[python] Re: Pivot Angle Summary (epic)

Am Freitag, den 13.10.2006, 20:58 +0200 schrieb JÃrgen Mages:
> Hello all,
> 
> in the recent time lots of new members have joined the list.
> Alltogether there are 124 members now. I imagine that lots
> of the newbies are a bit confused about the recent discussions.
> 
> Therefore I would like to give a brief status report about
> the results of the discussions about "The Angle":
> 
> 1. Why negative trail?
> 
> When riding a bike, it is good to have steering feedback and a
> force that pulls the steered wheel back into a centered position.
> 
> In normal bikes this centering force is realised by the caster effect
> caused by the pivot angle and the positive trail. This effect is
> zero when the bike is stopped and it is increasing with the speed.
> 
> When trying to build a very low center-steered recumbent one has
> to face the fact that, with the steering pivot being beneath the
> seat, one has to implement a very shallow pivot angle to achieve
> positive trail.
> 
> This shallow angle (around 30 deg) has big disadvantages:
> First the steered front wheel wants to tip into the curve by its own
> weight (wheel flop). A strong steering damper is needed to bring the
> wheel back to the center. Second the bike is very hard to maneuver
> because of its huge turning circle.
> 
> So what to do? Allowing a negative trail and thus obtaining bigger
> pivot angles resolves the mentioned problems.
> 
> But what about the centering force? The caster effect is gone but
> another force comes into play now: By turning the wheel, the pivot
> rises and as the rider sits above the pivot he is also lifted. As
> the lowest pivot position is the centered wheel, it is pulled back
> automatically (by gravity) after each steering action. This seat
> rising effect is present at any speed and also when the bike is
> stopped.
> 
> What is the best pivot angle?
> 
> By looking at this graph (credits to Dirk BonnÃ):
> 
> http://www.python-lowracer.de/pics/height_vs_aa.gif
> 
> one could naively conclude that the best pivot angle is around
> 53 degrees, because it yields the biggest seat rising effect.
> 
> This is true, but there is still the wheel flop which comes into
> play at shallow angles. I tested this geometry, resulting in a
> bad riding behaviour where the front part was constantly swinging
> from one side to the other. So I gradually increased the pivot angle
> until the bike became rideable at exactly 63 degrees.
> 
> This "Sweet Spot" was amazingly sharp bounded at its lower edge
> (two degrees lower and the bike was unrideable) and diffuse bounded
> at its upper edge (bigger pivot angles were still rideable, but the
> self centering effect declined).
> 
> So 63 degrees is the best pivot angle?
> 
> Not really, but it is close: It is exactly the angle where the whole
> front part (including the riders legs) is in equilibrium with the
> rest of the bike (including the rest of the rider). This is different
> with every bike and rider.
> 
> The heavier the rear part is in relation to the front, the closer the
> pivot angle may approach the desired maximum seat rising angle.
> 
> For those who want to be on the safe side I recommend a pivot angle
> of 65 degrees.
> 
> Sorry for the epic ;-)
> Any corrections and hints are welcome ...
> 
> Best regards,
> JÃrgen.

Thanks for this great summary. 
You could hint future subscribers to some kind of best-of email link
list within the response email they get :-)

Could you extend what you mean by equilibrium? Equilibrium between the
flop-force and the centering force?

Is the self-centering only dependend on the angle, or do i.e the
distances between wheel centers and pivot point matter as well?
If this would be the case, one could vary those distances while keeping
the optimum angle and potentially raise the centering effect...


regards,
Dirk

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