In David E.H. Jones's paper "The stability of the bicycle", an
unrideable bicycle (URB-I) is used to demonstrate that a bicycle can
be ridden without gyroscopic assistance. The URB-I has a second,
counter-rotating gyro mounted besides the bicycle's active (ground
contacting) front wheel. This is to counteract the gyroscopic effect
of the active front wheel. Jones demonstrates that the URB-I remains
rideable. A second bicycle, the URB-II had a tiny 1 inch diameter
wheel. This was used to demonstrate fork geometry in the absence of
gyroscopic stabilization.

This paper is heavily referenced in support of the premise of
gyroscopic forces contributing little to the stability of the bicycle.
I remain a little skeptical.

My question is a multi-part question, but I have lumped it together,
as you really can't answer one part without answering the others.

Is it possible to cancel the gyroscopic action of one gyro with a
second counter-rotating gyro, and if so, how does this cancellation
effect work?

Before answering, please refer to the related question "Why can I ride
my bike?" id=25883, asked by gruffgareth-ga and answered by
thx1138-ga, with helpful comments by daemon-ga.

Please also refer to David E.H. Jones, "The stability of the bicycle",
Physics Today 23(4),1970, pp34-40, (c)1970 American Institute of
Physics. Link below (9MB PDF file):

http://ist-socrates.berkeley.edu/~fajans/Teaching/MoreBikeFiles/JonesBikeBW.pdf

I will rate a complete and timely response *****. By complete, I mean
just enough detail so that I understand your answer and don't need
further research to be comfortable with it. References/ links are not
strictly necessary. I am familiar with basic physics and you don't
need to give an explanation of concepts like gyroscopic precession.

I will rate a fairly good, but timely answer ****. Otherwise, your
answer will be paid, but unrated.

If the two gyroscopes are not free to move relative to each other, and
if their total angular momentum is zero, there is no gyroscopic
effect.  Any torque supplied by one when the direction of the axis is
changed is exactly cancelled by the other.  In Jones' paper, he
describes a hoop with a counter-rotating inner part.  The hoop won't
roll like a regular hoop, but falls over because of lack of total
angular momentum.

I think there are 2 questions getting confused here; does a bicycle
(or a hoop) depend on gyroscopic stability, and can you cancel the
gyroscopic effect with contra-rotating disks. Ignoring the first
question (though I suspect the answer's "no"), we then have to ask
which gyroscopic effects are we trying to cancel? Assuming the disks
are identical apart from their direction of rotation, the precession
will be canceled. This configuration has been suggested as a means of
stabilising O'Neil type space colonies. In the case of a bicycle,
though, we're concerned with stability in the plane of rotation. In
this case there's no coupling between the gyros until an attempt is
made to disturb them, when they'll both oppose the movement. The
contra-rotating disks don't cancel each other, they act in concert.

Ian G.

PS  Given the length of time this problem's been running, I suspect
I'm missing something, somewhere. You have been warned :-)

Thanks for your comment Ian.

I'm not really referring to the necessity of gyroscopic forces in the
riding of a bicycle.  Perhaps it is possible to ride a bike infinitely
light wheels (or imagine a bike on ice-skates or roller-blades).
That's not really my concern,

I just want to know if the forces of two gyros can be made to cancel
out (in practical terms) without a linkage other than perhaps a common
spindle. I'm sure it is possible with a complex mechanical linkage.

The reason for my skepticism is AFAIK, the direction of rotation of a
gyro is unimportant. The gyro will exert a correcting force on an
impulse that attempts to move the axis away from true. Therefore, two
idential, extremely thin disks mounted very close together on the same
axis spinning with identical speed in opposite directions wouldn't be
expected to cancel out.

Instead they would, as you say, act in concert.

BTW, I think the issue with the space colony is not one of stability,
but the difficulty of motoring a massive spinning disk without the
constant use of thrusters.  Therefore, two counter-rotating torroids
could be used, because one acts as a counter-balance to the other,
giving each something to mechanically push against.  By locating the
counterbalance ring in the same plane as the habitat ring, some of the
torque effects of acceleration and deceleration are minimised.

That's not the same effect as David Jones' apparatus and my question
about cancelling the stabilization properties.

The more and more I think of it, the more I believe Jones' flawed
experiment has led the bicycling industry astray.

There's still plenty of scope for a researcher to come back with an
answer... Any takers?

Spurious

I think you're right to be skeptical!

Regarding the space colonies, I think we're both right - it's a 2 for
the price of 1 solution. My reason for raising the subject in the
first place was that a number of people on the web talk about
contra-rotating disks or cylinders cancelling each other's gyroscopic
effect when they're only referring to precession. The space colonies
pages give precession more focus.

Cheers

Ian G.

OK, let's get one thing straight:  the answer to the question "can two
counter-rotating gyros cancel each others' gyroscopic action?" is, as
I said before, perhaps not loudly enough, *** Y E S ***.  Two disks
spinning in opposite directions on the same axis have NO angular
momentum, and hence they behave in all respects as though they were
not spinning.  Imagine superimposing the two disks on top of each
other, so that somehow they were occupying the same space, but
spinning in opposite directions.  Essentially this is what a disk
standing still is: you can arbirarily define all the atoms whose
random thermal motions are carrying them one direction as part of the
first disk, and all those that are moving the other way as part of the
second.

RE:

The reason for my skepticism is AFAIK, the direction of rotation of a
gyro is unimportant. The gyro will exert a correcting force on an
impulse that attempts to move the axis away from true. 

The direction is important.  If you put a torque on a gyroscope, say
try to tip a gyro with a vertical axis over by pushing the top of it
to the north, the response of the gyro is to shift is axis in a
direction 90 degrees away from the direction the torque is pushing it
toward (that's why gyros under a constant torque from, say, gravity,
precess, rather than simply move toward the direction the torque
pushes them), so it would tip toward the east if the gyroscope were
spinning clockwise and toward the west if it were spinning
counterclockwise.  With two counterrotating disks, these responses
cancel.

RE:

does a bicycle
(or a hoop) depend on gyroscopic stability, and can you cancel the
gyroscopic effect with contra-rotating disks. Ignoring the first
question (though I suspect the answer's "no")

A hoop absolutely and unquestionably depends on gyroscopic stability
to roll without falling down.  The question of whether a bicycle does
or not is a complicated one, because so many factors work together in
the stability of a bicycle.

racecar-ga

You've just described precession - no argument, contra-rotating disks
cancel each other. I already said that. My contention is that the
other gyroscopic effect, gyroscopic inertia or "rigidity in space",
isn't canceled out.  I think the net angular momentum argument doesn't
apply in this case - the 2 gyroscopes aren't joined in any effective
way.

Let me throw something else into the pot. If you fix the front forks
of a bicycle so that the handle bars can't turn, it becomes
unrideable. I've seen this demonstrated. Several minutes playing with
a drinks coaster between my index fingers (I wish I could remember the
math!) seems to show that precession should be the main factor in a
bike's stability (by turning the bike to one side you correct the
toppling movement). But we've already shown that this isn't true....
Help!!!

Ian G.

There is no 'other gyroscopic effect'.  If you agree that precession
won't occur, than what can you possibly imagine is still acting as a
'gyroscopic effect'?  Do you think that no torque, however large, will
budge the axis of the gyroscope?  That's obviously not true.  But if
there's no precession, the axis must move in the direction of the
torque.  If there were some such thing as 'gyroscopic stability', a
non-zero torque would presumably be required to cause this movement. 
But if you have a non-zero torque which is causing a motion in the
direction in which it's acting, the torque is doing work.  Where do
you think that energy is going?  Is it speeding up the gyroscope's
rate of spin about its axis?  It can't.  Conservation of energy is
violated, and 'gyroscopic stability' (that occurs without precession)
is disproven.

This question has gone stale and I don't expect a researcher to pick
it up so far down the question list, so I'm going to withdraw it now.

In any case, while they don't agree in all respects, the commentators
seem to have thrashed out the principles.  In conclusion:

Two flywheels spinning on the same axis in the same plane (theoretical
answer) with the same angular momentum will exhibit no net precession
force (the force that acts in the plane of rotation at right angles to
the destabilzing force) because the opposing precession forces of the
two flywheels will cancel out. The flywheels will still oppose the
destabilizing force.

Hence the answer to the Question is no, gyroscopic destabilization (as
described - gyroscopic stabilization cancellation) is impossible.

This is not to say that an imperfectly balanced pair of flywheels will
not result in an unstable system.

Thanks to both racecar-ga and iang-ga for their helpful comments.