detailed computer program that is constantly referenced should be published along with the book to show that his equations do in fact represent a more rigorously defined dynamic model.

3b) Whitt, F. R. and D. G. Wilson (1982). Bicycling Science. Cambridge, The MIT Press.

4b) Timoshenko, S. (1948). Advanced Dynamics. New York, McGraw-Hill Book Company, Inc.

5b) Wilson, D. G. and J. Papadopoulos (2004). Bicycling Science. Cambridge, The MIT Press.

6b) Abzug, M. J. and E. E. Larrabee (2002). Airplane Stability and Control: A History of the Technologies The Made Aviation Possible. Cambridge, Cambridge University Press.

This is a great starting place for understanding the historical development of the airplane stability analysis and flying qualities. Chapters 3, 5, 6, 10, 18, and 21 were of particular interest and somewhat general enough to give some insight to bicycle handling characteristics. Azbug and Larrabee provide loads of references to the more specific topics discussed in the book.