# Gear train to convert a solar day to a sidereal day (or vice versa)

Discussion in 'Clock Construction' started by David Malphrus, Sep 1, 2014.

1. ### David Malphrus Registered User

Aug 27, 2014
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Last edited: Sep 1, 2014
Gear train to convert a solar day to a sidereal day (or vice versa)

Reference:

Title: The new definition of universal time
Authors: Aoki, S., Kinoshta, H., Guinot, B., Kaplan, G. H., McCarthy, D. D., & Seidelmann, P. K.,
Journal: Astronomy and Astrophysics, vol. 105, no. 2

It lists the conversion factor as: 1.002737909350795 for January 1, 2000. This value needs a "smidgen" of correction over time.

The algorithm is 1.002737909350795 + 5.9006 10^-11 T - 5.9 10^-15 T^2

Where T is the number of Julian centuries (consisting of 36,525 days of 86,400 seconds of dynamical time each) elapsed since JD 2451545 TDB.

The elapsed time to current is 14 9/12 years or .1475 centuries for T meaning the present conversion is:

1.002737909359498256638125 (for September 1, 2014).

But, if this is used you will have an error of X in your gear train in 100 years, so why not use a conversion factor that is correct 50 years into the future. Then you would start with an error of .5X, end with an error of .5X and have (practically) no error at 50 years.

September 1, 2064 = .6475 centuries for T.

Conversion factor: 1.002737909388998911388125

Now convert 1.002737909388998911388125 to un-vulgar/proper fractions for the gears while constraining the conversion to four fractions:

My method produces:

(233/359) * (346/317) * (358/304) * (363/302) = 1.0027379093889957827883714847908

with a gear-train error of: 0.0000000000000031286

Any thoughts, comments and/or corrections?

--David Malphrus

2. ### John MacArthur Registered User NAWCC Member

Feb 13, 2007
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#2
"gear-train error of: 0.0000000000000031286"

The sidereal day will likely change more than that over that length of time. It'd be a shame to have to adjust it......

Johnny

3. ### NigelW Registered User

Jan 2, 2015
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#3
Sidereal time and mean time are surely related by a constant ratio, but doesn't the conversion to solar time involve an equation of time adjustment?

4. ### NigelW Registered User

Jan 2, 2015
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Differential gearing to produce a solar time clock (theoretical exercise only)

I am interested in the theory of equation of time clocks and understand that there are at least three methods for generating solar time: a cam, differential gearing and pendulum length adjustment.

My paper exercise is to design a clock with a single escapement and pendulum but with two, separately driven trains - one showing mean time on a conventional dial and the other showing solar time on a second conventional dial (i.e. not just a + or - indicator or second minute hand), using differential gearing.

I have been searching the net for clues on how to do this but have not got very far. Any pointers would be most appreciated.

5. ### Tinker Dwight Registered User

Oct 11, 2010
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#5
No, Sidereal is relative to the stars. The equation of time
is caused mostly by the elliptical orbit of the Earth relative
to the sun. The Earth rotates at, mostly, a constant rate relative
to an inertial frame of reference. The stars are an inertial
frame of reference for all intensive purposes. The elliptical orbit is too
tiny compared to the distant stars to have any effect.
Sidereal and solar time are not the same.
Tinker Dwight

6. ### Tinker Dwight Registered User

Oct 11, 2010
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#6
Re: Differential gearing to produce a solar time clock (theoretical exercise only)

What part are you having troubles with?
Creating the cam or the gears?
Tinker Dwight

7. ### NigelW Registered User

Jan 2, 2015
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#7
I know that sidereal time is different from solar time, but true solar is time based on the sun reaching its height at noon every day.

My point is that sidereal time and mean time are pretty constant and can therefore be linked by a simple ratio but true solar time varies during the year because of the equation of time caused by a combination of the elliptical orbit of the earth and the tilt of the earth on its axis. I am currently interested in modelling this variation using differential gearing but have yet to find a design.

8. ### Tinker Dwight Registered User

Oct 11, 2010
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#8
Re: Differential gearing to produce a solar time clock (theoretical exercise only)

Lets try to keep to this one thread. It gets confusing if we have two threads
on the same subject.
To get some help on how to deal with things, look up tide machines. I think
you'll find a lot of useful information because they are solving similar problems.
Most of the newer ones have used Fourier transforms to create sine components.
The summing method are about the same. It will be difficult to do seconds
from the same pendulum but minutes and hours is not that hard.
Tinker Dwight

9. ### Allan Wolff Moderator NAWCC Member

Mar 17, 2005
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#9
Re: Differential gearing to produce a solar time clock (theoretical exercise only)

I have merged the two threads on solar and sidereal time since they are very similar (and interesting!)
Allan

10. ### GregS Registered User

Sep 4, 2008
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#10
NigelW, you may also want to contact Mark Frank who has commissioned an extensive astrological clock. His website can be found here:

www.my-time-machines.net

I'm sure you can contact him via info found on his site.
Cheers,
Greg

11. ### MartinM Registered User

Jun 24, 2011
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#11
Wow!

Just...
Wow!