Q/noise of Earth as an oscillator
Exciting the Earth with a new frequency (and an adeguate amount of
energy) sets a new rotational speed: you cannot retune a (for example)
quartz crystal in the same way...
On Wed, Jul 27, 2016 at 3:42 PM, Tom Van Baak tvb@leapsecond.com wrote:
Hi Michael,
I sympathize with both your and Attila's comments and would like to dig deeper for the truth on this.
Clearly both the earth and a pendulum (and many other periodic systems) exhibit a decay of energy, when you remove the periodic restoring force. And if you take the classic definition Q = 2 pi * total energy / energy lost per cycle then it would seem earth has a Q factor.
In fact, if you use real energy numbers you get:
- total rotational energy of earth is 2.14e29 J
- energy lost per cycle (day) is 2.7e17 J
- so Q = 2pi * 2.14e29 / 2.7e17 = 5e12, the same 5 trillion as my earlier calculation.
But your point about resonance is a good one and it has always intrigued me. Is this one difference between a pendulum and the earth as timekeepers?
On the other hand, if you swept the earth with an external powerful frequency in the range well below to well above 1.16e-5 Hz (1/86164 s) would you not see a resonance peak right at the center? Given the mass of the planet and its pre-existing rotational energy, it seems like there is a "resonance", a preference to remain at its current frequency. Plus it has a slow decay due to internal friction. This sounds like any other timing system with Q to me.
Or imagine a planet the same size as earth made from a Mylar balloon. Much less mass. Give it the same rotational speed. Much easier to increase or decrease its energy by applying external force. Far lower Q than earth, yes?
It might also be useful at this point, to:
read the history Q and its definition:
http://www.collinsaudio.com/Prosound_Workshop/The_story_of_Q.pdf
and read the patent in which Q first appeared:
http://leapsecond.com/pages/Q/1927-US1628983.pdf
or view the first paragraph in which Q appeared:
http://leapsecond.com/pages/Q/1927-Q-patent-600x300.gif
/tvb
----- Original Message -----
From: "Michael Wouters" michaeljwouters@gmail.com
To: "Discussion of precise time and frequency measurement" time-nuts@febo.com; attila@kinali.ch
Sent: Wednesday, July 27, 2016 5:43 AM
Subject: Re: [time-nuts] Q/noise of Earth as an oscillator
On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali attila@kinali.ch wrote:
"I am not sure you can apply this definition of Q onto earth."
It doesn't make sense to me either.
If you mark a point on the surface of a sphere then you can observe
that point as the sphere
rotates and count rotations to make a clock. If you think of just a
circle, then a point on it viewed in a rectilinear coordinate system
executes simple harmonic motion so the motion of that point looks like
an oscillator, so that much is OK.
But unlike the LCR circuit, the pendulum and quartz crystal, the
sphere's rotational motion does not have a
resonant frequency. Another way of characterizing the Q of an
oscillator, the relative width of the resonance, makes
no sense in this context.
It seems to me that the model of the earth as an oscillator is
misapplied and that the 'Q' is not a meaningful number.
I think the confusion arises here because of a conflation of a
rotation of the sphere (which marks out a time interval) with an
oscillation. Both can be used to define an energy lost per unit time
but the former doesn't have anything to do with the properties of an
oscillator.
Something else that indicates that the model is suspect is that the
apparently high 'Q' implies a stability which the earth does not have,
as Tom observes. Viewed another way, this suggests that the model is
inappropriate because it leads to an incorrect conclusion.
Time for bed. I'll probably lie awake thinking about this now :-)
Cheers
Michael
On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali attila@kinali.ch wrote:
Hoi Tom,
On Tue, 26 Jul 2016 12:36:37 -0700
"Tom Van Baak" tvb@LeapSecond.com wrote:
Among other things, the quality-factor, or Q is a measure of how slowly a
free-running oscillator runs down. There are lots of examples of periodic or
damped oscillatory motion that have Q -- RC or LC circuit, tuning fork,
pendulum, vibrating quartz; yes, even a rotating planet in space.
I am not sure you can apply this definition of Q onto earth. Q is defined
for harmonic oscillators (or oscillators that can be approximated by an
harmonic oscillator) but the earth isn't oscillating, it's rotating.
While, for time keeping purposes, similar in nature, the physical
description of both are different.
Attila Kinali
--
Malek's Law:
Any simple idea will be worded in the most complicated way.
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We have discussed quartz crystals which despite their high Q, may
suffer from periodic "jumps" in frequency do to what I assume are
imperfection that hardly affect Q. If they did affect Q, then that
would have been a good way to grade them for this behavior.
Temperature coefficient is also independent of Q. If I built a
pendulum out of a material with a high thermal coefficient of
expansion, it will not be very stable but the Q will be unaffected.
On Wed, 27 Jul 2016 22:43:04 +1000, you wrote:
On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali attila@kinali.ch wrote:
...
Something else that indicates that the model is suspect is that the
apparently high 'Q' implies a stability which the earth does not have,
as Tom observes. Viewed another way, this suggests that the model is
inappropriate because it leads to an incorrect conclusion.
Time for bed. I'll probably lie awake thinking about this now :-)
Cheers
Michael
If you consider viewing earth from above the equator at a long distance
and imagine a
spot on the surface of the earth. That spot will appear to have a
sinusoidal motion.
The frequency of the sinusoid exhibits a decay. That decay can be
considered as the Q
of the earths rotation.
Pete.
On 7/27/2016 9:00 AM, jimlux wrote:
On 7/27/16 5:43 AM, Michael Wouters wrote:
On Wed, Jul 27, 2016 at 8:08 AM, Attila Kinali attila@kinali.ch wrote:
"I am not sure you can apply this definition of Q onto earth."
It doesn't make sense to me either.
If you mark a point on the surface of a sphere then you can observe
that point as the sphere
rotates and count rotations to make a clock. If you think of just a
circle, then a point on it viewed in a rectilinear coordinate system
executes simple harmonic motion so the motion of that point looks like
an oscillator, so that much is OK.
But unlike the LCR circuit, the pendulum and quartz crystal, the
sphere's rotational motion does not have a
resonant frequency. Another way of characterizing the Q of an
oscillator, the relative width of the resonance, makes
no sense in this context.
There's also the thing that "things that resonate" typically have
energy transferring back and forth between modes or components: E
field and H field for an antenna; kinetic vs potential energy for
pendulums and weight/spring; charge and current (C & L, really E
field/H field again).
Spinning earth is more of an "rotational inertia and loss" thing, with
zero frequency, just the exponential decay term.
If you think of a single measurand in any of these scenarios you have
at the core some sort of exp(-kt)cos(omegat+phi) and we're relating
Q to the coefficient k.
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On Wed, July 27, 2016 8:58 am, Azelio Boriani wrote:
Exciting the Earth with a new frequency (and an adeguate amount of
energy) sets a new rotational speed: you cannot retune a (for example)
quartz crystal in the same way...
Does that imply that this value is not constant:
On Wed, Jul 27, 2016 at 3:42 PM, Tom Van Baak tvb@leapsecond.com wrote:
And if you take the classic definition Q = 2 pi * total energy / energy
lost per cycle then it would seem earth has a Q factor.
In fact, if you use real energy numbers you get:
- total rotational energy of earth is 2.14e29 J
- energy lost per cycle (day) is 2.7e17 J
- so Q = 2pi * 2.14e29 / 2.7e17 = 5e12, the same 5 trillion as my
earlier calculation.
My first intuition is that energy lost per cycle would not increase as the
square of angular velocity, but angular kinetic energy does increase as
the square of angular velocity. The energy losses are from a complicated
interaction of tidal forces and fluid friction between crust and
atmosphere/ocean and mantle and outer core, so I don't trust that my
intuition is correct at all. If however that turns out to be correct in a
rough sense then adding energy to speed up the rotation would change the
period and the Q, which isn't a property of most things with high Q that
we use as stable clocks.
Who has a globe on magnetic bearings in a vacuum chamber and will run the
experiment for us?
--
Chris Caudle
On Wed, Jul 27, 2016 at 11:33 AM, Chris Caudle chris@chriscaudle.org
wrote:
Who has a globe on magnetic bearings in a vacuum chamber and will run the
experiment for us?
The superconducting gyroscopes in the Gravity Probe B satellite did an
extraordinary job of eliminating frictional and other losses in a spinning
object, with a spin-down time constant of 15,000 years.
https://einstein.stanford.edu/TECH/technology1.html
--
--Jim Harman
I believe a phase noise plot deep into the uHz or lower would apply to the
rotation rate of the earth.
On Saturday, 23 July 2016, Hal Murray hmurray@megapathdsl.net wrote:
tvb@LeapSecond.com said:
Earth is a very noisy, wandering, drifting,
incredibly-expensive-to-measure,
low-precision (though high-Q) clock.
What is the Q of the Earth? It might be on one of your web pages, but I
don't remember seeing it. Google found a few mentions, but I didn't find a
number.
I did find an interesting list of damping mechanisms in a geology book.
Geology-nuts are as nutty as time-nuts. Many were discussing damping of
seismic waves rather than rotation.
I've seen mention that the rotation rate of the Earth changed by a few
microseconds per day as a result of the 2011 earthquake in Japan. Does
that
show up in any data? Your recent graph doesn't go back that far and it's
got
a full scale of 2000 microseconds so a few is going to be hard to see.
--
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Scott Stobbe wrote:
I believe a phase noise plot deep into the uHz or lower would apply to the
rotation rate of the earth.
Yup. You'll see lots of uHz to Hz noise plots by people working with seismic noise, for example. My introduction to the subject were the many plots and papers that describe the heroic effort LIGO goes through to measure tidal and seismic noise in order to keep their gravity wave servos locked. Short-term, the surface of the earth is a very noisy place. But if you can model or measure it before it hits the mirrors, you can mostly back it out.
One can use PN and ADEV statistics on earth rotation, just like any other clock or oscillator. And it seems we can also compute Q for the earth, as if it were a mechanical oscillator.
The remaining question in this thread is if earth Q measurement has actual meaning, that is, if the concept of Q is valid for a slowly decaying rotating object, as it is for a slowly decaying simple harmonic oscillator. And that's were get into the history and definition(s) and applicability of Q to non harmonic oscillators, such as coils, capacitors, atomic clocks, planets, pulsars, etc.
/tvb
I'am not sure how the big ring lasers have progressed over the past
years. It seems the big New Zeeland earthquake messed up the nice ring
lasers over there.
http://www.fs.wettzell.de/LKREISEL/G/LaserGyros.html
http://www.phys.canterbury.ac.nz/ringlaser/about_us.shtml
--
Björn
I believe a phase noise plot deep into the uHz or lower would apply to the
rotation rate of the earth.
On Saturday, 23 July 2016, Hal Murray hmurray@megapathdsl.net wrote:
tvb@LeapSecond.com said:
Earth is a very noisy, wandering, drifting,
incredibly-expensive-to-measure,
low-precision (though high-Q) clock.
What is the Q of the Earth? It might be on one of your web pages, but I
don't remember seeing it. Google found a few mentions, but I didn't
find a
number.
I did find an interesting list of damping mechanisms in a geology book.
Geology-nuts are as nutty as time-nuts. Many were discussing damping of
seismic waves rather than rotation.
I've seen mention that the rotation rate of the Earth changed by a few
microseconds per day as a result of the 2011 earthquake in Japan. Does
that
show up in any data? Your recent graph doesn't go back that far and
it's
got
a full scale of 2000 microseconds so a few is going to be hard to see.
--
These are my opinions. I hate spam.
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The main issue has been deemed to be safety- or lack of it, due to the ring
lasers location in an underground cavern that cannot continue to be used
because of a high risk of additional ground/rock failure. For the present
there has been no further ring laser work at canterbury university since the
2010/2011 quakes and cave access is not permitted.
DaveB,
Christchurch, NZ
----- Original Message -----
From: ""Björn Gabrielsson"" bg@lysator.liu.se
To: "Discussion of precise time and frequency measurement"
time-nuts@febo.com
Sent: Saturday, July 30, 2016 8:48 AM
Subject: Re: [time-nuts] Q/noise of Earth as an oscillator
I'am not sure how the big ring lasers have progressed over the past
years. It seems the big New Zeeland earthquake messed up the nice ring
lasers over there.
http://www.fs.wettzell.de/LKREISEL/G/LaserGyros.html
http://www.phys.canterbury.ac.nz/ringlaser/about_us.shtml
--
Björn
I believe a phase noise plot deep into the uHz or lower would apply to
the
rotation rate of the earth.
On Saturday, 23 July 2016, Hal Murray hmurray@megapathdsl.net wrote:
tvb@LeapSecond.com said:
Earth is a very noisy, wandering, drifting,
incredibly-expensive-to-measure,
low-precision (though high-Q) clock.
What is the Q of the Earth? It might be on one of your web pages, but I
don't remember seeing it. Google found a few mentions, but I didn't
find a
number.
I did find an interesting list of damping mechanisms in a geology book.
Geology-nuts are as nutty as time-nuts. Many were discussing damping of
seismic waves rather than rotation.
I've seen mention that the rotation rate of the Earth changed by a few
microseconds per day as a result of the 2011 earthquake in Japan. Does
that
show up in any data? Your recent graph doesn't go back that far and
it's
got
a full scale of 2000 microseconds so a few is going to be hard to see.
--
These are my opinions. I hate spam.
time-nuts mailing list -- time-nuts@febo.com javascript:;
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Thanks Tom, I would agree LIGOs efforts are beyond heroic, I will try to
find some of their phase noise plots.
Regarding Q of the earth, I would agree one could compute an UNloaded Q for
the earth as if it were a mass element in some form of a mechanical
oscillator. The first sticky point is which Q, a loaded Q (QL) would assume
it's oscillating (which as many have outlined) it's not, an unloaded Q
(1/DF, or X/R) would be a reasonable value to commute for some specific
frequency. It is interesting (although expected) I have arrived to similar
Q as you, though through different reasoning, but similar assumptions.
Taking inspiration from the many brilliant controls and analog Engineers
from the analog computing days, we can create a circuit equivalent model
for the rotational dynamics of the earth.
Some physical parameters:
omega_e = 7.3E-5 rad/s (angular rate of the earth)
alpha_e = -6.3E-22 rad/s^2 (angular deceleration of the earth)
J_e = 8E37 kg m^2 (Inertia of the earth)
Mapping the torque-(angular displacement) space to the volt-coulomb space
Capacitor - Torsional Spring
Q = C V, tau = k theta
Resistor - Damper / Friction
Qdot = V/R, tau = B thetadot
Inductor - Mass
Qdotdot = V/L, tau = J thetadotdot
In this circuit equivalent model the inertia of the earth would be
represented by an inductor of inductance
L = 8E37 kg m^2
An approximate rotational friction coefficient (tidal friction, doubt it's
a first order relation, but for the sake of Q, assume it is, and other
losses) can be found from the net angular deceleration.
B = J * |alpha_e|/omega_e = 6.9E20 Nm s
Solving as an equivalent resistance yields,
Rs = 6.9E20 Nm s
Finally the unloaded Q at 11 and change uHz,
Q = XL/Rs = (7.3E-5)(8E37)/(6.9E20) = 8.5E12
8.5 Trillion, not bad for an inductor at 11 uHz... Now if you really wanted
an 11 uHz oscillator you could ram a torsional spring up the earth's south
pole.
From a circuit perspective, the earth's rotation looks like a monster near
superconducting inductor that at some point and somehow was precharged to a
current Io, and then had its terminals crowbarred. Our solar time is like
watching a reference electron run round and round a coil.
Björn and Dave, thanks for the gyro reference I will take a look.
On Fri, Jul 29, 2016 at 1:19 PM, Tom Van Baak tvb@leapsecond.com wrote:
Scott Stobbe wrote:
I believe a phase noise plot deep into the uHz or lower would apply to
the
rotation rate of the earth.
Yup. You'll see lots of uHz to Hz noise plots by people working with
seismic noise, for example. My introduction to the subject were the many
plots and papers that describe the heroic effort LIGO goes through to
measure tidal and seismic noise in order to keep their gravity wave servos
locked. Short-term, the surface of the earth is a very noisy place. But if
you can model or measure it before it hits the mirrors, you can mostly back
it out.
One can use PN and ADEV statistics on earth rotation, just like any other
clock or oscillator. And it seems we can also compute Q for the earth, as
if it were a mechanical oscillator.
The remaining question in this thread is if earth Q measurement has actual
meaning, that is, if the concept of Q is valid for a slowly decaying
rotating object, as it is for a slowly decaying simple harmonic oscillator.
And that's were get into the history and definition(s) and applicability of
Q to non harmonic oscillators, such as coils, capacitors, atomic clocks,
planets, pulsars, etc.
/tvb
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