> Having a rake angle on the front wheel makes a bicycle self correcting (if the c.g. is on the right side of where the wheels contact the ground, then a right turn is induced in the front wheel by the rank angle)
No. If you actually read the paper linked (and the Supplementary Online Materials, which contains a lot of the actual information), it is shown that rake angle is not necessary for the bike to be self correcting. You can build a bike with a negative or zero rake angle that is still self-stable (at least, according to the bicycle dynamics modelling software they were using, JBike6; they didn't actually build this particular bike, but did build one that had small negative trail and no gyroscopic effects that was still stable).
As they demonstrate in the paper, none of rake angle, trail, or gyroscopic forces are either necessary or sufficient for self-stability. All of them can influence stability, so saying the gyroscopic theory has been proven wrong is not entirely right either; it is a part of the dynamics that adds stability, it is simply not necessary or sufficient on its own. In fact, the paper shows that on the "benchmark bicycle", removing the gyroscopic force makes it unstable, so on that particular design, the gyroscopic force is necessary for its stability (thus explaining why it was believed for so long that gyroscopic force is what provided stability).
What we know is that gyroscopic forces, trail, rake angle, and distribution of the center of mass of the fork and body of the bicycle all influence stability (in particular, the center of mass of the body of the bike being substantially higher than that of the fork); none of them alone are sufficient to provide stability, and likewise none of them alone are necessary as we can build bikes without them that are still self-stable.
> > Having a rake angle on the front wheel makes a bicycle self correcting ..
> No. If you actually read the paper linked ...
Please don't start replies with a "no", especially when you don't disagree! You reply that it "is not necessary" which does not negate your interlocutor's point!
(probably going to regret going meta, but the initial 'no' in forums and irc really bothers me)
No. If you actually read the paper linked (and the Supplementary Online Materials, which contains a lot of the actual information), it is shown that rake angle is not necessary for the bike to be self correcting. You can build a bike with a negative or zero rake angle that is still self-stable (at least, according to the bicycle dynamics modelling software they were using, JBike6; they didn't actually build this particular bike, but did build one that had small negative trail and no gyroscopic effects that was still stable).
As they demonstrate in the paper, none of rake angle, trail, or gyroscopic forces are either necessary or sufficient for self-stability. All of them can influence stability, so saying the gyroscopic theory has been proven wrong is not entirely right either; it is a part of the dynamics that adds stability, it is simply not necessary or sufficient on its own. In fact, the paper shows that on the "benchmark bicycle", removing the gyroscopic force makes it unstable, so on that particular design, the gyroscopic force is necessary for its stability (thus explaining why it was believed for so long that gyroscopic force is what provided stability).
What we know is that gyroscopic forces, trail, rake angle, and distribution of the center of mass of the fork and body of the bicycle all influence stability (in particular, the center of mass of the body of the bike being substantially higher than that of the fork); none of them alone are sufficient to provide stability, and likewise none of them alone are necessary as we can build bikes without them that are still self-stable.