Ships must practice celestial navigation

https://www.usni.org/magazines/proceedings/2025/january/ships-must-practice-celestial-navigation

by HR01 • 2 years ago

114 112 2 years ago

jas39• 2 years ago

A smartphone has all the sensors: tilt, clock, camera. Even compass, though hardly needed. This should be enough to build an app to determine position at sea.

bhhaskin2• 2 years ago

Those likely aren't anywhere near accurate enough. And accuracy matters when being off by a few degrees can mean hundreds of miles.

UniverseHacker2• 2 years ago

You’re right, but they can be used together with a sextant to instantly preform calculations that can be time consuming and difficult at sea.

I use an app to double check my hand calculations.

kragen2• 2 years ago

Cellphone clocks are quartz crystals. Ordinary quartz crystals have an accuracy of ±10 ppm. That's ±0.001%. That's plenty accurate unless you've been at sea for a long time. 10 ppm of a month is 26 seconds, during which time the equator rotates 12 km (6 arc minutes, 1.9 milliradians). That's not "a few degrees".

Of course if you have a GPS signal you can keep time to within nanoseconds, but I suppose we're assuming GPS is jammed.

Cellphone cameras typically have pixel pitch on the order of 250 microradians, but star trackers routinely deliver attitude information accurate to less than a tenth of a pixel, so 25 microradians, which is 5 arc seconds, not "a few degrees". Calibrating a star tracker for a mass-market camera with its nonlinear distortions is a pain in the ass but can be done. 25 microradians is 160 meters.

SatState from F-Droid shows that my cellphone's accelerometer (tilt sensor) seems to vary by ±0.01m/s² in each of its ≈200ms samples, which is about a milliradian of error, 40× worse than the camera error, about two weeks of clock drift. This isn't "a few degrees" either. Accelerometers can integrate over arbitrarily long periods of time to reduce noise; to reduce noise by 40×, assuming a Gaussian distribution, you need about 1600 samples (320 seconds, 5 minutes and 20 seconds) to average out to the same level as the camera error.

(It's easiest if the phone is sitting still during the averaging time, but both the gyros and the star tracker attitude information permit you to usefully average the accelerometer signal over time even when the phone is changing attitude.)

You probably do need to calibrate the angle between the accelerometer and the camera, but it probably won't change significantly over time for a given phone.

The clock seems like it could be the weak point here, but even the clock is only drifting a few hundred meters a day, and that only produces an east-west error.

saulpw• 2 years ago

But what happens when the smartphone is bricked by an EMP, or hacked by a nation-state virus? Haven't you ever seen Battlestar Galactica?

BenjiWiebe• 2 years ago

Can you actually brick a smartphone with an EMP? They don't have much capture area compared to the grid.

nayuki6• 2 years ago

The article opens with:

Any navigation equipment that used electricity was prohibited, including all GPS sources, the Essex’s electronic Voyage Management System (VMS), and the computer-based celestial navigation software STELLA.

That defines the scope of the exercise.

_xerces_• 2 years ago

Curious how navigation at night was not possible without expensive equipment, sounds like they were relying only on starts in the morning and evening? Are the measuring something like angle of those morning/evening stars or their set/rise times with respect to the sun?

UniverseHacker2• 2 years ago

It is not true- the authors sound very inexperienced with celestial navigation. There are many ways including the lunar distance method to get a position at night with regular equipment. The math is more complex than a simple noon solar sighting, but it can be done with just a regular cheap plastic sextant and a watch.

It’s also no big deal to go 12 hours with no position. If you know your speed and heading you can accurately estimate your position much longer than that.

Overall, they also made it sound almost impossibly difficult for a large team of professionals, when solo and otherwise short handed recreational sailors have been reliably sailing around the world with celestial navigation for more than a century- through all possible conditions.

danielvf• 2 years ago

Note that they were staying roughly 2 miles within the actual track, while having the bulk of the work being done by a combo of officers and newbs that they had just trained. That's high accuracy standards for celestial nav, not even counting that this is most of other people's first time doing this in anger.

quercusa• 2 years ago

And just how expensive is a bubble sextant?

wrycoder• 2 years ago

I have one I paid $150 for. But bubble sextants are usually only used on aircraft.

ianburrell• 2 years ago

I discovered that real Tamaya marine sextants are available on eBay for $100-150. They were 30x that new.

My understanding is that the sextants are coming from breaker yards in India where the sextants were left on ships and salvaged.

throw0101a7• 2 years ago

Curious how navigation at night was not possible without expensive equipment, sounds like they were relying only on starts in the morning and evening?

As a sibling comment notes, it is possible. There are tables for lunar distance:

* https://thenauticalalmanac.com/Lunar_Distance_Tables.html

* https://en.wikipedia.org/wiki/Lunar_distance_(navigation)

* https://www.starpath.com/resources2/brunner-lunars.pdf

The planets Venus, Mars, Jupiter, and Saturn can be used, as well as several dozen planets (lookup tables in an almanac)

* https://en.wikipedia.org/wiki/Nautical_almanac

* https://thenauticalalmanac.com

Two US military videos explaining the theory (ground points/GP, circle of position, etc):

* USAF: https://www.youtube.com/watch?v=UV1V9-nnaAs

* Army: https://www.youtube.com/watch?v=G4DRBi66cOA

The USAF has a video because that's how planes used to do navigation outside of radio range—sextants on the ceiling of the cockpit:

* https://www.youtube.com/watch?v=C7gAiI79nOY

* https://www.youtube.com/watch?v=xc3rAlCDf54

throw0101a7• 2 years ago

Training for this was discontinued, but brought back in 2016:

* https://www.npr.org/2016/02/22/467210492/u-s-navy-brings-bac...

Now if only the US (and others) would get their act together and build out a backup system to GNSS. China, for example, has built out an eLoran system:

* https://rntfnd.org/2024/10/03/china-completes-national-elora...

An old USAF video explaining how the theory works (it assumes a geocentric worldview: the Earth is the centre of the universe (but it's not flat :)):

* https://www.youtube.com/watch?v=UV1V9-nnaAs

dzhiurgis• 2 years ago

Now if only the US (and others) would get their act together and build out a backup system to GNSS

They are moving towards quantum navigation (esp subs)

throw0101a7• 2 years ago

They are moving towards quantum navigation (esp subs)

How does that help the merchant marine that is part of the logistical supply chain? Are container ships going to get this quantum nav boxes too? The US pays airlines a retainer to be a reserve fleet [1]: will they get these boxes as well in case of emergency?

What happens to all the civilian infrastructure that need navigation and timing signals?

Considering only the "military" ramifications of GNSS disruption is myopic.

[1] https://en.wikipedia.org/wiki/Civil_Reserve_Air_Fleet

pbhjpbhj• 2 years ago

The USA who just threatened to invade a few NATO allies? People working with USA for the next few years seems pretty foolhardy. Surely everyone else in NATO needs to be getting together and building it defense system that exclude USA.

scottLobster• 2 years ago

I'm pretty sure the threatened invasions are just distractions to change the conversation from the H1B debacle.

If for no other reason than Canada is a country a lot of Americans actually care about (many have relatives there), and without a formal declaration of war congress could step in at any time and declare the whole thing illegal, enabling the military to refuse orders relevant to the invasion.

But as an American who has been a little sick of Europe mooching off of our military overwatch (see various European nations running out of bombs during the Libya campaign), I'm all for an independent European military command with independent capacity. The Cold War is over, the Russian tank hordes that once threatened to roll across Western Europe haven't managed to roll halfway across Ukraine with even reluctant, intermittent, indirect western support. We don't need to be under some monolithic military command anymore, Europe does not (or at least should not) need US strategic overwatch to fend off Russia.

As for the "European militarization has historically led to world wars" argument, the UK, France, and Russia all have nukes. Germany could probably build a few in a long weekend if sufficiently motivated. We aren't going to see a WWI or WWII rematch unless the AI "revolution" actually turns out to be more than smoke and mirrors for dumb money and enables perfect missile defense or something.

So yeah, please get an ex-US NATO off the ground so we can focus on China.

throw0101a7• 2 years ago

For (e.g.) eLoran, each chain is independent of every other chain. So the network chain(s) run in the EU are not dependent on the chains in US/CA, are not dependent on the chains in Russia, or the Middle East:

* https://en.wikipedia.org/wiki/File:NGA-Atlantic_Loran.png

The chains run by Japan are not dependent on the chains run by South Korea, would not be dependent on chains run by AU or NZ:

* https://en.wikipedia.org/wiki/File:NGA-Pacific_Loran.png

* https://en.wikipedia.org/wiki/Loran-C#Limitations

India, China, and Pakistan could all run their own infrastructure:

* https://commons.wikimedia.org/wiki/File:Loranstationscrkl.jp...

The only agreement being the technical standards (frequencies) and timing offset for near-by chains.

(And I'm Canadian.)

erulabs2• 2 years ago

The question was “Greenland and Panama” and the answer was “I wouldn’t rule anything out”. It requires a pretty hard squint to convert that into a threat “to invade a few NATO allies”. This sort of intentional misunderstanding of an exaggeration does so much more harm than good.

A western defense system that excludes the USA is naive at best.

piokoch• 2 years ago

This is very simplistic way of interpreting what Trump said. I would advice to read a bit about the significance of the GIUK (Greenland, Island, UK) in view of warming climate and growing importance of Arctics - melting ice might provide a much better and faster route for trade.

The problem is who will control the entrance and exit to that route and GIKU is one of them. And here we are on the key problem: Denmark for years totally neglected building any security/military infrastructure on Greenland, which suddenly might become a crucial element of the World economy and trade.

Do you really want sadistic regimes like Russia or China to take control over key parts of the potential trade routes (80% of global trade goes through the sees and oceans)?

Whatever you think about Trump, he will be gone in 4 years, someone else can be elected if Trump/Vance fails to deliver. Do you think we can get rid of Putin and his dreams on conquests Europe that easily? Or Xi, who is speeding with extending military potential of China, including nuclear weapons, aircraft carriers? Try to guess why Xi is doing this.

belter• 2 years ago

The USA technical infrastructure can be shutdown entirely any time EU wants. Hint: ASML Machines and Remote Disable...

AceyMan• 2 years ago

It wasn't "the USA", it was our incoming president, who everyone knows speaks for no one but himself.

dylan6042• 2 years ago

Now if only the US (and others) would get their act together and build out a backup system to GNSS. China, for example, has built out an eLoran system:

What prevents other countries from using these other systems?

throw0101a7• 2 years ago

What prevents other countries from using these other systems?

Nothing.

Nothing also prevents other countries from using China's BeiDou GNSS or their eLoran network.

nayuki6• 2 years ago

Encryption. For example, GPS's P(Y) code is encrypted and only for military use. https://en.wikipedia.org/wiki/Global_Positioning_System

knifie_spoonie• 2 years ago

The US government can apparently turn off their GPS signals over certain parts of the world:

https://idstch.com/geopolitics/denial-gps-services-kargil-wa...

madphilosopher• 2 years ago

The main principle of celestial navigation is pretty easy to visualize.

Pick a celestial body that's in your sky right now, like the Sun. At any given time, the Sun is directly over a single point on the globe (the GP, or Geographic Position). So if you measure the Sun as being directly over your head, you know where you are exactly on the globe, after consulting your clock and almanac.

But, if you measure the Sun at a non-overhead angle, then you and everyone else with that same measurement must be on a circle whose centre is the Sun's GP. (Visualize the circle as the edge of a flashlight beam being pointed directly downward at the GP.) The rest of celestial navigation is refinements to figure out where you are on that circle.

Onavo• 2 years ago

You can also do it at night using star charts (or as you call it, an "almanac"). That's how most of the digital celestial navigation solutions work, they use the positions of bright stars to determine a fix based on observatory data.

You can try it yourself here:

https://nova.astrometry.net/

nonrandomstring• 2 years ago

Might I differ on "easy", from second hand experience of watching my father go through his advanced yachtsmanship RYA Astro Navigation exams and cursing at trig functions? In practice its a lot of paper and compasses.

Almondsetat• 2 years ago

the Earth is the center of the universe, though, just like any other point in space

cafard• 2 years ago

when celestial navigation is all but impossible without advanced, expensive equipment (i.e., a bubble sextant).

Compared to what the Navy usually steers by, how advanced and expensive are bubble sextants?

knallfrosch• 2 years ago

Probably they use a $500,000 computer that fills a room and could be replaced with a $50 Android smartphone with offline Google Maps.

HPsquared2• 2 years ago

Said Android smartphone relies on clear airwaves and billions worth of GPS satellites.

5555624• 2 years ago

A new Tamaya sextant can run about $3,000 and Chinese-made Astra sextants are about a third of that. (Bubble sextants aren't used at sea.)

That's the only "expensive" equipment needed for celestial navigation or at least that was the case when I learned it over 40 years ago.

arter4• 2 years ago

As The American Practical Navigator (aka “Bowditch”) states, “No navigator should ever become completely dependent on electronic methods. The navigator who regularly navigates by blindly pushing buttons and reading the coordinates from ‘black boxes’ will not be prepared to use basic principles to improvise solutions in an emergency.”

I wonder if this mindset is also applied, for example, to the rest of the military. Does the Army regularly practice land navigation? I know they get at least one landnav class, but it is a perishable skill. If you don't practice, you'll soon forget about it.

I guess this could also be useful to civilians. Being able to do stuff without relying too much on electronics.

nradov2• 2 years ago

Some Army units, particularly ground combat units, regularly practice land navigation with map and compass. I don't think they typically spend much time on celestial navigation beyond the basics of finding heading based on constellations. They're not usually carrying sextants.

i_am_proteus• 2 years ago

There's no real need for celestial navigation on land, the same way there's no need for celestial navigation in most coastal waters: if you can see lines of bearing to known landmarks/navigation markers, you can obtain a fix.

lupire• 2 years ago

Ships are far more isolated than land crews, and direction-finding is much harder at sea than on land. If you're part of an organization that cares where you are and wants you back, you are pretty easy to find your general location venture off on a land journey and get stuck. A single human might be hard to find under a rock or snow, but an army unit that wants to fund is easy to spot.

paganel• 2 years ago

The problem with getting lost as an army unit on land is that you might inadvertently get in your enemy's sights before anyone on your side might have had the chance to find you, and at that moment it is game over for said unit. There have been documented a few of these such cases in the war in Ukraine.

rickcarlino• 2 years ago

Have there been any computer vision systems that can approximate celestial navigation using common sensors like a camera, An electronic compass, and a tilt sensor? Something like a computer vision based auto sextant. This is an idea I have thought about for a while but I have zero background in this area.

walrus01• 2 years ago

I'm not aware of any specifically, but one of the instruments that can be used as a data point to further reduce error when navigating in a zero-GPS/zero-radio-signal environment is an INS. The very highest precision ones are quite classified and used on submarines.

https://en.wikipedia.org/wiki/Inertial_navigation_system

exe34• 2 years ago

https://play.google.com/store/apps/details?id=com.embarcader...

not tried it

Polizeiposaune• 2 years ago

Not exactly what you're looking for, but spacecraft can use optical star trackers which compare what they see to a catalogue of known stars to determine orientation.

See, for instance:

https://www.rocketlabusa.com/space-systems/satellite-compone...

https://en.wikipedia.org/wiki/Star_tracker

gmueckl• 2 years ago

The closest unit I can think of right now was the SR-71's celestial navigation unit. I don't know how it worked internally, but it supposedly navigated the spy planes to targets across the globe before GPS existed.

nine_k• 2 years ago

A number of ICBMs used / uses a similar approach. In space, stars are always visible well, and terrestrial navigation aids may have been jammed or destroyed when ICBMs are put to use.

ttepasse• 2 years ago

From one SR-71 memoir I remember the factoid that sometimes the electromechanical star tracker was sensitive enough to catch stars in the daylight while the plane was still on the ground. Makes one wonder what is possible now with modern digital photographic sensors and processing power. And miniaturisation of course, the 60s celestial navigation unit was the size of a fridge.

bigfatkitten• 2 years ago

Many aircraft, mostly numbers had similar systems.

kragen2• 2 years ago

Yes, starcams are standard equipment on satellites including Cubesats because they provide more precise attitude information than any other available sensor. There are numerous free-software packages for star tracking; a quick search finds https://github.com/spel-uchile/Star_Tracker. I don't know if there's, like, an Android app that will do the required sensor fusion to tell you where on Earth you are.

cguess2• 2 years ago

Yes, there's one mentioned in the article, STELLA. Here's a paper describing it https://adsabs.harvard.edu/full/1999naos.symp..239K

tgsovlerkhgsel2• 2 years ago

That's an amazing paper:

TL;DR star tracking is a thoroughly solved problem, the hard problem is finding "where is down" without looking at the horizon (which may not be visible). The solution to that is coupling into the ship's inertial navigation system, which still may drift up to an arcminute per hour, but if you feed the star tracker data back into the INS for corrections, it gets better.

tgsovlerkhgsel2• 2 years ago

I looked into it briefly, and while it may be easy at sea with a horizon reference, it becomes surprisingly hard without it (which also complicates testing). The article touches on this with the mention of the bubble sextant required at night, presumably because you can't see the horizon. You'd have the same problem over land.

The stars only give you the angle at which you're looking at the sky. If you know the angle to the center of the earth (or can relate the sky measurement to that) and the exact time, you know where you are, within the inaccuracy of your measurements. Being 1/60th of a degree (1 angular minute) off places you 1 nautical mile off.

A bubble sextant solves this by including a literal 2D bubble level. "When properly used, the bubble sextant gives good results, by which we mean an accuracy to within 5 miles." (https://www.usni.org/magazines/proceedings/1939/june/averagi...).

The obvious solution that immediately springs to mind is a tilt sensor/accelerometer. However, once you get to a useful accuracy, those start getting expensive - several hundred dollars for a 0.01 degree system, which would give you an error of about 1 km.

You'd then need a sufficiently rigid mount for everything, proper calibration (remember, some angle on your mount being 0.05 degrees off completely destroys all usefulness of your system!), and then a camera and a plate solver (software that turns a photo into sky coordinates) should give you a useful fix. I think you could build a system that gets you within a few nautical miles for about $1000 (parts, not labor).

Havoc• 2 years ago

Like others said SR71 etc.

Problem is those fly high enough that the sky is pretty dark and you can actually see stars.

That's not an assumption we can make for the avg plane

cromulent• 2 years ago

There is a lot of GPS jamming happening these days, especially in the Baltic around Kaliningrad. Makes a lot of sense.

nayuki6• 2 years ago

analog navigation techniques became relevant again

I'm not sure exactly what methods were used in this navigation exercise, but if they write down numbers with finite precision at any point in the process, then the method has at least some digital component to it. Note that digital means the use of digits, not necessarily any involvement of computers or electronics.

For example, if they take a reading on a sextant, write down a number, and manually transfer it to a coordinate on paper, then that is a semi-digital process. If they take a number and then look up some kind of trigonometric table, that is definitely digital and not analog. But if the navigation process entirely consists of analog mechanical linkages and at no point any number is read out, then I would deem it 100% analog.

using the radian rule, steering 1 degree off base course for 12 hours at a speed of 16 knots results in nearly 3.5 nm left or right of track (565 yards per hour)

This brings up a laughable feature of the US customary measurement "system", a hodge-podge of units with no coherent logic to it: 1 nautical mile ≈ 2025.371... yards, an awkward number that isn't even whole. This is because 1 nautical mile = 1852 metres exact and 1 yard = 0.9144 metre exact. Converting between these units would be a pain. (Whereas at least 1 mile = 1760 yards exact.)

Analogously, let's say you're piloting an airplane at an altitude of 15000 feet and have a horizontal distance of 7 nautical miles to your landing site. What would be the descent angle if you flew down in a straight line? The answer is not immediately obvious because you can't do trigonometry on different units. Whereas if I said you're 4572 m high and 12964 m horizontal distance away, then the angle is arctan(4572/12964) ≈ 19.4°. And even if distances are reported in kilometres, even a child knows that 1 km = 1000 m.

brookst2• 2 years ago

What a wonderfully pedantic takedown of the conflation of digital and electronic.

floren• 2 years ago

Much written, nothing said

nayuki6• 2 years ago

Can't tell if that's a compliment or a snark. Do you have anything else to add to the discussion?

Btw, digital logic can be made out of LEGO, fluidics, electromagnetic (not electronic!) relays, steel plates (old railway signaling logic).

xerox13ster• 2 years ago

Go ahead and tune to your favorite station on an analog FM radio without using any digits, please.

Do you mind sharing what that station is with the class, or where it is on the dial?

nayuki6• 2 years ago

tune to your favorite station on an analog FM radio ... dial

I mean, when an ad says "Listen to 123.4 FM!", they are literally conveying that information to you digitally; they are telling you the number to tune to.

A fully analog radio has markings to give you a rough guide of where the frequencies are, e.g. 99.0 MHz, 99.1 MHz, 99.2 MHz, etc. When you take the number in your mind and map it onto the markings, you are performing a digital-to-analog conversion (DAC). And because the dial is analog, you can make it fall between any marking you want; there are no steps that you're forced to take.

Meanwhile, a digital tuner would let you tune to 99.1 MHz and 99.3 MHz with nothing in between.

y33t3• 2 years ago

Knots and nmi are not US customary units. 1nmi is 1 arcminute along the Earth's surface -- 1/60 of 1 degree. Knots are simply nmi/hr. Navigation is really just the application of spherical geometry. Not sure why they're referring to yards, I've never heard of those used in a navigational context.

If you want odd American units you should check out surveying. Units vary by geographical region.

nayuki6• 2 years ago

Knots and nmi are not US customary units.

Uh yeah they are. They are _customarily used_ in the US, so they count. They're literally used on all ships and planes. Any unit that is broadly used in the USA is USC. Further, they are indeed listed under the USC page: https://en.wikipedia.org/wiki/United_States_customary_units .

y33t3• 2 years ago

Believe it or not, some people still use slide rules and books on trig tables for this very purpose. They use them too. No sense in having them if you aren't competent at using them.

fmajid2• 2 years ago

So does that mean USN ships are issued with a precision mechanical chronometer for longitude, like John Harrison's original marine chronometer that won the Royal Navy's Longitude Prize?

ls612• 2 years ago

An electric timekeeping device which is not networked would presumably be good enough for this purpose wouldn’t it? The concern is ewar not so much the ship not having electricity.

fmajid2• 2 years ago

In this application, I would also be concerned about resilience in the event of an EMP strike. Not sure a battery-powered quartz timepiece would survive such, even if it would survive a failure of the ship's electrical systems (not sure if that would matter, as I doubt the ship's propulsion could survive such).

bodhiandphysics• 2 years ago

you can just put a quartz watch in a faraday cage. That'll be more accurate than any mechanical timepiece. Mechanical clocks have a nasty habit of breaking.

cguess2• 2 years ago

It's really funny to watch a bunch of people contradict the US Navy when it comes to navigation at sea. No, a cell phone isn't going to work in the middle of the Pacific and no, the US Navy doesn't use Google maps. Go get on an actual boat sometime and sail out of sight of land, you lose cell signal way before you're even over the horizon.

wakawaka28• 2 years ago

Ships do use GPS and so do phones and other devices. What exactly are you trying to say?

myself2482• 2 years ago

A cellphone's GPS only relies on the network for a quickstart. With no network, it takes longer to get the initial fix, but then works perfectly fine.

throw0101a7• 2 years ago

A cellphone's GPS only relies on the network for a quickstart.

The point is not to rely on GPS/GNSS:

* https://gpsjam.org

Tor3• 2 years ago

Not always true. I have devices with GPS which not only relies on a network for getting ephemeris data for the satellites, but they can't function without it. In other words, they don't even try to get ephemeris data through the GPS signal. So, if there's no network, it doesn't work. One of my devices is even a tablet without a SIM card, it only has wifi.. so if I'm near a cafeteria with wifi I can get a fix, and keep it for a while, but without it it's totally stuck. Forever.

In any case, as others have said, in the ocean a cellphone is useless for navigation. At least use a standalone satellite navigator. And learn to use paper maps and a sextant, it's actually a lot of fun.

doodaddy• 2 years ago

CIC was to notify Lieutenant Commander Stanton if the Essex deviated more than 10 nautical miles (nm) from the planned track.

Pretty impressive! USS Essex would cover 10nm in about half an hour, so not much tolerance for going off-course.

gertrunde• 2 years ago

Somewhat related - https://oceangloberace.com/

A round-the-world yacht race where modern technology is not permitted. (Where 'Modern' = pretty much anything that wasn't in common use in 1970's/1980's).

A fair few of the boats that have taken part had previously run the Whitbread Race in 80's.

GPS isn't permitted outside of emergency situations, and neither are mobile phones/computers (which are sealed in a bag by race organizers for the duration of each leg).

Celestial navigation is required iirc.

Other banned items include: - Carbon Fiber - Digital Music (Only cassette tapes permitted!)

Ships must practice celestial navigation

Related Stories