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Uricanejack

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I did offer to post a template for a Longitude by Chronometer if anyone was interested. One person was.

Unfortunately while I have found a couple of my old sight books. I did not find one where I had used Long by Chrome. I also have not yet found my rather old dog eared set of Nories Tables. I put them in a safe place and can’t remember where it is.
I have to apologise it is over three decades since I used long by chrom. And I will have to sit down scratch my head and think and think a bit.
Most of my found sight books were from a time where I used a calculator. And or the short method tables for stars.

This is from back in the day when I did everything long hand. Using Nories Tables. By have sine formula using logarithm tables and traverse tables to calculate runs for DR’s

A Template for a Sun Sight run to Noon by Marc St Hiliar.
This template fit vertically into an A 4 hard note book. I would use the back page of the previous day for rough figuring and to figure out time of apparent noon.

Most of the templates I have seen have each section laid out separately all over the page. Makes it easy to mark in an exam setting.
Back in the bad old pre satellite days most of us used a vertical column layout. Which has a few advantages. One of which was taking 3 sights in quick succession and working them out together using the same DR.

I would start by figuring out a rough DR for Noon. From this determine the approximate time of apparent noon. Choose an approximate time to take am sight i.e. 2 hours before Noon whole numbers make the distance run easier. Sun preferably not to low i.e. less than 20 altitude. Lower the altitude the greater parallax and greater errors.
The total correction is an approximation and parallax varies with temperature.

The closer your azimuth is to 090 the better your noon cross and your longitude.

On a nice day, with a clear sky and a clear horizon I could be picky about time.
On a nasty day I’d look for the Sun and horizon all watch and take what I could get.

Use DR Noon longitude to determine time of apparent noon. You can use equation of time and Longitude
converted to time

or my preferred method next less.
LHA Apparent Noon = 000 Deg 00 Min
Add Longitude east positive west negative.
GHA of Sun at Apparent Noon.
From almanac take next less whole Hour GHA
Subtract from GHA at apparent Noon
Difference.
Enter increments with difference will give minutes and seconds after Whole hour.

GMT Hour minutes and seconds for apparent noon at DR

I would pre-calculate my approximate apparent noon sextant angle far right column.

By Nories tables using haversine formula and logarithms.

The advantage of the haversine formula and logarithms is everything is just simple arithmetic adding up no subtraction

Hopefully there are no misleading typos or other errors

I just realised I never posted the formula.
The haversin Formula for Marc St Hilaire

Hav. ZD=Hav. LHA Cos Lat Cos Dec+Hav(Lat +-Dec)

Where
Hav = haversin
ZD= Zenith Distance
LHA=Local hour Angle
 
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I would put a separate collum for each observation.

Chronometer.
Error.
GMT.

GHA
Inc
GHA
Long
LHA

Dec
d cor
Dec
Lat
Lat Dif Dec

Sextant Alt
Index E
Observed Alt
Dip
App Alt
Total Correction
True Alt.
90- Alt
True ZD.


Log hav sine LHA
Log Cos Lat
Log Cos Dec
Log Have sine
Natural Havrsine
N Haversine Lat Diff Dec
Natural haversine CZD
Calculated Zenith Distance.


Calculated Zenith Distance
True Zenith Distance
Intercept.

A Correction
B Correction
C Correction
Azimuth

From this point you can get a plotting sheet
Or continue with calculation.
 
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Chronometer.
Error.
GMT.

GHA
Inc
GHA
Long
LHA

Dec
d cor
Dec
Lat
Lat Dif Dec

Sextant Alt
Index E
Observed Alt
Dip
App Alt
Total Correction
True Alt.
90- Alt
True Zenith Distance.


Log hav sine LHA
Log Cos Lat
Log Cos Dec
Log Have sine
Natural Havrsine
N Haversine Lat Diff Dec
Natural haversine CZD
Calculated Zenith Distance


Calculated Zenith Distance
True Zenith Distance
Intercept.

A Correction
B Correction
C Correction
Azimuth

From this point you can get a plotting sheet
Or continue with calculation.
I used to use traverse tables as fastest.

DR Lat Long
Intercept x Azimuth D Lat Dlong
Intercept Terminal Point Lat Long

Use Traverse Tables again to run intercept terminal point to Noon.

Next bit is optional do you want a position at Apparent Noon or 12 Noon?
I would usually calculate a position for 12 Noon.

If you want a position at apparent noon. Run DR to time of apparent Noon

I would run my DR to 12 Noon. This would require me to run my observed latitude taken at apparent noon to 12 Noon.

This next part could be ether.

Intercept Terminal Point Lat Long
Run To Noon D Lat D Long
Noon DR Lat Long



This next bit might not make sense, but it works. Remember your intercept terminal point is just a position on your position line,

Observed Noon Lat
Run to noon or not

Observed Noon Latitude.
DR Noon latitude DR Noon Longitude.
Diff Lat

You can calculate the difference between your Noon Dr Longitude and the longitude your position line crosses your observed latitude using the C Correction.( The C Correction is the ratio of your position line)

Difference Lat x C Cor.= D Long D Long
Noon Latitude Longitude
 
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It might make more sense without my confusing notes


Chronometer.
Error.
GMT.

GHA
Inc
GHA
Long
LHA

Dec
d cor
Dec
Lat
Lat Dif Dec

Sextant Alt
Index E
Observed Alt
Dip
App Alt
Total Correction
True Alt.
90- Alt
True ZD.


Log hav sine LHA
Log Cos Lat
Log Cos Dec
Log Have sine
Natural Havrsine
N Haversine Lat Diff Dec
Natural haversine CZD
Calculated Zenith Distance.

Calculated Zenith Distance
True Zenith Distance
Intercept.

A Correction
B Correction
C Correction
Azimuth



DR Lat Long
Intercept x Azimuth D Lat Dlong
Intercept Terminal Point Lat Long

Intercept Terminal Point Lat Long
Run To Noon D Lat D Long
Noon DR Lat Long

Observed Noon Lat
Run to noon or not

Observed Noon Latitude.
DR Noon latitude DR Noon Longitude.
Diff Lat

Difference Lat x C Cor.= D Long D Long
Noon Latitude Longitude
 
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I usualy stuck this on the right hand side of My A4 note book.
It got all mixed up when I included it as part of template


Noon Dr Lat
Declination
Noon Dr ZD
DR True Alt
Total Cor
DR Apparent Alt
Dip
Dr Observed Alt
Index Error
DR Sextant Alt

Sextant Alt
Index Error
Observed Alt
Dip
Apparent Alt
Total Cor
True Zenith Dist

Noon Declination
d Cor Noon Declination
True Zenith Dist
Observed Lat.

Run To Noon
Obs Noon lat
 
The above must have been a huge effort to post, uricane. So thanks.

I love the little astro I have done, and only wish I had the deep understanding you display.
 
Found it

Longitude by Chronometer

Hav LHA =(Hav ZX- Hav(lat Dif Dec) )sec Lat sec Dec

Where
ZX = Zenith Distance.
Sec= Secant.

You might not have head of a Secant.
A secant is a sine for dummies. Back in the day cleaver people like actual mathematicians’ figured out the average professional seaman was really not very good at math probably having left school at 14.

So the invented secants which are 1/ sine the advantage of which is us dummies don’t have to do any division. Multiplying by a secant is the same as dividing by a sine.

There are also cosecants and cotangents for the same reason.

You might not have heard of a haversin either.

Half a versin. Which is of course as clear as mud.

A versin is 1 minus sine.

A haversin sine = (1 - sine)/2

The old long hand logarithm method of figuring out spherical trigonometry problems are based on the haversin formula.
The advantage of which it is always positive again trigonometry for dummies. It was all , so we did not have to figure out if we should add or subtract multiply or divide.

It was all look just it up and add it up.

Most of the template is much the same as for other methods of calculating a sight.
Just the order is a bit different.

I found this template in an old note book. In reality I would abbreviate it a bit but I left the extras in there things like date. Looking back at one of my old sight books where I left the date out. Is not very helpful.
Local time or LMT would normally be just part of my rough prep work. On the back page.
 
Template for longitude by chronnometer

Date
Dr Lat.
Dr Longitude

Local Time
Longitude
Approximate GMT

Chronometer
Error
Correct GMT

Declination
d correction
Declination

DR Latitude
Declination
Lat Diff Dec

GHA
Increment
GHA

Sextant Altitude
Index Error
Observed Altitude
Dip
Apparent Altitude
Total Correction
True Altitude
90- True Alt
True Zenith Distance.

Natural haversin TZD
Natural haversin Lat Diff Dec.
Natural haversine

Log haversine
Log Secant Latitude
Log Secant Declination
Log haversine LHA
LHA

LHA
GHA
Observed Longitude

A Correction
B Correction
C Correction
True Azimuth.
Position line


A Few notes.

If Sun is in the East use the Bottom of the page in the tables to determine LHA
If Sun is in the West use the top of the page in the tables to determine the LHA

Although I refer to the longitude as an observed longitude it is not your longitude.
What you have calculated from your observation of the altitude of the sun at an observed time is the longitude your position line crosses your DR Latitude.

To obtain an actual position or longitude you still have to do the Sun run to Noon which you can do to apparent noon. And plot on a plotting sheet. For apparent noon.
The Cross with your position line and your observed latitude from apparent noon will give you your longitude.

Or you can run to 12 noon

At Apparent Noon or 12 Noon you can still use the same trick with the C correction to calculate your longitude instead of plotting.
 
I was that one person who asked! Given that you've done me the courtesy of a response (huge effort, many thanks), I owe you the courtesy of trying to work through it.

Like oldvarnish, I've probably done the bare minimum to meet RYA course and exam requirements. I did the course one-to-one with a retired master mariner. I really enjoyed his anecdotes of a lifetime at sea.

Sitting in an office all day, I don't get too many opportunities to practice (hoping to fix this in the next couple of years, though:encouragement:). I do recall on a Biscay crossing doing all of the preparation in readiness for a star 3 point fix but come evening twighlight it had clouded over. Sun-run-sun with a MP thrown in at local noon aren't so bad, by comparison.

Thanks.
 
Uricanejack said:
Although I refer to the longitude as an observed longitude it is not your longitude.
What you have calculated from your observation of the altitude of the sun at an observed time is the longitude your position line crosses your DR Latitude.

To obtain an actual position or longitude you still have to do the Sun run to Noon which you can do to apparent noon. And plot on a plotting sheet. For apparent noon.
The Cross with your position line and your observed latitude from apparent noon will give you your longitude.
Click to expand...

I read the other thread too, and as near as I can tell, what you are calling "Long by chronometer" is not much more than taking the Long from a sunline and DR. IMO, "Long by chrono" specifically refers to Long calculation at merpass. A sun-run-sun, or any so-called "running fix" is not a fix per se; it's an EP (again IMO) as it's just an improved DR (a DR with an LOP, to be precise). The only reason I could think of to go through the effort of calculating the Long by time, would be if one hadn't obtained a recent fix (stars or sun and other body). Otherwise sun-run-merpass is reasonably acceptable. Done right, a noonsite with a Long calculation can be considered a fix - and I reckon with better than the 10nm accuracy that was suggested in the other thread. Bilbo posted the link in the other thread, but it's worth throwing it back up here - Bowditch chap 20 describes the Long calculation by averaging and graphing: http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002
 
Cruiser2B said:
I read the other thread too, and as near as I can tell, what you are calling "Long by chronometer" is not much more than taking the Long from a sunline and DR. IMO, "Long by chrono" specifically refers to Long calculation at merpass. A sun-run-sun, or any so-called "running fix" is not a fix per se; it's an EP (again IMO) as it's just an improved DR (a DR with an LOP, to be precise). The only reason I could think of to go through the effort of calculating the Long by time, would be if one hadn't obtained a recent fix (stars or sun and other body). Otherwise sun-run-merpass is reasonably acceptable. Done right, a noonsite with a Long calculation can be considered a fix - and I reckon with better than the 10nm accuracy that was suggested in the other thread. Bilbo posted the link in the other thread, but it's worth throwing it back up here - Bowditch chap 20 describes the Long calculation by averaging and graphing: http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002
Click to expand...

If all these methods, are achieving such accuracies, why did Chichester, rely upon finding an island, by 'running down a parallel of latitude', if he could fix his lat and long?

PS
Thanks urricanejack, most interesting.
 
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alant said:
If all these methods, are achieving such accuracies, why did Chichester, rely upon finding an island, by 'running down a parallel of latitude', if he could fix his lat and long?
Click to expand...

I can't speak for Sir Francis, but running down the parallel has no advantage in accuracy - it's just relatively simple.
 
alant said:
If all these methods, are achieving such accuracies, why did Chichester, rely upon finding an island, by 'running down a parallel of latitude', if he could fix his lat and long?

PS
Thanks urricanejack, most interesting.
Click to expand...

I asked Chichester a very similar question when he came to talk to our sixth form. His answer was that in sailing, same as flying, it is relatively easy to know your latitude, but aiming precisely at an island you could be a few miles to one side or another, guess wrngly and then turn away from it. His trick was to aim to one side or the other, the follow the p of lat, knowing that you had a much much higher chance, almost a certainty, of then running across the island. He called it a "deliberate miss" . It's a neat idea to reduce the probability of an error being compounded.
 
Cruiser2B said:
I read the other thread too, and as near as I can tell, what you are calling "Long by chronometer" is not much more than taking the Long from a sunline and DR. IMO, "Long by chrono" specifically refers to Long calculation at merpass. A sun-run-sun, or any so-called "running fix" is not a fix per se; it's an EP (again IMO) as it's just an improved DR (a DR with an LOP, to be precise). The only reason I could think of to go through the effort of calculating the Long by time, would be if one hadn't obtained a recent fix (stars or sun and other body). Otherwise sun-run-merpass is reasonably acceptable. Done right, a noonsite with a Long calculation can be considered a fix - and I reckon with better than the 10nm accuracy that was suggested in the other thread. Bilbo posted the link in the other thread, but it's worth throwing it back up here - Bowditch chap 20 describes the Long calculation by averaging and graphing: http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002
Click to expand...

You are correct; it is just a running fix and subject to error. The method faded from popular use being considered less accurate than Marc St Hillaire. Though it was still taught when I learned navigation.
I learned originally in the UK and there are more than a few differences in terminology.
I am not familiar with Bowditch; though one day I should get a copy.
It may be we use the term “Long by Chronometer” differently.

The accuracy of the method you describe is good enough.
I wouldn't make a quoted accuracy, There are to many variables, I would get an idea of my accuracy based on the conditions.
 
In another incarnation - and certainly in another century - I earned my crust, with my many colleagues, doing air-astro to a degree of precision which the Murricains just could not believe - and which is STILL Classified. There is no particular credit in that which attaches to me - that was down to the techniques and procedures invented and honed by my betters....

I remain in awe of those with the intellect and mental agility to consider, manipulate and then utilise the various tools that spherical trigonometry, algebra, topography, probability theory and a good handful of other mathematical disciplines offered to provide us 'peons' with Menus or Recipes, like Hayes 'How To Do It' Manuals, which would permit dummkopfs like me to navigate e.g. strategic bombers-with-payloads, strategic transports stuffed full of soldiers, VIPs, newshounds, important cargoes..... with an accuracy reliable enough for HM Queen to trust us routinely with her trans-oceanic comings and goings.

This was 'standing on the shoulders of giants' such as Sir Francis Chichester, who shot his sights from an open cockpit and both resolved them using a 'tubular slide rule' and plotted them on his knees, while flying the 'stringbag' aircraft with his shins. He knew and understood this stuff every which way, but had the rare genius of being able to 'simplificate and add lightness' ( to borrow a phrase ) so that others could follow and find the island, too.

Very much in the same vein is the deceptively-simple 'Reeds Astro Navigation Tables' by Lt Cdr Harry Baker, from Adlard Coles Nautical. Over the years I have used the simple 'look up' tables involving the Air Almanac and AP 3270, I have used the Nautical Almanac, I have used Nories and Burtons Tables.... and I have used a pre-programmed calculator. For my money, Harry Baker's 'Heavenly Body' Tables ( as he prefers to call them ) are the easiest to use and the most economic of space and of ££££.


'an important advantage of the versine method is that your sight is plotted from your EP, rather than from an assumed position, thus eliminating large intercepts and the consequent risk of plotting errors....'
Click to expand...

And so I would encourage others, those who have a 'sun-run-sun' or only a single 'sun LOP' in their logbooks, to take their interest just a little further. We inherit 'The Knowledge', which is hard-earned and needs to be practiced. Harry Baker's Tables make that a whole lot easier.


LatestScans-5.jpg



LatestScans_0001.jpg
 
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Uricanejack said:
You can calculate the difference between your Noon Dr Longitude and the longitude your position line crosses your observed latitude using the C Correction.( The C Correction is the ratio of your position line)

Difference Lat x C Cor.= D Long D Long
Noon Latitude Longitude
Click to expand...


Thanks for taking the time over this.
That method of calculating the D Long from D Lat x C Corrn is something I never understood, even though I used it, (my 30 yr old sight book is in front of me and that says I used it.
To my mind, D Lat x C Corrn would give departure.
I think I may have forgotten something over the past few years

Any way, here is my contribution, Ex Meridian Method using log tables

Hav (Lat~Dec) = Hav TZD - (Hav LHA x Cos Lat x Cos Dec)

In my sight book it is shown as

Log Hav LHA
Log Cos Lat
Log Cos Dec
__________
Log Hav X

Nat Hav TZD
Nat Hav X
___________
Nat Hav Lat~Dec
 
Uricanejack said:
The old long hand logarithm method of figuring out spherical trigonometry problems are based on the haversin formula.
The advantage of which it is always positive again trigonometry for dummies. It was all , so we did not have to figure out if we should add or subtract multiply or divide.

It was all look just it up and add it up.
Click to expand...

I can remember studying at Plymouth School of Maritime studies for my Second Mates ticket. I struggled to get my head around haversines and spherical trig. Loved it when I started using sight reduction tables ! Well done indeed for spending the time to post all this. I still have my old copy of Nories and a Burtons. Must start using them again when we set off deep sea.
Chris
 
oldbilbo said:
And so I would encourage others, those who have a 'sun-run-sun' or only a single 'sun LOP' in their logbooks, to take their interest just a little further. We inherit 'The Knowledge', which is hard-earned and needs to be practiced. Harry Baker's Tables make that a whole lot easier.
Click to expand...

Absolutely agree. Like, I think, most people who still practice the art, I do it for fun and because I enjoy it. I like taking moons upper limb, polaris etc. There is something very satisfying about a sun run sun position at noon which is less than 2 miles out from the gps. Not often I admit, but have done it !
Chris
 
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