<p>I realize there are boundless amounts of information as to the formulas to calculate solstices, equinoxes, and cross-quarter days, but I would like to design a gear-based mechanical solution for the same problem.</p>
<p>I already created a wood gear clock that includes an EOT (equation of time) dial, but that seems easy in comparison to my current challenge.  For EOT, a kidney cog was the solution to allow the varied offsets for LST (local solar time) vs. civil time.</p>
<p>Many folks seem to just take the easy way out by using the average date of the various events and are satisfied.  I prefer a more accurate approach.</p>
<p>For example, I build wood gear clocks that take into account leap years instead of just relying on the clock's owner to back up the date by a day in February once every four years.</p>
<p>The key to the answer I seek is simplicity wherever possible.  Calculating the size and shape of a kidney gear is fine.  But building something to rival Charles Babbage’s Analytical Engine is beyond the scope of my project.</p>
<p>Thanks in advance for any helpful suggestions, solutions or advice you may be willing to offer!</p>

CC BY-SA 4.0
2024-04-01T18:57:35.527Z
How can we help you? I have simple linear equations that give the time of the equinoxes and solstices, accurate to ~30 minutes (or better), over the next 50 years or so. But I have no idea what kind of arithmetic you can implement in clockwork. So you need to tell us what kinds of equations you can work with.
PM 2Ring
CC BY-SA 4.0
2024-12-11T17:23:13.267Z
On the one hand, I want the time displayed on the clock portion of the device to be LST which takes the equation of time into account.  As for the calendar portion, I need the mechanism to display the solar year instead of the civil calendar year.
Eriks
CC BY-SA 4.0
2024-03-18T06:02:39.643Z
I don't know much about clockwork computation, but I'm a bit puzzled. I expect it would be a little easier to calculate equinoxes and solstices (using the Right Ascension of the Sun) than to calculate the EoT, since the EoT is RA(mean sun) - RA(true sun).
PM 2Ring
CC BY-SA 4.0
2024-03-19T14:51:01.980Z
It is the variance of the date of those events each year that makes it challenging.  While we can consider gears with teeth to be kinda "digital", the solution to the EOT issue was to use a kidney gear (a curved cog along the side of which a lever rests against and goes up or down depending on the current position of the cog)--which is kinda like "analog"
Eriks
CC BY-SA 4.0
2024-03-20T00:16:01.013Z
What would be the input to the device?  The EoT is a continuous function throughout the year, but the equinoxes and solstices are only defined under certain conditions.  I would imagine a Fourier transform would be useful, where you make gears using the most dominate frequencies, which is how VSOP87 (an algorithm for computing the planets' positions) works.  But if you look that up, you'll see you'd be making a whole lot of gears.  Though that is accurate for a few thousand years.
Greg Miller
CC BY-SA 4.0
2024-03-20T05:31:54.700Z
Input?  The mechanism would be running on an ongoing basis and would be consistent with the current LST (local solar time).  Not sure what the planet positions have to do with solstices and equinoxes....?  (sorry if that's a stupid question, but please explain)
Eriks
CC BY-SA 4.0
2024-03-20T05:59:22.770Z
@Eriks Greg's point is that the usual way to calculate the precise time of the equinox or solstice involves computing where the Earth is in its orbit. But you don't need that level of precision.
PM 2Ring
CC BY-SA 4.0
2024-03-20T06:05:52.607Z
The time from one March equinox to the next is a [tropical year](https://en.wikipedia.org/wiki/Tropical_year#Length_of_tropical_year). The exact length of a tropical year varies slightly, but since you aren't trying to determine the time of the equinox with sub-minute precision, you can ignore that. So you can just use a mean value for the duration from the March equinox to the June solstice, etc.
PM 2Ring
CC BY-SA 4.0
2024-03-21T16:28:34.480Z
You might want to specify what type of accuracy you're looking for.  In your question you specify you want an accurate approach.  The USNO publishes it to the minute.  Obviously the more accurate you want, the more involved it will be.
Greg Miller
<equinox><solstice><clock>
How can I build a gear-based mechanism to calculate solstices, equinoxes, and cross-quarter dates?
Eriks
# How can I build a gear-based mechanism to calculate solstices, equinoxes, and cross-quarter dates?

(Asked by: username_0 on 2024-03-17)

I realize there are boundless amounts of information as to the formulas to calculate solstices, equinoxes, and cross-quarter days, but I would like to design a gear-based mechanical solution for the same problem.

I already created a wood gear clock that includes an EOT (equation of time) dial, but that seems easy in comparison to my current challenge. For EOT, a kidney cog was the solution to allow the varied offsets for LST (local solar time) vs. civil time.

Many folks seem to just take the easy way out by using the average date of the various events and are satisfied. I prefer a more accurate approach.

For example, I build wood gear clocks that take into account leap years instead of just relying on the clock's owner to back up the date by a day in February once every four years.

The key to the answer I seek is simplicity wherever possible. Calculating the size and shape of a kidney gear is fine. But building something to rival Charles Babbage’s Analytical Engine is beyond the scope of my project.

Thanks in advance for any helpful suggestions, solutions or advice you may be willing to offer!

**Tags:** equinox, solstice, clock

> **Comments:**
> **username_1**: I don't know much about clockwork computation, but I'm a bit puzzled. I expect it would be a little easier to calculate equinoxes and solstices (using the Right Ascension of the Sun) than to calculate the EoT, since the EoT is RA(mean sun) - RA(true sun).  
> **username_0**: It is the variance of the date of those events each year that makes it challenging.  While we can consider gears with teeth to be kinda "digital", the solution to the EOT issue was to use a kidney gear (a curved cog along the side of which a lever rests against and goes up or down depending on the current position of the cog)--which is kinda like "analog"  
> **username_2**: What would be the input to the device?  The EoT is a continuous function throughout the year, but the equinoxes and solstices are only defined under certain conditions.  I would imagine a Fourier transform would be useful, where you make gears using the most dominate frequencies, which is how VSOP87 (an algorithm for computing the planets' positions) works.  But if you look that up, you'll see you'd be making a whole lot of gears.  Though that is accurate for a few thousand years.  
> **username_0**: Input?  The mechanism would be running on an ongoing basis and would be consistent with the current LST (local solar time).  Not sure what the planet positions have to do with solstices and equinoxes....?  (sorry if that's a stupid question, but please explain)  
> **username_1**: @username_0 Greg's point is that the usual way to calculate the precise time of the equinox or solstice involves computing where the Earth is in its orbit. But you don't need that level of precision.  
> **username_1**: The time from one March equinox to the next is a [tropical year](https://en.wikipedia.org/wiki/Tropical_year#Length_of_tropical_year). The exact length of a tropical year varies slightly, but since you aren't trying to determine the time of the equinox with sub-minute precision, you can ignore that. So you can just use a mean value for the duration from the March equinox to the June solstice, etc.  
> **username_2**: You might want to specify what type of accuracy you're looking for.  In your question you specify you want an accurate approach.  The USNO publishes it to the minute.  Obviously the more accurate you want, the more involved it will be.  
> **username_1**: How can we help you? I have simple linear equations that give the time of the equinoxes and solstices, accurate to ~30 minutes (or better), over the next 50 years or so. But I have no idea what kind of arithmetic you can implement in clockwork. So you need to tell us what kinds of equations you can work with.  
> **username_0**: On the one hand, I want the time displayed on the clock portion of the device to be LST which takes the equation of time into account.  As for the calendar portion, I need the mechanism to display the solar year instead of the civil calendar year.  

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## 0 answers

