[python] Re: [python]
- From: George Durbridge <gdurbrid@xxxxxxxxxxxxxx>
- To: python@xxxxxxxxxxxxx
- Date: Fri, 20 Aug 2010 19:24:19 +1000
On Fri, 2010-08-20 at 02:18 -0500, Howard Stevens wrote:
> Hey Dirk!
>
> I made some modifications and it was most interesting. First I reduced
> the pivot angle to about 55degrees which reduced the PSI considerably
> and improved the ease of turning. Then I reduced it further to 50
> degrees and the PSI ceased altogether! Hooray!! Also the steering was
> even easier and the wheel tilting was moderate...I would hardly call
> it wheel-flop at all. This is not what I expected...I thought that the
> less the pivot angle, the more difficult the steering would be, but it
> was easier! So it seems you have solved my problem!
Dirk may have solved your problem a long time ago. The graphs on
Jurgen's frame geometry page from Dirk's program which calculates the
inverse pendulum effect suggest that the optimum effect will be at about
53 degrees, which is broadly consistent with what you have found. Only
broadly, because the graphs don't suggest much improvement between 62
degrees and 55 degrees, or any improvement between 55 degrees and 50
degrees. But they do suggest that 50 - 55 degrees will be better than
62 degrees, which in turn is better than 70 degrees.
It is interesting that the graphs fit your experience on a trike better
than they do Jurgen's and others' bikes, for which the optimum seems to
be around 63 degrees. As I understand it, Dirk's program makes no
allowance for the tilt or lean of a bike in a bend, which must interact
with the inverse pendulum effect. Because a trike doesn't lean, the
program may be a better fit for a trike than a bike.
Interestingly, Esko Meriluoto settled on 53.1 degrees as a suitable
pivot angle for a centre-steered trike, exactly in accordance with the
graphs. I don't hink he explains how he arrived at this angle, but his
first prototype was adjustable in many ways, so he probably tested this
out. Unfortunately, the projects and wiki pages don't seem to record
pivot angles of any Python trikes (except one of 80 degrees).
Jurgen also points out that the problem with a Python with a pivot angle
less than 60 degrees is wheel flop. But wheel flop is a much worse
problem with a bike than with a trike, because as the bike flops there
is a positive feedback effect, with the rear of the bike falling towards
the outside of the turn, which makes the problem worse. To correct the
flop, you really want the bike to fall to the inside of the turn. A
trike doesn't do either, but stays stolidly upright.
> I think the geometry and mathematics of all this is not simple, for
> many factors come into play, and to varying extents on different
> cycles. As you said, the pivot angle was quite significant and so is
> the position of the pivot. I also suspect that the Cof G of the
> bike/trike is also important as the percentage of the total load on
> the front wheel and pivot would also affect the centring forces and
> therefore the PSI. Perhaps bicycles and tricycles also behave
> differently...does anyone have any ideas on this?.
You are right on all of these points. The dynamics of keeping a bike
upright is very complex. As Jurgen points, out, the centring force from
the inverse pendulum comes from the rider's weight over the pivot. If
the CoG is moved back, reducing the weight over the pivot, the centring
force is reduced, but the road forces tending to push the front wheel
out of line seem to remain the same, so the trike will be less stable,
or will become unstable at a lower speed.
> I have about 35% of the weight on the front wheel and that seems ok
> even on steep ascents, but of course on gravel a steep ascent will
> lead to wheel slipping. I haven't found much problem with loading the
> trike, and suspect that it would make no difference at all, if it is
> placed directly over the rear axle.
>
> In my particular case it seems that it was necessary to decrease the
> pivot angle to counteract the PSI induced by the forward position of
> the pivot. Perhaps it also counteracted a PSI tendency because only
> 35% of the weight is on the front wheel. Another possible factor could
> be the amount of negative trail with different pivot angles and wheel
> sizes. It is starting to sound a bit like rocket science!!!
No, just sprocket science.
> Cheers Howard
>
> Hi M Channon or is it McHannon! Yes, your python pivot is pretty much
> where mine is, so it is interesting that you don't get PSI. I'm not
> sure what PIS is....your not taking the piss outa me are you? Cheers
> Howard
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