# Sundial question

Sorry if this is a bit dumb, but I started wondering about it quite late at night after quite a bit of wine, and I don’t know much about sundials.
Does sundial measurement vary with the seasons? Is there some sort of correction worked in for the difference in middle of summer shadows and times versus deep winter? Since a shadow might be similar at, say, 4 PM in December and 11 PM in July somewhere in the north. . . how is that accounted for?

Well, the sun is due south at noon in all seasons and moves 15[sup]o[/sup]/hr in all seasons.

How can that be? At what time is the sun due east? How does that time distance from noon manage to work out to 15 degrees per hour all year round? Or are days shorter because the sun rises at a different place further along on the horizon? I’m having a hard time visualizing this. Does the sun (pardon my imbecilic phrasing-- hopefully you get the point. I don’t really think Apollo is working a chariot up there) “move faster” through the sky in winter having risen and set at the same horizon points as usual, or does it just cover less distance in the sky, rising and setting at points closer together?

It rises and sets at points closer together. The only way it could possibly “move faster” would be if the rotation of the Earth somehow sped up in winter.

Ok, that’s what I suppose I was looking for. It all makes sense now. Sorry about the dumbassedness.

As to the 15º/hr. The sun appears to circle the earth going 360º in 24 hours. That’s 15º/hr in any season.

Noon is defined as the time when the sun is due south (actually when it is at its highest point which turns out to be due south), and I should have added, in the horthern hemisphere. So it would be due north in Tahiti.

I didn’t see it as “dumbassedness”, and if I gave the impression of any snark in my reply, I apologize. It was not intended.

Having read a bit of the link I see that the sun isn’t quite highest at local noon. We need a celestial navigator. I thought that navigators measured the sun’s height for a bunch of readings around noon and morked the highes point as noon. That set the local clock which they compared with the chronometer set to Greenwich time to get longitude. Where did I go wrong?

No no no, no snark perceived-- I’m just embarrassed that my sense of the way things work is so poor. For some reason I was sure that the sun always rose and set in the same places and I think I’d come up with some pre-Copernican, non-Euclidian rationale for why the sun could change apparent speed.

It’s news to me too, but from reading the link I note that the difference is all but unmeasurable and it appears (to me) to be rooted in the difference between celestial north and true north.

Yeah, the link said the difference is small. So for a ship traveling at even 25 knots, even a couple of minutes time difference wouldn’t result in a big enough error to be noticeable.

Having been an amateur astronomer and amateur sundial builder, I learned that the concept of how time is kept is very complex.
For example a sundial does not keep mean solar time which is what a regular clock does. The Sun can be directly overhead at different times at different times of the year. Clocks keep an average time. The Sun does not function on an average time.
Since you wanted to know about the amount of time that a sundial differs from a regular clock (or “civil time”) you will first have to learn about the equation of time.

For another thing, the time zones are averaged for 15 degrees of longitude on the surface of the Earth. So, Boston for example, (71 degrees longitude) has the Sun overhead 16 minutes (of time) before it would be overhead on the 75 degree longitude). This is called the local longitude difference.

Also, Daylight Saving Time must be taken into account.

Since celestial navigation has been brought into the topic, exact time does make an enormous difference in determining longitude. If you were at the equator, one degree of longitude is about 66.66 miles. The Sun goes through 15 degrees of longitude per hour. Therefore if your clock was 1 minute off, your longitude would be 16.66 miles in error.

I typed a lot of this from memory but I would suggest you consult a sundial tutorial - yeah this stuff is complicated.

Really? For instance, in much of the southern hemisphere, surely it’s due North at noon? And near the equator it can be due North or due South depending upon where you are and the time of year.

So I have a northern hemisphere bias, sue me. Anyway, I corrected this in a later post.

Perhaps a better way to visualize this is to look at an analemma. That’s a composite picture of the Sun taken from the same location at many different days through a full year, but at the same (mean solar) time each day. The shape is a result of the tilt of the Earth’s axis, and the fact that the Earth’s orbit isn’t circular: If the orbit were circular, the analemma would still be a figure-eight, but it’d be symmetric on both axes. Since perihelion is close to (but not exactly on) a solstice, it’s almost (but not quite) symmetric about the long axis, but the southern half is bigger than the northern half (since it’s the southern solstice). If the Earth’s axis were not inclined, but the orbit were still elliptical, the Sun would still move in the sky from day to day, but along a straight line (the sides of the figure-8 would be squeezed in). And if both the axis and the orbit were straightened out, the analemma would be reduced to a single point.

Ah, so it is a bit more complicated than simply “there’s no difference.” That’s very interesting, Chronos. Perhaps my gut instinct was correct but for the wrong reasons.

It’s always more complicated, isn’t it? The thing is that everyone east and west have different solar times. If I am standing west of you, when it is solar noon for you it isn’t quite solar noon for me because the sun hasn’t gotten to my meridian yet. What was done to avoid this jumble of times was to divide the earth into 24 time zones each one 15º wide. Noon by the clock in each of them is the same for the whole time zone and it is the time that is solar noon for a meridian, probably the center one, in the zone. That way, no one’s clock is more that 1/2 hour ahead of or behind solar time. So your sundial will be within 1/2 hour of your clock. Except, and there’s always an except, when you go on daylight savings time. In that case your clock can be up to 1½ hours ahead of the sundial.

As Quartz pointed out, within 23½º of the equator the sun can be north or south of you or directly overhead. When you are on the equator the sun is north of you during the daytime when it is summer in the northern hemisphere. If you are on the line of latitude called the Tropic of Cancer, which runs through Cabo San Lucas in Baja California, the sun is directly ovehead on the summer solstice, 22 June or thereabouts. That region from 23½º N to 23½º S is probably not the best place to use a sundial as a timepiece.

Chronos
Your explanation went into much greater depth than mine (and a good explanation it was).

I remember several years ago, a woman sent me an E-Mail stating that her son wanted to do a science project about sundials. I told her some of the concepts that have been mentioned here (equation of time, local longitude difference, etc). Also, I told her that to make the typical “garden variety” sundial (called a horizontal plane sundial), you would need to know the trigonometric formulas. (Actually those formulas are derived from spherical trig). Plus the fact that the gnomon (the sundial “pointer”) has to be aligned to celestial north and of course a gnomon of any appreciable width had to be taken into account when drawing the hour lines.
Needless to say, her son decided on some other science project.

As someone said in posting #12 “yeah this stuff is complicated”.

Bingo! Here, for the first time, we alight on the true complexity of the sundial.

All of this talk about the Equation of Time, deviation from the 15-degree meridian, and Daylight Savings Time is well and good, but those are the easy things to correct for. You can, if you wish, ignore them and say that your sundial measures time before and after apparent local noon.

But even to accomplish that much, you have to worry about spherical trig. The length and direction of the shadow cast by a solid object are a function of the altitude and azimuth of the Sun, and these change in a complicated manner depending on your latitude and the season. It’s nothing so simple as 15 degrees per hour, unless you’re Santa Claus or a South Pole scientist. Unfortunately, I’m not nearly sophisticated enough mathematically to explain it.

Oh, you can do it with no math at all. Just poke a stick in the ground at any old place, and then take your watch out at 1-hour intervals one day and mark where the shadow is each hour. It’ll only be right for that day, but it’ll be right.

If you’re really determined, you could do the same thing for many days through the year, and then just remember what set of marks to use at what time of year, and maybe interpolate between them. Or just draw a line (actually an analemma figure-8, but if you were lazy, you could approximate it as a line) for the curve traced out by the tip of the shadow at each hour. Bingo, accurate sundial, usable any time of the year, with no math required.