nor cal ride sometime??

[Weaver, Mark]

thinking about doing an overnight norcal ride in mendocino nat'l forest (2 hrs or so north of san francisco). my preference would be to start early enough to get somewhere entertaining and camp (perhaps bear creek, ifyou know where that is) and still have time to go exploring for a couple hours with unladen bikes. the area i have in mind is easily accessible with a loaded klr (i drove there with my wife on the back and about half our gear). it's pretty much all good dirt roads. there are some motorcycle trails and fairly rugged jeep trails in the area that are suitable for exploration. if you're interested, please respond with some ideas on dates that work for you. i could do it any weekend in august, or possibly july 1-2. -mark weaver

[Jeffrey L. Walker]

> I never claimed that there isn't a POINT of instantaneous zero velocity, > just that the entire contact patch does not have zero velocity relative to > the pavement. >

Nope, just the great majority of it, where the tire is flattened to the pavement. There is an "entry region" and "exit region" where their will be some slippage between the two surfaces, but this is very small in comparison to the area of the contact patch. Consider this extreme example of a similar system; a tank's tracks. All along the bottom of the track where it is flat their is no relative velocity between the surfaces. Also, bear in mind that as an element of the tire (a differential mass if you will) enters the contact patch, it is not only translating, but rotating, therefore moves up or down rather rapidly, so the amount of time that it slips is very short in comparison to the amount of time that element spends in the contact patch. Yes, the slippage that occurs is a wear mechanism, but I don't think that you have described why tires cup. This wear mechanism you describe would provide even wear on the tire, not uneven wear. I consider the dynamic system like this; With vulcanized rubber and pressurized air in the tire, there is a coefficient of restitution, or spring constant for the system. There is also a damping constant, (which I have no clue as to what it is, but it must exist and offhand I'd say the system is underdamped.) The normal force between the tire and the surface, and the force due to static friction contribute to the forcing function. (Alternating stresses on each side of the contact patch, compression and tension.) Therefore, this is an oscillatory system. I don't know how many degrees of freedom. I do know that the natural frequencies of the system are influenced by the rotational velocity of the tire, and the tire tread pattern. Perhaps it is then a "beating phenomenon" that creates the tire cupping, or simple resonance. This I don't know. As Tom pointed out, this is a very complicated dynamic system, so I'm sure I don't have much hope creating a mathematical model, even with finite element analysis. So you see, it is because of the zero velocity point that tire cupping occurs, as this is the point at which the forcing function occurs, and my original explanation is valid, with refinement. Mr. Morehead, I might respectfully suggest that you check the validity of your own arguments before you make disparaging allusions to the intelligence of others. I am not infallible, and I do appreciate corrections to any theory I might propose, as this is a very important part of the learning process and I still have much to learn. However you came across as rather unprofessional. If you have any doubt as to the professional conduct and ethics of an engineer, then I refer you to the National Society of Professional Engineers Code of Ethics: http://www.nspe.org/ethics/eh1-code.asp More specifically: Engineers shall: 6. Conduct themselves honorably, responsibly, ethically, and lawfully so as to enhance the honor, reputation, and usefulness of the profession. and 7. Engineers shall not attempt to injure, maliciously or falsely, directly or indirectly, the professional reputation, prospects, practice, or employment of other engineers. Respectfully, Jeff Walker