Celestial Navigation


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Has anyone here done lunar distances?? I tried one in Tenant's Harbor, ME, some years ago, was devoured by mosquitoes which no doubt affected my sights, and discovered that we were in Australia! Andrew
Roger Harris
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A brief description from Cotter, “The Complete Nautical Astronomer” (1969), pp. 135 and 136:

“Chronometers for a long time after they became available were expensive and, therefore, scarce. The lunar problem, for about a century after its introduction, appears to have been the standard method for finding longitude at sea by astronomical methods. The problem of longitude, which the early Nautical almanacs were specifically designed to facilitate, involved measuring, by means of a sextant, the angle between the Moon and the Sun or a selected star lying in or near the Moon’s monthly circuit of the heavens. The observed lunar distance had then to be reduced, by which is meant computing the angle at the Earth’s centre between straight lines terminating respectively at the Moon’s centre and that of the second body. The process of doing this, in which corrections for refraction and parallax were to be made, was calling clearing the lunar distance. The cleared distance was then to be compared with tabulated distances given against G.M.T. In the Nautical Almanac. Having found the G.M.T., an ordinary altitude sight, taken at the time at which the lunar distance was measured, enabled the observer to find his ship’s longitude provided that the ship’s Latitude was known.
“The lunar distance problem was not at all an easy problem for most navigators. So that until the time when chronometers did become common - about the middle of the 19th century - and the methods of modern position-line navigation had been discovered, the generality of navigators observed the noonday Sun for Latitude, and relied largely on D.R. navigation for longitude.”

Roger Harris
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To answer the original question: while I have owned a copy of “Stark Tables for Clearing the Lunar Distance”, 3rd rev’d ed. (2010) for almost seven years, I confess that I’ve yet to put in the grind to learn how to use them. If the ongoing Covid-19 restrictions continue throughout the current year (perish the thought!), perhaps I will run out of excuses and finally get stuck in.

P.S. Might be of interest: a reasonably-detailed explanation of how to clear lunar distances is contained in John Letcher’s “Self-Contained Celestial Navigation with H.O. 208” (1977), pp. 87-95. Helpfully, several questions are posed to confirm the reader’s understanding (answers are supplied at the end of the book).

P.P.S. Letcher’s book contains a separate chapter entitled “Time by Lunar Lines of Position” (pp. 9-106). Below are introductory paragraphs explaining the concept:

“The basic idea is to check whether lines of position from moon sights agree in longitude with lines of position from sights of other bodies. As long as the chronometer is right, the moon will attest to the fact by being in the right place in the sky, so lunar lines of position are consistently in agreement with sun and star sights. If the chronometer is wrong, and you work the sights as if it were right, the moon lines of position will lie consistently to either the eastward or westward of the other lines, depending on whether the chronometer is fast or slow on GMT? Again, we are using the relatively rapid known motion of the moon as a time standard, but in this procedure, we measure its motion relative to the horizon by an ordinary altitude sight. In case the lunar line is found to disagree with the other lines, a time can be found that will bring them into agreement, and this procedure finds the true GMT and chronometer error just about as accurately as lunar distance sights would....

“[R]easonably accurate time can be found if good, accurate altitudes are taken of the moon and the other bodies. The moon and other sights are worked and plotted into lines of position by completely standard, habitual methods, but for this purpose it is essential to work to very high standards of accuracy attainable: care in taking the sights, and applying sight corrections, carrying the tenth of minutes throughout, and plotting with great precision.”


Roger Harris
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More on lunars, this time from Jonathan Raban's Passage to Juneau (1999), pages 56-58:

In 1792, more than thirty years after John Harrison unveiled his marine chronometer, longitude was still a much more troubling problem than most popular books on the subject (like Dana Sobel’s Longitude) have generally conveyed. The new chronometers worked well on short voyages of three or four weeks; but on longer ones they fell so far out of sync with Greenwich Mean Time as to be useless, unless they were continually corrected by some other means of ascertaining time.

One of Vancouver’s commissions on the voyage south from Falmouth to Cape Town had been to experiment with a new method of determining longitude that was being touted around the Admiralty. This involved measuring the exact magnetic variation of the compass at a given latitude and locating it on a chart of all the variations observed on a particular ocean. Vancouver tested this cheap and easy solution, and found it foolhardy and dangerous. That the Admiralty should be promoting it at all, so late in the navigational day, says a lot about the dubious reliability of the Harrison clock.

There remained an ingenious and reliable method known as “lunar distance”. Because the sun and the moon travel around the earth on different orbits and at different speeds (it is the navigator’s necessary fiction that the sun, like every other heavenly body, circles the earth and not vice versa), they can be thought of as a pair of clock hands. By calculating the distance between them at any given moment, you can find the exact time at Greenwich, and therefore your longitude.

The working of a lunar distance was the navigator’s piece de resistance. It required very accurate sights with a quadrant or sextant, followed by some horrible arithmetic. Midshipmen dreaded the exercise, and few captains were confident of their mastery of it. George Vancouver excelled at lunar distances, their finical quadrant handling and abstruse mathematics. When he wrote about his “lunars” in his Voyage, he did so in the tone of an evangelist. “I hope to see the period arrive, when every sea-faring person capable of using a quadrant, will, on due instruction, be enabled by lunar observations to determine his longitude at sea.”

...

At nearly noon, ship’s time, the moon bore 0970/T. Its observed altitude, by quadrant sight, was 29004’. The sun bore 1790, at an altitude of 54050’. Now came the brain-cudgeling part. You had to solve a devilish spherical triangle. Your ship lay on a latitude just short of 490N. The sun, reduced to its zenith point on the earth’s surface, lay on a spot in mid-Pacific, roughly 2,700 miles west of Costa Rica. The moon lay – more roughly still – somewhere close to Providence, Rhode Island. Your job was to calculate the distance between those two geographic points, along with all the angles in the triangle formed by the ship, the moon, and the sun....

Some work on the nascent, partially-drawn chart, with soft pencil and boxwood parallel ruler – and there you were. Latitude: 48013’N. Longitude: 235059’E (Vancouver always measured his Pacific longitudes by going eastabout from Greenwich). Most importantly of all, the time at Greenwich when the observations were taken turned out to have been exactly 8.13’.06” P.M. After thirteen months at sea, Discovery’s main chronometer, made by Larcum Kendall of London, was running fast by 45 minutes and 46 seconds.






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Link to an example of lunar longitude measurement:
https://www.starpath.com/downloads/May_7_2000_lunar.pdf

Link to Jan Kalivoda's detailed review of Stark Tables for Clearing the Lunar Distance, 2nd ed. (2007):
https://www.starpath.com/catalog/books/StarkTables.htm
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Mystic Seaport Museum annually offers a nine-hour course on lunar techniques. The 2021 dates have not yet been announced, but it usually takes place in August. "Special topics includ(e) Grand Canyon Lunars, Slaver Tables, Legendre Trick".

Lunars: Finding Longitude by Lunar Distances

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Roger Harris - 27 Feb 2021
Mystic Seaport Museum annually offers a nine-hour course on lunar techniques. The 2021 dates have not yet been announced, but it usually takes place in August. "Special topics includ(e) Grand Canyon Lunars, Slaver Tables, Legendre Trick".

Lunars: Finding Longitude by Lunar Distances

Hi all,
I guess this takes the form of a personal position paper on the use of celestial navigation. These thoughts are on the receiving of training in celestial navigation and, simply put, are to advocate that the learning of celestial navigation be undertaken for possible emergency use (a lightening strike for example) or for a wonderful hobby, but not for primary navigational use (by primary, I mean that determining boat position is done solely by celestial without referring to GPS).
The only celestial instructor I knew well had circumnavigated twice using only a sextant: once with friends and once with family. The sextant was, at this time, state of the navigational art and all he had available. Teaching celestial decades later he insisted that his training not be used for primary navigation. He felt it was just far more accurate and, more important, far safer to determine position with GPS.
Going to sea navigating solely by sextant could be motivated by 1. A romantic notion and identification with past practices, 2. Placing a feather in the skipper’s cap of accomplishments, 3. A personal navigational challenge, 4. Some sort of challenge/stunt. Navigating by sextant is well understood and has been practiced over time and many locations, so I can see no scientific reason to further document its capacities.
All of the above, and others, are possible reasons, but navigating solely by sextant, while in no way a guarantee, does clearly make more likely that the skipper, crew and boat might get into trouble. Another way of saying this is that it is just not as safe.
I read of skippers who go to sea intending to use celestial as their primary navigational tool. My concern with skippers who go to sea without such a fundamental safety device as GPS is (at least) 3-fold. First is my concern that SAR personnel will be hurt or killed in a rescue attempt. Secondly, there may be crew on the boat who ill equipped with the experience or skills to judge the degree of risk they are undertaking, and thirdly, the environmental damage, that might occur if wrecked, say, on a reef with a load of fuel.
There is a way around at least a couple of points of concern. Although I would try to talk them out of the endeavor, I would have no problem if skippers met at least a couple of conditions: they went alone (or all crew knew celestial and practiced sights at sea regularly and were aware they were giving up a degree of safety), and if the boat carried no EPIRB or other communication devices to call for help. By this they would be acknowledging that they were choosing a risky endeavor and had no wish to have other people (SAR in particular) put in danger’s way by their choices.
My best, Dick Stevenson, s/v Alchemy


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Dick - 2 Mar 2021
I guess this takes the form of a personal position paper on the use of celestial navigation. These thoughts are on the receiving of training in celestial navigation and, simply put, are to advocate that the learning of celestial navigation be undertaken for possible emergency use (a lightening strike for example) or for a wonderful hobby, but not for primary navigational use (by primary, I mean that determining boat position is done solely by celestial without referring to GPS).

Hello Dick,

Thank you for your post. I appreciate your contribution, though I cordially disagree with your conviction.

Like all navigational methods, celestial undoubtedly has its limitations:
  1. It takes a relatively long time to produce a 'fix', especially when using the sun-run-sun technique;
  2. That fix will probably only be accurate within a few miles or so (which, it should be said, is quite sufficient for practical purposes);
  3. It requires measuring the altitude of celestial bodies, which are invisible in overcast conditions;
  4. Whilst sight reduction calculations are not particularly difficult, they can be tedious and silly errors are prone to occur (especially when the navigator is tired or seasick);
  5. And probably a few additional modest challenges that don't immediately occur to me.

All that said, groundings are generally caused not by systems limitations but by poor situational awareness. A vessel can be equipped with the finest, most modern electronic equipment known to man, and still go on the rocks if no one is monitoring what is actually happening ... it happens more often than it should.

Dick - 2 Mar 2021
Going to sea navigating solely by sextant could be motivated by 1. A romantic notion and identification with past practices, 2. Placing a feather in the skipper’s cap of accomplishments, 3. A personal navigational challenge, 4. Some sort of challenge/stunt.

There are many possible reasons for contemporary reliance on celestial navigation. It is certainly not "some sort of challenge/stunt" (which some might consider disrespectful of navigators like Bert ter Hart and Leo Gooden).

Using a sextant is fun! Sight reduction helps keeps one's arithmetic up to the mark. Celestial nav. exposes us to the wonders of the universe. Finally, making an expected landfall without the aid of GNSS is deeply satisfying, and promotes self-reliance.

Here's a link to a StFYC webinar that includes a recent documentary film about the above: Celestial (2020).

Dick - 2 Mar 2021
[N]avigating solely by sextant, while in no way a guarantee, does clearly make more likely that the skipper, crew and boat might get into trouble. Another way of saying this is that it is just not as safe.



As acknowledged above, celestial navigation has its limitations. Provided only that one is aware of those limitations, there's no reason for it to be significantly less safe than any other form of ocean navigation.

The Marion-Bermuda Race has for many years (possibly since its 1972 inception?) offered a "celestial election" yielding a 3% handicap (see Notice of Race, and see generally the documentary film linked above). Whilst there have been a few accidents in that race - accidental gybes, etc. - to the best of my knowledge none have related to celestial navigation.

The (celestial-only) 2018 Golden Globe Race is a similar example. Accidents, certainly. Navigation issues, zero.

The alternative ('safer') form of navigation was unspecified, but is presumably satellite-based. GPS, GLONASS and Galileo are technical marvels but are certainly not foolproof, and people who blindly depend on them can go badly astray. The well-known phenomenon of "Death by GPS" on land has nautical equivalents, Team Vestas Wind’s 2014 grounding on the Cargados Carajos Shoals probably being the best known.

Dick - 2 Mar 2021
I read of skippers who go to sea intending to use celestial as their primary navigational tool. My concern with skippers who go to sea without such a fundamental safety device as GPS is (at least) 3-fold. First is my concern that SAR personnel will be hurt or killed in a rescue attempt. Secondly, there may be crew on the boat who ill equipped with the experience or skills to judge the degree of risk they are undertaking, and thirdly, the environmental damage, that might occur if wrecked, say, on a reef with a load of fuel.



1) I know of no specific examples of SAR being called out due to celestial navigation errors aboard a yacht.

2) I agree that inexperienced crew are always ill-equipped to judge the risks attendant with offshore or ocean sailing (the vast majority of which have nothing to do with navigation). In any event, again, celestial has not proven to be less safe than other forms of navigation.

3) I'm bemused by the suggestion that celestial navigators run an increased risk of causing "environmental damage, that might occur if wrecked, say, on a reef with a load of fuel". I can think of at least one example of that happening: viz., the 1965 grounding of the USS Frank Knox on the Pratas Reed (southwest of Hong Kong). On the other hand, there are multiple examples of GNSS-reliant vessels causing environmental substantial harm. A few cases, all from the US Navy to stay consistent:
  • in 2009, the USS Port Royal went aground on a reef near Pearl Harbor, Hawaii, causing over US$7 million damage to coral;
  • in 2014, the USS Taylor leaked 175 gallons of fuel from a damaged propeller shaft after going aground while entering Samsun, Turkey; 
  • in 2015, the US federal government paid substantial compensation to the Philippines for environmental damage caused to the Tubbataha Reef when the USS Guardian went aground after relying primarily on an inaccurate Digital Nautical Chart (DNC)® coastal chart;
  • in 2017, the USS Antietam grounded on shoals in Tokyo Bay, causing a spill of 4,200 litres of hydraulic oil.
Again, the navigation system in use is essentially inconsequential. What matters is situational awareness. 

Dick - 2 Mar 2021
I read of skippers who go to sea intending to use celestial as their primary navigational tool.... Although I would try to talk them out of the endeavor, I would have no problem if skippers met at least a couple of conditions: they went alone (or all crew knew celestial and practiced sights at sea regularly and were aware they were giving up a degree of safety), and if the boat carried no EPIRB or other communication devices to call for help. By this they would be acknowledging that they were choosing a risky endeavor and had no wish to have other people (SAR in particular) put in danger’s way by their choices.


I agree that crew redundancy is always desirable. Not just with navigation, either: ideally, everyone aboard should know how to reef and steer, maintain and repair the engine and the boat's various systems, provision and cook underway, operate the radar, obtain and interpret marine forecasts, deploy distress signals, provide first aid, etc.

Of course, not everyone has the inclination or time to learn all aspects of passage-making. With respect to celestial navigation, the noon sight for latitude is quickly learned and easily performed; that, plus a practical knowledge of DR should be sufficient for back-up navigators.

Celestially-navigated vessels might for whatever reason choose not to carry EPIRBs or other means of communication, but should in no way feel pressure to do so: that would be absurd. For one thing, most emergencies have nothing at all to do with navigation: piracy, health issues, down flooding up flooding, dismasting, etc. etc. For another, celestial navigators pay the same taxes as everyone else and are entitled to the same protection - such it is, offshore - as any other mariner.

In conclusion, we all have our own opinions and levels of comfort with different methods ... and that's entirely fine. Again, thanks for sharing your perspective.

Best wishes, Roger

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Roger Harris - 4 Mar 2021
Dick - 2 Mar 2021
I guess this takes the form of a personal position paper on the use of celestial navigation. These thoughts are on the receiving of training in celestial navigation and, simply put, are to advocate that the learning of celestial navigation be undertaken for possible emergency use (a lightening strike for example) or for a wonderful hobby, but not for primary navigational use (by primary, I mean that determining boat position is done solely by celestial without referring to GPS).

Hello Dick,

Thank you for your post. I appreciate your contribution, though I cordially disagree with your conviction.

Like all navigational methods, celestial undoubtedly has its limitations:
  1. It takes a relatively long time to produce a 'fix', especially when using the sun-run-sun technique;
  2. That fix will probably only be accurate within a few miles or so (which, it should be said, is quite sufficient for practical purposes);
  3. It requires measuring the altitude of celestial bodies, which are invisible in overcast conditions;
  4. Whilst sight reduction calculations are not particularly difficult, they can be tedious and silly errors are prone to occur (especially when the navigator is tired or seasick);
  5. And probably a few additional modest challenges that don't immediately occur to me.

All that said, groundings are generally caused not by systems limitations but by poor situational awareness. A vessel can be equipped with the finest, most modern electronic equipment known to man, and still go on the rocks if no one is monitoring what is actually happening ... it happens more often than it should.

Dick - 2 Mar 2021
Going to sea navigating solely by sextant could be motivated by 1. A romantic notion and identification with past practices, 2. Placing a feather in the skipper’s cap of accomplishments, 3. A personal navigational challenge, 4. Some sort of challenge/stunt.

There are many possible reasons for contemporary reliance on celestial navigation. It is certainly not "some sort of challenge/stunt" (which some might consider disrespectful of navigators like Bert ter Hart and Leo Gooden).

Using a sextant is fun! Sight reduction helps keeps one's arithmetic up to the mark. Celestial nav. exposes us to the wonders of the universe. Finally, making an expected landfall without the aid of GNSS is deeply satisfying, and promotes self-reliance.

Here's a link to a StFYC webinar that includes a recent documentary film about the above: Celestial (2020).

Dick - 2 Mar 2021
[N]avigating solely by sextant, while in no way a guarantee, does clearly make more likely that the skipper, crew and boat might get into trouble. Another way of saying this is that it is just not as safe.



As acknowledged above, celestial navigation has its limitations. Provided only that one is aware of those limitations, there's no reason for it to be significantly less safe than any other form of ocean navigation.

The Marion-Bermuda Race has for many years (possibly since its 1972 inception?) offered a "celestial election" yielding a 3% handicap (see Notice of Race, and see generally the documentary film linked above). Whilst there have been a few accidents in that race - accidental gybes, etc. - to the best of my knowledge none have related to celestial navigation.

The (celestial-only) 2018 Golden Globe Race is a similar example. Accidents, certainly. Navigation issues, zero.

The alternative ('safer') form of navigation was unspecified, but is presumably satellite-based. GPS, GLONASS and Galileo are technical marvels but are certainly not foolproof, and people who blindly depend on them can go badly astray. The well-known phenomenon of "Death by GPS" on land has nautical equivalents, Team Vestas Wind’s 2014 grounding on the Cargados Carajos Shoals probably being the best known.

Dick - 2 Mar 2021
I read of skippers who go to sea intending to use celestial as their primary navigational tool. My concern with skippers who go to sea without such a fundamental safety device as GPS is (at least) 3-fold. First is my concern that SAR personnel will be hurt or killed in a rescue attempt. Secondly, there may be crew on the boat who ill equipped with the experience or skills to judge the degree of risk they are undertaking, and thirdly, the environmental damage, that might occur if wrecked, say, on a reef with a load of fuel.



1) I know of no specific examples of SAR being called out due to celestial navigation errors aboard a yacht.

2) I agree that inexperienced crew are always ill-equipped to judge the risks attendant with offshore or ocean sailing (the vast majority of which have nothing to do with navigation). In any event, again, celestial has not proven to be less safe than other forms of navigation.

3) I'm bemused by the suggestion that celestial navigators run an increased risk of causing "environmental damage, that might occur if wrecked, say, on a reef with a load of fuel". I can think of at least one example of that happening: viz., the 1965 grounding of the USS Frank Knox on the Pratas Reed (southwest of Hong Kong). On the other hand, there are multiple examples of GNSS-reliant vessels causing environmental substantial harm. A few cases, all from the US Navy to stay consistent:
  • in 2009, the USS Port Royal went aground on a reef near Pearl Harbor, Hawaii, causing over US$7 million damage to coral;
  • in 2014, the USS Taylor leaked 175 gallons of fuel from a damaged propeller shaft after going aground while entering Samsun, Turkey; 
  • in 2015, the US federal government paid substantial compensation to the Philippines for environmental damage caused to the Tubbataha Reef when the USS Guardian went aground after relying primarily on an inaccurate Digital Nautical Chart (DNC)® coastal chart;
  • in 2017, the USS Antietam grounded on shoals in Tokyo Bay, causing a spill of 4,200 litres of hydraulic oil.
Again, the navigation system in use is essentially inconsequential. What matters is situational awareness. 

Dick - 2 Mar 2021
I read of skippers who go to sea intending to use celestial as their primary navigational tool.... Although I would try to talk them out of the endeavor, I would have no problem if skippers met at least a couple of conditions: they went alone (or all crew knew celestial and practiced sights at sea regularly and were aware they were giving up a degree of safety), and if the boat carried no EPIRB or other communication devices to call for help. By this they would be acknowledging that they were choosing a risky endeavor and had no wish to have other people (SAR in particular) put in danger’s way by their choices.


I agree that crew redundancy is always desirable. Not just with navigation, either: ideally, everyone aboard should know how to reef and steer, maintain and repair the engine and the boat's various systems, provision and cook underway, operate the radar, obtain and interpret marine forecasts, deploy distress signals, provide first aid, etc.

Of course, not everyone has the inclination or time to learn all aspects of passage-making. With respect to celestial navigation, the noon sight for latitude is quickly learned and easily performed; that, plus a practical knowledge of DR should be sufficient for back-up navigators.

Celestially-navigated vessels might for whatever reason choose not to carry EPIRBs or other means of communication, but should in no way feel pressure to do so: that would be absurd. For one thing, most emergencies have nothing at all to do with navigation: piracy, health issues, down flooding up flooding, dismasting, etc. etc. For another, celestial navigators pay the same taxes as everyone else and are entitled to the same protection - such it is, offshore - as any other mariner.

In conclusion, we all have our own opinions and levels of comfort with different methods ... and that's entirely fine. Again, thanks for sharing your perspective.

Best wishes, Roger

Hi Roger,
I will respond with a few separate comments on your comprehensive response, but to start:
I might have prefaced my comments by saying, that I am clear that some may see me as a bit of a gadfly around the subject outlined below.
In various venues, including OCC, I have written about my concerns that too many boats are going to sea poorly prepared: either the skipper has not the experience and skills for the passage chosen or the boat was poorly prepared and/or poorly fitted out. I pay only a bit of attention to sailing news, but even this casual attention leads, once or twice a year, to my thinking, “That boat and crew should not have been there in the first place.” Often these reports catch my attention only because SAR crews were sent out to assist them.
As just said, sometimes these boats (who might reasonably be argued should not be out there in the first place) initiate call-outs of SAR resources. SAR personnel know they have potentially dangerous work and we are very fortunate that they are willing to do the rescues they do. I believe that, as recreational sailors, we are obligated to go to sea in boats that are prepared to meet reasonably expected conditions that might be met and that skipper and crew have the experience and skill necessary to handle the boat and crew safely in those potentially challenging conditions in addition to the challenges of everyday life while cruising.
Now, I am clear that any mariner may experience bad luck and need assistance: that is what an EPIRB is for. But calling for help is never to be done lightly nor should it be done by skippers whose boat (and boat gear) is arguably not appropriate to the task at hand. I would argue that a boat going to sea without a GPS intending to use celestial for primary navigational position fixing, while fine in the open ocean, is unnecessarily courting trouble when the hard bits, land, is around. Whether this is a landfall or whether it rounding a headland, or navigating near reefs, atolls and islands: it can certainly be accomplished safely, but there is clearly an increased likelihood of trouble when doing navigation solely by celestial.
I know that every time there is an SAR call-out, there is the possibility of injury or worse. I believe we, as recreational sailors, are obligated to do our cruising in the safest reasonable manner. Open ocean, fine, use celestial, but near the hard bits, if using celestial gets the boat and crew in trouble, putting SAR crews in jeopardy coming to your rescue should not occur.
My best, Dick Stevenson, s/v Alchemy

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