From:                              Bob Goethe

Sent:                               November 4, 2017 12:24 PM

To:                                   'Bill Anderson'; 'Carly Butler'; 'Brian Hehn'

Subject:                          NASA:  a question of precision


Dear Friends:


Brian wrote me and ask for clarification around time.  I realized that by talking about the importance of accurate timepieces, I had *implied* something about the kind of precision in time we were looking for in CNav, but I was not explicit.  His question was the genesis of what follows.


Wow...the title of this email sounds like a title from one of Carly’s art works.



Precision of Time


The importance of precision in time varies with just where you are on the face of the earth, and just where your celestial object is.  The worst case scenario is that a 4 second error in time will lead to a 1 nm error in your fix.  That’s a 15 nm error for being 1 minute out.  


When we go for a rule-of-thumb re time, we always use this particular worst-case scenario as the general rule, since the math to actually work out the actual error would be complicated beyond imagination when taking a fix of, say, three stars in different parts of the sky.


Further, if in doubt, the navigator will always go to the worst-case scenario, and seek to address whatever safety issues arise from that scenario.


My goal for you all is that you should be able to sail from Halifax to Bermuda and get there using only celestial navigation. is an account of a sailboat race that has a division for boats navigating by celestial alone. 


The highest point of Bermuda is only 259 feet high.  This means you can just BARELY see it on the horizon at 19.2 nm.  If you have a 2 minute error in time, this translates into a positional error of 30 nm...which means you could pass by Bermuda without ever seeing it.  More than one person sailing from N. Am. to Europe with a stop in Bermuda has missed Bermuda completely and had to sail on direct to Europe.


To put it another way, the mouth of the Strait of Juan de Fuca is 11 miles wide.  If you aim for the exact middle, and plan to arrive at 10 AM, you will do just fine if you are ±5 nm.  You can see where you are, and just adjust your course by eye when you are a few miles out.


What you DON’T want to do is to wake up at 4 AM to the sound of waves crashing on rocks, to discover that you have inadvertently sailed in among the islands near Bamfield.  Having the correct time will help protect you from this sort of navigational adventure.


If we cannot get correct time, we work with what we have.  A bad fix is better than no fix at all.  But if we can get it, we go for accuracy to the nearest second at all times.  Differences of less than ½ second, we don’t worry about. 


What if I have no accurate time? 


If all you have is a bad fix and it is night, you will probably choose to heave-to while still 50 nm offshore from Juan de Fuca, and arrange to arrive during daylight. 


Further, even arriving in daytime you might also aim well north of Juan de Fuca, so you don’t have the ambiguity of wondering if you are making landfall 30 miles NORTH of Juan de Fuca, or 30 miles SOUTH of it (all those rocks look very much alike).   If you know you are well north of Juan de Fuca, then you can turn to the SE and sail parallel to the coast until you come up on the strait.


So the good navigator knows what she/he doesn’t know...and makes allowances for his ignorance. 


If you have this kind of ambiguity of location and your target is Bermuda rather than Juan de Fuca, your best bet is to get yourself down to 32° 18’ N latitude as quickly as you can, and then turn directly east.  Just keep yourself on that latitude, and you will eventually bump into Bermuda. 


It will be an advanced topic for our learn how to determine your latitude without accurate time.


Without accurate time, you cannot know longitude at all.  We will eventually get into this as well.


Carly, on NavList you have run into people talking about “lunars”.  It is possible to get time, after a fashion, and hence longitude (also after a fashion) by measuring the distance between the moon and a given star.  But practically speaking, that is quite a bit easier to do from ashore than from the deck of a moving vessel.  Even so, lunars give you – at best – a time error that could still see you missing Bermuda over the horizon.


Most sailors without an accurate timepiece have done “latitude sailing” – i.e. getting your boat on the latitude of your destination, and then sailing straight east or west to be assured of hitting your destination.


Of course, many arrived at their destinations but did so unexpectedly, at midnight instead of noon, and died in consequence.  But this is a way of saying that “longitude is important”, and  that accurate time signals by radio and quartz watches have increased safety on the sea.


Precision of Distance


Many of the things I will tell you are mostly true...or rather, are treated as absolutely true given the context of celestial navigation.  For example:


1 nautical mile (abbreviated by navigators variously as nm, NM, M, m, mi, or mile) is not precisely equal to 1 minute of latitude (what it is precisely equal to is 1,852 meters).  But the difference in the length of a nautical mile is minimal:  1,849 meters at the poles and 1,855 meters at the equator.  Only 6 meters different...a difference that is insignificant to the celestial navigator, who is ecstatic if he can get a fix that is accurate to within 3 miles.


This is also why we don’t worry about time except to the nearest second.  Any attempts to be more accurate than that would be lost in the noise of a method that can almost never “see” a positional difference of less than a couple of thousand meters.


Oh yes...and “mile” for a navigator never ever means the statute mile of 5,280 feet.  It always means a nautical mile of 1,852 meters or 6,067 feet.


So for the purposes of celestial navigation generally, and this course in particular, we will treat a nautical mile as being precisely equal to a minute of latitude at all times...and we will treat the earth as a sphere with a perfectly smooth surface rather than an ellipsoid that has bumps on it like an orange. 


And in terms of finding  Bermuda where you expect it, this assumption works just fine.


Since 1 knot = 1 nautical mile per hour, all our measurements are made – both speed and distance – without making any reference to meters. 


You will occasionally see “knots per hour” in print.  Although this phrase was used – though rarely – in the 19th century, if somebody says “knots per hour” today it is generally a tip off that they don’t know squat about navigation or the sea.




Precision of Results


When ashore, and particularly when using an artificial horizon (which we will eventually get to in our class), I aspire to accuracy within 1 nm of my GPS position, but am generally satisfied if I am within 3 nm. 


On a vessel, “finding Bermuda successfully” defines the practical accuracy that is required most of the time.  Once you get within visual range of your destination, celestial navigation’s job is done. You start using your hand-bearing compass and depth sounder to determine your location. 


So while on board, you can tolerate (just barely – you may miss Bermuda!) fixes that are 20 nm off.  10 nm is OK.  5 nm is terrific. 


Once, while sailing from Hawaii to Victoria, I had a shot where my line of position ran directly over the top of my GPS position on the plotting sheet.  I was accurate to within the width of the pencil lead I was using.  If that happens, you end up saving that plotting sheet so you can look back on it and reminisce during a dark winter day in Edmonton.


Where you guys take sights from a beach or shoreline, we will aim for eventual accuracy of 5 nm or better.





Brian will not be joining us (Bob/Carly/Bill) for our regular classes in January.  He plans to be in the Bahamas in January, building experience toward his goal of being a professional captain for large yachts.  In January, he will be in and out of port, and when in port may have questionable wi-fi, and even when his connections are good, his time-zone difference will put him out of sync with us here in W. Canada.  In consequence of all of this, I will instruct him separately. 



Bob Goethe


"As I sail, I praise God, and care not."
            Luke Foxe, Arctic Explorer, 1634


I desire no more delight
Than to be under sail and gone tonight.

           Gratiano, in Act 2, Scene 6, The Merchant of Venice

           By William Shakespeare, 1596


Some day you will read in the papers that D.L. Moody, of East Northfield, is dead. Don't you believe a word of it! At that moment I shall be more alive than I am now.
           D. L. Moody (1837-1899)





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