Author Topic: Sunrise, Sunset and Solar Azimuth  (Read 10257 times)

captain paranoia

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #15 on: September 18, 2013, 07:11:11 PM »
> People were doing this stuff before modern mathematics.

'Modern mathematics', as pointed out by MoonMan, is actually quite old, especially this sort of stuff.

> I am not knocking anyone's enthusiasm or knowledge but can we possibly have it in simple English?

I'm trying my best to express myself in school-level mathematics, and trying to make the terms I use as clear as possible, and provide pictures to support my words.  Sorry if I'm failing :-(

> Are you trying to work out the time of sunrise/set or location of sunrise/set?

Yes to both.

Well, I'm trying to reproduce the mathematical model to give figures as accurate as the NOAA site I linked in the first post.  I'm doing this to help me think through and understand the mathematics, and the real world behaviour.

adi

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #16 on: September 18, 2013, 08:00:26 PM »
If you are trying to find bearing of sunrise then it is quite simple.

Firstly, calculate how many minutes between sunrise and midday.
Then Divide the figure by 4
Finally subtract number from 180 to give bearing to sunrise.

So 180 - (S/4) = bearing of sunrise.

I am trying to rack my brains to remember how to work out time of sunrise. I am sure I have come across a simple way to work it out but I just cant remember.

And now-a-days I use apps to tell me. My favorite is the Apple app the Photographers ephemeris for time and direction of both sun and moon rise and fall. 
"We do not belong to those who only get their thought from books, or at the prompting of books - it is our custom to think in the open air, walking, leaping, climbing or dancing, of lonesome mountains by preference, or close to the sea, where even the paths become thoughtful." Friedrich Nietzsche

Skills4Survival

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #17 on: September 18, 2013, 10:45:29 PM »
Great stuff.



Some of the 80,000 or so words that were not included in my book (88,000 were) included a big section of bearings at Sunrise and Sunset and for two reasons:
1.   If you do not have a compass or are in an area where your compass may be unreliable.
2.   To determine your local magnetic declination if your maps are old or do not display this information.

Here is some of this copy and also the prototype of a creditcard sized tool I developed to determine where the sun will rise/set according to the time of the year. You only need to know the current date and your latitude. (The tool would need to be scaled and drawn more accurately)

We all know that the sun rises in the east and sets in the west; what is less known is that no matter where you are in the world:
•   The sun only rises true east and sets true west on two days, September 21 & March 21: The Equinoxes. 
•   The sun rises/sets north of these points from March to September.
•   The sun rises/sets south of these points from September to March.
•   The amount it rises/sets further north or south varies by location.
•   This variation is always the same for sunrise and sunset.

To determine east/west using the sun you need to use Sunrise/Sunset Chart.
1.   Using this chart find the latitude nearest to the one where you are.
2.   Read beneath your latitude the maximum amplitude of the sun.
3.   Scale the horizontal bar from 0 to this amplitude on the side of the chart with the month you are in.
4.   Draw a line from today’s date, parallel with the vertical bar of the chart.
5.   Where this line intersects on your scale is the sun’s amplitude for that day.
6.   In the Northern hemisphere, subtract this number from 90° to find sunrise and add this number to 270° to find sunset.
7.   In the Southern hemisphere, add this number to 90° to find sunrise and subtract this number from 270° to find sunset.

To ascertain local Magnetic Declination:
1.   Using the steps above determine the bearing the sun will rise or set where you are.
2.   When it rises/sets take a bearing on it.
3.   The difference between your compasses bearing and the bearing you derived from your chart is the local magnetic declination.

Using the tool.

This is the front of the credit card sized tool (possibly with a light grid overprinted on it)



This information is printed on the reverse



At 55 degrees latitude in the northern hemisphere you divide the horizontal bar into 44 equal sections.



Using todays date, in this example October the 30th, you draw a horizontal line down from the date.



From this you can easily calculate that:
Sunrise will be at 70 degrees (90-20)
Sunset will be at 280 degrees (270+20)
Ivo

Lyle Brotherton

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #18 on: September 19, 2013, 10:26:00 AM »
Thanks Ivo and good to hear from you. Cal says you may have developed an alcohol problem ;)

CP I cannot personally take credit for the origin of this tool, this honour must go to the sadly late Hiroshi Sato, Leader of Special Rescue Teams, Tokyo, Japan, a tremendous SAR expert and terrific personality, sadly missed.

Hiroshi had been a mariner (your clue Adi) and was used to working with sextants and star almanacs.

Hiroshi had invented a sunrise/sunset disc.

It was built out of plywood, around 300mm in diameter, and at the centre had a small hole drilled through which was threaded a length of red nylon line.

Around the circumference of this disc markings had been made at 10° intervals. These were then grouped in segments of three, starting from 10° from the ‘north’. 

Each block of three segments were marked with the consecutive months of the year, starting with October at 10°to 40° followed by November between 40° and 70° and so forth.

He had then separately calculated the suns maximum amplitude in 1° intervals from 5° to 62° latitude; these values were the same for both hemispheres and put the results into a table format.

Using this disc on October 21, 2008 in Tokyo, Japan (Northern Hemisphere) Hiroshi found the Sun’s maximum amplitude at the latitude we were at.

He then scaled the north-south baseline of the disc for the maximum amplitude each side of the centre.

Then he found October 21 on the circumference of the disc and he pulled the red nylon line from the centre of the disc across it.

Holding the line on this date, he pulled its tail toward and perpendicular to the baseline. The intersection on the baseline gave him the sun’s amplitude.

To calculate the Sun setting at the horizon he subtracted the north amplitude from 90° east.

To calculate the Sun setting at the horizon he added the north amplitude to 270° west.   

I made notes about his design and asked if I could try and create a handy tool from his design which he kindly agreed to.

However, when I tried to replicate his results I failed. It was only when a friend, who reads Japanese, informed me that I had put the month names in the wrong place that I got it to work.

My design was to try and continue the handy creditcard sized designs I have for my other tools, as these are easy to carry in your wallet and almost everyone I know takes their wallet onto the hill with them!

I also condensed his table from 1° intervals to 5°
« Last Edit: September 19, 2013, 01:38:25 PM by Lyle Brotherton »
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captain paranoia

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #19 on: September 19, 2013, 06:18:23 PM »
> It was built out of plywood, around 300mm in diameter

Ah, now, if it was round, that would make more sense, and I was thinking that a circular device would work.

With a circular scale, you can project down from where the radial arm meets the date, and thus read off a value for any date.  Since the date scale is circular, the vertical projection will be down to a point on the horizontal scale that is proportional to the cosine of the date (expressed as an angular fraction of a year) from winter solstice, mimicking the behaviour of the Sun in the sky.

For your rectangular device, what do you expect to do for dates between mid-November and mid-January, and between mid-May and mid_July?  You cannot project a vertical line down from them to the horizontal bar, because the date scale is already vertical.

You might add a vertical scale to cover the required range, and project horizontally for these dates instead, but the horizontal and vertical scales would have to cover the appropriate ranges (not the full range of amplitude); the vertical scale would have the maximum amplitude in the centre (which the solstice dates would project to).

If we consider the amplitude to vary as a perfect sinusoid*, starting from zero (sin(0 degrees)) at the spring equinox, rising to a maximum at the summer solstice (sin(90 degrees)), and falling to a minimum at the winter solstice (sin(270 degrees)), we note that the positions of the corners are at the 45 degree points of the cycle.  Since sin(45)=0.7071, we can say that the horizontal scale must be of length 0.7071*k, and the length of the vertical scale must be (1-0.701)*k, or 0.2929*k, where k is an arbitrary tool scale factor.  The horizontal scale would cover the range 0-0.7071*max_amplitude, and the horizontal scale the range 0.7071*max_amplitude to max_amplitude.  That would work!  To fit the device onto an arbitrary rectangle (e.g. a credit card), we could re-scale the vertical axis to fit the available form factor.

* although I don't think it does; close, but not exactly.  Probably near enough for a tool this approximate.

BTW, if you used a circular dial, you could add a second rotating dial behind the first, with scaling tick lines to represent the amplitude at different latitudes, and a slot window in the scale at the front.  You'd have an outer dial that selected the current latitude.  At a push, you might even manage this for a rectangular tool, with two sets of scaling tick lines.  Since latitude varies over 90 degrees, the horizontal and vertical tick scale lines wouldn't overlap...  Essentially, you'd have made a circular slide rule calculator.

Skills4Survival

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #20 on: September 21, 2013, 10:57:59 PM »
Lets just say I am becoming very interested in grapes and surrounding science. I am also waiting for temperature to drop and go on a hike, I need it. Since Cascade Designs have understood the necessities in life (I had a straight and hard talk with them) they came up with something which actually makes life better, even when crawling under your shelter.

http://www.cascadedesigns.com/en/platypus/wine-preservation/category

best regards,
Ivo



Thanks Ivo and good to hear from you. Cal says you may have developed an alcohol problem ;)

CP I cannot personally take credit for the origin of this tool, this honour must go to the sadly late Hiroshi Sato, Leader of Special Rescue Teams, Tokyo, Japan, a tremendous SAR expert and terrific personality, sadly missed.

Hiroshi had been a mariner (your clue Adi) and was used to working with sextants and star almanacs.

Hiroshi had invented a sunrise/sunset disc.

It was built out of plywood, around 300mm in diameter, and at the centre had a small hole drilled through which was threaded a length of red nylon line.

Around the circumference of this disc markings had been made at 10° intervals. These were then grouped in segments of three, starting from 10° from the ‘north’. 

Each block of three segments were marked with the consecutive months of the year, starting with October at 10°to 40° followed by November between 40° and 70° and so forth.

He had then separately calculated the suns maximum amplitude in 1° intervals from 5° to 62° latitude; these values were the same for both hemispheres and put the results into a table format.

Using this disc on October 21, 2008 in Tokyo, Japan (Northern Hemisphere) Hiroshi found the Sun’s maximum amplitude at the latitude we were at.

He then scaled the north-south baseline of the disc for the maximum amplitude each side of the centre.

Then he found October 21 on the circumference of the disc and he pulled the red nylon line from the centre of the disc across it.

Holding the line on this date, he pulled its tail toward and perpendicular to the baseline. The intersection on the baseline gave him the sun’s amplitude.

To calculate the Sun setting at the horizon he subtracted the north amplitude from 90° east.

To calculate the Sun setting at the horizon he added the north amplitude to 270° west.   

I made notes about his design and asked if I could try and create a handy tool from his design which he kindly agreed to.

However, when I tried to replicate his results I failed. It was only when a friend, who reads Japanese, informed me that I had put the month names in the wrong place that I got it to work.

My design was to try and continue the handy creditcard sized designs I have for my other tools, as these are easy to carry in your wallet and almost everyone I know takes their wallet onto the hill with them!

I also condensed his table from 1° intervals to 5°
Ivo

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Re: Sunrise, Sunset and Solar Azimuth
« Reply #21 on: April 16, 2014, 04:46:08 PM »
Thanks for posting that info Lyle, looks like a good addition to the nav card set.
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