

12022013, 03:41

#46

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Join Date: Feb 2012
Posts: 2,441

Re: Coordinate Math Question
Daddle: you claim that "The question as phrased by the OP is not formed properly"If so, why were you in such a rush to answer it for him? I think you need to reread the OP. Maybe you're going from memory ... The only tiny sliver of ambiguity is easily resolved by assuming the implied word "due" before the word west. (As you did in your first post)In which case the problem can perfectly well be answered.The other matter is frankly a complete nonstarter. By longstanding convention, which you alluded to a bit fuzzily in your first answer: there is a very close approximation accomodated by the definition of a nautical mile, which allows distance and angle to be related for navigational purposes, as opposed to, say pinpoint surveying, where Growley's point would be valid.Growley and you might both do well to read the wikipedia entry on "Nautical Mile", which makes it clear that the length of said nautical mile was chosen for the exact purpose of allowing the latitude scale of charts to be used as a measure of distance at sea, with a maximum error of less than plus minus 0.5% (at the equator or at the poles, not where the OP is)It's just as well, because otherwise most paper charts would have been unusable without a calculator, slide rule or trig tables. That is patently not the case.Furthermore, a chart which is accurate to better than 0.5% on distances between every detail has yet to be drawn. That's three decimals on EVERY feature. The International Nautical Mile, adopted by the US, is the average length of a minute of latitude, rounded to the nearest metre. The UK Hydrographic authorities, for reasons best known to themselves, have come up with a figure exactly one metre different from the international nautical mile. Perhaps that's what Growley is on about       You made it clear in your subsequent posts that your chief motive in answering the OP's question, having partaken of a drink or three, was to gain bragging rights. It seems to me it's more helpful to clearly describe the process so the OP can solve it, than to answer it by solving it for him. In which case one does not need to know the exact data. The data will be different each time the problem crops up, in any case, so it's the process which seems to be what's needed (teach a man to fish, etc...)But, if you are somehow right and the question was NOT properly formed, that suggests that the OP is not yet ready to frame that question.In which case it seems to me the helpful thing to do would be to lay down some fundamentals so the OP at least knows enough to frame such questions unambiguously.
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12022013, 04:14

#47

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Join Date: Dec 2012
Location: New Orleans
Boat: 1976 Cal 227
Posts: 1,003

Re: Coordinate Math Question
Not flaming, Andrew. And I am not saying that you can't use the latitude scale for distance. It is done all the time, of course. It is certainly close enough for Mercator charting. But the OP has to understand that Lat and Long are actually angular, which is why a minute of Longitude, on a (Mercator) chart, is practically never representable by a mile, nor does it represent a mile.
Now, for the OP...
Let me make this simple. And yet, not so simple. I would have you think a little, and truly understand the problem so the solution is repeatable with logical thinking and a little math.
For a very small distance, say 100 miles or less, it may be acceptable to simply regard the Earth as flat, and do this using plane geometry. For distances as small as a mile or less, there is no practical difference between polar and rectangular solutions except in the extreme polar regions. BUT... you still need to understand that longitude does not correspond directly to distance. As long as you understand that, we can fudge things a bit and take some technically false assumptions as a basis. In other words, sometimes it might be okay to compare apples and oranges.
Here is a highly nontechnical way to do your problem. Construct a plotting sheet. Draw a line through the middle of a sheet of paper, parellel to the long edge. Near the center point of that line, draw a circle with a compass. The bigger, the better but not all the way out to the edge of the paper. Draw another line parallel to the first one, that passes through the exact bottom of the circle, and another one at the top. Determine the mid latitude of the area in question. Let's say you are at 30 degrees North Latitude. With your protractor, draw a light line from the center of the circle, angled upward 30 degrees from the horizontal. It must intersect the circle. Draw another one angling 30 degrees upward from the horizontal centerline going toward the other side of the circle. Where these lines intersect the circle, draw another line on each side, up and down. The horizontal lines are latitude and the vertical lines are longitude. If you assume The distance between the lower latitude line and the center latitude line to be a minute of latitude, then the distance between the right or left longitude line and the center point is a minute of longitude AT YOUR MIDLATITUDE. If a degree, then a degree. If 1/10 minute, then ipso sameo.
Now further refine your scale. Take a ruler and pick off 10 units. Lets say your latitude lines are 1' apart. Place your zero mark on one latitude line. Place the 10th mark on the next one. Make a tick at each ruler division, on the paper. With your triangle aligned with a longitude line, move the triangle up or down so the upper leg is adjacent to the tic mark, and make another mark at the edge of the paper, or the center longitude line. Wherever. You are establishing a scale. Do this for all the other marks. Repeat the process for the longitude so you also have a graduated longitude scale.
ASSUME a minute of latitude to equal a Nautical Mile, while remembering, of course, that latitude is actually an angular measurement. Now you can plot lat and long on your plot sheet, and also measure distance and angle.
Let's say you are rubbing right up against bouy "A". You have bouy "B" on the radar at .5 miles, bearing 045 True. You want to know the lat and long of bouy "B".
Plot your position on the plot sheet. Using the latitude scale, and assuming a minute of latitude equals a Nautical Mile, pick off the distance of .5 miles with your dividers. With your triangle, (hopefully it has protractor markings on it) align it to pass through your position and at the correct orientation to draw a line representing 045 True. With your dividers set at .5NM, make a prick or mark at 045, guided by your triangle. Wa La. Now with your triangles or parallel rules or whatever, find the Lat and Long from the scales of your plot sheet. Easy Sneezy.
You can buy pads of universal plotting sheets that all you have to do is draw the longitude lines. Use pencil and draw lightly, so you can erase.
Obviously, you can do this graphical solution on an actual chart, too. But now you have a better understanding of the relationship of lat/long lines on a Mercator chart, and in an assumed flat earth model. Plus you didn't have to clutter up your chart. Plus, you can use a bigger scale for better accuracy in plotting and measuring.
Of course you could simply use your GPS magic box to do this for you, but this is more fun and could be a handy skill some day.
Notice that when you drew the 30 degree line to the edge of the circle, and drew a vertical line through the intersection, you constructed a triangle, and that this triangle describes the planar relationship between Lat and Long at your Latitude. You probably know the formulae for finding the length of the sides or angles of a right triangle, right? All that Sine/Cosine/Tangent stuff? Now that you have seen the relationship graphically, maybe you can figure out how to solve the problem mathematically by a simple method. The result will be you will understand the solution instead of simply follow the textbook recipe steps to derive it. This understanding will help you to become familiar and comfortable with the solution, and not forget it.
Forget? All you got to do is figure it out again. No biggie.
This understanding of basic plane geometry and how it applies to Navigation is a good first step in becoming an actual Navigator. Spherical trigonometry can wait a while, if you are not crossing oceans.
Hope this helps. Anyway it occupied my mind and typing fingers for a few minutes.
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GrowleyMonster
1976 Cal 227 sloop, MR WIGGLES
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12022013, 05:30

#48

Registered User
Join Date: Nov 2007
Location: Probably and anchorage or a boatyard..
Boat: Ebbtide 33' steel cutter
Posts: 2,753

Re: Coordinate Math Question
These little chats always lead to learning something. i always thought a nautical mile was a exactly minute of latitude and would vary slightly between the tropis and the poles.
Apparently not, but..
Quote:
By international agreement, it is 1,852 metres......
.... The Imperial (UK) nautical mile, also known as the Admiralty mile, was defined in terms of the knot, such that one nautical mile was exactly 6,080 international feet (1,853.184 m):[6] it was abandoned in 1970[6] and, for legal purposes, old references to the obsolete unit are now converted to 1,853 metres exactly.[7]

Nautical mile  Wikipedia, the free encyclopedia
Which is close enough to a minute of lat with my pencil on a chart anyway
Always stuff to learn
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12022013, 05:31

#49

Moderator
Join Date: Oct 2009
Location: Manchester, UK
Boat: Beneteau 473
Posts: 4,440

Re: Coordinate Math Question
No one has mentioned Traverse Tables, very handy set of tables useful for distances up to about 600 nm. You can get the course and distance between two separate waypoints, or find the D.Lat and D.Long given one waypoint and a bearing and distance.
Also useful for calculating the Intercept Terminal Point for those still using sextants.
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Beneteau 473
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12022013, 07:55

#50

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Join Date: Apr 2006
Posts: 12,077

Re: Coordinate Math Question
Jammer, you raise a good point about teaching skills and I think few of us teach navigation. And probably we each do things a different way having selected one method and forgotten the rest. You ask "how to lay out points on a distance and bearing mathematically from a known point? " and I would tell you, literally, you've answered your own question on that.
You can go to Weems & Plath to see the special tools, often simple tools, that navigators use to do this. What they call a "course plotter" Course Plotter  Weems & Plath is among the simplest. A protractor and ruler combination so if you are trying to get the lat/lon of a point that lies at a set distance and bearing, you plot that position with a tool like this, then just drop lines to the two borders of the chart and read the lat/lon equivalent position.
If you are in charted waters, yes, it is "plot then read". In open ocean...you can fake it with plotting sheets and hopefully you aren't requiring the same precision at sea.
Navigation tools often overlap drafting tools. Drafting arms, or rolling rulers, triangles, protractors and compasses, pretty much the same tools with the same purposes. "Doing it" the analog way with extended lines and on paper, works just as well as "doing the math" and generating the results that way. Each way gives headaches to some people.<G>
And just as in carpentry, as in cabinetry or finish carpentry, you've got to be aware of the limits in the numbers and solutions. You can design and lay out a bookcase down to 1/64th of an inch in your measurements, but if you start the job in cool dry weather and finish it in hot damp weather, your work will be screwed up as the wood swells and the dimensions change. In navigation that's always a prime consideration. Not just "where are we" but what circle of error is in that position, and why. With a mark or buoy, that would always start with the swing from the mooring, so an accuracy within 100 yards might be all you'd ever need, or find.
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12022013, 08:08

#51

Registered User
Join Date: Nov 2010
Location: Lafayette, Louisiana
Boat: Ketch, Hardin 45
Posts: 440

Re: Coordinate Math Question
There are a few ways of finding the distance & course from from one lat/long to another.
1. Plain sailing;
2. Mercator sailing;
3. Plotting on an appropriate size chart and stepping it off.
4. Great Circle Sailing.
Have used all 4 methods depending on the distance and what I want to use at the time... I have a tendency to know and use more then one method. A. for the practice of Navigation and for for the simple reason, I take pride in being able too.
And you can use Bowditch to find a couple of more methods also... I love Scienific Caculators, they really make it easier to do the math. But you can use the tables in Bowditch if want instead of a caculator.
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12022013, 08:09

#52

cruiser
Join Date: Jan 2013
Posts: 72

Re: Coordinate Math Question
Quote:
Originally Posted by hellosailor
You can go to Weems & Plath to see the special tools, often simple tools, that navigators use to do this. What they call a "course plotter" Course Plotter  Weems & Plath is among the simplest. A protractor and ruler combination so if you are trying to get the lat/lon of a point that lies at a set distance and bearing, you plot that position with a tool like this, then just drop lines to the two borders of the chart and read the lat/lon equivalent position.
If you are in charted waters, yes, it is "plot then read". In open ocean...you can fake it with plotting sheets and hopefully you aren't requiring the same precision at sea.
.<G>
.

OP asking classic "great circle sailing" question and you came out with rulers, protractors, triangles...plotting sheets, what plotting sheets. i wonder in which school you are teaching "navigation".
this is answer for OP question..no more, no less.
How to Calculate the Distance Between Two Latitude/Longitude Points  eHow.com
http://www.movabletype.co.uk/scripts/latlong.html
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12022013, 09:13

#53

Registered User
Join Date: Dec 2012
Location: New Orleans
Boat: 1976 Cal 227
Posts: 1,003

Re: Coordinate Math Question
Scimitar, he answered. His solution is to simply step it of on a chart, and it works.
BTW I find a good pair of triangles to be fastest and easiest. I don't like all the other rollarulers, parallel rules, etc stuff. Most ships will have a pair of triangles sitting on the chart at any given time.
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1976 Cal 227 sloop, MR WIGGLES
Now with clean, dependable electric propulsion!



12022013, 09:20

#54

Registered User
Join Date: Dec 2012
Location: New Orleans
Boat: 1976 Cal 227
Posts: 1,003

Re: Coordinate Math Question
Here is a sample plot sheet. Turn it sideways... the graduated scale is latitude of course. Later when I have a better connection I will post a small program for custom printing your own sheets with better resolution. You tweak the settings and it sends data to a virtual printer object rather than printing a pixelated image from the screen. They come out pretty nice if I say so myself. Meanwhile you can amuse yourself with this gif file.
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1976 Cal 227 sloop, MR WIGGLES
Now with clean, dependable electric propulsion!



12022013, 17:13

#55

cruiser
Join Date: Dec 2012
Location: Seattle
Posts: 1,130

Re: Coordinate Math Question
Okay, more questions.
First, I see no relationship between this circle and the Tyee Shoal Light. But then, I didn't see a relationship between exterior sheathing and sheetrock the first time I framed, either. So I took sixteen inch centers on faith. Worked then, it'll probably work now.
I've attached a picture. I hope it works.
Note that I subdivided by six, not ten, hoping to get seconds. Or at least unit of ten seconds. Or something. Because I'm at least as bright as the apprentice who brought me a rope when I asked for a wrench. Don't ask. At least he found the truck and didn't come back empty handed.
Now, here's my next question: my problem is laying out a dimension in yards, and deriving coordinates in degrees, minutes and seconds.
So if I lay this grid out by six, for ten seconds, and every major division is one minute of latitudelongitude, how do I then set my dividers for 200 yards?
P.S. I have no idea why the picture rotated 90 degrees. Which is one reason I don't want to lay it out on a magic black box. Magic black boxes are rarely either, although they are occasionally boxes.
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12022013, 17:16

#56

cruiser
Join Date: Dec 2012
Location: Seattle
Posts: 1,130

Re: Coordinate Math Question
Man, that picture sucks. I see I have to draw heavier lines and use bigger lettering if I'm going to post a picture to the internet.
Some of the text says that I used 47 degrees, because the Tyee Shoal light is at 473634.6N, 1222915.2W.
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12022013, 18:37

#57

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Join Date: Apr 2006
Posts: 12,077

Re: Coordinate Math Question
"my problem is laying out a dimension in yards, and deriving coordinates in degrees, minutes and seconds."
Well, it is only fair to mention that while we sailors putz around with archaic and traditional DDMMSS notations, the actual newfangled (1020 years old?) ISO standard is to plot position information as simply degrees to five decimal places, that is DD.ddddd which elimates all sorts of opportunities for conversion errors as well. Just saying, DDMMSS is not the only way to do it. DDMMmm is also out there, using decimal minutes, just to make sure navigators lose sleep.
And again, you are not necessarily deriving coordinates, you will be approximating them, and you have choices of how to approximate them and what accuracy to approximate them with.
"So if I lay this grid out by six, for ten seconds, and every major division is one minute of latitudelongitude, how do I then set my dividers for 200 yards? " Fast answer: You can't. Unless you are at the equator, you can set your dividers to mark off 200 yards of longitudebut not latitude. So now you chose. Do you want to average out the two? Pick the length of a degree of latitude at your approximate latitude, average that out with longitude, and punt with a compromise?
Or, do you set them for longitude, mark off your longitude offset, and then reset them for latitude, and mark off you latitude offset? Two operations.
You might decide that since one minute of longitude is about 6000 feet, and 200 feet is one tenth of that (six degrees) that you can just set your divider to six degrees on your scale/grid, and then measure 200yeard increment that way. And then, as above, either reset for latitude, or just say "good enough for government groundings" and accept that there will be a larger circle of error in your final plot.
There isn't just one way to do things. Well, there is, if you're using spherical trig and aiming for exact numbers and such. Computers and calculators have really taken out a lot of the donkey work in that. A PDA like the old Palms or a smartphone running software to do that, really can do a fine job. (I still like the Palms because they're too dumb to make creative mistakes. Cheap now, too.)
Speaking of pictures and bolder linesthe lines are part of the equation also. Quite seriously. You may chose to draw plots with a .5mm pencil or a .7mm pencil or a blunt No.2 or even a crayon. No matter what you use, no matter what the scale, the width of the lines themselves also adds to position error, or can be chosen to indicate/allow for it. Whether you use analog means or digital to plot positions, there's all kinds of stuff going on that affects the size of "we are here".
A slow, boring, traditional book, carefully written by a trained and experienced teacher, will tend to make you aware of all that stuff. Going back to frmaing carpentry: It doesn't matter how good your carpenters are, if the house isn't built on a solid foundation. And what is solid enough, varies with where you are building. The books will go into that, a fast onpoint answer online would miss it.
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12022013, 19:21

#58

cruiser
Join Date: Dec 2012
Location: Seattle
Posts: 1,130

Re: Coordinate Math Question
Alright, let me rephrase.
If I want to do latitude and longitude as separate operations, how do I set my dividers for 200 yards of latitude after laying out my grid to read in degreesminutesseconds?
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12022013, 20:02

#59

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Join Date: Apr 2006
Posts: 12,077

Re: Coordinate Math Question
Speaking of rephrasing, I got spun (or decaffienated) and the reference to LONGitude above should be LATitude. The length of each degree of LATitude stays almost the same from equator to pole. The length of each degree of LONGitude shrinks on the way from the equator to the poles.
Calculation of Distance Represented by Degrees of Latitude and Longitude
is one explanation of how to calculate the changing length of one degree of longitude, based on your local latitude. They use DD.dddd decimal degrees and convert for one mile, so you'll need to adapt that or modify the formula a bit.
Length of 1 degree of Longitude = cosine (latitude) * length of degree (miles) at equator is the fomula they are using and their example is for latitude 33.1519:
1° Longitude = cos (33.1519) * 69.172 mi = 57.912 miles * 5280 feet · mile1 = 305,775 ft Basically, they take the cosine of the local latitude, multiply out, and use that to adjust the length of one degree of longitude.
Using this same formula you can find out the length of one degree (or minute, etc.) of longitude at your location. Mark it, set your divider for 200 yards worth, and you're in business. Cosines? Oh, right, every navigator has a book of trig values, sinces and cosines and all that good stuff.
And if you don't want to use a calculator to replace the tables, there's always the handy dandy analog calculator: The slide rule ain't dead yet! <G>
Got one in the bottom of my bag, mainly to keep the silicon life forms scared and on their proper behavior.
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12022013, 21:52

#60

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Join Date: Dec 2010
Location: B.C.,Canada
Boat: 29'
Posts: 2,368

Re: Coordinate Math Question
Quote:
Originally Posted by Jammer Six
Alright, let me rephrase.
If I want to do latitude and longitude as separate operations, how do I set my dividers for 200 yards of latitude after laying out my grid to read in degreesminutesseconds?

The answer is: Don't use yards as a measure.
Yards are on sailing ships.
They are not a unit of measure on a chart.
in return, I won't use fathoms in carpentry,ok?
What is it you are trying to do again? Convert a bearing and distance to Lat and long?
since the quick answer didn't help, Draw it on a paper chart. A mercator chart. It's the simplest and most common. Google "mercator projection". Use the easy measures it offers you. degrees,minutes,seconds,or maybe "cables"( a tenth of a minute)
Not some tailor's idea of selling cloth based on a unit of archery.
Latitude and Longitude are a grid system. Figure out your new position from the grid numbers at the sides of the chart.
Done.
You don't need feet yards metres to do this. You just need two positions and a ruler and dividers.... and a new outlook on this new and apparently strange world.
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