[python] Re: Trail

On Fri, 2007-03-02 at 06:08 +1000, Henry Thomas wrote:
> George Durbridge wrote:
> > A factor which seems not to be taken into account in any of the Python
> > discussions is the extent to which the lean of the bike in a turn
> > increases the hanging pendulum effect.
> >   
> 
> I have often wondered about this, and came to the conclusion in at least 
> my mental theory on python dynamic stability that when the python is 
> turning at speed, and the rider is leaning into the curve then the 
> hanging pendulum effect must in a essence be helping the bike hunt for 
> the correct line in the curve, rather than exhibiting oversteer or 
> understeer. Or does the Python want to steer straight.

I don't know, but I hope Dirk has a view.  One way of looking at it is
that the sum of gravity and centripetal force acts on the mass of the
machine in the plane into which it is tilted, in the same way as gravity
acts on it when upright and moving in a straight line, so the hanging
pendulum effect will not be altered, except that it is increased in
proportion as the sum of the forces is greater than gravity alone.

> There should be other forces as work too. As the Python leans, the point 
> of contact of the tires with the ground would be moving to the side of 
> the tires, but what also tends to happen (on positive trail bikes at 
> least) is that the contact patch starts to move forward around the front 
> rim and backward around the read rim thus extending the wheel base and 
> changing dynamic forces pushing on the tires on the sides of the tires, 
> and at different angles than on an upright bike. On the Python does the 
> point of contact with the front tire on the leaning bike actually move 
> forward or does the negative in some way cause it to move differently? 

I think that both front and rear contact points in effect move forward
at speed, on bikes and trikes of all sorts, and that this is a generic
effect with pneumatic tyres.  The effect of this movement on wheelbase
will be trivial (probably nil), but there seems to be a significant
effect on trail, reducing it on positive trail machines, and presumably
increasing it on negative-trail machines.  This will affect the force
due to the slip angle, reducing its stabilizing effect on positive-trail
bikes and tending to increase its destabilizing effect on negative-trail
machines.

I am not sure whether contact patch movement will affect the hanging
pendulum much, since that depends on the pivot angle, which in turn
depends on frame geometry.

> What influence to you think this has on the cornering dynamics. On a 
> positive trail bike, there is a point where an extreme lean will in fact 
> neutralize the effect of positive trail to the point where it actually 
> becomes negative and causes instability, but generally the pivot angle 
> is set at such an angle that this is only a theoretical risk.

Movement of the contact patch clearly reduces the stability of
positive-trail bikes at speed, although designers allow for it.  I think
it must increase the instability of negative-trail bikes at speed.  If
it increases the hanging pendulum effect on Pythons, however, there will
be a stabilizing effect which partly offsets the slip angle effect.

I cannot see that lean, apart from steering movement, will affect trail
at all.  Distances along the bike's fore and aft axis on the ground are
unaffected by rotating the bike around that axis.  In the cases which
matter most (high speed turns, at high lean angles) the steering tends
to be turned through only a small angle.  Large steering movements are
usually at very low speeds, with correspondingly low lean angles.  Large
steering movement at high lean generally means a crash.  Many front
wheel drive racing recumbents have severe interference between the chain
and the front tyre at quite moderate steering angles.  They would be
useless in a parking lot, but are fine for racing.

> > There are interesting discussions of trail in books on bike design by
> > Mike Burrows and Tony Foale.  Both have conducted experiments (on
> > positive-trail machines) which satisfied them that steering rake is
> > important only for ergonomic reasons, and that the only important factor
> > in the dynamics of the bike is the mechanical trail.  This conclusion
> > was applied by Burrows to the steering of the Windcheetah, which has
> > negligible rake and about an inch of trail.
> >   
> 
> By rake here are you are talking about the pivot angle or fork offset?

Pivot angle - the angle between the steering axis and the horizontal.
(To be exact, rake is generally measured from the vertical, so let's
refer to pivot angles, since they are the convention in this forum.)

> > By contrast, steering rake is critically important to the dynamics of
> > Pythons.  On Robert's machine, we changed the rake by fitting different
> > sized rear wheels (pity about the brakes ...) and could feel clear
> > differences in the stability.
> >   
> 
> The effect being that you changed the pivot angle with the different 
> tire size and as such the handling characteristics. Did you draw any 
> conclusions as to which angles you felt were better from this? If you 
> posted it here I am afraid I must have missed it.

Yes, we swapped a 24" wheel for the 26" rear wheel, which reduced the
pivot angle, probably by about 2 degrees, and made the bike noticeably
less twitchy.  I think on another occasion, Robert tried a 20" rear
wheel, and I'll ask him about the effect.  Nothing was posted, because
the machine was converted before we could make any real measurements.
I'm afraid I don't even know what the pivot angle was with two 26"
wheels.


-- 
George Durbridge
+61 3 9481 3500
+61 409 413 945

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