Lost tech of Ancients

Q and A break. Is it clear about the formula? or do I need to explain it differently?

 

Just to be clear for a reader in the future, I'll break it down.
You take a Dr (dead reckoned) position. I like to pre-calculate before morning stars. it's something to do in the small hours of a night watch, presuming the radar scope is clear of contacts.
Take the longitude of your projected position, and convert it to GHA. Remember that 180 degrees or less longitude is the same in GHA, Just relabel GHA. To get GHA of a star we expect to shoot, We need to calculate from it's SHA in the almanac. I was going to cover that in next part, Lesson #7, but since the topic comes up, I'll cover it here.

The stars don't move in relation to each other. Not in our short lifetimes. To save space and repetition, astronomers devised "First Point of Aries". To the naked eye, it's an empty spot in the sky. It's square one. All stars have their degrees of westing measured from this point. Sidereal means star, so Sidereal Hour Angle or SHA. The First Point of Aries, symbol V with curved points like ram horns, has GHA tabulated for all hours of the day in almanac. The SHA of the stars is listed once. Adding a stars SHA to GHA of V=stars GHA.
Subtracting our GHA from stars GHA gives us LHA, local hour angle. If the star is east of us, add 360 to stars GHA and subtract our GHA.

I'll continue in next post

 

Ok. We have our projected latitude and LHA. We look up the declination of the star we are going to shoot. It's the same all day long.

Ignore the sin-1 left of the equals. Thats the answer we are going to calculate.

enter the latitude, hit DMS changing it to decimal degrees.
sto 1
hit sin.
times or X
enter declination of star, DMS
sto2
hit sin
=
sto3
ce (clear entry)
recall mem1 (decimal latitude)
cos
X (times)
recall 2 (dec)
cos
X(times)
enter LHA, DMS
cos
=
+
recall 3
=
We now have our answer but its in form of a sin. to change to an angle, depending on calculator, press inv then sin, or on some alt sin.
We now have decimal degrees.
DMS converts back to degrees, minutes, seconds, and this is the altitude we expect to see the star.
We preset our sextant to this angle and at predetermined minute, remember advance DR, look through it in the appropriate direction, and there is our star.
Wait, its not touching horizon, or maybe its in the water. So we adjust till it just touches horizon when arcing. We scribble down the sextant altitude, hs, correct to ho, observed altitude, and subtract lesser from greater, ho from hc, or hc from ho.
Eureka we have @
@ is intercept.
It's the difference between where we are, and where we thought we would be.
A wonderfull thing about navigation (and topic in a later post) is, one minute of arc = one nauticle mile.
If ho is 3 minutes larger than hc, we move our lop 3 nm in direction of star. LOP discussed very soon in a post

Have I thoroughly confused everybody?

 

Lesson #7
LOP, GP, parallax, and nautical miles.
Great Britain had the greatest empire the world has ever known, untill WWII. Britania ruled the waves for 300 years, from the time of Queen Elizabeth I, untill again, WWII.
So maybe it's not surprising England played a huge role in advancements in seamanship and navigation. Like Greenwich time being Universal time?

The english statute mile could easily have become standard measurement of distance for the world. A small mistake inhibited it. Originally, it was proposed, that the ideal measurement, would be a minute of arc of the earth surface, and so it was decreed, and the statute mile was invented. Great idea, flawed only by the court astronomers faulty estimate of the size of the earth. He was off about 15%. Too small. When the error was discovered, it was too late, the statute mile was entrenched. So, they invented the nautical mile, which IS a minute of arc of earth surface. Multiply nm by 1.15 to get stm. Shame, would have been much more sensible than the meter.

GP and LOP.
GP is geographical position. Latitude and longitude of your location is your GP. The heavenly bodies have a GP. How? They aren't on the earth?
First lets talk parallax. After I explain it, you can forget it.
If you alternately close one eye and open the other, then swap, again and again, the scene before you shifts right, left, right, ect.
It's because each eye sees from a different angle. That's good. Gives us 3D and depth perception. It's called parallax. In the night sky, the distances are so great, that parallax becomes an infinitely small angle. Exception the moon and the sun. They are close enough to have a visible, measurable disk. More on them later. Back to the stars. Because of the vast distances, we can pretend our eye is located at center of the earth, and that distance from earth surface to center wouldn't matter, the angle so tiny because of the distance to the nearest star. So forget parallax in star navigation.
Assume our eye WAS at the earth center, and the earth was transparent glass with lines of longitude and latitude etched on it's surface. When we saw a star, we would see it through some point on the earths surface. The GP of the star. If we stood on that point back up on the surface, our feet would point to earths center, and the star would be in our zenith, directly overhead. So, GP is where, a line between the star and earths center, intersects the surface.
Gp is measured in GHA and declination as formally discussed. And is constantly moving. Bless the inventors of the clock and navigation. They gave both the hour and the degree 60 minutes. Darned convenient.

Step back a ways, and the star isn't in our zenith anymore. We could walk around a circle equidistant from that GP, and see the star at a constant altitude from every direction, as long as we were standing on that circle. That's called a circle of equal altitude. The bigger the circle, the lower the elevation, or altitude we observe the star. But we still observe at the same height from any place on the circle.
Now imagine a huge circle of equal altitude. So huge, that plotting just a short segment of the circle, appears to be a straight line on the chart. We can't see the circle now, just a line. A line of position. LOP.
Any where on that line, we will see the star at the same altitude, because, really it's a segment of a huge circle of equal altitude.
Heres the best part. When you have two lops crossing at or near right angles, You are on both lops at the same time, and the only place you COULD be on both at same time is where they cross. X marks your spot!

Goodnight, more tomorrow

 

Dont often use the sextant anymore. When Students are on board ,preparing for testing, I break out the HO 208 tables. These are the most compact of the sight reduction tables, about 75 pages.

Longitude at noon was my favorite.

Finding time and date from a known position is also a good exercise.

Constructing plotting sheets from standard graph paper is a great chapter.

Ive carried John Letchers, Self contained Celestial Navigation with HO 208 my whole life. Great book if you can find it. Contains the sight reduction tables and fits into a sexant box.

 

Thanks Michael
I have 3 more "lessons" to post. Introduce the azimuth formula for intercept sight reduction, running fixes, which Gonzo was headed for earlier, and Great Circle Sailing using same formulas, the final chapter.
I hope nobody thinks my "tone" is condescending.
I'm no babe, 63 years young, and I suffer from sensory overload sometimes. I have assisted hands going up for original licenses many times with this lecture. I bet most of them weren't as smart as the men on this forumn, so I apologize if I seem to be pre-chewing the morsels as I feed them. Well, I believe if it ain't broke, don't fix it. And you can't eat a steak in one gulp. Hopefully, these 10 posts will encourage further study on some members part, and alleviate the terror of the mathematics.
Please kibitz, expound, correct, improve, or enhance my "lessons"
with respect to all, Dave

 

For close in navigation...when celestial is not usable...distance off by horizontal sextant angle is very accurate and simple. The plastic davis sextants do a great job...better than handbearings from an unstable compass. Before accurate lat long charts this technique was often used. I still have British Admiralty charts on board...not old, 1986, that have no lat long grid ,only the known position of a prominent landmark noted on the chart . Landfall was all about bearings of this known position and depth. Making landfall Azores was typically a sextant elevation of Mt Pico to determine distance off then cross it with an RDF bearing . The Caribbean and areas like the Labrador Coast were notorious for lat long positions on the charts

I think the problem with any modern navigation..as opposed to watching the gps move your boat across the screen...is that its a full time job. The job is not difficult, but its relentless.

I grew up before automated navigation systems...electronic aids like LORAN A, OMEGA and transit sat nav needed a full time navigator and accurate DR position. I doubt if any boat out there these days has thier speed log and compass calibrated enough to give a meaningful DR, let alone a sharp pencil, stop watch,parallel rules and navigation discipline.

One thing I notice with modern small craft seagoing is that since the full crew is no longer needed to keep a navigation schedule and monitor radio transmissions they fall asleep .

To give you an idea of how far navigation skills have atrophied, last fall I was involved with a MAYDAY RELAY. The yacht in distress kept trying to relay its position as lat long numbers in highly accented english and bad radio reception. The complication was that I was straddling East and West longitude. It would have been normal not many years ago to state..position 55 miles SSW MENORCA..position 55 miles SSW Menorca...position 55 miles SSW MENORCA.....

 

Exactly Michael. We are both from the same old school. I still remember when radio direction finder was our only electronic navigation. Remember the miracle of Loran A, manually adjusting the sine waves to coincide and get the time difference, and then loran C, Omega, sat-nav, eventually GPS.

I tell hands to sit down before you fall down, but even 30 years ago, the only bridge chair was exclusively the old mans. When you stood a watch, you STOOD your watch, harder to fall asleep a pie. (on your feet in spanish) I constantly admonish the young officers working with me "Be the navigator, You are the navigator, not the electronics!" Most don't fall asleep on the bridge, but they'll play solitare card games that are packaged inside windows.

My agendas for this thread, is Don't let sextant nav be a lost art. Don't be a slave to the electronics (robots taking over ala Asimov?). Be the master of yourself and your vessel. Don't be mentally lazy. Death waits down that road.

Ok. Rant over. Y'all can come back out from where you ducked.

 

Probably a good lesson would be how to use a perpetual almanac . Its become almost impossible to purchase a nautical almanac on the waterfront.

 

Piloting is another lost art, or nearly. Navigation by bearings is piloting. Doubling angle on the bow? Distance run is equal to distance off. Example, what's your range from the lighthouse 2 pts on the starboard bow? Mark the time, and when the light is 4 pts, mark again. Calculate how far you ran in the intervening time, thats your distance off at the 2nd bearing. The classic doubling angle is, Bow/Beam. 45 degrees on the bow, mark, distance run=distance off when abeam.
Whens the last time you saw a pelorus or adelaide on a modern vessel?

 

All almanacs are perpetual, just need to change the dates, skip ahead so many days depending how long ago issue date. I forget. I'll look it up. I think I remember it/s in the addendum after the daily pages, between sections, in the almanac.

 

yes and no. There used to be this handy addendum...GHA and DEC of the sun for years 1953 2000. Now my modern almanac simply states, for use in.....,then a series of obtuse directions for either adding or subtracting time and angle. Would probably make your head spin if you actually had to use it.

 

here you go

(1) The back cover AP3270 - Sight Reduction Tables for Air Navigation (UK version) contains a 50 year almanac for the sun.

(2) Self- Contained Celestial Navigation with H.O. 208 (John S. Letcher) , contains an 'long term' almanac for 1975-2000.

(3) Bowditch, Vol_1 (1984), appendix 'H' is a perpetual almanac, based on a four year cycle.

 

All I have at present is NP 314 , the Admiralty almanac, plus concise reduction tables HO 208. Perhaps I have an AP 3270 buried somewhere in all the old nav paper.

 

Oh, I fogot! Sucess thru intimidation. Have a cabin boy swing an hour glass on a string inmagical figure 8s where you plan to stand to take your LAN sights. Examine the sun through binoculars (tightly shut your eyes) to see if it;s "Ripe" to be shot. Pile books on deck to consult afterwards, Ho 229s good for this. When finally, you announce to ship's company the noon position, you will have honored the age tarnished tradition of keeping navigation a dark mystery. And an added benefit, it's less likely you'll be tosses in the sea if you decide to flog or hang one of the crew.