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    Re: Sextant accuracy and possibility of future improvement
    From: Lu Abel
    Date: 2016 Jul 19, 19:55 +0000

    I was about to comment on this question until I saw your reply which was, as usual, much more comprehensive than my proposed comments.

    One thing I would add, though -- the ability to hold a sextant steadily on a vessel.

    Maybe a gyro-stablized cruise ship affords stability on par with standing on land.   On the other hand, my experience in shooting celestial sights from my 36' sailboat, even in fairly calm conditions, is that accuracy of even a minute (much less than a fraction of a minute) is difficult to achieve due to the boat's motion. 

    Lu Abel

    From: Frank Reed <NoReply_FrankReed@fer3.com>
    To: luabel@ymail.com
    Sent: Tuesday, July 19, 2016 12:33 PM
    Subject: [NavList] Re: Sextant accuracy and possibility of future improvement

    The real mystery with sextants in manual navigation might perhaps be that they are much more accurate and more versatile than necessary. The design of the modern sextant was mostly driven by the requirements of shooting lunars two centuries ago. Today's sextants can measure angles with an accuracy of 0.1' if adjusted and handled very carefully (and certainly within a quarter of a minute of arc), and over range up to 120°, which is quite un-necessary for nearly all of celestial navigation. These and other features made sense for lunars. In the early 19th century, most ocean-going navigators had access to two types of instruments: a fine metal sextant for shooting lunars, that is not so very different from a modern sextant (see below) and also a wooden octant, which was used for ordinary altitudes of the Sun and other bodies. After roughly 1820 in the British culture of navigation and after 1850 in the American culture, lunars were done, almost never used at sea. But the instrument that survived was the sextant! Wooden octants were no longer manufactured and were soon seen as archaic, worthless things. The sextant is much too accurate for the needs of normal celestial navigation and more versatile, too. So why did that fancy, expensive instrument win out?
    Sextants have evolved in small ways since the 19th century. The biggest change, by far, was the introduction of the micrometer and along with it the milled arc (which the worm gear of the micrometer fits into). This was a radical improvement in usability, yet even so, habitually conservative navigators were stubborn converts to the new technology. Post-war, sextants optics changed noticeably with bigger apertures on telescopes and correspondingly larger mirrors. These changes arose from the popularity of twilight multi-star fixes --a fashion which has become so ingrained in the now global culture of celestial navigation, that many navigators think of the twilight fix as the primary methodology of celestial navigation. Along with the optical modifications, sextants also acquired built-in lighting systems, which honestly are rather ugly and ad hoc modification in the early post-war years. But that's about it for improvements in sextants. As you note, Francis, things haven't changed much. A modern sextant is scarcely different from a sextant produced in 1946, seventy years ago...
    Let's split celestial navigation into two broad categories: manual celestial practiced at sea (and therefore necessarily near sea level), and everything else, including navigation in the stratosphere, navigation on solid ground, and any and all automated systems.
    Let's start with manual celestial at sea. Modern nautical sextants, like the ones most of us have used, are limited by the fundamental limiting problem of celestial navigation: the sea horizon. Since the sea horizon has a natural variability due to variable surface refraction and also due to uncertainty in height of eye due to waves and swells on the order of a quarter to half a minute of arc, the modern nautical sextant is simply good enough. There's no reason to measure better angles because we would just be measuring noise in the system. The modern metal nautical sextant is good enough for this task. Arguably, it's even too good, which explains the popularity of plastic sextants among many bluewater sailors.
    There have been attempts, prototypes and specialty models, to produce sextants that are basically similar to the manual nautical sextant but which bypass the uncertainty in the horizon. I have never seen any that have made it to market in any significant way, but there have been attempts to determine the vertical using semi-inertial systems. In principle, this could yield a highly accurate celestial navigation system at least ten times more accurate, and reasonably 100 times more accurate, than traditional manual celestial. So why don't we all own such systems? First, they're expensive. So unless there's a real navigational benefit, they'll never succeed in the market. And here's where we remember the most fundamental limit of traditional manual celestial navigation at sea: when it's cloudy, it's useless. Sometimes we forget this while typing our messages in our homes, seeing days at sea filled with perfect weather --in our heads... But this is a profound limitation of traditional celestial navigation at sea level or at any altitude within the troposphere. A system of navigation that only works in good weather is simply too crippled for modern use compared to satellite navigation, inertial systems, and a variety of other systems (primarily available to military users). There's no way that an expensive improvement in finding the vertical (and thus bypassing the horizon and allowing a substantial improvement in position fixing) will make any headway so long as it suffers from this basic limitation. It doesn't work on a cloudy day.
    Beyond common nautical sextants as used at sea, it is, in fact, possible, even easy, to go beyond the limits. Just today Philip Sadler posted about a remarkable instrument for terrestrial position-fixing that could achieve high accuracy seventy years ago. Why didn't that become more popular (an open question -- probably many answers so please, speculate away)? And as we have discussed many times before, modern military aircraft, like US B2 bomber, that fly in the stratosphere, have automated celestial navigation "turrets" built into their wings which can scan dozens of stars per minute generating continuous high-accuracy fixes under many circumstances --don't try this in a dogfight, and, just as above, it won't work down in the troposphere if you're flying under clouds.
    It's worth noting that any form of celestial navigation which goes beyond the typical half mile to one mile limit of traditional manual celestial navigation must contend with the difference between astronomical latitude and longitude and true geodetic (a.k.a. "GPS") coordinates. The Earth's gravitational field is a wobbly mess when you get down to coordinate differences smaller than about a mile. Astronomical navigation "pulls down" the perfect coordinates of the celestial sphere, but it does so using the local vertical as a reference in nearly every case, and that local vertical is a property of the local gravitational field. We can map this -- it is a correctable "error"-- but it can't be ignored with high-accuracy fixes.
    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

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