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Henry:

I think we are in agreement, with any perceived disagreement based on 
hidden assumptions.

If you were a navigator on commercial vessels than you likely have wrung 
more salt water out of your socks than I've sailed over in a lifetime of 
recreational boating, so I deeply admire your expertise and opinion.

One of the great things I get out of our group is not only learning 
about new things but sometimes having my eyes opened on things I thought 
I already knew.   George's posting about the fallacy of the cocked-hat 
was one of the latter.

If I may struggle to explain things in my own words, any measurement is 
subject to two sorts of error.  One is systematic error; an excellent 
example of this is Index Error.  With proper calibration, systematic 
errors can be eliminated from most observations.  The second kind of 
error is simply random errors due to instability or uncertainty in the 
measurement itself.

What this whole discussion has made me realize personally is that the 
issue of these latter kinds of errors is rarely emphasized in 
navigational texts.  For example, we are taught that crossing two LOPs 
at right angles is best because it "minimizes potential errors in 
position" (and some texts go so far as to show a square/diamond 
indicating uncertainty around the crossing of two LOPs), but few texts 
discuss errors experienced in real navigation.  We are taught to cross 
two compass bearings in coastal piloting to get a fix, but rarely is 
there a discussion of the accuracy of bearings in real practice (and, 
again, I speak of recreational craft being tossed about and not the 
rock-solid platform of an aircraft carrier).  Start plotting bearings � 
2 degrees on a chart and most navigation students are surprised to see 
how large the error box gets!

In fact, I suspect some of the visceral dislike of GPS felt by old-time 
navigators is that the magic box just displays a number, take it or 
leave it.  Working with bearings or sights, the experienced navigator 
gets a feel for the accuracy of his/her work.

Likewise, there is a innate comfort in seeing a cocked hat.   "Surely, I 
must be somewhere inside that triangle."  George's post was a call for 
reconsideration.  I've learned from that....

On a side note, I suspect that the "experimental Loran stations" you 
mentioned were a way of measuring systematic Loran errors.  Knowing 
one's position accurately using Loran requires knowing the speed of 
light very precisely.  The speed of light is 300,000 km/h (or 186,000 
MPH) only in empty space.  The atmosphere, refraction, and even the 
conductivity of the earth (influenced by things such as moisture 
content) affects the speed of radio waves.  Loran designers could 
compensate for some of this with calculations, but effects caused by 
things such as ground moisture required experimental measurement. 
Without knowing these systematic errors, Loran had great repeatability 
(coming back to an exact set of Loran coordinates would typically bring 
one to within � 50 feet of the position where they were originally 
measured) but initially poor absolute accuracy (L/Lo as calculated by 
the box and/or from TD LOPs plotted on charts) (typically 1/4 mile or 
more). (I remember my first Loran set was typically off by 1/4 mile, but 
the "offness" was a very consistent systematic error and I soon learned 
to compensate for this just as one compensates for Index Error; my last 
set was so spot on with its L/Lo's I could detect the movement of a buoy 
in 100' of water as it swung with the tide.)

Thanks for all your insights, Henry.

Lu Abel

halboth wrote:
> Hi Lu,
> 
> Let's clarify one thing before going any further. This discussion has
> related, I think, to the intersection of lines of position obtained by
> celestial observation, not to the accuracy of the resultant position which
> may not be reflected by the nicety of intersection. One criterion sometimes
> applied is that of "repeatability" , i.e., the coincidence of multiple
> positions obtained in a static location over a period of time and obtained
> by the same means - some years ago, the USCG established experimental Loran
> stations for just this purpose, and the results seemed rather amazing as
> respects the divergence of the resultant positions. Although they have
> almost certainly been done, I know of no similar experiments with GPS, or
> for that matter any other form of position finding - potential accuracy
> would certainly be better served by such work, rather than by repeated
> quotations from texts, the authors of which may well have never have
> navigated a ship at sea and are published with the dollar market uppermost
> in mind. It should be remembered that, until relatively recent time, most
> charts were constructed on the basis of celestial observation, usually but
> not always utilizing the artificial horizon. Most of these charts, albeit
> not all, have been proved to be amazingly accurate - as a matter of simple
> fact, in the late 1940s, there being no other charts immediately available,
> I was obliged to use a 1908 BA blueback chart to navigate portions of the
> West African coast, and found no appreciable discrepancy of position
> anywhere.
> 
> For years, my only gauges of position accuracy were that the ship remained
> always afloat, and the accuracy of any particular landfall. I have had
> perfectly wonderful looking fixes and, a few hours later made the intended
> landfall 6-miles or so either side of the intended course line while at
> other times it was dead on. On one occasion, it was predicted that we would
> raise Green Point Light at about 0600 - I was called at 2400 with Green
> Point and Slangkop clearly above the horizon and the 3rd Mate in a bloody
> panic; cross bearings quickly established that we were some 52-miles off
> Green Point and with plenty of time for a good snooze before arrival. It was
> the most significant case of refraction that I recall witnessing at sea.
> 
> Any position established at sea by whatever means must be viewed with
> suspicion and the navigator must use every trick in his bag, the price of
> safety being eternal vigilance - and nothing could be truer as respects
> navigation. That being said, I simply refuse any static textbook definition
> of sight accuracy - such definitions, in my humble opinion, lead to sloppy
> if not careless workmanship and demean the potential of celestial
> navigation; generally they lead to excessive "rounding off" which in itself
> is conducive to accumulated errors. I have had good, bad, indifferent and
> wonderful results with celestial navigation and it was my job to be able to
> differentiate, based on existent conditions whatever they might be.
> Normally, I endeavored to work to the accuracy permitted by commercially
> available plotting sheets, and am of the opinion that average results, under
> good conditions of horizon and ship steadiness, were probably in the range
> of 2.5-miles of the truth with more often than not good LOP intersections.
> Let there, however, be no mistake, there were also bad results - just not
> too many.
> 
> Regards,
> 
> Henry
> ----- Original Message ----- 
> From: "Lu Abel" 
> To: 
> Sent: Monday, December 11, 2006 12:56 AM
> Subject: [NavList 1881] Re: Position lines, crossing
> 
> 
> 
>>With deepest respect, Henry, a previous poster pointed out that most
>>texts suggest that LOPs taken at sea are at best good to +/- 2 NM and
>>that for small craft +/- 5 NM is more likely.   I agree.   So I'm
>>wondering under what conditions your sights were taken and/or what scale
>>you used in plotting them!
>>
>>I don't mean in any way to demean your skill, I just am reflecting the
>>track of this discussion, which is that any navigator worth his salt
>>will not only be able to plot a LOP on a chart, but also fully
>>understand the uncertainties associated with it.
>>
>>Lu Abel
>>
>>halboth wrote:
>>
>>>Hi Peter,
>>>
>>>I most certainly am Peter, and have hundreds, if not thousands, of
>>>positions in my navigation workbooks to demonstrate this fact.
>>>
>>>Regards,
>>>
>>>Henry
>>>
>>>    ----- Original Message -----
>>>    *From:* Peter Fogg 
>>>    *To:* NavList@fer3.com 
>>>    *Sent:* Sunday, December 10, 2006 11:55 PM
>>>    *Subject:* [NavList 1877] Re: Position lines, crossing
>>>
>>>    Henry wrote:
>>>
>>>        In my opinion, "cocked hats" are most often the result of
>>>        altitude errors induced by varying horizon conditions due, in
>>>        the case of stars, to failing light conditions.
>>>
>>>
>>>    Henry, are you saying that given ideal conditions (as you have
>>>    described) LOPs can in practice meet, or almost meet, at a common
> 
> point?
> 
>>>
>>>
>>>
>>>    >
>>
> 
> 
> > 
> 

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