Re: Zenith angles and hours to sunset

[Steve Lelievre]

Willy, thanks.

I'm travelling away from home now, so can't respond in full - but your 
chart helps me and gives me an idea that I will combine with Gian's rule 
of thumb and post on the list later.


Steve

On 2017-11-08 10:10 AM, Willy Leenders wrote:

Hello Steve,

Based on your discovery and to prove that from the vernal equinox to 
the autumnal equinox for a certain time to sunset the sun altitude is 
*/approximately/* equal, I made calculations and a graph showing that 
this is the case for 1, 2, 3 and 4 hours to sunset.


Willy Leenders
Hasselt in Flanders (Belgium)

Visit my website about the sundials in the province of Limburg 
(Flanders) with a section 'worth knowing about sundials' (mostly in 
Dutch): http://www.wijzerweb.be





Op 6-nov-2017, om 02:15 heeft Steve Lelievre het volgende geschreven:

I have been doing some calculations for an Hours To Sunset dial (that 
is, an Italian Hours dial with the numbering running backwards). I 
discovered that the maximum altitude for a given hour does not occur 
at the summer solstice.  I was a little surprised to discover this - 
not amazed, but surprised enough to make me wonder if I have done my 
calculations wrong.


The attached diagram is for the example case of 4 hours before 
sunset. I'm getting a double maximum occurring a little after the 
vernal equinox and a little before before the autumnal equinox. I get 
similarly shaped curves for others hours, with less separation 
between the peaks when I use higher (italian) hour numbers.


Assuming that I have in fact graphed the altitude correctly, it means 
is that there is a period over the summer months when the altitude 
for any given hour to sunset stays /approximately/ the same. In my 
case, at 49N, it seems that over the summer months, the solar 
altitude for 1 hour to sunset is approximately a little under 10 
degrees, 2 hours to sunset is approximately a little under 20 
degrees, and so on at a little under 10 degrees per hour, at least 
for the last 5 to 6 hours of the day.


In this day and age, I think we would demand greater accuracy, but 
have there ever been sundials or other devices that exploited this 
approximation?


Steve


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Re: Zenith angles and hours to sunset

[Willy Leenders]

Hello Steve,

Based on your discovery and to prove that from the vernal equinox to the 
autumnal equinox for a certain time to sunset the sun altitude is approximately 
equal, I made calculations and a graph showing that this is the case for 1, 2, 
3 and 4 hours to sunset.

Willy Leenders
Hasselt in Flanders (Belgium)

Visit my website about the sundials in the province of Limburg (Flanders) with 
a section 'worth knowing about sundials' (mostly in Dutch): 
http://www.wijzerweb.be





Op 6-nov-2017, om 02:15 heeft Steve Lelievre het volgende geschreven:

> I have been doing some calculations for an Hours To Sunset dial (that is, an 
> Italian Hours dial with the numbering running backwards). I discovered that 
> the maximum altitude for a given hour does not occur at the summer solstice.  
> I was a little surprised to discover this - not amazed, but surprised enough 
> to make me wonder if I have done my calculations wrong.
> 
> The attached diagram is for the example case of 4 hours before sunset. I'm 
> getting a double maximum occurring a little after the vernal equinox and a 
> little before before the autumnal equinox. I get similarly shaped curves for 
> others hours, with less separation between the peaks when I use higher 
> (italian) hour numbers. 
> Assuming that I have in fact graphed the altitude correctly, it means is that 
> there is a period over the summer months when the altitude for any given hour 
> to sunset stays approximately the same. In my case, at 49N, it seems that 
> over the summer months, the solar altitude for 1 hour to sunset is 
> approximately a little under 10 degrees, 2 hours to sunset is approximately a 
> little under 20 degrees, and so on at a little under 10 degrees per hour, at 
> least for the last 5 to 6 hours of the day.
> In this day and age, I think we would demand greater accuracy, but have there 
> ever been sundials or other devices that exploited this approximation?
> 
> Steve
> 
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 

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Re: Zenith angles and hours to sunset

[Steve Lelievre]

Thanks, Gian, for validating my calculations, and for that story.  It 
must be based on the rule of thumb that the thickness of a finger (or 
maybe a thumb?) is 2 degrees. For my latitude, that would mean that each 
fist is about one hour to sunset.  I must remember to try it next summer.


Cheers,
Steve






On 2017-11-06 12:28 AM, Gian Casalegno wrote:

A similar result can be obtained by means of Orologi Solari.

The attached pdf shows a dial at 49.2 N where hours to sunset lines 
and sun height lines are drawn.
The asymptotes of the sun height lines are parallel to the hour lines 
in the afternoon i.e. sun height is nearly constant for a fixed time 
to sunset value.


The attached image shows a shepherd dial with the last seven time to 
sunset lines drawn.
Hour lines 1 to 5 are nearly horizontal in the right side of the graph 
(summer).

The result is so again confirmed.

Therefore time to sunset can be deduced in summer from the height of 
the sun on the horizon.


This fact reminds me about a trick that someone told me a long time ago.
It was said that sailors used to estimate the time by measuring with 
their fingers the height of the sun above the line of the horizon.
I always thought it was a fake but now I see it can work, at least in 
the evening in summer time.

Of course the relation between height and time depends on the latitude.

Ciao.
Gian


 
	Mail priva di virus. www.avast.com 
 




2017-11-06 2:15 GMT+01:00 Steve Lelievre 
>:


I have been doing some calculations for an Hours To Sunset dial
(that is, an Italian Hours dial with the numbering running
backwards). I discovered that the maximum altitude for a given
hour does not occur at the summer solstice.  I was a little
surprised to discover this - not amazed, but surprised enough to
make me wonder if I have done my calculations wrong.

The attached diagram is for the example case of 4 hours before
sunset. I'm getting a double maximum occurring a little after the
vernal equinox and a little before before the autumnal equinox. I
get similarly shaped curves for others hours, with less separation
between the peaks when I use higher (italian) hour numbers.

Assuming that I have in fact graphed the altitude correctly, it
means is that there is a period over the summer months when the
altitude for any given hour to sunset stays /approximately/ the
same. In my case, at 49N, it seems that over the summer months,
the solar altitude for 1 hour to sunset is approximately a little
under 10 degrees, 2 hours to sunset is approximately a little
under 20 degrees, and so on at a little under 10 degrees per hour,
at least for the last 5 to 6 hours of the day.

In this day and age, I think we would demand greater accuracy, but
have there ever been sundials or other devices that exploited this
approximation?

Steve


---
https://lists.uni-koeln.de/mailman/listinfo/sundial






---
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https://lists.uni-koeln.de/mailman/listinfo/sundial

Zenith angles and hours to sunset

[Steve Lelievre]

I have been doing some calculations for an Hours To Sunset dial (that 
is, an Italian Hours dial with the numbering running backwards). I 
discovered that the maximum altitude for a given hour does not occur at 
the summer solstice.  I was a little surprised to discover this - not 
amazed, but surprised enough to make me wonder if I have done my 
calculations wrong.


The attached diagram is for the example case of 4 hours before sunset. 
I'm getting a double maximum occurring a little after the vernal equinox 
and a little before before the autumnal equinox. I get similarly shaped 
curves for others hours, with less separation between the peaks when I 
use higher (italian) hour numbers.


Assuming that I have in fact graphed the altitude correctly, it means is 
that there is a period over the summer months when the altitude for any 
given hour to sunset stays /approximately/ the same. In my case, at 49N, 
it seems that over the summer months, the solar altitude for 1 hour to 
sunset is approximately a little under 10 degrees, 2 hours to sunset is 
approximately a little under 20 degrees, and so on at a little under 10 
degrees per hour, at least for the last 5 to 6 hours of the day.


In this day and age, I think we would demand greater accuracy, but have 
there ever been sundials or other devices that exploited this approximation?


Steve

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