rcgldr said:
The test results at 30 kph (8.33 m/s) conflicted with the mathematical model ... capsize mode.
A.T. said:
I wanted to follow up on this, because I exchanged e-mails with some of the involved:
The capsize mode predicted by theory above certain speed is not very prominent and remains around zero. It basically means that the bike fails to straighten up and recover from the turn. You cannot show this on a treadmill, because the bike cannot do a long continuous turn there. My own idea: The perturbation they introduce on the treadmill above capsize speed is more like the weave mode for low speeds, which might explain why it doesn't grow at high speeds, and the bike appears stable.
One possible issue I've wondered about; did the mathematical model take into account that the tires are not infinitely thin? When the bike is leaned over, the contact patch moves off center, providing a small amount of torque that would oppose lean, and if capsize mode was close to zero, then that small amount of corrective torque could be enough to prevent capsize and perhaps enough for some self-correction, but it seems unlikely it would result in the rapid correction shown in the video at 8.33 m/s (30 kph). I'm also thinking that if there is a capsize speed for that bicycle, it's significantly higher than the 8 m/s that the model predicted.
I'm thinking the reason for the transition into "lean" stablity (tendency to hold a lean angle) at high speed is due to the gyroscopic forces (at front and rear tire) resisting any change in lean angle, and dominating the self-correction tendencies. Also at high speed, the rate of precession and reaction to leaning (roll axis to pivot axis coupling) of the front wheel will be reduced, because of the relatively large amount of angular velocity in the tires forward rotation compared to the angular velocity along the roll (lean) axis. The bike may actually be falling inwards or outwards, but the rate of change in lean angle is so small that it's imperceptible by the rider.
A.T. said:
Others did experiments with releasing a bike above capsize speed bike in free terrain, and the bike remained in a circular turn until it slowed down to stable speeds. Then it straightened up again. I suggested to use electric powered bikes to see what happens if the bike doesn't slow down.
In the case of sport type or racing motorcycles, at high speeds (100+ mph 161+kph), the motorcycles tend to hold a lean angle as opposed to straightening up. This would be similar to what you described with the bike holding a turn at high speed, but I wonder what the required speed was before this behavior appeared. My guess is that it was well above the 8 m/s speed originally predicted by the model. Also, capsize mode predicts the bike will slowly fall inwards, not hold a lean angle and remain in a near circular turn. Again, I wonder if the width of the tires and the offset contact patch is playing a role here.
A.T. said:
You can have a self stable "bike" without castor and gyroscopic effects.
As I mentioned in post #3, weight distribution can also be used. In the video, the specialized "bicycle" has the center of mass (weight) in "front" of the pivot axis, so the front tire will steer in the direction of lean, which the author states that the key aspect of self-stability (designing a bike so the front tire turns into the direction of lean). Not mentioned in the video, but noticable in the video is that the special test bike has very thin "tires", which I assume was done to minimize any effects related to an offset contact patch when the test bike was leaned.
