[python] Re: gyro forces
- From: "25hz" <25hz@xxxxxxxxxx>
- To: <python@xxxxxxxxxxxxx>
- Date: Sun, 16 Oct 2005 20:49:58 -0400
I was thinking about some of the other posts have said, and this comment by
Daryl:
"When I tried pivoting the wheel on an axis through the center of the wheel
(like a normal fork) it "fought" me."
plus the link Jurgen posted, finally has given me a little "light".
The primary requirement to feel or use the gyroscopic effect, is how close
your steering pivot point is located to the wheel's axle, and for the
python, I think the front wheel is the most "important" wheel as far as
handling, gyro effect, etc are concerned. Go to the link Jurgen posted and
look at the picture for the "Details of Precession", and I'll use it as my
reference. In my non-technical/non-mathematician description, I think the
following is the case:
- to set the basics, X axis is the axle. Z axis goes fore and aft THROUGH
the axle(X axis) and Y axis goes up and down, but again, THROUGH the axle's
center.
- on the python, only one axis coincides with this picture and that is the
axle itself. So, at this point, we only have 1/3 of the axes lining up to
produce a noticeable/strong gyroscopic effect.
- I don't think it matters if all 3 axes are rotated in any direction, just
so long is the point that they all intersect is a) the same point, and b)
they all maintain a 90 angle to each other. On the python, there is no
common axis or point where all three cross each other.
- because of traill, the Y axis is displaced to the rear and no longer
coincides with any point along the X axis. I think the further the Y axis
is away from X, the more diminished the gyro force is, even if the Z axisis
still interecting the X axis. By holding the python suspended, Y axis
doesn't turn the front wheel at all, but physically moves the whole thing
left and right.
- Z axis is the lean on the python when you turn, and for argument sake, we
can rotate it backwards so it at least intersects the Y axis at 90 degrees.
I don't know for sure if this is a valid assumption or not, but I imagine
the Z axis will automatically be assumed to align itself with the X axis. I
do know that if I draw the Z axis perpendicular to the Y axis on my BHP, it
passes below the X axis (the axle) by about 3.5 cm. The Z axis doesn't
produce the turning action though, because by rotating the Z axis counter
clockwise(for example), it makes the pivot drop to the left, the front wheel
points to the right, and the bike falls over. Rather, the Z axis is used by
the rider to try to get his CoG back to the direction he/she wants to turn
and likely inboard of the tires' contact patches.
So, this means exactly what?
Dimensions:
I plugged the following dimensions into the page for a 26" and 20" wheel:
Density: 100 (which gives a wheel weight of 1kg - about what my front and
rear wheel weighs)
Radius: .33(26") and .25(20")
Depth: .03 (width of a rim. Might be a little narrow by averaging the
whole wheel width, but won't do anything but make all the values a little
lower across the board)
RPM: 425 for a .33R wheel (52.87kph), and 561 for a .25R wheel (52.87kph)
Degree change: 30 (that might be high when considering normal steering
correction input)
Time in Seconds: 1
Distance between bearings: .135 (the standard width of an ordinary rear
wheel these days)
- a 26"(.987 @ 52.8kph) wheel produces about 40% the gyroscopic torque of a
20"(2.245 @ 52.8kph) wheel at the same speed in kph
- a 26" wheel produces about 50% of the gyroscopic torque of a 20" wheel at
the same RPM
- the increase in gyroscopic torque is linear to the increase in RPM and
speed. So, the torque produced at 10kph, is half that produced at 20kph.
The effect is linear for both, and likely all, wheel sizes.
I used the formulae page so I could definitively see how the math worked
out, so I now know that gyroscopic force isn't an exponential one like some
of the fluid dynamics formulae are. The force values produced are fine, but
that only applies to a rotating mass with all 3 axes coinciding at the same
point in 3D space - which the python does not have. So, what's next? I
went out to the garage, of course :)
I grabbed a 20" and 26" rear wheel. By the force numbers produced, there is
about 6 to 7 foot pounds of gyro torque on the axle ends at 50kph. At the
speed I was spinning the wheels, likely 1/4 of that. So, I did the
following while holding both ends of the axles with both hands at shoulder
height:
1. spun both wheels at arm's length and tried to rotate them on the Y, and
then the Z axes
2. spun both wheels at arm's length while I pivoted using my torso as the Y
axis, not the wheel's axle as the Y axis
3. spun both wheels at arm's length while I tilted sideways using my waist
as the Z axis
4. using the 20" wheel, I repeated the same exercises but with my arms bent,
bringing the wheel as close to my chin as possible, but still keeping it at
shoulder height
So, using my rough "analog" tests, I found the following:
- For the 1st test, I really couldn't detect much difference in gyro torque
between the two wheel sizes. Looking at the force numbers for the torque,
they'd be around 3 ft/lbs no that would likely be below my "finesse" level
and unable to feel the difference that was obviously there
- For the second test, the gyro torque produced was considerably less than
the first test, but again, both wheel sizes felt pretty much the same. If I
tried to twist faster, the gyro torque was geater, but again, much less than
test 1. Additionally, some small instability produced by my arms not being
completely rigid and parallel likely added to the torque by moving slightly
in more than 1 axis at once.
- For the third test, same results as the second - very light/weak gyro
torque felt.
- For the 1st test repeated at half arm length, no change in apparent gyro
torque
- For the 2nd test repeated at half arm, the apparent torque felt stronger
than at full arm's length, but still much weaker than at full arm's length
- For the 3rd test repeated at half arm, the same result as above. The
apparent gyro torque felt stronger than at full arm's length, but no where
near test 1's strength.
While my method might not have been very strict, I don't think I need a
fancy test rig to be able to see that the closer the twisting motion (in
eith Y or Z axes) is to the X axis, the stronger the gyro force is. In the
end, traill seems to be the biggest gyro killer. Following close to that is
the pivot angle, I think, because the pivot angle makes steering input sweep
the whole wheel in an arc, back and down, which further moves the forces
away from the X axis. If I had the wheels as rigidly mounted as they are in
a python frame, by themselves, it doesn't surprise me at all that the gyro
forces couldn't be felt at all when I tried it a few days ago. Any gyro
torquing action would have to make it past the ability of the chainstays to
absorb the wheel's torquing action before it could be felt at either the
pedals or the seat. A python and rider would be, on average, 180 to 200lbs?
Even a 16" wheel at 52kph produces about 18 ft/lbs of torque (when all axes
are aligned). So when you factor in the counteracting levering force
produced by the rider weight at the distance of the pivot from the axle,
plus the diminished gyro force because the Y (possibly Z axis too) axis is
out of alignment, how much would you actually feel?
So, the shorter the trail, the stronger the gyroscopic forces will be felt.
The closer the Z axis is to the actual axle height, the stronger the gyro
forces will be felt. And, according to the gyro formula page, the smaller
the wheel, the stronger the gyro forces will be for any given speed, but
again, all three axis need to be aligned to produce the strongest force.
Mention of the wheel size changes on the Flevo is interesting. Looking at
the design of them, 2 other things would have immediately changed as well.
The amount of trail and the seat height, unless the frame was redesigned to
put these two dimensions back at their original values. Was the 28" seat
height and trail compared to the 26" seat height and trail, or did they just
assume that gyroscopic forces were the culprit? Keeping the same frame
geometry, did it change the handling again when switched to 24" or 20"
wheels too?
If gyro forces are actually at work, one now has three options to produce a
more stable python. Low pivot angles, optimum wheelbase, and small
diameter - high RPM wheels. So, counter-intuitively, switching from big
wheels to small wheels doesn't diminish the gyro force, it increases it by
double or more. If the gyro force was at work, that should produce a torque
that you can feel at high speed, but my problem, especially downhill, is
that I don't have hardly ANY torque/weight/feel telling me what the python
is doing.
Sorry for the epic :)
> It´s good that Dirk brought back the gyro effect into discussion.
>
> The flevoracer was reported to have "strange high speed behaviour"
> once it had 28" wheels. Therefore the company changed the wheelsize
> to 26" thus solving the problem.
>
> Not knowing exactly what happened, one could presume that
> the stronger gyro force lead to a scary feeling at higher speeds.
>
> When I find the time I will wrap the spokes of my front wheel with
> lead tape (the ones, used in curtains) and make some experiments.
>
> http://www.gyroscopes.org/math.asp
>
> is a good site that calculates various aspects of gyro force.
>
> Cheers,
> Jürgen.
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