How to calculate the gear ratio of this moonphase watch

[Don Wong]

I would like to calculate the gear ratio of this moonphase watch, however i cannot calculate the exact day of its mentioned. What's wrong with my calculation?
https://www.ochsundjunior.swiss/watches/moon-phase/tech-specs/

my calculation is 1/(2/12*14/18*14/109)/2=30.03
which is different from its result 29.53089 days.

 

[Mech_Engineer]

I recommend you take a closer look at the numbers you're using in calculation. It might be worth doing some reading on the specifics of lunar phases, maybe try here: https://en.wikipedia.org/wiki/Lunar_phase#Calendar

 

[Don Wong]

I recommend you take a closer look at the numbers you're using in calculation. It might be worth doing some reading on the specifics of lunar phases, maybe try here: https://en.wikipedia.org/wiki/Lunar_phase#Calendar

I have read that wiki before, but i think this question doesn't require the knowledge of the lunar phase system. It is just the calculation of the gear ratio as it states in the website.

 

[Baluncore]

Don Wong.
Your ratio is assuming that the arm with the gears is fixed while the 109 tooth ring rotates. That is back to front. The arm that carries the moon rotates counter-clockwise once each lunar cycle, complete with the gear train. You must allow for that one turn advance of the first gear over each lunar period.
12 hours is half a day so a quick estimate gives a period closer to 30.03 – 0.5 = 29.53 days.

 

[Baluncore]

Every 12 hours, the 12 tooth input gear is advanced by not one, but by two teeth as the pin passes.
So the compound gear ratio becomes;
(12/14) * (18/14) * ( 109 / 2 ) = 60.0612244898
Next remove the epicyclic backward turn of the arm from the simple ratio;
60.0612244898 – 1 = 59.0612244898
The input period is 12 hours = 0.5 day, so the output period is;
59.0612244898 * 0.5 day = 29.5306122449 days.

 

[hussein]

Every 12 hours, the 12 tooth input gear is advanced by not one, but by two teeth as the pin passes.
So the compound gear ratio becomes;
(12/14) * (18/14) * ( 109 / 2 ) = 60.0612244898
Next remove the epicyclic backward turn of the arm from the simple ratio;
60.0612244898 – 1 = 59.0612244898
The input period is 12 hours = 0.5 day, so the output period is;
59.0612244898 * 0.5 day = 29.5306122449 days.

Can I ask you for something?

In Muslim using 12 months and every month 29 or 30
How can it doing with your calculate

Every 12 hours, the 12 tooth input gear is advanced by not one, but by two teeth as the pin passes.
So the compound gear ratio becomes;
(12/14) * (18/14) * ( 109 / 2 ) = 60.0612244898
Next remove the epicyclic backward turn of the arm from the simple ratio;
60.0612244898 – 1 = 59.0612244898
The input period is 12 hours = 0.5 day, so the output period is;
59.0612244898 * 0.5 day = 29.5306122449 days.

I liked what you wrote. Is it possible to ask a question in the Islamic, the Hijri month depends on twelve months, and the month ranges from 30 days to 29 days on the appearance of the moon, is it possible to explain in the same way

 

[Baluncore]

Welcome to PF.

The lunar clock fitted with the correct gear ratio will accurately predict the lunar months of the Hijri calendar for Mecca. The numerical explanation will be exactly the same.

But there may be some problems in countries with significantly different longitudes to Mecca, where the New Moon is not always FIRST seen on the same solar day as in Mecca. I believe that causes some months to start at midnight while others start at midday. Different Muslim countries have different conventions.

The 12 Lunar months of the Hijri calendar make one lunar year of 354 or 355 days. That is because 29.530589 * 12 lunar cycles = 354.367068 days. I guess you probably use the Gregorian calendar for your civil calendar, which is quite independent of the Lunar month, and so slides past the Hijri calendar.

 

[hussein]

Thank you so much for your goodness

 

[hussein]

Welcome to PF.

The lunar clock fitted with the correct gear ratio will accurately predict the lunar months of the Hijri calendar for Mecca. The numerical explanation will be exactly the same.

But there may be some problems in countries with significantly different longitudes to Mecca, where the New Moon is not always FIRST seen on the same solar day as in Mecca. I believe that causes some months to start at midnight while others start at midday. Different Muslim countries have different conventions.

The 12 Lunar months of the Hijri calendar make one lunar year of 354 or 355 days. That is because 29.530589 * 12 lunar cycles = 354.367068 days. I guess you probably use the Gregorian calendar for your civil calendar, which is quite independent of the Lunar month, and so slides past the Hijri calendar.

But when you make design the month 30 days and the pointer move to complete the month or make it 29 days
I ask about that and how mechanism work and how to make it and another pointer change to month when complete month (29 or 30) full cycle
Sorry for long message

 

[Baluncore]

I think I understand the problem. It is easy to solve with a computer.

I will need to think carefully about how the spiral "day of the month" ring works, with the short diagonal marker that shows through the holes.

Here is an example of the months with 29 or 30 days.

Yr Days in lunar months
0 30.000000 30.469411 29.938822 30.408233 29.877644 30.347055 29.816466 30.285877 29.755288 30.224699 29.694110 30.163521
1 29.632932 30.102343 29.571754 30.041165 30.510576 29.979987 30.449398 29.918809 30.388220 29.857631 30.327042 29.796453
2 30.265864 29.735275 30.204686 29.674097 30.143508 29.612919 30.082330 29.551741 30.021152 30.490563 29.959974 30.429385
3 29.898796 30.368207 29.837618 30.307029 29.776440 30.245851 29.715262 30.184673 29.654084 30.123495 29.592906 30.062317
4 29.531728 30.001139 30.470550 29.939961 30.409372 29.878783 30.348194 29.817605 30.287016 29.756427 30.225838 29.695249
5 30.164660 29.634071 30.103482 29.572893 30.042304 30.511715 29.981126 30.450537 29.919948 30.389359 29.858770 30.328181
6 29.797592 30.267003 29.736414 30.205825 29.675236 30.144647 29.614058 30.083469 29.552880 30.022291 30.491702 29.961113
7 30.430524 29.899935 30.369346 29.838757 30.308168 29.777579 30.246990 29.716401 30.185812 29.655223 30.124634 29.594045
8 30.063456 29.532867 30.002278 30.471689 29.941100 30.410511 29.879922 30.349333 29.818744 30.288155 29.757566 30.226977
9 29.696388 30.165799 29.635210 30.104621 29.574032 30.043443 30.512854 29.982265 30.451676 29.921087 30.390498 29.859909

 

[hussein]

I think I understand the problem. It is easy to solve with a computer.

I will need to think carefully about how the spiral "day of the month" ring works, with the short diagonal marker that shows through the holes.

Here is an example of the months with 29 or 30 days.

Yr Days in lunar months
0 30.000000 30.469411 29.938822 30.408233 29.877644 30.347055 29.816466 30.285877 29.755288 30.224699 29.694110 30.163521
1 29.632932 30.102343 29.571754 30.041165 30.510576 29.979987 30.449398 29.918809 30.388220 29.857631 30.327042 29.796453
2 30.265864 29.735275 30.204686 29.674097 30.143508 29.612919 30.082330 29.551741 30.021152 30.490563 29.959974 30.429385
3 29.898796 30.368207 29.837618 30.307029 29.776440 30.245851 29.715262 30.184673 29.654084 30.123495 29.592906 30.062317
4 29.531728 30.001139 30.470550 29.939961 30.409372 29.878783 30.348194 29.817605 30.287016 29.756427 30.225838 29.695249
5 30.164660 29.634071 30.103482 29.572893 30.042304 30.511715 29.981126 30.450537 29.919948 30.389359 29.858770 30.328181
6 29.797592 30.267003 29.736414 30.205825 29.675236 30.144647 29.614058 30.083469 29.552880 30.022291 30.491702 29.961113
7 30.430524 29.899935 30.369346 29.838757 30.308168 29.777579 30.246990 29.716401 30.185812 29.655223 30.124634 29.594045
8 30.063456 29.532867 30.002278 30.471689 29.941100 30.410511 29.879922 30.349333 29.818744 30.288155 29.757566 30.226977
9 29.696388 30.165799 29.635210 30.104621 29.574032 30.043443 30.512854 29.982265 30.451676 29.921087 30.390498 29.859909

Thank you so much

 

[Baluncore]

I believe the "ochs und junior" lunar watch displays the Gregorian calendar day of the month, not the day of the hijri month.

Traditionally, the first day of each hijri calendar month is the day of the first sighting of the hilal, (the crescent new moon), after sunset. Note that hijri days and months conveniently begin at sunset.

I use this site to identify the present Lunar Phase. https://www.heavens-above.com/moon.aspx
After setting my location and time zone, I see the next new moon will be on 06 October 2021 at 22:05 local time. Future new moons will follow every 29.530589 days.
The time of sunset for the observer will also be needed, it can be found for the day in question on https://www.heavens-above.com/sun.aspx

Since 22:05 is after sunset, the hijri calendar month will begin for me on the next day, 7 October at sunset. The number of days in a hijri calendar month does not follow a fixed pattern. It must be calculated by extrapolation each month by adding 29.530589 days = 29 days, 12 hours, 44 min, and 2.9 sec, to the instant of the previous new moon. The time instant must then be examined to identify if the astronomical new moon is before or after sunset. That will decide if sunset today or tomorrow will become the first day of the hijri month, and therefore the number of days in the previous hijri month.

Thank you so much

Perhaps you can ask a more specific question.
Will you use the "ochs und junior" lunar watch ?
Will you make your own mechanical gear hijri clock ?
Will you need a computer program ?

 

[hussein]

I believe the "ochs und junior" lunar watch displays the Gregorian calendar day of the month, not the day of the hijri month.

Traditionally, the first day of each hijri calendar month is the day of the first sighting of the hilal, (the crescent new moon), after sunset. Note that hijri days and months conveniently begin at sunset.

I use this site to identify the present Lunar Phase. https://www.heavens-above.com/moon.aspx
After setting my location and time zone, I see the next new moon will be on 06 October 2021 at 22:05 local time. Future new moons will follow every 29.530589 days.
The time of sunset for the observer will also be needed, it can be found for the day in question on https://www.heavens-above.com/sun.aspx

Since 22:05 is after sunset, the hijri calendar month will begin for me on the next day, 7 October at sunset. The number of days in a hijri calendar month does not follow a fixed pattern. It must be calculated by extrapolation each month by adding 29.530589 days = 29 days, 12 hours, 44 min, and 2.9 sec, to the instant of the previous new moon. The time instant must then be examined to identify if the astronomical new moon is before or after sunset. That will decide if sunset today or tomorrow will become the first day of the hijri month, and therefore the number of days in the previous hijri month.


Perhaps you can ask a more specific question.
Will you use the "ochs und junior" lunar watch ?
Will you make your own mechanical gear hijri clock ?
Will you need a computer program ?

Thank you for all information
But first I try hard to help friends to collect all information about that and ratio like antikythera mechanism
But for hijri the same but give day and month
Thank you so much for your patience and help

 

[hussein]

Welcome to PF.

The lunar clock fitted with the correct gear ratio will accurately predict the lunar months of the Hijri calendar for Mecca. The numerical explanation will be exactly the same.

But there may be some problems in countries with significantly different longitudes to Mecca, where the New Moon is not always FIRST seen on the same solar day as in Mecca. I believe that causes some months to start at midnight while others start at midday. Different Muslim countries have different conventions.

The 12 Lunar months of the Hijri calendar make one lunar year of 354 or 355 days. That is because 29.530589 * 12 lunar cycles = 354.367068 days. I guess you probably use the Gregorian calendar for your civil calendar, which is quite independent of the Lunar month, and so slides past the Hijri calendar.

dear sir
I found that link I hope useful for you
https://russianpatents.com/patent/242/2427927.html