# Is sundial time entirely dependent on solar azimuth?

I've visited several "how sundials work" sites and can't seem to get a clear answer to this: is "sundial time" just a linear function of solar azimuth? More specifically:

• When the sun is due south (northern hemisphere), it is sundial noon. All sites I've visited agree on this.

• When the sun is due west (azimuth 270 degrees), I say the sundial time is 6pm, a quarter turn/day from noon. However, I can't find a site that actually says this, and some sites seem to disagree with this. Same for it being 6am sundial time when the sun is due east.

I know there are different types of sundials, but had always assumed they would give the same sundial time. Is that not true?

As a note, the sundial I describe above can be fairly inaccurate at times, which makes me question whether I'm correct.

EDIT (to clarify question): Forgetting entirely about clock time for a moment, suppose I build a sundial. When the sun is due west, my sundial reads 6pm. When the sun is due east, my sundial reads 6am. When the sun is due south, my sundial reads noon. My question: have I built my sundial correctly? The type of answer I'm hoping to get:

• No. When you build a sundial, it should read (something else) when the sun is due west.

• There are many different types of sundials. Depending on type, your sundial may or may not read 6pm when the sun is due west.

• It depends on your latitude: sundials are latitude-specific. There's no such thing as a global sundial.

• Yes, your understanding of a sundial is correct. Sundials can be off by as much as (some number/formula) from mean solar time, depending on your latitude. They can be as much as (some number/formula) from clock time, depending on your longitude and time zone.

Any sundial that gives the same result as this is correct and any other is wrong (but sometimes close enough):

                    _      /############
/|    /#############
skewer        /     /##############
(central) v       /     /###############
|  north     /################
| (S in S.  /#################
| hmsphre) /##################
________|________ /###################
hoop      |        /##### LEVEL  #######
(from the | side) /###### GROUND #######
|      /####### (SOIL) #######
latitude--|-    /#######################
(use      ||   /########################
protractor)|  /#########################
|V /##########################
| /###########################
|/############################
j#############################
,|#############################
/#|#############################
/##|#############################
/###|#############################
/####|#############################
/#####|#############################
/######|#############################
/#######|#############################
/########V#############################
/#######################################
########################################


write noon on hoop's inside closest to ground, midnight opposite, 6 pm on the east side, 9 pm midway between the last two, and so on (hours only occurring in darkness optional).

If your sundial reads 6 pm at due west all the time then you're doing it wrong. Let's say I put a vertical stick in the ground, draw a 24 hour clock face around it, put noon poleward and think it's a sundial. In New York City, it could literally be saying 6 am when a genuine sundial says 9 am. That's just middle latitudes. At the equator on the equinox, it would read 6 am all morning and 6pm all afternoon at the equator. If you go 1 mile south of where the next noon, summer solstice and Tropic of Cancer coincide, it would say about 4:30am at sunrise, go forwards at first, then backwards, finally showing the middle 6 hours of the night passing in 7 seconds. Backwards. At noon. Then it will run forwards again until it reaches 7:30pm at sunset. If you place the stick right, you can even make it stay between 4:30a and 6a all morning, stop at 6 am at the instant of noon then instantly become midnight, run infinity years per second backwards for an infinitely short amount of time, go almost 6 hours backwards in seconds, then later forwards again very slowly until it shows about 7:30pm at sunset. This is why sundials cannot be made that way.

(of course, this is theoretical, there are no infinitely thin, vertical, and straight sticks, shadows are fuzzy, they can be too short to see, the Earth wobbles a bit, the speed of light is not infinite, this would only be true if only the Sun and Earth existed, even a flea jumping in Russia moves the Earth etc.)

And yes, the sundial time can be up to 16 minutes away from mean solar time (the equation of time), easily noticeable, but if you wanted correct local clock time instead of correct sundial time then you could put as many dates as needed on another dial and rotate the hour scale until the arrows point at the current time of year. The shadow then shows mean solar time.

That should be close enough to mean solar time that you wouldn't care for a number of centuries, certainly a century if you're real picky. As for clock time, what sundial disagreements are possible is limited only by the whims of man. The sundial is several hours wrong in West China. Cause they use the zone that's good for Shanghai (or Tokyo when daylight savings).

And all sundials without moving parts are latitude specific. Some are adjustible, though. Some designs are more suited for some latitudes or even become impossible in some places, like the kind with a wedge or rod on a level face. They will also not work on days with polar night. Though you could use a moondial if it's also not polar moon's below the horizon for days or weeks. Yes, moondials exist! You need to correct for moon phase and time of year or they're useless.

• @MikeG This looks really helpful - is it possible to also add a punch-line or tl;dr somehow? Suppose I believe it unconditionally and don't need proof - but I need a short-cut to the point. Can it be summarized somehow? – uhoh Aug 26 '16 at 5:18
• Just cleaning up the ASCII art here. I added a separate answer. – Mike G Aug 26 '16 at 12:55

The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic.

Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasonal change on earth. Yet the highest altitude of the ecliptic will always be due south, which means noon is well defined every day of the year.

Now to answer the question; if the day length (from sun-rise to sun-down) is exactly 12 hours, the sun will rise at an azimuth of 90 degrees and set at 270 degrees. However, this happens only twice a year, namely at the vernal equinox (first day of spring) and the autumnal equinox (first day of fall).

At the longest day, the summer solstice, both sun-rise and sun-down azimuths will be at their highest shift northward. On the other hand, during the shortest day, the winter solstice, the azimuth-shift will be maximally southward. This last bit applies to the northern hemisphere, for the southern hemisphere the seasons and therefore day lengths are reversed.

So in short, you have to account for what place on earth your sundial is at and what time of year it is.

The sun is not on the same Azimuth for the same hour (not even at noon!). You need to take the analema figure (http://en.wikipedia.org/wiki/Equation_of_time) into your accounts. If you do not, your clock will be exact only 4 times a year.

The shadow of a vertical stick would show the Sun's azimuth, but that's not really a sundial. A proper sundial's gnomon is aligned with the celestial poles so that the shadow indicates the Sun's hour angle. Then the great circle of hour angle $\pm$90$^\circ$ is projected onto the sundial plane as an east-west line; the shadow falls on that line at 6am or 6pm local apparent solar time regardless of the Sun's declination. Unless the sundial is an equatorial type, the other hour marks are spaced closer together around noon and farther apart around 6am and 6pm.