Ships must practice celestial navigation
56 comments
·January 10, 2025throw0101a
dylan604
> 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?
nayuki
Encryption. For example, GPS's P(Y) code is encrypted and only for military use. https://en.wikipedia.org/wiki/Global_Positioning_System
dylan604
But that’s what the three letter agencies are supposed to do. Surely there’s a good guy back door to that encryption /s
throw0101a
> 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.
pbhjpbhj
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.
throw0101a
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.)
erulabs
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.
FireBeyond
It’s not a hard squint.
If these countries were our Allie’s the answer would be “I have no idea why you wood even be thinking that question”, not “we won’t rule anything out”
scottLobster
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.
dageshi
My impression is the US has pretty consistently tried to dissuade the EU from developing any kind of capable military organisation and to instead do it as part of NATO.
Although I have to assume that with Trump as president for a second time a lot of people in europe are going to have to worry that the US can't be relied on in the way it could in the past so I think you might get your wish.
Where that leaves NATO afterwards, I don't know.
jltsiren
> So yeah, please get an ex-US NATO off the ground so we can focus on China.
If the US does not care about its European allies, it no longer has the economic power to "focus on China". From an European perspective, China is far away and not particularly threatening. If there are no specific reasons to support the US, it's better to not take sides and trade with both sides.
BRICS is already a serious challenge to the Western hegemony. If the US thinks that "the West" has no longer a reason to exist, it will be seriously outnumbered by those who don't share its ambitions.
vlovich123
> 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.
I’m pretty sure that war requires congressional approval BEFORE an invasion full stop. Congress in recent history has been fairly cavalier about letting the executive launch military action and looking the other way, but it’s not actually supposed to work this way.
> 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
This is a gross mischaracterization of the situation that significantly underplays what actually happened I think. Without what Biden did right before the war saying “it’s going to happen” and mustering broad domestic and international support as well as using sanctions to freeze Russian assets and use them to pay Ukraine for reparations, Ukraine wouldn’t exist today.
We’re talking about $70B of military HW and $23B in terms of economic and humanitarian aid and another ~87B for the Ukrainian government to keep the lights on. That’s from the US alone. The international community has also contributed another $100B.
> 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.
It’s a slower burn. Putin isn’t going to try to take everything at once. It’s the Hitler annexation strategy over a longer time period. A little Georgia here, a little Crimea there, now it’s the entirety of Ukraine. Partly because his country is weaker but also because war is more expensive to prosecute than 100 years ago due to technology and the resistance is much better prepared for such an attempt.
Where do you think Eastern and Western European civilians will flee if any of those countries is drawn into conflict with Russia? Conflict forces desperate immigration which then creates anti-immigration counter responses in domestic populations here in the US.
China is important but what are we going to do there? Do you think we’re going to successfully defend an invasion of Taiwan when it happens? Cause that’s going to be their first military action. And if people are complaining about supporting Ukraine, how do you think they’ll fair regarding Chinese nationalists?
Finally, I’m pretty sure the troops and equipment we need there are also fairly different. If China is delivering huge numbers of land troops to Taiwan in the first place I’d say the battle is very lost. It’s going to be a sea/land siege so if the US gets directly involved it’ll be a meeting of the navies.
dzhiurgis
> 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)
throw0101a
> 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.
cromulent
There is a lot of GPS jamming happening these days, especially in the Baltic around Kaliningrad. Makes a lot of sense.
null
arter4
>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.
nradov
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.
lupire
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.
fmajid
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?
y33t
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.
rickcarlino
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.
kragen
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.
gmueckl
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
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.
null
Polizeiposaune
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...
walrus01
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.
nayuki
> 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.
y33t
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.
nayuki
> 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 .
y33t
Sorry, I meant that they aren't exclusively US units like US has its own unique pound, etc. Nmi are widely used because elevation of a celestial body can be directly translated to it's Geographical Point's distance from your own. Handy.
brookst
What a wonderfully pedantic takedown of the conflation of digital and electronic.
nayuki
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).
floren
Much written, nothing said
xerox13ster
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?
nayuki
> 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.
_xerces_
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?
UniverseHacker
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
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.
throw0101a
> 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:
quercusa
And just how expensive is a bubble sextant?
ianburrell
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.
wrycoder
I have one I paid $150 for. But bubble sextants are usually only used on aircraft.
cafard
> 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?
5555624
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.
knallfrosch
Probably they use a $500,000 computer that fills a room and could be replaced with a $50 Android smartphone with offline Google Maps.
jas39
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.
nayuki
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.
bhhaskin
Those likely aren't anywhere near accurate enough. And accuracy matters when being off by a few degrees can mean hundreds of miles.
kragen
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. 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.
The clock seems like it could be the weak point here, but even the clock is only drifting a few hundred meters a day.
UniverseHacker
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.
bhhaskin
At that point though you are using a sextant and a fancy calculator =P
saulpw
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?
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