Just pondering a bit more about this, if you think about it the restoring
force is zero when the wheel is straight. Ideally the road force is too. In
reality any little pebbles/dirt/wind etc will try to initiate a sideways
force. I think these forces would be like AC "noise" (both directions left &
right). As speed increases the magnitude of this AC noise increases. Because
the road force is AC noise it may try to initiate a left turn, say, but then
get batted back to the right by something else. I think at low speed this
all happens unnoticed below the restoring force. As you get to "Vcritical"
the AC component begins to become predominant and the "squirrelly" feeling
becomes noticable. Above Vcritical you enter a realm of positive feedback
(instability).
An analogy;
Slow speed is like the stable situation of rolling a marble on a track in a
gully. If you push it off its stable position at the bottom it will always
return to the bottom of the gully. Negative feedback, Stable. The front
wheel returns to the straight position.
Vcritical is a momentary theoretical limit, a perfectly flat track. Neutral
stability. The front wheel has no preference for any position.
High speed is like the unstable situation of rolling a marble on a track on
the top of a hill. If you push it off its stable position at the top it will
immediately take off to the bottom gaining speed as it goes, never to return
to its initial position. Positive feedback, Unstable. The front wheel gets
ripped sideways.
Thus as you ride and increase speed it is like you are slowly bending the
track from a gully into a hill. In fact as you approach a flat track the
ball swings so widely most people wisely back off.
Using my analogy my point was that the best you can do is to slightly delay
the point at which the track gets bent flat but that when the track is *near
flat* the geometry doesn't matter too much. i.e. the geometry will affect
the degree of flatness but the feeling of approaching very flat and slightly
flat is essentially the same.
Cheers Daryl
From: "daryl bender" <darylbender@xxxxxxxxxxx> Reply-To: python@xxxxxxxxxxxxx To: python@xxxxxxxxxxxxx Subject: [python] Re: front-end - "my zero is twice the size of your zero" Date: Wed, 16 Nov 2005 21:53:49 -0500
You know I think it's suddenly dawned on me in a new way. All this talk about pivot angles and trails may be of little consequence at speed. If you look at the last graph;
http://www.python-lowracer.de/pics/height_vs_ab.gif
You can see that for small steering changes the restoring force at *any* (neg) trail or pivot angle is 1) very small (approaching negligible) and 2) almost the same for each case. They only diverge noticeably beyond 10deg turn!I At a 10deg turn the road force trying to turn the front sidways would be incredible! Way way beyond the restoring force. I suspect they are proportionately larger right down to 0deg (the asymptote). Hence the instability. The limiting factor is at what speed (reduction) the restoring force wins out again.
And here I was sketching a variable pivot angle design this morning. Hmmmmmm........ I'm thinking now this won't change too much in the overall scheme of things as the road force (curve) will rise exponentially but the restoring force (curve) is essentially constant. My variable pivot idea may slightly defer the instability but it will always arrive.
I'm thinking now that if you were to have enough force to prevent this the python might not be a good handling bike. Hmmmmm.... This is like battle of the limits in calculus. A "my zero is twice the size of your zero" kind of thing as you are working at the asymptote for both forces.
Cheers Daryl
From: Jürgen Mages <jmages@xxxxxx> Reply-To: python@xxxxxxxxxxxxx To: <python@xxxxxxxxxxxxx> Subject: [python] Re: frontend Date: Wed, 16 Nov 2005 13:41:15 +0100
The curse of NT is the decreasing stability when coasting high speed downhill. 60 kph is kind of a limit for this.But the way I understand it, that is the curse of NT in general. When you have more NT, you get more stability and I would expect downhill speed to improve as well. Or am I wrong?
Unfortunately I am not good ad technical mechanics, but I assume the following:
As Dirk's calculation shows:
http://www.python-lowracer.de/pics/height_vs_trail.gif
the seat rising increases almost linearly with the NT, thus is the self centering force. With increasing NT, the coasting force that wants to turn the front part backward will increase as well - most probably much more than the centering force, thus easily zeroing this force out.
I wish some ingenious physicist will join this list and help us calculating
these effects ;-)
Jürgen.
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