[python] Pivot Angle Summary (epic)

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 Bonné):

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,
Jürgen.

PS: Native speakers please correct me per PM if the text is badly
readable.

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