Navigation the Rite Way.. or Is GPS Reliable???

[Captain Smollett]

before or after makes no difference.how ever a difference between"minus point five" or  two to five  is a huge difference resulting in as much as 2-5 miles.still I will swear by my garmin 12,which yeilds an error of 6 feet,or about.001  nautical mile

Look, Eric, I don't know what you are talking about.  If you correct for the Index Error by subtracting it out, IT INTRODUCES NO ERROR IN YOUR FIX.

Prove to me otherwise, mathematically, that if you have a measured angle that you KNOW is too small by X and you add X to the measured value, how is that not the REAL VALUE?

The error in fix in CN comes mostly from two places: error in taking the measurement itself and in knowing the time that the site was taken.  CN can reliably give a fix to wthin 4 nm (which historically was 'good enough' since that is less than the visible radius from the maintop of a square rigger, or even from the deck of an Ariel).  While metal sextants do tend to be a little better, if you know the limitations of a plastic sextant (ie, determine the index error for each site), they are about as good.

That four mile precision using CN is true whether you have an Index Error of 0 minutes or 10 degrees - IF you KNOW what the IE is.  It does not matter.

Many professional navigators, as evidenced by years worth of articles in Ocean Navigator, do not rely SOLELY on GPS; in fact, they recommend against relying on any one technique alone.  Further, many of these same professional navigators keep plastic sextants as backups or even as the primary tool in the 'abandon ship' gear.  CN is a great hobby, and a useful one.  And there is no need to drop $500+ on a high grade metal sextant while learning the art when a $120 plastic model will serve just fine.

CN vs. GPS is another discussion completely. No one is claiming CN to be as precise as GPS, but please don't cloud the issue with nonsense that KNOWN Index Error cauaes an error in the computed fix.  I don't think you really believe this to be true, since I gather from your discussion of CN that you really do understand it.

[starcrest]

index correction is the amount of error in the arc itself.simple changes in air temp makes the actual material that the instrument is made of  change ist shape --in heat it expands in cold it contracts,plastic is very unstable in this sense.when using my david white ww2 navy surplus,it would be in the box in the relative coolness of shade.once brought out into the hot sun the metal the it is made of would expand....not in the way you could see by eye.....but this is very definite when looking thru the horison mirror."if its on its off,,,,,if its off its on"in otherwords some times the error is negative (then its added)and vise-verse.I am basing my experience on 15000 mile of celestial nav use.

[Captain Smollett]

index correction is the amount of error in the arc itself

Not exactly. 

It is a mirror alignment problem that is very easily measured, should always be measured, and once you know the IE, it's effect on the instrument introduces no error in the fix obtained from a given site.

Index error is the the reading on the instrument when the horizon is 'nulled.'  That is, when you are looking through the sextant and you see one solid image, the sextant is 'nulled.'  If you must adjust the sextant to a non-zero reading to get this single uniform image, that reading is the Index Error.  It is trivial to measure, and if you determine the IE right before you take a site, the thermal properties of plastic have nothing to do with it.  Any changes to the shape of the sextant in the few seconds from measuring the Index Error to taking your site will contribute less 'error' than a human's ability to precisely drop a celestial body to the horizon.

Good and Brief Description of Index Error
Or Here  (scroll about 2/3 way down the page)
Or Here  Notice that it says to determine the IE before each use.
Or Here Again "you check for IE each time you use the sextant."
And Finally Here, Too

This is my last post on the topic, since we are getting nowhere.  You can think what you want about plastic sextants and index error, and I'll continue using my Mark 15 to get fixes acceptable to me.

[starcrest]

getting nowhere ...sounds good ...remember even if you are nowhere you are never more than 5 miles from......

[CapnK]

Hey guys -

Don't stop talking yet - the discussion, though frustrating it may be to be at loggerheads about part of it, is yielding some good info and links for those of us who are rank n00bies at CN. :)

$120 for a plastic sextant? Too expensive!!! My Davis 15 cheapo was only $35. ;D (Just kidding, I know what you are talking about...) Supposedly the 15 has been/gets used by people as their primary sextant, and as a liferaft tool as well. Personally, if it's accurate enough to get me close enough to somewhere that I could do coastal piloting, I think that that is pretty darned good. Better than what Magellan, Cook, Colon, Polynesians, and others had back then, and look what they did! ;D

It's good that GPS does what it does, reliably and accurately, and I admit that I use it extensively, but having all my navigational eggs in one electrical basket for an ocean crossing wouldn't make for a whole lot of peace of mind in my case. I do want to have a KISS method to determine where (even if only approximately) I am. I think I would like to make sights manually, and then check my sights afterwards against what the GPS says. That way I could know that I had become proficient at the non-electrical, reliable "old school" nav in case the "new school" nav went out, either because of failure on my recieving end, or because of some other reason, ie another big terrorist attack that would cause the military to scramble signals, or perhaps due to an EMP-induced failure of the system.

One thing about GPS accuracy - yes, they will tell you your position to within a few feet, *BUT* people put blind faith on what the little chart on the GPS screen shows them as to where that position is, and that is possibly seriously misplaced faith in tight quarters, in my opinion and experience. I've read and seen that the errors possible in what a chartplotting GPS displays can be as much as several hundred feet, given that 1) charts are not always accurate or up-to-date in what they show (especially charts for other parts of the world, and 2) that how the chart is scanned in to and then rendered by the GPS on its screen can induce further errors.

I've seen this myself at times, with my WAAS GPS pulling in good signals from several satellites. I have been on the ICW, dead-center of the channel, looking at a course saved from just a few days/weeks earlier that, if I followed it blindly, would have required wheels or tank treads to have been installed on my boat, since it was several hundred feet or yards off to one side of where the water actually was.

My favorite nav instruments are the good old Mark I Eyeball, and Common Sense and Reasoning. ;D

[Lars]

http://164.214.12.145/index/index.html


http://www.tecepe.com.br/nav/almanac.html-ssi



Here are some links someone may find usefull..sight reduction tables and natical almanac.. there are also full size pilot charts and light list ..everything in pdf format

[starcrest]

I would think that there are hardly few boats in the 26 -30 foot  size range that would have the capability to run computers 5 miles from the bottom .....unless you had a very long land line connection.even then itsa nufangled  electric gizmo.computors are not infallable.when some thing goeth rongo on the one I yooz atwoik,I can make sure it never has to be fixed again with the application of relatively primitive hardware.....a sledge hammer(that should be woit some applause hmmmmmmmm?)

[Captain Smollett]

I would think that there are hardly few boats in the 26 -30 foot  size range that would have the capability to run computers 5 miles from the bottom .....unless you had a very long land line connection.

There's a lot you can do with a laptop, by battery, that you don't need any external connection.

I use several different computer based almanac/calculators in my CN practice.  Of course, I also do site reductions by hand, too (no reduction tables, crunch numbers with raw equations, either with small hand held calculator or with a slide rule).

I think I linked to several sites that offer such computerized tools higher in the thread.

Even if you need a connection to external servers, there are satellite based ISP's, or even HAM based if you have radio gear on board.  I don't think this necessarily comes under the KISS principle, but the resources/capability is there if one chooses to use it.

[starcrest]

actually I have seen those satellite dome type antennae on some large houseboats here.but I wonder how the actual hardware would stand up thru time to the ravages of the marine environment(not the artificial reef type) but the high humudity ,heat and salt air of the average small boat.I can never forget the pounding of the way north from hawaii.....man that was not fun.infact on the triton my vector loran had a problem with the lat/lon #2 button.it would not give a read out.I havent done much sailing lately but I have great gps fun with the garmin 12 in the car.the up/down/left /rite arrow button has been acting up.like any electronic gizmo it too is not infallable.half way there on the schooner I left the short wave receiver on the deck.It got ruined from the sea spray that could have been disasterous,but like magic someone produced a branspankinnu RDF that had tha ability of  getting wwvh on 2.5 mhz.

[Zen]

http://www.marineplanner.com/bowditch/bowditch.cfm

[svosprey]

Free open source stargazing program. Awesome!!!

Try zooming the nebulas!

http://www.stellarium.org/

[Rockdoctor]

You may also like Celestia, it is free as well. You can fly to the planets, add spaceships, and make great movies. I use both in my astronomy class and Celestia is as much fun as Google Earth
http://www.shatters.net/celestia/

[CapnK]

Cool, guys, both of ya! :D

Karma pops...  ;D

[Zen]

First a disclaimer:

I am not saying go out an make this for using on a trip! It is of interest value only. Maybe  of some use for understanding basics.
end of disclaimer.

That was for StarCrest wherever he is, so when he comes back and reads this, he will not have a cow. "that does happen not just on TV " ( by the where  r U dude?) ;D ;D ;D ;D

anyway  found this:
http://www.tecepe.com.br/nav/CDSextantProject.htm

[AdriftAtSea]

A couple of other things...

Tania Aebi wrote about how she had a lot of trouble using plastic sextant, and had not realized how much it had warped from sitting in the sun.  The fact that it had warped was not easily apparent and the source of her problems with it.  Once she switched to a metal sextant, much progress was made in celestial navigation.

A heavier sextant is often easier to aim, but more tiring to hold.

A good starfinder is worth its weight in gold...too bad they're not very heavy. ;)

A good book to get as a reference, is "The Complete On-board Celestial Navigator" by George G. Bennett.  It has all the tables and forms you'll need to do celestial nav through the end of next year...I'd imagine a new version is due shortly.

Most of the better metal sextants are shipped with a little chart that gives you any index errors at various points along the scale.  I consider myself fortunate that mine doesn't have any index error at all.  But this can change over time.

BTW, I use an Astra IIIB.  I got it on sale at Westmarine, but their prices for it are not normally the best.

If you do try to use an artificial horizon, remember that there is no dip error correction for height as the artificial horizon removes the need for it.  Water is a lousy liquid for an artificial horizon—I'd use thinned molasses or soy sauce instead... especially if I was going to do sun sights.

Moon sights are a royal pain in some ways, as there are many more corrections for the moon than there are for any other celestial body.  YMMV.

A few other points...
1)  GPS has been shut down by the US military before...around the time of Desert Storm IIRC, and it could happen again.
2)  Also, most of the GPS satellites are past their designated operating lifespan, and could fail catastrophically, like the Hughes IntelSat IV did about six years ago, and wiped out 80%+ of the paging service in the country by doing so... same thing could happen to GPS. 
3)  GPS and Celestial Navigation are both tools... and one is a good backup/check for the other...but the Mark I Eyeball is also pretty good...and when you're near the coast, it should also be used. 
4)  Just remember the little picture on the GPS isn't really a representation of where you boat is...it is a representation of where the electronic satellites are telling they think the cartographer who made the map thinks your boat should be... and some of the maps are based on data from the 1890s still... so they should be thought of as somewhat inaccurate. 

Just soem food for thought.  I personally think that anyone who goes on bluewater without a GPS and a sextant, and all the necessary paper books for it is crazy... :D

[Captain Smollett]

I like solving Navigation problems, and I'm currently working on calculator solutions to many of the problems that can be solved with the trusty old Bowditch.  These are good techniques to have, imo, as all of our wonderful modern electronic gadgetry can fail.

You might say "ah, but your electronic calculator can fail, too."  Yes, indeed.  That's why I have a non-electronic, no-batteries needed slide rule in my nav kit.  Just In Case (tm).  And I'll bet I can do sight reductions by hand with the slide rule ALMOST as fast as many can do them with HO 249.

So here's a practice problem I am working out, and to keep things simple I'll make a few (ridiculous) assumptions.  The set-up is a sail from Georgetown, SC to Portland, ME, long enough that we possibly don't have a single Mercator Chart with both endpoints.  We are going to ignore Massachusettes and the fact that Georgetown is several miles inland from the ocean.  Let's just pretend we want to sail from the lat-long of Georgetown to the lat-long of Portland over 'open' water.

Also, I'll give the lats and longs in decimal degrees (rather than degrees decimal minutes) just to make punching on the calculator a bit easier.  The problem: Given initial and final Lat-Long, Require rhumb line course to steer and distance.

Georgetown:  32.22 N, 79.17 W
Portland:  43.40 N, 70.16 W

Solution:

A Mercator chart has the properties that a straight line on the chart is a constant compass course.  This is not technically the shortest distance between two points on the earth (unless along a N-S line or the equator itself), but is 'easier' to steer.  This course is a rhumb line.

Why don't we want to use a single small scale Mercator chart, or chain together many small ones?  The problem is that for a Mercator Chart, the flat distance represented by the lat and long are not the same, and the 'ratio' of lat to long varies with distance from the equator.  This is a mathematical property of the projection.  If you took a chart of Georgetown and a chart of Portlant, laid them so their corners are in the 'right place' and tried to strike a rhumb line, your course would not be correct since the 'ratio' of lat to long for the two charts would be different.

To calculate the distance, we need the course first.  And, it turns out, the course is harder to compute.  The equation is simple looking,

C = arctan ( DLo / m )

where arctan is the arctangent function, DLo is the change in longitude and m is the meridional difference, M2 - M1.  Here, the M's are the meridional parts for our two latitudes, which can be computed using:

M = 7915.704468 log ( tan ( 45 + lat/2 ) ) - 0.23268932 sin ( lat ) - 0.052500 sin^3 ( lat ) - 0.000213 sin^5 ( lat )

M is a quantification of the relationship between latitude and longitude on the projection, and it should be noted that this formula is approximate (as most are that are used in practice for computing M).

So, for the problem at hand,

M2 (Portland)      = 2031.5533
M1 (Georgetown) = 2880.0139
m = M2 - M1 =  848.4606

When this m and DLo is plugged into the equation for the course to steer, we get C = N 32.5 degrees E, or 32.5 degrees True.

That notation for the course means 32.5 degrees East of North, and is necessary since the 'quadrant' of course computed is determined by how the endpoints are situated.  It is similar to figuring out the azimuth quadrant in a celestial sight reduction.

With the Course in hand, it is relatively simple to compute the distance:

d = l / cos ( C )

where l is the latitude difference, L2 - L1 and C is the course we computed above.  So,

d = 795.4' = 795.4 nm.

Incidentally, the Great Circle Course for this 'trip' is 794.1 nm, only about 1 mile shorter!

Okay, so why bother with all of this?  Strictly speaking, we should not prick the chart to get distances (unless a fairly large scale chart) unless the course lies due E-W.  This is because a minute of longitude is not only not 1 nm, but it is not constant!  That's what those M's correct.

But we often don't have to compute the course to steer as we did here.  The course betwen two endpoints on a Mercator Chart is an accurate rhumb line course.  So, you could simply measure the angle using course protractor (or other whatever is your prefered method for laying courses on the chart) and use it in the equation for distance given above.

This is a tremendous back-up, in my opinion, against putting ALL your navigational eggs into one GPS basket.  The math is not that complicated if you have the formulas written down.  And even better, there are downloadable programs for pocket electronic calculators available (as well as javascript based web pages) to handle the math.

To help learn how these equations work, I am writing my own set of programs for the TI Voyage 200 calculator.  The V-200 is $172, which makes it over $300 cheaper than CelestiComp ($499).  I have the sight reduction, noon lat and rhumb distance programs 'done' and testing, and will post these and others for free download soon.

If anyone on the board has an older TI calculator (TI-89 or 90), I'd like to port the programs to them.  Unfortunately, it is my understanding that V-200 programs are not downwardly compatible, so we'd have to recode for the older calculators.

[Zen]

 :-[  :-\   :'(

[Captain Smollett]

Rhumb lines are what the GPS computes fro what we commonly call "waypoints."  If you know the lat-long of the waypoints along your route, you can compute your own course-distances for each leg.

You know, if the GPS is broken.

;)

[Pixie Dust]

Say it isn't so... GPS's break or stop working?  Please don't tell me that gadgets aren't perfect.  :o  ;D :D
I might have to do math??   :o  I think Jimmy Buffett has a song titled Math Sucks.   :)

PS- I actually enjoy Math.   ;)

[Cmdr Pete]

Even simple math makes my brain hurt.

Anybody use a nautical slide rule like this one?

http://www.weems-plath.com/cgi-bin/showCollection.cgi?categoryKey=23&subCategoryKey=36&itemNumber=105