The Equation of Time, old time navigation know-how in the modern world

If you ever messed with celestial navigation, you probably understand why even a perfectly installed sundial can be off by more than 15 minutes at some times of the year. But let’s recap on this shortest and darkest of days — in the Northern Hemisphere, that is — and I’ll also discuss how my old celestial nav skills recently helped with some very modern technology.

While it seems logical that the sun will pass due south of a fixed spot on earth at the exact same time every day, it does not. The calculated differences between Mean Solar Time (our fundamental 24-hour-day metric) and Apparent Solar Time (what actually happens) goes by the ancient and elegant name Equation of Time.

In celestial navigation, the Equation of Time must be accounted for every time you swing a sextant to measure the altitude of the sun to get a Line of Position, except for the special case of a Noon Sight when the precise time of the event is not needed to then calculate your latitude. (Which is why Dava Sobel’s fabulous book on the 18th-century race to build accurate chronometers is titled Longitude.)

But you do need to look up the Equation of Time if you want to know in advance when the sun is truly dead South (or North) of your position — known as Local Apparent Noon (LAN) in celestial or Solar Noon on the handy NOAA Solar Calculator website seen above.  So why was I using the calculator with the lat/long of my house on Dec. 4? Please allow me to babble a bit more about celestial mechanics first.

Equation of Time animations by Rob Cook via Wikimedia Commons

Understanding celestial navigation well means learning a lot about how the heavenly bodies appear to move versus what’s actually happening, and you too may relish the terms involved. So, as Wikipedia well explains, the Equation of Time is caused by two astronomical effects that each cause “a different non-uniformity in the apparent daily motion of the Sun relative to the stars” — the Orbit Eccentricity of the Earth’s annual trip around the Sun and the Ecliptic Obliquity of the Earth’s daily rotation (that 23.44° degree tilt highlighted today).

Besides for the Equation of Time, the combined effects can also be seen in the Analemma, an age-old diagram of the Sun’s annual positions in the sky as seen from a fixed point and showing the (Equation) time difference between Mean and Apparent Noon as well as altitude differences (Declination) from the Ecliptic.

And, yes, for reasons unknown, we in the Northern Hemisphere experience a lot more non-uniformity in the apparent daily motion of Sun in winter than we do in summer. The Equation does moderate around both Solstices, but sunrise/sunset tables still don’t always show what most people would predict around this shortest day.  I’ll stop now, but I’m not the only geek Having Fun with the Equation of Time.

Determining the true bearing of my home’s south side.

Here’s the question I had earlier this month: Back in 1979 — when I used a box compass, local Magnetic Variation, and that day’s Equation of Time (from The Nautical Almanac in print form) to establish 180°T for the crew hired to build the foundation for my passive solar home to be — how close did I get? I certainly know after all these years that the house works like a giant sundial, and I enjoy the earth/solar symmetry of straight back shadows from all the south-facing windows at or near Local Apparent Noon. But I’d never double-checked the azimuth precision, despite all the high-tech Heading devices that have passed through the shop below.

But I didn’t have a gadget handy on December 4 and why not use the Equation of Time to check where True South really is relative to the built house? The sunlight was crisp, the kitchen table above was already perpendicular to the south wall, and the books helped with a sharper shadow. It was just a matter of employing the Equation in a different way.

First I used the NOAA Solar Calculator to figure out the local time of Solar Noon — 11:26 because we’re far East in our standard time zone and also because the Equation puts the Sun almost 10 minutes fast in early December (see animated Analemma) —  and then I started minding the shadows beforehand. True local noon came and went before the sun’s azimuth shadow seemed most perpendicular to the table at 11:39, but then it was just a matter of tapping the “Use Current Time” button on NOAA’s site to get the results seen in the screen at the top. According to this test, my home bears 183°, not bad for an amateur with a box compass.

Revision Energy field designer on my roof with Solmetric SunEye solar panel tool

The point of all this was the prospect of turning my nearly 40-year-old passive solar home into an active solar home. And of course the bright young field designer from Revision Energy who did the initial assessment brought along a tool that quickly duplicated my work and much more. The Solmetric SunEye 210 “incorporates a calibrated fisheye camera, electronic compass, tilt sensor, and GPS” along with software that must include the same ephemeris work behind The Nautical Almanac to calculate solar access for a specific photovoltaic install location.

Solmetric SunEye 210 solar access analysis of my roof

The SunEye even let the designer paint in the seasonal leaves that will reduce solar gain a bit. But the cost/efficiency of solar panels is so good these days — plus the wise 30% U.S. Federal tax credit that may expire after next year — that even marginal roof exposures in Maine arguably make sense. My exposure is quite good and please note how the modern gadget’s Azimuth calculation is only one degree different from my Equation of Time shadow work.

A magazine recently interviewed me about marine electronics and I wasn’t too surprised when asked if they’ve somehow degraded proper navigation practices.  I suspect yes, somewhat, for some people, but always find it a hard question because I started navigating with hardly any electronic aids. I don’t think that traditional navigation should over-romanticized — just look at all the charted wrecks, or read about scary near-misses like my early tangle with Cape Cod — but I firmly believe that celestial and paper chart navigation taught me things about the physical world that continue to enrich my life.

By the way, I’ve signed on the dotted line for both a home solar panel system and a Pika Energy islanding/backup battery system. The technology is not marine-related yet, but my continuing good experience with boat solar helped with the decision, and maybe someday we’ll be joining a smart grid when we plug into shore power (and the awesome Victron Venus GX I just installed on Gizmo is already capable).

If nothing else, all this is fun to contemplate on the year’s shortest day, and here’s wishing you all an excellent Winter Solstice, belated Happy Hanukkah, and Merry Christmas. We just turned the Analemma low point once again, and the sunlight will return (to this Hemisphere).

Ben Ellison

Ben Ellison

Panbo editor, publisher & chief bottlewasher from 4/2005 until 8/2018, and now pleased to have Ben Stein as a very able publisher, webmaster, and editing colleague. Please don't regard him as an "expert"; he's getting quite old and thinks that "fadiddling fumble-putz" is a more accurate description.

15 Responses

  1. DougP says:

    Thanks Ben!!!
    This brings back some wonderful memories!!
    Makes me want to haul out my Tamaya Spica and take a round of sights!! 😉

    • Ben Ellison Ben Ellison says:

      Thank you, DougP. You inspired me to pull out and lubricate the Heath Hezzanith I bought almost new on a St. Thomas dock in 1971. It could use new mirrors but I think it could still work. I also have a Walker Excelsior IV Taffrail Log that I recall as old school even in the 70’s. It too got oiled and seems fully functional (if I found the right line to replace the one some garage critter destroyed).

      You might also enjoy this old entry about celestial mechanics and why observed sun altitude at LAN subracted from 90° plus or minus Sun Declination equals your Latitude (which is also visible in the NOAA Solar Calculator results):

      And/or Charlie Doane’s “Celestial Reasoning…”

      • DougP says:

        A Taffrail log??? Now that IS seriously Cool! AND Seriously old school!!!
        Like me!
        I kept the Spica onboard for years long after putting a Decca 801 (?) Satnav (TRANSIT) on the Luna 50 I bought in France to bring her back to SoFL in ’85, but I still took a noon site, just to keep my hand in. The Transit systems were pretty cool, often giving you a 1/2 mile fix every fifteen minutes to a few hours! 😉
        When we flew to France to pick up the boat, I also took my old TI Loran with me.
        Loran C AND SATNAV on a 50 foot sailboat, with a Vetus jet bowthruster!! Were we hot stuff or what???

        • Ben Ellison Ben Ellison says:

          You can sort of see the Walker at work in this 1978 offshore photo…

          …but I will honor it more in a future EdBlog. It certainly improved our DR work.

          I also still have that DIY plywood fishing reel, and sometimes we dared trail both at once. The SOP was no sharp turns and haul in the log before the fish, but we still endured some terrible tangles.

          • DougP says:

            GREAT PIC! truly old school! What vane was that? Looks like it far predates the old Sailomat which as the only vane I have any experience with.

          • Ben Ellison Ben Ellison says:

            I can’t remember the brand name, Doug, but think it started with an R. Nicely self-contained, simple vertical vane to trim tab, but aluminum parts caused some trouble I recall. This was the last offshore trip on Alice (daughter on her way) and I’d just installed the vane a few months before, so I didn’t get to use it very much.

  2. Ben Ellison Ben Ellison says:

    An interesting tidbit from the stellar Wikipedia Equation of Time entry:

    “The right time was originally considered to be that which was shown by a sundial. When good mechanical clocks were introduced, they agreed with sundials only near four dates each year, so the equation of time was used to ‘correct’ their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this ‘correction’.”

    It must have been hell on airline schedules.

  3. Larry Hall says:

    Thanks for the article, Ben, and Happy Holidays! Old enough to have used HO 214, 229, and 249 for sight reduction I now revel in the use of a $15 app for my iPhone called ‘Celestial’ by Navimatics. Check it out!

    • DougP says:

      Hi Larry,
      The reduction apps are amazing.
      Do you remember the small, 1980s, sight reduction calculator that came in a small wood box to match our sextants? I can’t remember the brand, but I thought I’d died and gone to heaven when I got that! 😉

      • Ben Ellison Ben Ellison says:

        “Tamaya” maybe? I never owned one but spent time offshore jealous of those who did. The StarPilot looks like the ticket now:

        • DouP says:

          Tamaya might have sold them but didn’t make them.
          But I just found it on Google:
          Celesticomp complete with the mahogany box!
          I was truly kickass with that! 😉
          That Starpilot is very nice with the graphing capability! Would be wonderful for sites in rough conditions!

          • Andrew Howe says:

            Unfortunately, the Celesticomp is no longer made or serviced/updated….I found this out when mine died in the middle of the 2015 Marion Bermuda Race. Luckily a crew member had brought a spare so I was spared the drudgery of the tables (which were on board as well). For the 2017 race I downloaded the “Celestial” iPhone app from Navimatics, which works great! For quick practical work the app can’t be beat, but it is still fun (and smart) to recall and explore the mechanics behind celestial navigation. Sort of like keeping paper charts at hand, and actually putting a pencil mark on a chart once in awhile!

  4. JB says:

    Perihelion — Earth’s closest approach to the Sun — is in very early January. So, during northern hemisphere winter, the Earth is moving around its orbit faster than it is in summer (Kepler’s second law “equal areas in equal times”), which means that the angular position of the Sun relative to the stars changes more quickly in winter, hence the area of that portion of the figure 8 analemma is larger.

    13000 years from now the situation will be reversed owing to precession of the equinoxes.

  5. Wil Bailey says:

    It turns out I now have two ‘sunguns’ – one given, one inherited, neither actually been used yet. There’s an Astra IIIB ( presented to me by HRH ) and a Zeiss Trommel ( bought by boatbuilder F-in-L before his last illness ). Which one to keep?
    I also had 3 trailing or taffrail logs. I gave one to a would-be GGR competitor, who didn’t go further than Spain. Maybe I’ll do better….

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