On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with
it is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing, so for the half cycle where the phase is
adjusted by abridging the swing by the hit of the hit and miss
stabiliser, the frequency of the slave is, indeed, changed.

The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

.... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!

On 08/05/17 19:14, Gareth's Downstairs Computer wrote:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with
it is that it doesn't adjust the phase by adjusting the frequency of
the slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing, so for the half cycle where the phase is
adjusted by abridging the swing by the hit of the hit and miss
stabiliser, the frequency of the slave is, indeed, changed.

The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!



This just won't go away, will it :-). Here we are, arguing over the
semantics of phase locked loops, but the term pll didn't come into
wide use until the 1960's, decades after the Shortt clock. I'll
continue to think of it as a hit and miss governor, as it was
originally described...

Chris

Chris wrote on 8/5/2017 4:06 PM:
On 08/05/17 19:14, Gareth's Downstairs Computer wrote:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with
it is that it doesn't adjust the phase by adjusting the frequency of
the slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing, so for the half cycle where the phase is
adjusted by abridging the swing by the hit of the hit and miss
stabiliser, the frequency of the slave is, indeed, changed.

The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!



This just won't go away, will it :-). Here we are, arguing over the
semantics of phase locked loops, but the term pll didn't come into
wide use until the 1960's, decades after the Shortt clock. I'll
continue to think of it as a hit and miss governor, as it was
originally described...

And that is what it is, not at all unlike a PLL using a bang-bang phase
detector.

--

Rick C

On 05/08/17 20:14, Gareth's Downstairs Computer wrote:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with
it is that it doesn't adjust the phase by adjusting the frequency of
the slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing, so for the half cycle where the phase is
adjusted by abridging the swing by the hit of the hit and miss
stabiliser, the frequency of the slave is, indeed, changed.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!



You seem to be confusing two different things

The error you refer to is due to the pendulum not actually taking a
direct line between the ends of its travel, the error is small for small
amplitudes. There was a famous experiment by a Frenchman in, I think
Paris, he hung a huge pendulum and let it trace its path in sand, rather
than it going 'to and fro' it actually went in arcs as it went to and fro.

The effect is minimised by reducing the amplitude.

As you correctly say, the frequency of a pendulum is given by the
formula you state. If you 'give it a nudge' you may shorted one swing
but the overall frequency is still determined by the formula.

The 'nudge' will change the phase of the swing, not the frequency- ie it
will shorten one cycle.

Brian Reay wrote on 8/5/2017 5:10 PM:
On 05/08/17 20:14, Gareth's Downstairs Computer wrote:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with it
is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing, so for the half cycle where the phase is adjusted
by abridging the swing by the hit of the hit and miss stabiliser, the
frequency of the slave is, indeed, changed.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!



You seem to be confusing two different things

The error you refer to is due to the pendulum not actually taking a direct
line between the ends of its travel, the error is small for small
amplitudes. There was a famous experiment by a Frenchman in, I think Paris,
he hung a huge pendulum and let it trace its path in sand, rather than it
going 'to and fro' it actually went in arcs as it went to and fro.

The effect is minimised by reducing the amplitude.

I believe you are thinking of the Foucault pendulum. This had nothing to do
with elliptical paths of pendulums. This was a pendulum free to swing along
any axis. As the earth rotates the pendulum continues to swing in its
original path and the earth turns beneath it. Of course the pendulum
appears to rotate the plane of swing.


As you correctly say, the frequency of a pendulum is given by the formula
you state. If you 'give it a nudge' you may shorted one swing but the
overall frequency is still determined by the formula.

The 'nudge' will change the phase of the swing, not the frequency- ie it
will shorten one cycle.

Yes, that is right. The change in frequency (phase change rate) is only
momentary.

--

Rick C

Gareth's Downstairs Computer wrote on 8/5/2017 3:14 PM:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with it
is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing,

All *uncorrected* pendulums have circular error. The Fedchenko clock has a
mounting spring for the pendulum that corrects for circular error.


so for the half cycle where the phase is adjusted by
abridging the swing by the hit of the hit and miss stabiliser, the frequency
of the slave is, indeed, changed.

This has nothing to do with the circular error.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!

This equation is an approximation which ignores the higher terms of the
power series of the full equation. It is only truly valid for no swing at all.

--

Rick C

On 05/08/2017 22:24, rickman wrote:
Gareth's Downstairs Computer wrote on 8/5/2017 3:14 PM:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have
with it
is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing,

All *uncorrected* pendulums have circular error. The Fedchenko clock
has a mounting spring for the pendulum that corrects for circular error.

Hadn't heard of that one. At the BHI lecture there was mention of
another correction of circular error by a colied spring attached
somewhere at the bottom, but I wasn't paying full attention at
that point.

There were also other means such as cycloidal cheeks around the
suspension spring.

so for the half cycle where the phase is adjusted by
abridging the swing by the hit of the hit and miss stabiliser, the
frequency
of the slave is, indeed, changed.

This has nothing to do with the circular error.

It has everything to do with the circular error and the variation
in frequency that comes with varying amplitude of the swing.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!

This equation is an approximation which ignores the higher terms of the
power series of the full equation. It is only truly valid for no swing
at all.

.... which is virtually the range where sin( theta) = theta.

Gareth's Downstairs Computer wrote on 8/5/2017 5:57 PM:
On 05/08/2017 22:24, rickman wrote:
Gareth's Downstairs Computer wrote on 8/5/2017 3:14 PM:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with it
is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing,

All *uncorrected* pendulums have circular error. The Fedchenko clock has
a mounting spring for the pendulum that corrects for circular error.

Hadn't heard of that one. At the BHI lecture there was mention of
another correction of circular error by a colied spring attached
somewhere at the bottom, but I wasn't paying full attention at
that point.

There were also other means such as cycloidal cheeks around the
suspension spring.

so for the half cycle where the phase is adjusted by
abridging the swing by the hit of the hit and miss stabiliser, the frequency
of the slave is, indeed, changed.

This has nothing to do with the circular error.

It has everything to do with the circular error and the variation
in frequency that comes with varying amplitude of the swing.

You seem to be completely misunderstanding the operation of the Shortt
clock. The slave pendulum has no need for correction of circular error. It
is a good pendulum, but not a great one. It doesn't need to be great, it is
corrected every 30 seconds by the electromechanical escapement of the master
pendulum. It only has to be good enough to provide an appropriately timed
release of the gravity lever.

So the small circular error has no bearing on the slave pendulum.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!

This equation is an approximation which ignores the higher terms of the
power series of the full equation. It is only truly valid for no swing at
all.

... which is virtually the range where sin( theta) = theta.

Exactly. This *is* the range where sin(theta) = theta. Anywhere other than
zero it is an approximation.

--

Rick C

On 05/08/2017 23:25, rickman wrote:
You seem to be completely misunderstanding the operation of the Shortt
clock. The slave pendulum has no need for correction of circular
error.

I'm sorry, but you totally misunderstood what I was saying, which was
that because all pendulums exhibit circular error, when the hit occurs
in the hit and miss synchroniser and foreshortens the swing, then, for
that half-cycle, and only that half cycle, the frequency is
changed, as it must be.

Just as in the electronic PLL, instantaneous changes of phase have
instantaneous changes of frequency, no matter how short lived,
associated with them.

Gareth's Downstairs Computer wrote on 8/6/2017 5:26 AM:
On 05/08/2017 23:25, rickman wrote:
You seem to be completely misunderstanding the operation of the Shortt
clock. The slave pendulum has no need for correction of circular error.

I'm sorry, but you totally misunderstood what I was saying, which was
that because all pendulums exhibit circular error, when the hit occurs
in the hit and miss synchroniser and foreshortens the swing, then, for
that half-cycle, and only that half cycle, the frequency is
changed, as it must be.

Just as in the electronic PLL, instantaneous changes of phase have
instantaneous changes of frequency, no matter how short lived,
associated with them.

What you say about frequency vs. phase is true and how the Shortt clock
adjusts phase, but it has nothing to do with circular error of the pendulum.
The correction of the phase is from the added spring resistance shortening
the time as well as the travel of the pendulum. The fact that the swing is
shorter and the second order circular error will create a tiny error in the
timing is pretty much irrelevant. The real change is from the added spring
constant changing the first order effect in the pendulum equation. The
coefficient of the gravitational constant is effectively changed by the spring.

Is that more clear?

--

Rick C