Another confessional - Astro?

[scotty123]

I find it difficult to understand how you can fix your longitude position, using a clock alone.

Yes, I understand GMT & how the GHA of the Sun, can, at any precise time, give the exact position of that heavenly body, marking its Geographic Position (GP) on a longitude meridian. This position, is the same, whichever direction you head & is only determined by reference to Greenwich Time. Hopefully, using a sextant & working back from this GP position, will give some indication of your longitude.

However, if you head West from Greenwich, lets say for 3 days, your longitude position will be different, when you set off along the 0 deg meridian (equator),than it would be if you set off from any higher latitudes, so your 'West' position, cannot be determined just by looking at your GMT clock. Should you on this westward progress, head in any other direction (even East), the elapsed time will also be the same as if you had continued West.

Reference to your 'ships' clock, is imprecise, since it is adjusted by an hour every 15degrees of longitude (estimated by DR), thus giving imprecise data against which to compare with GMT & thus obtaining longitude position.

Even a Meridian Sun Sight, which will give latitude at 'local' noon, cannot help, since the time of local noon, will be the same at any longitude.

I''d be obliged if anyone can clarify this for me.

 

[Barnacle Bill]

Well you don't use a 'ship's clock' adjusted to local time: you use a chronometer, set to UT, checking from time to time how many seconds fast or slow it is.

If you can measure the time of local noon, you can then work out how many degrees and minutes east or west of Greenwich you are. (360 degrees = 24 hours, thus every 4 seconds of time is one minute of longitude angle.)

For example. if local noon is 1300 UT, then you are 360/24=15 degrees west of the Greenwich meridian.

This is 'built in' to the sight reduction methods. Have a look at http://www.aztecsailing.co.uk/newaztec/ocean%20theory/ch1/astronav.html

 

[scotty123]

Well you don't use a 'ship's clock' adjusted to local time: you use a chronometer, checking from time to time how many seconds fast or slow it is.

If you can measure the time of local noon, you can then work out how many degrees and minutes east or west of Greenwich you are. (360 degrees = 24 hours, thus every 4 seconds of time is one minute of longitude angle.)

This is 'built in' to the sight reduction methods. Have a look at http://www.aztecsailing.co.uk/newaztec/ocean%20theory/ch1/astronav.html

"If you can measure the time of local noon"

Exactly how?
Yes, I fully understand how to convert time into degrees/mins, but "local noon" is imprecise.
Your Noon Sight, is used to determine latitude, NOT longitude, precisely because "local noon", is 'the same time at any longitude'.

 

[Barnacle Bill]

Best method is to take a series of altitude measurements with the sextant, and then interpolate to get the time of the greatest altitude.

Sorry if I was unclear. You are trying to measure the time when the sun is at its highest. So you use a sextant to measure the altitude (angular distance from the horizon) of the sun, and when this is at its greatest value, that is local noon.

If you take a series of measurements of the sun either side of noon - when altitude is increasing and then when it is reducing again - you can plot the angle against time on graph paper, to give a more accurate estimate of the exact time the sun was at its highest.

Oh, and the sun’s meridian passage to Greenwich isn’t precisely at 12.00 GMT. The Nautical Almanac gives you the difference (called the Equation of Time) for each day of the year.

 

[scotty123]

Best method is to take a series of altitude measurements with the sextant, and then interpolate to get the time of the greatest altitude.

"I find it difficult to understand how you can fix your longitude position, using a clock alone."

 

[oldvarnish]

"If you can measure the time of local noon"

Exactly how?
Yes, I fully understand how to convert time into degrees/mins, but "local noon" is imprecise.
Your Noon Sight, is used to determine latitude, NOT longitude, precisely because "local noon", is 'the same time at any longitude'.

To measure the time of local noon you must observe the rising sun until it stops rising, hovers for a very short while (or appears to) and then starts to fall. This will give you the time of local noon, although it is quite tricky to do, and any lack of precision will be on the part of the observer.

This http://en.wikipedia.org/wiki/Longitude_by_chronometer answers your next question, if I have understood you correctly. (Scroll down to 'longitude by noonsite')

 

[nigel1]

The usual method of determining longitude (using the sun) is to take a series of sights.
You need a chronometer, sextant, almanac, and a means to reduce the sight.
Say you take a sights at 0900 and 1000 local time. You then take your noon sight to determine latitude. Then the next step is to run up the two previous sights to the time of local noon (a running fix), and that gives you the position.
The more precise your sights, and your estimate of course and speed made good, the more precise your position.
You can of course take a set of star sights at twilight, this will give a more precise position, as the time between sights is much less.

Another method
Take a series of sights say aprrox 15, 10, and 5 mins before local noon, record the time and sextant altitude.
Then after local noon, set your sextant to the angle measured at the 5 mins before noon sight, and record the time when the sun is at the same angle. repeat for the 10 and 15min sights.
You can now, by means of averaging, work out the GMT of local noon.( when the suns LHA is 000)
With that GMT, enter the almanac and extract the GHA of the sun for that time, and convert the GHA to longitude.
It wont be precise, but it will be close enough.
It can also be done without the almanac, but you will need to know the Equation of time for the day

 

[Alan ashore]

"I find it difficult to understand how you can fix your longitude position, using a clock alone."

Well, if you meant without also using a sextant or something similar to observe precisely the time at which, on that clock, something predictable happens in the heavens, then I'd say the task is broadly impossible, so I wouldn't worry about not understanding how it's done!

 

[BelleSerene]

You're not using the clock (chronometer) as a log to estimate distance travelled based on your speed. You're using so that whatever your longitude, you know the time at which the sun was at its highest point ('zenith') at Greenwich - and so passed over the Greenwich longitude.

At the Greenwich meridian (basically) the sun's at its highest at 1200 GMT. The further west you go, the later that happens. By carrying the GMT-based chronometer with you, you know when the sun passed over Greenwich. By watching when the sun's at its highest above the horizon (that's what we call the noon sight) you know when it's 'local noon' - i.e. when the sun's passing over your own longitude. The difference between the two is*the time it's taken the sun to go as far westwards from Greenwich as you happen to be. As 360 degrees takes 24 hours, it's heading west at 15 degrees an hour or one degree west every 4 minutes.

 

[chal3oye]

So you use a sextant to measure the altitude (angular distance from the horizon) of the sun, and when this is at its greatest value, that is local noon.

If you take a series of measurements of the sun either side of noon - when altitude is increasing and then when it is reducing again - you can plot the angle against time on graph paper, to give a more accurate estimate of the exact time the sun was at its highest.????

 

[Buck Turgidson]

Tricky on a rocking platform but sticking a pole in the ground and marking the shadow length against time will give your local "High noon". Handy if you're shipwrecked on a tropical island ;-)

 

[Neil_Y]

With practice all the sights get better, but taking several sights as others have said before and after local noon you can get quite an accurate longitude. You record the time accurately on your casio set to GMT I experimented with setting the sextant at a fixed setting and watching the sun come up to that point and then after noon falling to the same angle. As you have the same angle and a time for each I could get longitude quite accurate with just two sights. You do have to sit there looking through the sextant for four or five minutes so you don't miss it. Impossible to get the time at local noon with one noon sight as its passage flattens off and it doesn't appear to move for a couple of minutes and you need accuracy to a second or so.

Without doing the maths to any accuracy at a latitude of Plymouth a second out on measuring local noon is less than 1/4 mile, so an accuracy of +/- 4 seconds is 2 miles or there abouts.

Does that help?

 

[alant]

You're not using the clock (chronometer) as a log to estimate distance travelled based on your speed. You're using so that whatever your longitude, you know the time at which the sun was at its highest point ('zenith') at Greenwich - and so passed over the Greenwich longitude.

At the Greenwich meridian (basically) the sun's at its highest at 1200 GMT. The further west you go, the later that happens. By carrying the GMT-based chronometer with you, you know when the sun passed over Greenwich. By watching when the sun's at its highest above the horizon (that's what we call the noon sight) you know when it's 'local noon' - i.e. when the sun's passing over your own longitude. The difference between the two is*the time it's taken the sun to go as far westwards from Greenwich as you happen to be. As 360 degrees takes 24 hours, it's heading west at 15 degrees an hour or one degree west every 4 minutes.

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

"Longitude cannot accurately be measured at noon, when it is very easy to determine the observer's latitude without knowing the exact time. At noon the sun's change of altitude is very slow so determining the exact time that the sun is at its zenith is impossible to measure to the degree of accuracy necessary to give an accurate longitude.

Corrections to the process[edit]Unfortunately, the Earth does not make a perfect circular orbit around the Sun. Due to the elliptical nature of the Earth’s true orbit around the Sun, the speed of the Sun’s apparent orbit around the Earth varies throughout the year and that causes it to appear to speed up and slow down very slightly. Consequently, noon at the Prime Meridian is rarely if ever exactly at 1200 UTC, but rather it occurs some minutes and seconds before or after that time each day. This slight daily variation has been calculated and is listed for each day of the year in the Nautical Almanac under the title of “Equation of Time”. This variation must be added to or subtracted from the UTC of local apparent noon to improve the accuracy of the calculation. Even with that, other factors, including the difficulty of determining the exact moment of local apparent noon due to the flattening of the Sun’s arc across the sky at its highest point, diminish the accuracy of determining longitude by chronometer as a method of celestial navigation. Accuracies of less than 10 nautical miles (19 km) in position are difficult to achieve using the "longitude by chronometer" method. Other celestial navigation methods involving more extensive use of both the Nautical Almanac and sight reduction tables are used by navigators to achieve accuracies of one nautical mile (1.9 km) or less"

 

[snowleopard]

In the absence of a sextant, local noon is when the bearing of the sun is 180°T. If you have a compass that can take the bearing, apply Variation and deviation to work out the compass bearing that equates to 180. Failing that, a rough bearing can be obtained using the shadow of a vertical straightedge across the compass.

With a sextant you can take a sun altitude shortly before noon, noting the UTC time, then take the time at which the sun descends to the same altitude after noon. Half way between the two times was local noon. Much more accurate than trying to gauge exactly when the sun is at the zenith.

 

[oldvarnish]

I experimented with setting the sextant at a fixed setting and watching the sun come up to that point and then after noon falling to the same angle. As you have the same angle and a time for each I could get longitude quite accurate with just two sights.

That's a good idea!

 

[oldbilbo]

If you take a series of measurements of the sun either side of noon - when altitude is increasing and then when it is reducing again - you can plot the angle against time on graph paper, to give a more accurate estimate of the exact time the sun was at its highest.

All well and good, if you have nothing better. And the already limited accuracy of the 'Longitude by Equal Altitudes' is made worserer at middle- to high-latitudes, when the Rate of Change of Altitude in the period before and after local noon - when you would be determining the first and second.... of the pair(s) of equal altitudes' you'll use - is flatter than optimum, hence the accuracy of determining 'like with like' is degraded.

Another, arguably more accurate, technique is to take, resolve and plot a sight when the sun ( or another identifiable body ) is rising through the Prime Vertical i.e. due east, as the resultant N-S Line of Position will give your longitude. Same thing applies in the evening... and one can/should also do a compass deviation check 'about then' by means of Sun's Amplitude. That LOP, run up to the Noon Latitude by DR, should give a reasonably satisfactory fix. By similar working, a late sun sight on the westerly Prime Vertical, run back to the preceding noon, should give an indicator of the accuracy of your DR process.... and of your Noon Fix.

Perhaps your best bet is to read and explore the technique given in Bowditch, Para 2011 here: http://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-20.pdf

 

[Barnacle Bill]

All well and good, if you have nothing better. And the already limited accuracy of the 'Longitude by Equal Altitudes' is made worserer at middle- to high-latitudes, when the Rate of Change of Altitude in the period before and after local noon - when you would be determining the first and second.... of the pair(s) of equal altitudes' you'll use - is flatter than optimum, hence the accuracy of determining 'like with like' is degraded.

Another, arguably more accurate, technique is to take, resolve and plot a sight when the sun ( or another identifiable body ) is rising through the Prime Vertical i.e. due east, as the resultant N-S Line of Position will give your longitude. Same thing applies in the evening... and one can/should also do a compass deviation check 'about then' by means of Sun's Amplitude. That LOP, run up to the Noon Latitude by DR, should give a reasonably satisfactory fix. By similar working, a late sun sight on the westerly Prime Vertical, run back to the preceding noon, should give an indicator of the accuracy of your DR process.... and of your Noon Fix.

Perhaps your best bet is to read and explore the technique given in Bowditch, Para 2011 here: http://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-20.pdf

Or get a GPS!

 

[Skylark]

Reading the thread motivated me to find my copy of Bowditch. As mentioned by oldbilbo, section 2011 (page 311 of my 2002 Bicentennial edition) outlines two methods for obtaining LAN with a precision sufficient for determining Longitude, (1) the graphical method, and (2) the calculation method.

 

[Uricanejack]

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

"Longitude cannot accurately be measured at noon, when it is very easy to determine the observer's latitude without knowing the exact time. At noon the sun's change of altitude is very slow so determining the exact time that the sun is at its zenith is impossible to measure to the degree of accuracy necessary to give an accurate longitude.

Corrections to the process[edit]Unfortunately, the Earth does not make a perfect circular orbit around the Sun. Due to the elliptical nature of the Earth’s true orbit around the Sun, the speed of the Sun’s apparent orbit around the Earth varies throughout the year and that causes it to appear to speed up and slow down very slightly. Consequently, noon at the Prime Meridian is rarely if ever exactly at 1200 UTC, but rather it occurs some minutes and seconds before or after that time each day. This slight daily variation has been calculated and is listed for each day of the year in the Nautical Almanac under the title of “Equation of Time”. This variation must be added to or subtracted from the UTC of local apparent noon to improve the accuracy of the calculation. Even with that, other factors, including the difficulty of determining the exact moment of local apparent noon due to the flattening of the Sun’s arc across the sky at its highest point, diminish the accuracy of determining longitude by chronometer as a method of celestial navigation. Accuracies of less than 10 nautical miles (19 km) in position are difficult to achieve using the "longitude by chronometer" method. Other celestial navigation methods involving more extensive use of both the Nautical Almanac and sight reduction tables are used by navigators to achieve accuracies of one nautical mile (1.9 km) or less"

I think you are mixing up two different things.
The method of determining longitude by taking a sight a equal altitude before and after noon as described by several poster's is imprecise for the reasons you have posted along with two other important errors being introduced.
Both your Boat and the Sun moved during the interval.

This is not the Longitude by Chronometer method of calculating a sight.
While I Personally chose to use the Marc St Hillarie. or intercept terminal point method. which is more modern. than the older longitude by chronometer method.
both have similar accuracy the difference is in the calculation not the observation.

In the Longitude by chronometer method.
You take the sight in the same way.
Instead of calculating the DR distance from the sun and comparing to your observed distance from the sun to find the nearest point through which your position line passes.
You use a different calculation to determine the longitude on your DR latitude through which your observed position line passes. you can then run this up to Noon for a noon DR to use the same way as with the intercept method.

I have used both with equal success or lack of success. In the end I preferred the intercept method finding it easier.

 

[BelleSerene]

I think you are mixing up two different things.
The method of determining longitude by taking a sight a equal altitude before and after noon as described by several poster's is imprecise for the reasons you have posted along with two other important errors being introduced.
Both your Boat and the Sun moved during the interval.

Of course the sun moved during the interval - that's not a cause of error in the measurement; it's WHY it works!