[time-nuts] ARRL FMT results

Magnus Danielson cfmd at bredband.net
Fri Jan 5 20:28:42 UTC 2007


From: "Tom Van Baak" <tvb at leapsecond.com>
Subject: Re: ARRL FMT results
Date: Fri, 5 Jan 2007 10:26:37 -0800
Message-ID: <002301c730f7$0a9a7ae0$148c8843 at computer>

> Magnus,

Tom,

> OK, let me rephrase what I meant - yes, the FMT
> transmissions do experience a Sagnac effect (a
> time synchronization propagation delay), as would
> any other form of EM transmission: RF or optical.
> 
> But the key thing here is that since the FMT event
> is a *frequency* measurement, any constant path
> delays cancel. Because transmitter and receiver
> are stationary, the Sagnac effect is constant. Any
> fixed phase offset drops out of a frequency calculation.
> And so the Sagnac effect has no effect on FMT.

Yes. I fully agree.

However, if you rely on a reflected wave in the atmosphere and the effective
point of reflection moves up or down, you will both experience doppler and
Sagnac effect from that movement.

> > If you say that it could silently be ignored I would agree, but mostly
> because
> > there seem to be some discussion about the actual frequency and stability
> of
> > their transmissions to start with.
> 
> It turns out to be rather small, about 200 ns for a
> full 40 000 km around-the-earth trip at the equator.

Actually, 207 ns. :-)

> But no matter how great or small the effect is, it
> cancels when you do you frequency measurement.

Frequency measurement with fixed transmitter and receiver relationship, yes.
This include transmission path changes.

> A good analogy is measuring a time/frequency
> receiver against your house standard. If you are
> measuring time accuracy, then the cable length
> makes a big difference and it has to be taken into
> account for accurate results.

Indeed. The Sagnac effect will effect your cablelength. See it as a form of
length dilation. :-)

> On the other hand, if you are measuring frequency
> accuracy any cable will do, long or short, as long
> as you don't change the cable during the test.

Indeed. Very good analogy.

> > The fiber optic gyro is actually a good explanation here. The transmitter
> and
> > receiver sits VERY FIXED in the same frame. However, as the optical wave
> goes
> > through the fiber, any turning of that fiber-roll will be effected by the
> > Sagnac effect and much like a coil, the total area (turns x average area
> per
> > turn) will be a direct measure on how sensitive they are. Direct laser
> gyros
> > work the same. They sit in commercial airliners, tactical robots and the
> space
> > shuttles to give a few examples. The more sensitive ones has a constant
> shift
> > in them since they feel the earth turning and the most sensitive ones also
> > measures the resonances in that turning.
> 
> Cool. What sort of sensitivity does one get out of
> these things? Do you need three of them; one for
> each axis?

Yes, one for each axis. They are cool things indeed. They are also part of
everyday life even if we don't see them. This just to make the point that the
Sagnac effect is a real thing and not only a nuace, but also a resource.
You could do it with basically any electromagnetic transmission, such as a
10 MHz signal through a coil of coax. However, the small time differences for
a certain resolution becomes such a small phase change that you would like to
operate at a very high frequency and preferably with a larger area. Optical
wavelengths as well as either a clear path, block of glas or fiber solution
will allow for very sensitive instruments. In one such they had a single block
of very stable glas and used a red HeNe laser for the interferometric solution.
The effective area for that device is 317 m^2. They measure the resonances in
the rotation of earth with that one.

> Right.
> 
> The GPS receiver knows where the SV is but the
> SV cannot know where the receiver is. So Sagnac
> corrections must be done by the party with all the
> information: the GPS receiver.

Exactly.

> The SR and GR corrections, on the other hand are
> done in the SV since the altitude/velocity information
> is known to the SV (by design or even by dynamic
> measurement).

Indeed.

> The other reason the SR and GR corrections must
> be made in the SV is because they affect the GPS
> clock frequency; it's a redshift.

Indeed. The SV is actually slightly low in frequency before lauch, it is set to
-4.467E-10 below the nominal correct frequency to compensate the gravitational
potential difference. This is a static compensation which eats up most of that
effect. This means that the vehicles is set to 10.22999999543 MHz rather than
the 10.23 MHz we expect them to have in orbit.

> Thanks, I'll look into the Parkinson & Spilker book.

Do so. Volume I, Chapter 18.

> I re-read my sources on the Sagnac effect also
> when I did the Mt Rainier relativity experiment last
> year. Since that was a round-trip road experiment,
> the net Sagnac effect was zero. But during various
> parts of the trip it would (predicted, not measured)
> amount to about +/- 100 ps depending on how far
> west or east I was from home.

Makes sense.

Maybe we all should calculate the Sagnac effect to know the time loss or time
gain for each travel? :-)

Cheers,
Magnus




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