# Why do sundial times vary with the latitude? **URL:** \ **Category:** Factual Questions\ **Created:** [January 29, 2021, 2:39pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774 "2021-01-29T14:39:48Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\ **Post date:** [January 29, 2021, 2:39pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/1 "2021-01-29T14:39:48Z")
I just came across this statement: “A sundial created for use at one latitude will give inexact times at other latitudes.” While I understand how longitude affects the times on a sundial, isn’t it the exact same time along any line of longitude, regardless of the latitude? And wouldn’t a sundial show that? What am I missing? ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [January 29, 2021, 3:05pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/2 "2021-01-29T15:05:07Z")
At noon, a vertical gnomon will cast a shadow due north anywhere along any line of longitude. But, that angle of the shadow is different for all other times, Think about a sundial sliding along a line of latitude several degrees east of Noon. The shadow will point due east on the equator, and rotate towards north the farther north the sundial is moved. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [January 29, 2021, 3:14pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/3 "2021-01-29T15:14:58Z")
> [@beowulff](#): > > Think about a sundial sliding along a line of latitude several degrees east of Noon. The shadow will point due east on the equator And this would actually only be true on the equinox. If it were the summer solstice for the northern hemisphere, then it would point south-east. > [@beowulff](#): > > and rotate towards north the farther north the sundial is moved. To make an extreme example, a sundial in the northern hemisphere that points straight north at noon on the equinox would point south in the southern hemisphere. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [January 29, 2021, 5:24pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/4 "2021-01-29T17:24:45Z")
> [@beowulff](#): > > But, that angle of the shadow is different for all other times, Think about a sundial sliding along a line of latitude several degrees east of Noon. The shadow will point due east on the equator, and rotate towards north the farther north the sundial is moved. Yes, this is true only at the equinoxes. But your basic point is well-taken and I wish I had thought of it when I was trying to come up with an explanation. In fact, a sundial is pretty useless at the equator and I wonder if it is much use anywhere in the tropics. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [January 29, 2021, 7:11pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/5 "2021-01-29T19:11:38Z")
> [@Hari\_Seldon](#): > > In fact, a sundial is pretty useless at the equator and I wonder if it is much use anywhere in the tropics. Huh? Why would a sundial be useless at the equator? [Here’s an example of a famous sundial at a location on the terrestrial equator](https://en.wikipedia.org/wiki/Quitsato_Sundial), which works just fine. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [January 29, 2021, 7:25pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/6 "2021-01-29T19:25:41Z")
That one is “useful” as a calendar. Would not be all that useful as a clock. If nothing else, the face of the clock would need to be re-calibrated almost daily. You _could_ tell time on it, but only if someone who already knows what time it is has made sure that the indicators are set up correctly. Or if you feel like doing a spot of math. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [January 29, 2021, 8:28pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/7 "2021-01-29T20:28:25Z")
> [@k9bfriender](#): > > That one is “useful” as a calendar. Would not be all that useful as a clock. If nothing else, the face of the clock would need to be re-calibrated almost daily. Not more so than sundials elsewhere. No matter where you are on the earth, you see the sun rising either somewhat north or somewhat south of the due east point, traveling westward in the sky on what is more or less a non-great circle parallel to the celestial equator (the projection of the terrestrial equator in the sky), and setting somewhat north or south of the due west point. (At equinoxes the sun is more or less on the prime vertical circle or due east-west line, of course.) So the sundial gnomon’s shadow is going to make some kind of nonzero angle with the east-west line at all times on all days, at any latitude, except when the sun is right on that prime vertical circle. You can test out some sample sundial shadow traces for various dates and latitudes [on this Science Pickle “Using Sundials” app](https://sciencepickleapps.com/SundialShadowsV1-0-0/) to see what I mean. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 29, 2021, 8:57pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/8 "2021-01-29T20:57:54Z")
If that sundial sits on the equator, and the gnomon points straight up, then the only “problem” with it is that it is not an equatorial sundial in which the gnomon is parallel to the Earth’s axis (which can be constructed in the tropics as well as anyplace else), but that is not the unique way to make a useful sundial. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 29, 2021, 9:11pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/9 "2021-01-29T21:11:28Z")
The only “recalibration” you might need is to display the Equation of Time, but that is not a function of latitude. ---
**Author:** ![Kedikat](https://avatars.discourse-cdn.com/v4/letter/k/ed655f/32.png) [@Kedikat](https://boards.straightdope.com/u/Kedikat)\ **Post date:** [January 30, 2021, 6:46am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/10 "2021-01-30T06:46:08Z")
Wouldn’t a sundial work at any latitude if you had the right demarcations on the baseplate? I imagine them to be curved lines. Oh oh. Now I am trying to imagine those lines curving and hooking up right from Equator to a pole. Midsummer at the north pole, you have 24 lines equally dividing the circle around a vertical pole. Totally circular. At the Equator you are horizontal. So maybe not… ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [January 30, 2021, 8:05am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/11 "2021-01-30T08:05:54Z")
> [@Kimstu](#): > > Not more so than sundials elsewhere. No matter where you are on the earth, you see the sun rising either somewhat north or somewhat south of the due east point, traveling westward in the sky on what is more or less a non-great circle parallel to the celestial equator (the projection of the terrestrial equator in the sky), and setting somewhat north or south of the due west point. (At equinoxes the sun is more or less on the prime vertical circle or due east-west line, of course.) I don’t understand your point here. Compare summer and winter at a northern latitude. In summer the sun rises in the NE, but it rises very early, so that’s where you mark the 5am. By the time it gets to 8am, the sun has moved around to the SE, which is about where it rises in winter - at 8am. Naturally the shadow will be longer in winter. Whereas on the equator the sun is going round to the north for half the year and south the other half, so the same kind of sundial just wouldn’t work. ETA: in practice it won’t match up because of summer time, but that’s just us messing with the clocks. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 30, 2021, 7:57pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/12 "2021-01-30T19:57:49Z")
> [@Kedikat](#): > > Wouldn’t a sundial work at any latitude if you had the right demarcations on the baseplate? I imagine them to be curved lines. Oh oh. Now I am trying to imagine those lines curving and hooking up right from Equator to a pole. Midsummer at the north pole, you have 24 lines equally dividing the circle around a vertical pole. Totally circular. At the Equator you are horizontal. > > So maybe not… It works fine; the sun keeps moving at 15 degrees per hour no matter where you are. The only question is how you want it to look. If you are near the equator (or anywhere, really) but want a horizontal sundial, you might choose a different design. Or adapt the design slightly: look at this example of an equatorial sundial in Singapore [![](https://upload.wikimedia.org/wikipedia/commons/f/f0/Sundial%2C_Singapore_Botanic_Gardens.jpg) ](https://upload.wikimedia.org/wikipedia/commons/f/f0/Sundial%2C_Singapore_Botanic_Gardens.jpg) vs one in Beijing [![](https://upload.wikimedia.org/wikipedia/commons/3/35/Beijing_sundial.jpg) ](https://upload.wikimedia.org/wikipedia/commons/3/35/Beijing_sundial.jpg) ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 30, 2021, 11:05pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/13 "2021-01-30T23:05:11Z")
Example of a “calibrated” sundial which displays mean time instead of solar time. There are various ways to do this; in this case you “calibrate” it by swiveling the shadow-casting plate so it points towards the sun: [New Millennium Sundial](http://www.swanstrom.net/sundial/NewM/index.htm) [http://www.swanstrom.net/sundial/NewM/NewM01.jpg](http://www.swanstrom.net/sundial/NewM/NewM01.jpg) ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [January 31, 2021, 5:30am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/14 "2021-01-31T05:30:07Z")
> [@DemonTree](#): > > Whereas on the equator the sun is going round to the north for half the year and south the other half, so the same kind of sundial just wouldn’t work. If what you mean is that the dial of a sundial generally needs to be calibrated differently for different latitudes, that’s true (and is basically what motivated this OP in the first place). But if you’re claiming that a sundial intrinsically won’t “work” at all just because the latitude is zero degrees, that’s not true. See for yourself by looking at the [Science Pickles “Using Sundials” app](https://sciencepickleapps.com/SundialShadowsV1-0-0/) that I linked to before. Click the “Shadow Trace” box, and then play around with the “Day” and “Latitude” settings to compare the path the shadow traces out on the dial during the day at different latitudes at different times of year. You’ll see that the shadow traces out a hyperbolic path between sunrise and sunset, wherever and whenever you’ve picked. The differences in date and latitude change the curvature of the hyperbola, which is why you have to re-calibrate the dial for different latitudes (and why, even at the same latitude, sundial readings won’t always be consistent with clock time throughout the year). But even at zero latitude, the shadow is tracing out a hyperbolic path and making different angles relative to the east-west line at different times of day. So you could put hour lines on the dial and read off those different directions as times. I.e., the sundial “works”. (The one exception is around the equinoxes, when the sun is traveling more or less due east-west overhead, so the shadow is falling right along the east-west line of the dial instead of making an angle with it.) Try out the app and then let me know if you still aren’t understanding why sundials can work at the equator. (In practical terms, of course, there are plenty of functional sundials in cities on or near the equator. E.g., in Singapore which is at less than 1.5 degrees of latitude.) ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [January 31, 2021, 7:25am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/15 "2021-01-31T07:25:06Z")
I know there are sundials that work in the tropics, but they are of a different design, as shown in the pictures @DPRK posted. I am saying the standard ‘garden sundial’ with an angled gnomon and horizontal dial marked out like a clock face (but with unequal angles) would not work on the equator. Your explanation seemed to imply this kind of sundial would not work at _any_ latitude, which I’m sure was not what you intended to say. I found this site which has a helpful explanation and diagrams of shadow paths, and includes a nice animation of how the shadow paths through the year can be used to determine the ‘hour lines’ for a given latitude: > **[Google Sites: Sign-in](https://accounts.google.com/v3/signin/identifier?dsh=S469961305%3A1675653819376873&continue=https%3A%2F%2Fsites.google.com%2Fsite%2Fsites%2Fsystem%2Ferrors%2FWebspaceNotFound%3Fpath%3D%2Fkhavrus%2Fpublic-activities%2FSolarEng%2Fsolengshadd&followup=https%3A%2F%2Fsites.google.com%2Fsite%2Fsites%2Fsystem%2Ferrors%2FWebspaceNotFound%3Fpath%3D%2Fkhavrus%2Fpublic-activities%2FSolarEng%2Fsolengshadd&passive=1209600&service=jotspot&flowName=GlifWebSignIn&flowEntry=ServiceLogin&ifkv=AWnogHfayCkxyelNyNrvY5VNC9M2_Xc-IyJ_wY3SKsD0qtB9Udfr2XeKM2Fi5AnIXpSj0ybkPG7o8Q)** > > Access Google Sites with a personal Google account or Google Workspace account (for business use). ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [January 31, 2021, 8:06am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/16 "2021-01-31T08:06:18Z")
> [@Kimstu](#): > > You’ll see that the shadow traces out a hyperbolic path between sunrise and sunset, wherever and whenever you’ve picked. The differences in date and latitude change the curvature of the hyperbola, which is why you have to re-calibrate the dial for different latitudes (and why, even at the same latitude, sundial readings won’t always be consistent with clock time throughout the year). To add to my earlier post, it’s true that sundial readings don’t always match clock times, but AIUI this is due to the earth’s orbit being slightly elliptical rather than a perfect circle, which means it is moving faster in its orbit at certain times of year. If not for this effect (and summertime) the sundial would match the clock all year round. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 31, 2021, 8:33am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/17 "2021-01-31T08:33:04Z")
> [@DemonTree](#): > > I am saying the standard ‘garden sundial’ with an angled gnomon and horizontal dial marked out like a clock face (but with unequal angles) would not work on the equator. That is correct — at least, if you start with the construction where the face of the sundial is parallel to the ground and the stylus points towards the celestial poles, at the poles of the Earth the hour lines evenly emanate from a point at the centre. As you move towards the equator this point of intersection moves away until at the equator you end up with something resembling this [![](https://www.shadowspro.com/images/polar1.png) ](https://www.shadowspro.com/images/polar1.png) where the lines are all parallel, at which point you could say it no longer looks like a clock face. See eg here for an illustration of the effect on a horizontal sundial of continuously varying the latitude: [https://www.mysundial.ca/tsp/horizontal\_sundial.html](https://www.mysundial.ca/tsp/horizontal_sundial.html) I cannot deny that any sundial needs to be calibrated for latitude by inclining the face and gnomon and constructing the lines and other conic sections correctly. I like to think that this is part of designing and installing it; a good sundial will tell time accurately and need no daily (or any) adjustment after it is fixed in place. On the other hand, if you insist on a portable sundial then you will need to align and rotate a couple of bits into place before you can read off the correct time. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 31, 2021, 8:50am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/18 "2021-01-31T08:50:57Z")
> [@DemonTree](#): > > To add to my earlier post, it’s true that sundial readings don’t always match clock times, but AIUI this is due to the earth’s orbit being slightly elliptical rather than a perfect circle, which means it is moving faster in its orbit at certain times of year. If not for this effect (and summertime) the sundial would match the clock all year round. This is called the Equation of Time and results from the Earth’s orbit being elliptical and also the tilt of the planet with respect to the orbital plane. Precision sundials will just tabulate this in some way [![](https://upload.wikimedia.org/wikipedia/commons/a/a0/Derby_Sundial_C_5810.JPG) ](https://upload.wikimedia.org/wikipedia/commons/a/a0/Derby_Sundial_C_5810.JPG) or you could indicate clock time directly by incorporating a weird-shaped gnomon [![](https://upload.wikimedia.org/wikipedia/commons/8/86/ROE-2012-05-07-0010.jpg) ](https://upload.wikimedia.org/wikipedia/commons/8/86/ROE-2012-05-07-0010.jpg) [![](https://upload.wikimedia.org/wikipedia/commons/0/01/Sundial_with_Equation_of_Time_correction.jpg) ](https://upload.wikimedia.org/wikipedia/commons/0/01/Sundial_with_Equation_of_Time_correction.jpg) or wavy instead of straight lines on the face. ---
**Author:** ![DemonTree](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/demontree/32/8646_2.png) [@DemonTree](https://boards.straightdope.com/u/DemonTree)\ **Post date:** [January 31, 2021, 9:55am UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/19 "2021-01-31T09:55:07Z")
> [@DPRK](#): > > That is correct — at least, if you start with the construction where the face of the sundial is parallel to the ground and the stylus points towards the celestial poles, at the poles of the Earth the hour lines evenly emanate from a point at the centre. As you move towards the equator this point of intersection moves away until at the equator you end up with something resembling this > > where the lines are all parallel, at which point you could say it no longer looks like a clock face. See eg here for an illustration of the effect on a horizontal sundial of continuously varying the latitude: Ah, I wondered if the lines would become parallel at the equator (and the gnomon need to be horizontal). That site helps visualise what is going on. > [@DPRK](#): > > This is called the Equation of Time and results from the Earth’s orbit being elliptical and also the tilt of the planet with respect to the orbital plane. Precision sundials will just tabulate this in some way Yeah, I’ve seen a couple of sundials that had the equation of time marked on. Can’t remember where I heard about it. The versions with the analemma gnomon are cooler. I also thought this was a fun design, reversing the usual concept, although I have no idea how accurate it is: [![](https://i.pinimg.com/originals/2e/10/66/2e106666dc2e8b502829bd0bcb538cc7.jpg) ](https://i.pinimg.com/originals/2e/10/66/2e106666dc2e8b502829bd0bcb538cc7.jpg) ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [January 31, 2021, 5:11pm UTC](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774/20 "2021-01-31T17:11:47Z")
> [@DemonTree](#): > > I am saying the standard ‘garden sundial’ with an angled gnomon and horizontal dial marked out like a clock face (but with unequal angles) would not work on the equator. Well, the issue there is that the correct angle of the gnomon to the dial surface depends on the latitude. Sure, a dial-gnomon combination calibrated for one latitude won’t work properly for a different latitude (which is why most one-size-fits-all “garden sundials” aren’t particularly accurate unless the latitude value happens to coincide with their angle), and its malfunctioning is worst at zero latitude. But since beowulff in post #2 referred to a “vertical gnomon”, and Hari Seldon’s post #3 asserted that “a sundial is pretty useless at the equator” without qualification, it sounded to me as though the claim was that any sundial wouldn’t work at the equator, which is not true. [Next page](https://boards.straightdope.com/t/why-do-sundial-times-vary-with-the-latitude/931774.md?page=2)