# Small hand marking Leap Year

Hi to all
Let’s see if anyone can help me. Some times, in real watches, i see dials more or less like this

with a small hand marking “Leap year”.
Now, if i would do something similar, which formula should i insert in the rotation of the small hand to properly indicate the Leap year?
Thanks in advance for any help
Cheers

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@diavo Hi I would love thelp you but Epoch stuff it beyond me. You could try inoke @mikeoday or @andrew.dowden. I hope they will forgive my cheek. I know it gets complex every 100 years and Millennium.
Those watches probably have a Moon Phase because a Perpetual Callander is required for both . All done with Gears. Staggering but then so is the Maths. All the best with that one.

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The hand on your image turns 1/4 circle each year. It covers the main definition of leap year, which is (in Gregorian calendar) each year which is an integer multiple of 4 (except for years evenly divisible by 100, and not by 400, which wont occur anytime soon). So we can make the hand rotate by the year number like:
((#Dy#%4)*90+(starting angle))

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Good stuff. I struggle to understand what % does. Here is a fine example for me to take apart. I think I understand what this one is doing. I was not sure when the adjustments are made. Did we get two on the Millinium ?

Hi @petruuccios and @russellcresser
A big thank to petruuccios for his help and to russellcresser for his interest.
I never thought it was so hard to make a hand marking leap year. Being the worst mathematician in the world i would have many asks

1. in the formula of petruucios there is +(starting angle) but…which is the starting angle? I.E. for the dial in the picture
2. How can i calculate the starting angle? In case of a different dial I.E a half circle
Thx for further help
Cheers
P.S: As russel told the real watches that I have seen all have the moonphase dial and perpetual calender
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@davio I don’t know abut a half circle ( jump dial ). In the case above if the hand ( needle ) is drawn pointing up the start angle would be 0. In which case the formula would be.

((#Dy#%4)*90+(starting angle))

2 Replies

3

russellcresser

1h

Good stuff. I struggle to understand what % does. Here is a fine example for me to take apart. I think I understand what this one is doing. I was not sure when the adjustments are made. Did we get two on the Millinium ?

diavo

petruuccios

20m

Hi @petruuccios and @russellcresser
A big thank to petruuccios for his help and to russellcresser for his interest.
I never thought it was so hard to make a hand marking leap year. Being the worst mathematician in the world i would have many asks

1. in the formula of petruucios there is +(starting angle) but…which is the starting angle? I.E. for the dial in the picture
2. How can i calculate the starting angle? In case of a different dial I.E a half circle
Thx for further help
Cheers
P.S: As russel told the real watches that I have seen all have the moonphase dial and perpetual calender

@davio
I don’t know what is happening with this messaging app.
It is a little all over the place for me. I will go back to my laptop.

I find it easier to make a test than talk about it.

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For the dial in the image the starting angle should be like -45 if the original hand image is pointing up
Edit: the small hand in the first picture looks to me like it was moving with each month - the xpression would be like `((#Dy#%4)*90+#DM#*90/12-93.75)`, not only once a year, but it also could be just somehow miss-alligned.

I answered similar question in other forum like this:
In plain english remember when you learned division of numbers before you learned decimals? There was a/b meaning how many times the whole b can be subtracted from a and how much reminds of it after that. This reminder is what [tag]%x gives, like no mater how many times you can subtract whole x from the tag, main thing is what reminds after that.

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Peter. Thanks for the clear explanation. I usually get there in the end. Topic Bookmarked.

The ‘%’ is simply the modulo math operator. In plain English, “the remainder”. So `year%4` would return a remainder of 0, 1, 2 or 3.

@diavo, et al

The formula provided will NOT work for year 2100 (or 2200, 2300), but we can just ignore that.

I would suggest using: (for a full circle)

``````(#Dy#%4)*90-45
``````

So, modulo returning 0 points to 45 degrees left (of vertical).

For a half circle:

``````(#Dy#%4)*60-90
``````

So, modulo returning 0 points to 90 degrees to left.

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Thanks so much to all of you for your help. I never thought it was matter for Mr. Einstein. LOL
2 last things;
Is there a way to test formulas? I tried advancing months in the Time Machine untill a new year, but that does not worked. Is there a different way?
2nd If i have understood well the @petruuccios formula ((#Dy#%4)*90+#DM#*90/12-93.75) should advance the small hand one shot every month. Correct?
About year 2100-2200-2300 I don’t want to put limits on providence, but I think I can ignore it
Many thanks, i wish everyone a good day

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If you Click once on the year on the Callander of the Time Machine then click on the Left or Right arrows ,then click on a day in the month , you will advance or retard the years.

For your original “real watch”, the blue hand shows the current month.

The formula would be:

``````(#DM#-1)*30
``````

Or, are you somehow intending to use a single hand to show both month AND leap / non-leap years?

Hello,
I was just trying to point out, that the red hand did not point into middle of the year field, and it could be because of bad hand alignment, or by the movement of the red hand being 1/4 of the blue hand movement.

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On a mechanical watch I should think that little hand was not a jump hand. It will be Intresting to get what @diavo is looking for with a smooth movement then a jump at the end of the leap year.
Just Saying : )

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Perhaps, we could try: (for red hand)

``````(#Dy#%4-1+#DD#/366)*90
``````

which quadrant: (multiple of 90 degrees)

• Year %4
• ((previous) -1) *90

smooth portion, of that quadrant (fraction of 90 degrees)

• Day_in_Year / 366
• (previous) *90
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Ok, just check the example

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@andrew.dowden @petruuccios . Master Class . Amazing .
I don’t know what time it is for you guys .I have only just had my Breakfast.
I am so glad we can bookmark stuff on here.

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Hi @andrew.dowden
No, no, i do not intend a single hand for month and leap year. The only hand that must marks the leap year is the one on the left.

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