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

On 06/08/2017 17:18, rickman wrote:
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?


You continue to misunderstand. Any pendulum swinging with circular error
speeds up for shorter amplitude; speeding up means increased frequency.
Therefore, for the half cycle inwhich there is a hit, a shorter
amplitude and hence instantaneous higher frequency exists.

Gareth's Downstairs Computer wrote on 8/6/2017 1:37 PM:
On 06/08/2017 17:18, rickman wrote:
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?


You continue to misunderstand. Any pendulum swinging with circular error
speeds up for shorter amplitude; speeding up means increased frequency.
Therefore, for the half cycle inwhich there is a hit, a shorter amplitude
and hence instantaneous higher frequency exists.

I understand perfectly and explained it for you in excruciating detail. The
change in phase of the Shortt clock slave pendulum is due to the FIRST ORDER
change in the effective gravitational constant in the pendulum equation by
engaging the leaf spring. While the reduced amplitude of the swing *will*
cause a SECOND ORDER effect in the motion of the pendulum, it will be MUCH
SMALLER than the FIRST ORDER effect.

What part of this do you not understand or not agree with?

--

Rick C

On 06/08/2017 18:37, Gareth's Downstairs Computer wrote:
On 06/08/2017 17:18, rickman wrote:
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?


You continue to misunderstand. Any pendulum swinging with circular error
speeds up for shorter amplitude; speeding up means increased frequency.
Therefore, for the half cycle inwhich there is a hit, a shorter
amplitude and hence instantaneous higher frequency exists.



Nothing in any of rick's posts he does understand the above, or anything
else. Plus, what you have posted is exactly what I explained to you
earlier.

It is clear you are on the edge of resorting to your normal abuse.