How accurate can the shadow of a large sundial be?

[tech99]

How to aim sun dial pointer at solar 12 noon? I think magnet north is wrong. True north is about 4 degree from magnet but which direction?

Magnetic Variation (UK) or Deviation (USA) is given on maps and sea charts. It varies a little with the exact location and also each year.

 

[Baluncore]

At any time at night, you could line the gnomon up with the pole star. If you extend the style of the gnomon as a straight line it should point directly at the pole star.

A magnetic compass will not always give good results. The easiest way to first set up an experimental sundial is simply to set the shadow to 12 noon at midday.
To do it more accurately you will need to know the time of your local solar noon. You would need to adjust for the equation of time (±15minutes) using the date and analemma diagram, and you need to adjust for your position (±30 minutes) relative to the reference longitude of your time zone.

 

[gary350]

At any time at night, you could line the gnomon up with the pole star. .

To do it more accurately you will need to know the time of your local solar noon. .

That is what I was asking, how to find solar noon at my location? Few days ago I looked up, sun rise & sun set at my zip code, chart shows time all day and at 12:50pm solar angle peaks. 12:50pm and 12:51pm are the same angle. I was looking for this chart again but can not find it I need to double check solar time.

I should have known to use north star I read in the Bible north star is only star in the sky that does not move. People at sea use north star for navigation. That will be hard in the dark and I live in TN we lots of tall trees. My back yard is donut circle of in center of trees.

 

[Baluncore]

Few days ago I looked up, sun rise & sun set at my zip code, chart shows time all day and at 12:50pm solar angle peaks.

That tells me that you now have "daylight saving", as the clock is 1 hour fast and reads about 1 PM when it is solar noon.
If you cannot align the gnomon with the pole star, then set the sundial to cast it's thin shadow on 12 noon when the sun is at it's highest point during the day.
Remember that a sundial reads local solar time which wanders through the year according to the analemma.

 

[gary350]

Can't find the original information but I found this, almost as good plus it lists solar noon as 12:50:54pm

https://sunrise-sunset.org/us/murfreesboro-tn

 

[gary350]

Can't find the original information but I found this, more accurate plus it lists solar noon as 12:50:54pm

It is interesting solar noon changes from 12:50 to 12:51 then 12:52 then 12:51 and so on. Some where I read this has something to do with Earth wobble & orgit not being perfect circle.

https://sunrise-sunset.org/us/murfreesboro-tn

 

[Baluncore]

Some where I read this has something to do with Earth wobble & orgit not being perfect circle.

Take a look at this page on wikpedia. It shows the time corrections and height of the Sun.
https://en.wikipedia.org/wiki/Equation_of_time#Graphical_representation

 

[Jonathan212]

Answering my own question, the -6 dB is at v = 0 below. Ie even in the straight line from a point source to the knife edge and to an aligned observer there is already attenuation by a factor of 4.

where v is defined as

where in the case of the sundial we plug in d1 = infinity. Source: http://www.waves.utoronto.ca/prof/svhum/ece422/notes/19-diffraction.pdf

But what happens at v = 1 where diffused light is 14 dB or 25 times weaker? The v = 1 isosurface of d2-versus-h is actually parabolic, not flat (d2 = 2/wavelength * h^2). A bit of a surprise:

So putting the observer a long way from the edge does not spread light very much, h does not increase in proportion. At d2 = 10 metres, h is still just 2 millimeters for red light. The sun's transition with the sun's diameter of 0.5 degrees would be 87 mm wide at the same distance.