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Old 11-02-2013, 07:58   #31
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Re: Coordinate Math Question

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OK, now I'm confused. The distance scale on charts is normally in 10ths for lat, so I plot using degrees and minutes and decimals, rather than seconds, and for longitude, isn't the scale sized to accomodate the particular location the chart is based?
Exactly what is confusing you Shorebird?

On a Mercator projection chart (i.e. the usual one), lat and long are both parallel lines (obviously at right angles to each other) and both are defined in degrees and minutes (and often 1/10ths of a minute).

Distance is scaled off the lat lines (1 minute = 1 nm) and must be read at the approximate latitude in question and never off the long lines.

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Old 11-02-2013, 09:04   #32
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Re: Coordinate Math Question

Your Trig Fu is OLD! I will defeat you easily! BWAAAAAAhahahahaha!!!!
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Old 11-02-2013, 09:07   #33
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Re: Coordinate Math Question

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without google!!!!!!

Maybe....

New Lat = Old Lat +(cos(course*dist)

New Long= Old long + (sin(course*dist)*90/oldlat

Better hit send quick before someone else gets in, haven't checked that yet ....
You are missing some parenthesis.
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Old 11-02-2013, 09:21   #34
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Re: Coordinate Math Question

Had a friend that was messing up his navigation until I told him to look carefully at the compass rose. NOAA makes a chart pack called the small craft series for Puget Sound. The charts are all rotated as necessary to fit. He was taking his distance measurements along the up and down sides of the chart not realizing that north/south was left/right.

Chart 18445b
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Old 11-02-2013, 14:59   #35
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Re: Coordinate Math Question

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Exactly what is confusing you Shorebird?

On a Mercator projection chart (i.e. the usual one), lat and long are both parallel lines (obviously at right angles to each other) and both are defined in degrees and minutes (and often 1/10ths of a minute).

Distance is scaled off the lat lines (1 minute = 1 nm) and must be read at the approximate latitude in question and never off the long lines.

The confusion results from the mercator projection. In a spherical representation, longitude cannot be measured the same as latitude... since the distance between them varies markedly as one moves North or South from the equator. since, with latitude, 1 minute equals one NM, the same cannot be true for longitude, since the spacing is near zero as one approaches the poles. Since the spacing for longitude is the same as latitude at the equator, this appears to me to be the only place where a minute is a mile. If I understand the complexities of the mercator, it seeks to keep the scale the same, and thus either one changes the definition of a nautical mile, or the geography must distort to accomodate, and consulting my original sailing manual, that is indeed the case, as it references the geographic distortion that increases as one approaches the poles. In the scale marine charts use, the distortion is likely minimal, but does indicate some shortcomings in any method compressing 3 dimensions into 2. But, lets get back to the part confusing me. If both lat and long use the same common dimension (1 NM=1/60 degree) then why, using a mercator chart, can't one use the scale for both, instead of just the lat scale?
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Old 11-02-2013, 15:13   #36
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Re: Coordinate Math Question

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The confusion results from the mercator projection. In a spherical representation, longitude cannot be measured the same as latitude... since the distance between them varies markedly as one moves North or South from the equator. since, with latitude, 1 minute equals one NM, the same cannot be true for longitude, since the spacing is near zero as one approaches the poles. Since the spacing for longitude is the same as latitude at the equator, this appears to me to be the only place where a minute is a mile. If I understand the complexities of the mercator, it seeks to keep the scale the same, and thus either one changes the definition of a nautical mile, or the geography must distort to accomodate, and consulting my original sailing manual, that is indeed the case, as it references the geographic distortion that increases as one approaches the poles. In the scale marine charts use, the distortion is likely minimal, but does indicate some shortcomings in any method compressing 3 dimensions into 2. But, lets get back to the part confusing me. If both lat and long use the same common dimension (1 NM=1/60 degree) then why, using a mercator chart, can't one use the scale for both, instead of just the lat scale?
Shorebird: I think I understand what lies at the root of your question, but please correct me if wrong:

Are you saying "Why do I need trig, if I have a chart?"
To which my answer is "Yes, indeed"

But to answer your SPECIFIC question at the end of the quote above:

You are right to say that the distance between any two points will be at the same scale on a mercator chart, whether those points are disposed E-W, or N-S, or anywhere in between.

You are also right to assume that a nautical mile measures the same everywhere, for all practical purposes.

HOWEVER: because a nautical mile is NOT the same as a minute of longitude*, it's not possible for the two scales on a chart to be the same as each other, AND for both to represent nautical miles. It's a logical impossibility.

given

A = B , and
A does not = C

then B cannot = C


*except at exactly one value of latitude
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Old 11-02-2013, 15:24   #37
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Re: Coordinate Math Question

"If both lat and long use the same common dimension (1 NM=1/60 degree)"
Those [lat & lon] are not dimensions. They might better be called orientations, or some other term. And where, in what context, have you ever seen either of them formally defined with an assignment of nautical miles to degrees?

Really, Bowditch, or Mixter's Primer of Navigation, or some other formal grounding pays off if you want to navigate. It is frightening, but when the light bulb goes off and you realize spherical trigonometry serves a purpose and nothing else will do the same job, it all starts to make sense.

Or, it never makes sense, and eventually you run aground.
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Old 11-02-2013, 15:46   #38
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Re: Coordinate Math Question

(I was typing this while hello was posting)

I re-read your post again more carefully and I think I spotted your misapprehension:
<<If both lat and long use the same common dimension (1 NM=1/60 degree)>>

Not true. Distances in the lat and long directions use a common scale, which could be expressed as 1NM= x.xxx mm, on a mercator chart; but the lat and long scales will not resemble each other, increasingly as you move away from the equator.
It is only the Lat scale for which 1 NM=1/60 degree holds true

The 'squares' on the globe become increasingly 'keystone' shaped, to use digital projector terminology, as the poles are approached.

You could think of Mercator as correcting the keystone effect, back to squares, by distorting the true shapes. This becomes so problematic near the poles that charts in very high latitudes can no longer use Mercator with satisfactory results.

I attach a scrap which I've annotated showing the top RH corner of the chart covering the location where sailing vessels have most closely approached the geographic South Pole. There is clearly no way the same scale can be used for distance.

It must ALWAYS be the scale at the side - the scale for latitude
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Name:	Lat vs Long near Poles.PNG
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Old 11-02-2013, 17:38   #39
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Re: Coordinate Math Question

Lat and Long are ANGULAR measurements, not linear. They correspond to a linear measurement unit in the same way that a broken clock tells the correct time twice a day.
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Old 11-02-2013, 20:00   #40
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Re: Coordinate Math Question

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Originally Posted by shorebird View Post
The confusion results from the mercator projection. In a spherical representation, longitude cannot be measured the same as latitude... since the distance between them varies markedly as one moves North or South from the equator. since, with latitude, 1 minute equals one NM, the same cannot be true for longitude, since the spacing is near zero as one approaches the poles. Since the spacing for longitude is the same as latitude at the equator, this appears to me to be the only place where a minute is a mile. If I understand the complexities of the mercator, it seeks to keep the scale the same, and thus either one changes the definition of a nautical mile, or the geography must distort to accomodate, and consulting my original sailing manual, that is indeed the case, as it references the geographic distortion that increases as one approaches the poles. In the scale marine charts use, the distortion is likely minimal, but does indicate some shortcomings in any method compressing 3 dimensions into 2. But, lets get back to the part confusing me. If both lat and long use the same common dimension (1 NM=1/60 degree) then why, using a mercator chart, can't one use the scale for both, instead of just the lat scale?
The geography IS distorted on a mercator map- any mercator map of the world will show you that. Greenland is NOT that big.
Mercator maps are compromises. but Distortion is less as the scale increases. ie: as it covers a smaller area........
xtra info: Often the mercator map will give you a central latitude around which top and bottom are distorted to straighten those longitude lines! so obviously using the horizontal scale from the map edges must be distorted . Plus, the central latitude needn't even be on your map, by the way.
Anyways, You can't use the "horizontal" scale much on a globe either so get over it.

As you go far north,plain-jane Mercator gets pretty ugly because of the increasing distortion caused by beating the orange-slice-like longitude at the poles flat and a different projection is used.

Google is your friend. Look up map projection or the like to see the various ways cartographers flatten the earth but keep it accurate.
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Old 11-02-2013, 21:39   #41
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Re: Coordinate Math Question

The borders of the two charts I use, 18446 and 18449 are both laid out in degrees, minutes and seconds.

On both charts, there are separate scales for yards and nautical miles. The nautical miles on those scales are laid out in tenths of a mile. Those scales run horizontally at the bottom and the top of the charts.

There is no tenths of a minute scale on either latitude or longitude.

Both latitude and longitude borders have separate scales for minutes and seconds.

You can plot distance against the latitude scale, or you can use the distance scale provided. You do not use the distance scale vertically, nor, therefore, is the vertical scale the only scale to use when measuring distance.

I am not measuring distance.

I am laying out waypoints, by distance and bearing from a known point, and looking for accurate latitude and longitude for those waypoints.

Being a carpenter by trade, I know how accuracy diminishes every time a dimension is laid out. There are at least four primary ways inaccuracy is created every time a dimension is laid out. There is also half a dozen more mistakes that most people make when laying out dimensions. Not to mention that mistakes appear to be an art, and a creative person can invent any number of ways to lay out dimensions inaccurately while maintaining an appearance of stringent accuracy. That is why dimensions are calculated rather than laid out on large projects, or when precision matters.

Therefore, I am reluctant to lay out and then measure-- that is the source of many an apprentice's error. The folks on my crews who would lay out and measure, or measure a scaled drawing were the same folks who would tell me there are nine cubic feet in a cubic yard. I never let them order the concrete. In fact, by the end of my career, as the projects grew in size, I calculated and ordered all the concrete personally.

It strikes me that perhaps most of you learned to do this so long ago you've forgotten how to explain it. Or, since explaining it is quite different from knowing it, you never knew how to explain it. Teaching is a separate skill, and a very difficult one to master. As this thread demonstrates. In light of that, perhaps I should re-phrase my question.

Is there anyone here who can teach how to lay out points on a distance and bearing mathematically from a known point?
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Old 11-02-2013, 21:42   #42
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Re: Coordinate Math Question

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Lat and Long are ANGULAR measurements, not linear. They correspond to a linear measurement unit in the same way that a broken clock tells the correct time twice a day.
The clock analogy is hyperbole, and frankly fanciful. Beyond growley, I would have thought.


A broken clock is completely useless, whereas the approximation that takes 1nm to be a minute of latitude is completely satisfactory.

Most people do not even know, or ever need to know, that it's an approximation.

A fair comparison would be with a clock whose time keeping varies either side of standard time by a few seconds in the course of a day, but nevertheless keeps time within a few seconds over the long term.

- - - -

If you're a practical navigator in a smallish boat, using paper charts, how would YOU suggest measuring or plotting a distance off, a DR distance for a running fix, or any linear distance measurement, expressed in nautical miles?

I would go to the side of the chart. If I was in deep latitudes, I would be careful to go to the side of the chart midway between the latitudes of the two ends of the line whose distance I was establishing.

I have not thought this worth mentioning hitherto, but I perhaps should have, because the kludge inseparable from any Mercator-type projection, which is implied by the earlier posts, will have been puzzling those paying close attention.

I need to confess that I was fudging when I referred to a scale of 1nm= x.xxmm:
there is no such unique scale factor on ANY Mercator chart, although the lack is absolutely imperceptible on any small scale chart anywhere near the equator.

Here's why:

I have amended my scrap of chart to show the bottom corner of the deep south chart posted above. I hope the annotations will make my point clear. Pondering the previous posts will probably provide the raw material to work out why.

Anyone who is particularly interested in this topic should note that this chart, because depths are in metres, also includes a scale graduated in kilometers, outside the Lat scale. The top can just be seen in my scrap.
The graduations, much like the longitude scale, expand as you travel south.

However THIS scale extends only half way down the chart. Which makes it useful only for that top half.


Growley's contention relates to something altogether more subtle variation, which is this (correct me if I'm wrong, please!)

Separate from (but additive to) the Mercator issue illustrated on the attached scrap, there's a reason the angle subtended at the centre of the earth CANNOT be used as a highly accurate length standard: the earth flattens towards the poles.

I made a solid model once to see how visible it was, and the answer is: not much.

- - - - - - - -

I would turn Growley's contention, for PRACTICAL PURPOSES, around, like this:

A nautical mile is NOT, for general small vessel navigation, using paper charts OR celestial position fixing, a distance measure: it should be thought of as a measure of angle, renamed.

Which is why it's ridiculous for armchair sailors to talk of "metrication of the nautical mile": it's not in any practical sense an imperial measure, any more than 360 degrees in a circle is.

When you plot celestial sight reductions, you plot the intercept on the EXPLICIT basis that one minute of angle, subtended at the centre of the earth, represents a nautical mile.

If you're trying to position a salvage crane over a blowout preventer on an aborted drill string, Growley's point is valid: you might need to correct for the oblate spheroid, and even for local bumps on that idealised shape, if you determine that the latter discrepancy will be problematic.

There is a table in Nories (and presumably Bowditch) which simplifies the (former) correction required for the small variation in the distance subtended by a minute of LATITUDE as you travel away from the equator.
In the southern hemisphere you really don't ever need to worry about it: there's too much land in the way to get far enough south.

My copy of Nories is currently in a shipping container: my library was in the mezzanine of my workshop which collapsed in a recent earthquake, so I can't check the exact discrepancy, but from memory it was less than 1%, and that's AT THE POLE.

Presumably the scale in kilometres I was dissing above actually takes account of this, in which case ALL THE MORE REASON for it to extend right to the bottom of the chart (sigh....)

97% of sailors don't know that a minute of latitude is not EXACTLY the same thing as a nautical mile, and 99 percent won't ever need to ... at least that's my guess. Start a poll if you want to prove me wrong, I'd be interested to know.

(Note that my figure implicitly excludes people who didn't know of any such relationship, or who thought it applied equally to longitude)
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Old 11-02-2013, 21:59   #43
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Re: Coordinate Math Question

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The two charts I use, 18446 and 18449 are both laid out in degrees, minutes and seconds.

On both charts, there are scales for yards and nautical miles. The nautical miles on those scales are laid out in tenths of a mile. Those scales run horizontally at the bottom and the top of the charts.

There is no tenths of a minute scale on either latitude or longitude.

Both latitude and longitude borders have separate scales for minutes and seconds.

.....
Being a carpenter by trade, I know how accuracy diminishes every time a dimension is laid out. There are least four primary ways inaccuracy is created every time a dimension is laid out. That is why dimensions are calculated rather than laid out on large projects, or when precision matters.

....

Is there anyone here who can teach how to lay out points on a distance and bearing mathematically from a known point?
If you want to do it mathematically, you already have at least one correct answer. (the trick is, deciding which one, but asking for even more seems likely to compound the problem of: "too much information".

I suggest picking the one you most NEARLY understand, and PM them. Try their method, lay it out on the chart, and compare results.

I personally don't think you should concentrate on accuracy for small boat navigation in the same way as laying out a construction: even GPS has appreciable error, and there's not much point being ten times as accurate with your plotting. Charts are also riddled with misplaced dangers: if you kid yourself that you can thread the needle you'll find that out the hard way. If you're going to keep amply safe margins, it simply doesn't matter if you're a pencil line or two from where theory suggests.

I convinced myself, early on, that in a small boat, it's far preferable to be approximately right* than to be exactly wrong.

*(and KNOW that it's only approximate)

Donning flame proof suit now (sigh....)

- 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0

To anyone with a similar problem who DOES want to solve it the quick, easy and reliable way: (by plotting on the chart):

(I don't have any US charts to check these points): If they don't show tenths of a minute on the latitude scale, they clearly belong to a different school of thought from the Admiralty charts used in most of the rest of the English speaking world.

Are the scales at top and bottom EXACTLY the same length overall?
It will depend what latitude you're in)

If they're different, I would personally use the scale at the top for plotting in the top half, and at the bottom for the bottom half.
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Old 11-02-2013, 22:30   #44
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Re: Coordinate Math Question

Jammer Six:

Thinking about your question: Better still, get a good "Practical Navigation for Small Boats" text, written for your US-only situation, which covers such topics in a clear and simple way.

I really don't think a www forum is a satisfactory resource for this sort of learning.

It's so hard to evaluate the quality of the advice, unless you already know enough that you don't actually need it.

And you tend to get flooded with quantity, which is no substitute.

(And you get fights among crusty curmudgeons breaking out on the sidelines, like the one I just started, which add NOTHING to the thread from your point of view, and for which on this occasion I apologise.)
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Old 12-02-2013, 03:51   #45
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Re: Coordinate Math Question

Andrew ... The question as phrased by the OP is not formed properly. (The OP can ignore this academic exercise) There is no correct answer.s Frankly, I'm surprised you have not remarked on this in your exhaustive commentary. As GrowlyMonster sagely pointed out the units of yards and degrees are incompatible. Also the bearing is ambiguous as we do not know if said bearing was sighted from the buoy to the point or v/v. Indeed a point plotted 200 yards WEST of a buoy might at the same instant observed to be NORTH of the buoy, no?
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