Re: Unusual bi-annual sundial

[John Goodman]

Won’t the factors that necessitate the addition of a leap day prevent this 
alignment from happening at exactly 11/11 11:11 every year? From year to year, 
that calendar date occurs at a slightly different fraction of the year’s days.

November 11 is the day 316 of 366 in 2016 and 315 of 365 in 2017. Will the sun 
have precisely the same alignment to this sculpture at a time that’s 316/366 of 
the year vs. 315/365? Close enough for the difference to be imperceptible?

The dates and times of the solstices and equinoxes vary from year to year. If 
these events shift relative to our timekeeping, how can the angle of sunlight 
required by this sculpture occurs at 11/11 11:11 every year? 

The beauty of math and the beauty of symbolism may not align here.

> Date: Wed, 18 Jan 2017 22:41:15 +
> From: Art Krenzel mailto:phoenix98...@msn.com>>
> To: "sundial@uni-koeln.de " 
> mailto:sundial@uni-koeln.de>>
> Subject: Unusual bi-annual sundial
> 
> I have been to Arizona many times but never saw this "working sundial" of 
> sorts.  It is on my bucket list now.
> 
> 
> I thought you might enjoy watching the beauty of math, the sun and time all 
> coming together.  There is a 30 second video of the solar display near the 
> bottom of the opening page at this URL.
> 
> 
> http://www.onlineatanthem.com/anthem-veterans-memorial 
> 
> 
> Anthem Veterans Memorial | Online At 
> Anthem >
> www.onlineatanthem.com 
> Reserve the Anthem Veterans Memorial area for a special ceremony or event. 
> Please refer to the ACC Board Policy Manual for a complete list of facility 
> rules and ...
> 
> 
> Enjoy!
> 
> 
> Art Krenzel

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Re: Unusual bi-annual sundial

[Frank King]

Dear John,

I wondered when someone would spot that there is a
whole can of worms waiting to be opened here...

> Won't the factors that necessitate the addition
> of a leap day prevent this alignment from
> happening at exactly 11/11 11:11 every year?

Quite so.  No doubt you looked at the time-lapse
video and spotted that the circle of light DIDN'T
properly centre itself on the Great Seal of the
United States.  This is surely only one step less
sinful than being disrespectful to the US flag?

OK, take a deep breath and see what we are up
against...

First we need to be clear what is meant by the
time 11:11?  I assume this is clock time in
Anthem, Arizona, and a little research suggests
they are on Mountain Time there and that they
don't observe Daylight Saving.  [Just think how
the whole scheme could be wrecked if they did
go over to Daylight Saving and the clocks didn't
go back until after 11 November!]

To me, their interest is at 18:11:00 UTC but that
is a detail.

The big difficulty is that, at this exact time of
day, the solar declination varies with the leap
year cycle and there is a steady drift.  As a
result both the solar altitude and solar azimuth
vary from one year to the next.  Let's see by
how much...

I'll take it that the Geographical Coordinates
of Anthem are:

   33° 51' 15" N 112° 7' 30"

Using GCstudio I determined the following data
for 10 years starting in 2016, a leap year:

  2016  -17°41'09"  +36°25'01"  +161°40'45"
  2017  -17°37'11"  +36°28'55"  +161°39'53"
  2018  -17°33'13"  +36°32'52"  +161°39'05"
  2019  -17°29'12"  +36°36'55"  +161°38'33"
  2020  -17°41'38"  +36°24'36"  +161°41'11"
  2021  -17°37'47"  +36°28'23"  +161°40'14"
  2022  -17°33'48"  +36°32'21"  +161°39'31"
  2023  -17°29'52"  +36°36'14"  +161°38'36"
  2024  -17°42'18"  +36°23'55"  +161°41'16"
  2025  -17°38'23"  +36°27'48"  +161°40'23"

The four columns show: year, declination, alt, az
as they are at Anthem at 11:11:00 Mountain Time
on 11 November in the 10 years shown.

Take declination first.  You see that starting in
2016 the declination gets about 4 minutes less
negative on successive years until there is a
sudden jump back which is A LITTLE TOO BIG.
This sets the pattern.  We become less negative
until 2024 when there is another jump.

The jumps back over-compensate because the tropical
year is slightly less than 365.25 days.

You will see that the solar altitude increases by
just under 4' a year before falling back just over
12' in a leap year.  You will see that even in this
little table the range of altitudes is about 11'
and this will be noticed by careful observers.

The azimuth varies too of course but by not so
much and its main effect is to make you have to
worry about just how to align the slabs.

OK, what should they have done?

Well one approach is to settle on the 2016 figures
and note that over the next 36 years the data for
2016 will be somewhere near the middle.  After
that the drift will become more noticeable but the
designer will probably be dead and won't care.

Things gradually get worse and worse until The
Great Correction over the years 2096 to 2004
when the omission of a leap year in 2100 will
reverse some of the damage.

Most people know that the Gregorian Calendar
was an improvement over the Julian Calendar but
almost all readers of this list will live their
entire lives enduring pure Julian Drift.

This is a massive imposition and we should all
be lobbying for a much better 33-year Calendar
originally designed by Omar Khayyam in 1079,
long before John Dee and others rediscovered
it.  This was over 500 years before Pope
Gregory's tinkering in 1582.  Why didn't
Pope Gregory do a proper job then?

That's a long story but the result is that we
are lumbered with an unhelpful calendar which
is, I suppose, upward-compatible with its
predecessor.

I share the view that "upward-compatibility is
the business of deliberately not putting right
someone else's mistakes".

Many apologies.  Another rant I fear!

Very best wishes

Frank

Frank King
Cambridge, U.K.

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Re: Unusual bi-annual sundial

[John Goodman]

Thank you, Frank. You’ve sharpened my vague suspicions with mathematical 
clarity.

> On Jan 19, 2017, at 11:33 AM, Frank King  wrote:
> 
> OK, take a deep breath and see what we are up against...

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Re: Unusual bi-annual sundial

[Patrick Powers]

John,

There is also this that describes (a little) the thinking that was behind the 
way they attempted to accommodate the small changes that still occur year to 
year.

http://www.onlineatanthem.com/news/memorial-science

Patrick


From: John Goodman 
Sent: Thursday, January 19, 2017 5:01 PM
To: Frank King ; Sundial List 
Subject: Re: Unusual bi-annual sundial

Thank you, Frank. You’ve sharpened my vague suspicions with mathematical 
clarity.

> On Jan 19, 2017, at 11:33 AM, Frank King  wrote:
> 
> OK, take a deep breath and see what we are up against...

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Re: Unusual bi-annual sundial

[John Goodman]

Thank you, Patrick. The link you sent shows that the designer clearly 
considered the time-variation problem. His comments sound like a fair enough 
conclusion to me:

"I would say that it is perfect if you recognize the plus or minus 12 time 
second difference for 11:11:11 a.m."

> On Jan 19, 2017, at 1:05 PM, sundial-requ...@uni-koeln.de wrote:
> 
> Date: Thu, 19 Jan 2017 17:59:21 -
> From: "Patrick Powers"  >
> To: "Sundial List" mailto:sundial@uni-koeln.de>>
> Subject: Re: Unusual bi-annual sundial
> 
> John,
> 
> There is also this that describes (a little) the thinking that was behind the 
> way they attempted to accommodate the small changes that still occur year to 
> year.
> 
> http://www.onlineatanthem.com/news/memorial-science 
> 
> 
> Patrick
> 
> 
> From: John Goodman 
> Sent: Thursday, January 19, 2017 5:01 PM
> To: Frank King ; Sundial List 
> Subject: Re: Unusual bi-annual sundial
> 
> Thank you, Frank. You?ve sharpened my vague suspicions with mathematical 
> clarity.
> 
>> On Jan 19, 2017, at 11:33 AM, Frank King > > wrote:
>> 
>> OK, take a deep breath and see what we are up against...
> 

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Re: Unusual bi-annual sundial

[Geoff Thurston]

Thank you, Frank, for that comprehensive analysis of the problem. However,
I wonder if the errors might be masked by the 32 arc minute  solar penumbra.

Best wishes,

Geoff

On 19 January 2017 at 16:33, Frank King  wrote:

> Dear John,
>
> I wondered when someone would spot that there is a
> whole can of worms waiting to be opened here...
>
> > Won't the factors that necessitate the addition
> > of a leap day prevent this alignment from
> > happening at exactly 11/11 11:11 every year?
>
> Quite so.  No doubt you looked at the time-lapse
> video and spotted that the circle of light DIDN'T
> properly centre itself on the Great Seal of the
> United States.  This is surely only one step less
> sinful than being disrespectful to the US flag?
>
> OK, take a deep breath and see what we are up
> against...
>
> First we need to be clear what is meant by the
> time 11:11?  I assume this is clock time in
> Anthem, Arizona, and a little research suggests
> they are on Mountain Time there and that they
> don't observe Daylight Saving.  [Just think how
> the whole scheme could be wrecked if they did
> go over to Daylight Saving and the clocks didn't
> go back until after 11 November!]
>
> To me, their interest is at 18:11:00 UTC but that
> is a detail.
>
> The big difficulty is that, at this exact time of
> day, the solar declination varies with the leap
> year cycle and there is a steady drift.  As a
> result both the solar altitude and solar azimuth
> vary from one year to the next.  Let's see by
> how much...
>
> I'll take it that the Geographical Coordinates
> of Anthem are:
>
>33° 51' 15" N 112° 7' 30"
>
> Using GCstudio I determined the following data
> for 10 years starting in 2016, a leap year:
>
>   2016  -17°41'09"  +36°25'01"  +161°40'45"
>   2017  -17°37'11"  +36°28'55"  +161°39'53"
>   2018  -17°33'13"  +36°32'52"  +161°39'05"
>   2019  -17°29'12"  +36°36'55"  +161°38'33"
>   2020  -17°41'38"  +36°24'36"  +161°41'11"
>   2021  -17°37'47"  +36°28'23"  +161°40'14"
>   2022  -17°33'48"  +36°32'21"  +161°39'31"
>   2023  -17°29'52"  +36°36'14"  +161°38'36"
>   2024  -17°42'18"  +36°23'55"  +161°41'16"
>   2025  -17°38'23"  +36°27'48"  +161°40'23"
>
> The four columns show: year, declination, alt, az
> as they are at Anthem at 11:11:00 Mountain Time
> on 11 November in the 10 years shown.
>
> Take declination first.  You see that starting in
> 2016 the declination gets about 4 minutes less
> negative on successive years until there is a
> sudden jump back which is A LITTLE TOO BIG.
> This sets the pattern.  We become less negative
> until 2024 when there is another jump.
>
> The jumps back over-compensate because the tropical
> year is slightly less than 365.25 days.
>
> You will see that the solar altitude increases by
> just under 4' a year before falling back just over
> 12' in a leap year.  You will see that even in this
> little table the range of altitudes is about 11'
> and this will be noticed by careful observers.
>
> The azimuth varies too of course but by not so
> much and its main effect is to make you have to
> worry about just how to align the slabs.
>
> OK, what should they have done?
>
> Well one approach is to settle on the 2016 figures
> and note that over the next 36 years the data for
> 2016 will be somewhere near the middle.  After
> that the drift will become more noticeable but the
> designer will probably be dead and won't care.
>
> Things gradually get worse and worse until The
> Great Correction over the years 2096 to 2004
> when the omission of a leap year in 2100 will
> reverse some of the damage.
>
> Most people know that the Gregorian Calendar
> was an improvement over the Julian Calendar but
> almost all readers of this list will live their
> entire lives enduring pure Julian Drift.
>
> This is a massive imposition and we should all
> be lobbying for a much better 33-year Calendar
> originally designed by Omar Khayyam in 1079,
> long before John Dee and others rediscovered
> it.  This was over 500 years before Pope
> Gregory's tinkering in 1582.  Why didn't
> Pope Gregory do a proper job then?
>
> That's a long story but the result is that we
> are lumbered with an unhelpful calendar which
> is, I suppose, upward-compatible with its
> predecessor.
>
> I share the view that "upward-compatibility is
> the business of deliberately not putting right
> someone else's mistakes".
>
> Many apologies.  Another rant I fear!
>
> Very best wishes
>
> Frank
>
> Frank King
> Cambridge, U.K.
>
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>
>
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