Could this be a mathematical way to obtain longitude without clock? Please help

[antonio glez]

archeoastronomist are bufled at polinesian finding out longitude without a clock

here the concept i just found out how to prove:

you have a dial with two geared counterotating needles you move by hand

every rotation of the sun around you you rotate a needle ten times with which the other needle will rotate another ten times in opposite sense

a question i think easy is how many times will cross each needle the sun?

well, like one follows the sun and the other goes against it one will count one more and the other one less that is 9 and 11

how many would they count along 10 days?

90 and 110

and how many will they count in those ten days if besides you give a revolution to earth(warning tricky question)

well my minds so weak i have to simplify i know in greenwhich they count 110 and 90 but i can't make in my mind the simultaneous rotation around the globe so i make first the ten days stopped and ill move in a second around the globe in the end and check the count

now my weak mind can see that

in greenwhich i count 110 and 90 for each needle crossing the sun, now i make a light fast trip around the globe:


so if both needles are at 12 and i make a light fast revolution following the sun going east the sun will move with respect to BOTH needles west but for one needle going west counts as POSITIVE while for the other going west counts as NEGATIVE, for theyre counterotating so ill have to add one and substract one to each other to whatever count

so if i count 110 and 90 in greenwhich traveling around the globe ill count one more and one less of each, 111 and 89 or 109 and 91 depending the sense i travel, which will allow me to know longitude


i think there's an easier demonstration:

in greenwhich one needel will move with speed x with respect to the sun clockwise and the other with speed y counterclockwise with respect to the sun

so as soon as you change longitude speeds will be x+z and y-z for the added velocity of the sun counts as clockwise in x and counterclockwise in y

 

[mfb]

a question i think easy is how many times will cross each needle the sun?

Sure, but where is the point in turning those needles?
The sun does not rotate around you. And you do not count rotations of Earth with that device, you count "days" as seen by your (probably changing) longitude.

so if i count 110 and 90 in greenwhich traveling around the globe ill count one more and one less of each, 111 and 89 or 109 and 91 depending the sense i travel, which will allow me to know longitude

No, you'll see 11 or 9 days (depending on the direction, while Greenwich sees 10), and have [120 and 100] or [100 and 80] crossings.

Unless you use a clock to power those needles to rotate 10 times in 24 hours. But then you don't need the needles any more, as you have a clock.

 

[jedishrfu]

Are you talking about the antekythera device?

http://en.wikipedia.org/wiki/Antikythera_mechanism

 

[antonio glez]

maybe the antichitera did this who knows

the idea is based in this concept, basically you have one needle which points to a VIRTUAL stellar body that rises east and sets west and the other needle aims to a VIRTUAL stellar body which rises west and sets east

then as phileas phog depending of going west or east youll count one more of one virtual star and one less of the other virtual star, and viceversa if you had gone opposite sense:

http://upload.wikimedia.org/wikipedia/commons/a/a4/Verne_Denoument.jpg

edit:

if you have a handclock with counterotating needles and you spin the whole clock youll count an extra turn from an outside reference in one needle and lack one turn in the other needle, and if you turn the clock the other sense viceversa

 

[antonio glez]

No, you'll see 11 or 9 days (depending on the direction, while Greenwich sees 10), and have [120 and 100] or [100 and 80] crossings.

well even in the worse case that shows my idea to work if not as well as i wish just with certain aproximation:

if you go one sense you get a ratio for crossings of 120/100 while the other sense 100/80, while in greenwhich you always get a ratio 11/9=12.222...so though not with high precision, in the worse of cases, checking the ratio of crossings you could find out longitude, though i believe with this method if works as i think you can get high precision

if you go around the globe in one sense you get 120/100=1.2

the other sense 100/80=1.25

so if you had a ratio of 1.2125 you traveled 180º(and this neglecting the verne effect)

 

[0xDEADBEEF]

You cannot get an absolute longitude with your device, which should be clear due to the elemental symmetry of the problem, so you could only measure deviations when you move from a known longitude to another longitude like from Greenwich to somewhere else, but even that doesn't work. You will always need a clock. You see the sun moving because you are in a rotating reference frame. If you move on the surface of the Earth changing the rotation speed of your reference frame the sun simply moves slower or faster. The position of your cogwheels is the result of geometry, and will look the same if the sun has moved by the same angle with respect to you, regardless of the time it took to do so. Maybe the advantage of that Polynesian device is that you just need high precision of your clock and not high accuracy, but I doubt that Polynesians had clocks of the necessary precision.

 

[sophiecentaur]

Whatever methods the Polynesians used for their navigation, we have no idea of how reliable they were. What percent of the journeys actually took them where they wanted to go? Also, they were probably as ingenious as we are (probably more so, out of necessity) so they would have made a virtue of necessity and, if they actually made landfall, they got on with life where they had arrived.

 

[mfb]

@antonio glez: Your concept always needs a clock, even if it turns 10 times per day instead of 2 times (like a conventional 12h-clock). If you check your arguments carefully, you already assume that those needles are a clock.

 

[sophiecentaur]

There were alternative ideas for navigation which involved observing the Moon and the Jovian Moons to establish a 'universal time' without carrying a clock with you. They weren't a total failure either and could probably be better nowadays with decent telescopes.

 

[mfb]

They weren't a total failure either and could probably be better nowadays with decent telescopes.

Sure, you can measure those moons to get the current time with a precision of a second with a good telescope today. But if you can use modern technology, wouldn't it be easier to use a GPS receiver ? This gives your location with an uncertainy of a few meters (and time with nanosecond precision, if you like).

 

[sophiecentaur]

I can't see the North Koreans being able to blow the moons of Jupiter out of the sky, though. (Or an extremist US government holding us all to ransom, either).

 

[antonio glez]

the big problem for me is that i can't solve this problem for I am dislexic so its very difficult for me to distinguish clockwise from counterclockwise

if in greenwhich its alway 90 and 110 crossings during ten days and as if someone pointed traveling around the globe would be 120 and 100 or 100 and 80 that backs up my idea as working

for it not working you should get 121 and 99 for 121/99=110/90

the idea is this concept adding it a counterotaing needle



edit:

by the way there's missinformation on this subject, the usefull solution to the longitude problem wasnt using a mechanical clock for they acumulate error and voyages lasted maybe years

the solution was using the angle between sun and and moon as a 28 day universal clock

 

[mfb]

I can't see the North Koreans being able to blow the moons of Jupiter out of the sky, though. (Or an extremist US government holding us all to ransom, either).

Well, use a modern clock then. If the US government (or North Korea) has and uses enough bombs to break all clocks on Earth (including wrist watches), latitute estimation is probably not your most urgent problem.

if in greenwhich its alway 90 and 110 crossings during ten days and as if someone pointed traveling around the globe would be 120 and 100 or 100 and 80 that backs up my idea as working

Yes, if you have a clock. Or a local man telling you the longitude so you can calculate the expected number of crossings for that longitude.

 

[jedishrfu]

There is a way to use a ship's sextant to compute the longitude but using a clock was way simpler:

http://en.wikipedia.org/wiki/Sextant

with some details of how it was done here:

http://en.wikipedia.org/wiki/Longitude

in contrast the polynesians used information from the stars and waves to navigate to known islands having discovered them by chance:

http://en.wikipedia.org/wiki/Polynesian_navigation

 

[antonio glez]

thanks a lot with your help i figured out where i went wrong:

basically if one virtual star to which a needle points to half its speed as you change longitude the other halfs it as well with which doesn't work

but imagine you use a mechanical clock with counterotating needles:

the clock has such an speed that during a day one needle crosses the sun 9 times and the other 11

if the clock during 10 days has a delay of 24 hours, huge delay, needles will cross the sun 90-1 and 110-1 times, expecting in greenwhich 90 and 110 crossings while after a revolution to Earth it would be expected 89 and 111

so 110/90=1.22222:expectted ratio of crossing in greenwhich
109/89=1.22471:ratio of crossings in greenwhich with a 24 hour mistake in clocks during 10 days
111/89=1.24719:expected ratio of crossings after a revolution to Earth with no error in the clock

so 1.22222 is a 0º as 1.24719 is at 360 so 1.24719-1.22222=0.02497

1.22471-1.22222=0.00249

so 0.02497 variation of crossings is at 360º variation of longitude

as 0.00249 variation of croosing is at the error of estimated longitude in greenwhich with a 24 hour error in the clock along ten days 9.971%

with this system with a 24 hour error in the clock that traditionally would lead to a 360º error in longitude you just get 0.09971*360=35.89907º

so with the traditional system a 24 hour error implies a 360 º error in longitude while with my system implies a 35º error

 

[mfb]

The traditional way would be to compare the clock (keeping Greenwich time) to the position of the sun or stars (giving access to a local time). Precision is just limited by the precision of the clock and the observations of the sun. With a wrist watch, the shadow of a roof and some stones to mark positions, it is possible to get a precision of <5 minutes. This corresponds to ~1° or about twice the diameter of the sun. This gives a maximal deviation of ~100km. With better devices, you can reduce the uncertainty a lot.

 

[antonio glez]

i recall reading don't rememeber where that the captains of the royal navy had orders to light an explosive charge in the navigation instruments case the ship was captured

as i see it, if I am right in my last point, with this opposite needle clock method you could diminish the expected error, 10 times, in the traditional method of comparing local and greenwhich time, something similar to magnify precision of the sextant with a nonius

so if the moon is actually a 28 day universal clock its precision can be magnified ten times with this method with which it becomes a 2.8 day clock for the effects

so i think the polinesian could have figured this out and use the moon-sun angle dial to power clocks with opposite sense needles and by keeping count of time wit respect to the sun or moon obtain longitude quite precisely with a very basic mechanical device

 

[mfb]

There is no expected error in the traditional method with a clock. Your method does not represent the traditional method, and would lead to a large error not present there.

 

[sophiecentaur]

Well, use a modern clock then. If the US government (or North Korea) has and uses enough bombs to break all clocks on Earth (including wrist watches), latitute estimation is probably not your most urgent problem.Yes, if you have a clock. Or a local man telling you the longitude so you can calculate the expected number of crossings for that longitude.

It's longitude that's the problem. If you can see the Sun at midday and you have a working calendar then you know your latitude.
With a set of ephemeris tables, a telescope and a sextant and a bit of time, you could decide where you were even if you had been asleep for an unspecified time. The time would be needed to get yourself into the right month of the right year.
Of course it's not necessary today but, when the bomb drops and you need to find that tiny island in the middle of the ocean, the clock-less and GPS-less solution is always there - and it's surprisingly accurate. And, hey, it's not the most random and pointless procedure that I've read on these fora!

 

[antonio glez]

yes there's an expected error in the traditional method and its the error of the clock

if the clock has an error of 24 hours along 10 day youll make an error in your position of exactly 360º

now with my system of virtual stars rotating opposite sense in the sky from a 24 hour error in the clock along 10 days you misspoint longitude in 36º

unless I am wrong of course that's why i post

 

[sophiecentaur]

yes there's an expected error and its the error of the clock

if the clock has an error of 24 hours along 10 day youll make an error in your position of exactly 360º

now with my system of virtual stars rotating opposite sense in the sky from a 24 hour error in the clock along 10 days you misspoint longitude in 36º

unless I am wrong of course that's why i post

The system still relies on an accurate time measurement - however you dress it up. You still need to know where these "Virtual stars" are supposed to be at the time you do your observation.

 

[mfb]

Well, use a modern clock then. If the US government (or North Korea) has and uses enough bombs to break all clocks on Earth (including wrist watches), latitute estimation is probably not your most urgent problem.

It's longitude that's the problem.

:(
Used the wrong word one time and you found it. Actually, the statement is even more accurate that way .@antonio glez: What you call "expected error" is the actual method to determine longitude.

 

[sophiecentaur]

:(
Used the wrong word one time and you found it. Actually, the statement is even more accurate that way .


@antonio glez: What you call "expected error" is the actual method to determine longitude.

I thought it was a slip!

 

[antonio glez]

well by error i meant a clock measures 25 hour where an atomic clock measures 24

the longitude is obtained traditionally by comparing LOCAL time from GREENWHICH time

the way i see the polinesian kept track of the virtual stars, the needles, by the angle sun-moon which is an UNIVERSAL 28 day clock and then augment precision with this system i try to explain

i insist using the moon-sun as a 28 day clock(with which you have greenwhich time to compare to your local time) was the solution to the longitude problem most extended until radios to syncronize clocks appeared

oh i forgot:

local time: position of the sun at where you are, sun in the top noon, 1200

greenwhich time : position of the sun in greenwhich

 

[sophiecentaur]

When we look at evidence of what ancient people achieved we really need to get things in context. We cannot do experiments on them - we can only see the surviving evidence of their successes. What routes did they actual travel reliably? If they stuck to voyages with constant latitude then they would not have needed to do the longitude thing at all. If they put in an easy North South dog-leg, by island hopping etc., they could then have taken an East West route over the horizon and been able to retrace their path to get home, reliably. We know about smart navigation by birds and fish. It's quite possible that humans could have followed the directions of flocks of seabirds to reach destinations way over the local horizon. Ocean swell can be stable in height, wavelength and direction for days and days at a time, giving direction and even an idea of distance (counting waves).

Is there any point in writing a hypothetical history of their navigation methods when there was probably a much better way - more suited to what the technology they had and involving a lot of ingeuity? I think one thing is certain and that is that they would have had an awful lot of failures; more than we would be prepared to accept these days. History does not record those failures.