Trigonometry question...

[dougdaniel]

Originally Posted by StuM

????? I was talking about a minute of longitude v NM! As I said it gets smaller as you move poleward.

I see. If I were to measure the distance between longitudes in minutes, I would use latitude. Since I am only interested in distance in nautical miles, I use minutes of longitude taken from the longitude markings on the chart. I have never found any reason to measure the distance between lines of longitude since it has no value that I know of.

Certainly a minute of latitude is less than a nautical mile where I have sailed.

If you believe that the distance between lines of longitude is called longitude and not lattitude, then I think the only thing we can agree on is that we disagree.

All the best to you in your future navigation.

[StuM]

Originally Posted by dougdaniel

I see. If I were to measure the distance between longitudes in minutes, I would use latitude. Since I am only interested in distance in nautical miles, I use minutes of longitude taken from the longitude markings on the chart. I have never found any reason to measure the distance between lines of longitude since it has no value that I know of.

Certainly a minute of latitude is less than a nautical mile where I have sailed.

If you believe that the distance between lines of longitude is called longitude and not lattitude, then I think the only thing we can agree on is that we disagree.

All the best to you in your future navigation.

You are not making sense!

The Latitude markings are the number which run up to sides of your chart.
The Latitude lines are the horizontal lines running across the chart.
The Longitude markings are the numbers which run across the top and bottom of your chart. The Longitude lines are the vertical lines running up and down the chart.


Say for argument's sake that I am at Long 0° Lat 0°.

If I move 1 degree of Latitude due north. I am now at Long 0° Lat 1°N
My longitude has not changed but my latitude has - by 1 degree. I have moved approximately 60NM

If I move 1 degree of Longitude due East, I am now at Long 1° Lat 0°. My Longitude has change by 1 degree but my latitude has not.
I have moved approximately 60NM


Now let's do the same thing starting at Long 45°N Lat 45°E

If I move 1 degree of Latitude due north. I am now at Long 45°E Lat 46°N
My longitude has not changed but my latitude has - by 1 degree. I have moved approximately 60NM

If I move 1 degree of Longitude due East, I am now at Long 46°'E Lat 45°N. My Longitude has change by 1 degree but my latitude has not.
I have moved approximately 40NM

So to reiterate.
I degree of Latitude = 60NM regardless of where you are.
1 degree of Longitude varies in length according to latitude.

Edit - Initial post mixed up degrees and minutes

[secrabtree]

What we have here is a very common misunderstanding. I didn't realise how common that misunderstanding is until I taught navigation in college.


A line of constant longitude (often lazily shortened to longitude) is a great circle going through the poles. Since all lines of constant longitude meet at the poles the measurement between them varies from a maximum at the equator to zero at the poles. "Longitude" is the term used for the measurement between the lines of longitude, that line of longitude going through Greenwich is the "Prime Meridian" (meridian also being another name for a line of constant longitude). The longitude of any particular point on earth is considered to be the angular measurement between the Prime Meridian and the meridian going through that point.


A line of constant latitude is a line (not a great circle, parallel to the equator, called a parallel. The latitude of any particular point on earth is the angular measurement between the equator and the parallel going through that point.


So Longitude is measured between the meridiansl (lines of longitude) along the parallel (line of latitude).


And latitude is the angular measurement between the equator and the parallel going through the point along a meridian.


By convention a minute of latitude or longitude, or any minute along a great circle, any great circle. Most commonly the only great circles that appear on the chart, the meridians and the equator. And because the earth is not a true sphere these minutes of a great circle vary in length by a small amount. That amount is almost always insignificant for marine navigation, offhand I cannot think of an exception.

[StuM]

> By convention a minute of latitude or longitude, or any minute along a great circle, any great circle.

You may like to rephrase that. I don't know what you meant to say.

[monte]

These links may be worth a quick browse to clarify the above comments
http://en.m.wikipedia.org/wiki/Mercator_projection
http://boatsafe.com/navigation/divide1.htm

[OldFrog75]

dd, I don't know where you sail since there is no information with your screen name but you can test this empirically with a local chart.

If you use your dividers to measure 1 minute of latitude along the vertical scale on your chart and then compare it to the horizontal longitude scale at the top of your chart, you should see a difference in degrees, minutes, or seconds; perhaps insignificant but a difference nonetheless.

Likewise, if you use your dividers to measure the distance between two points on the chart and then compare that to the latitude and longitude scales, you should see a difference in the degrees, minutes, or seconds between the two.

These differences become more pronounced the further away from the equator you go, hence most people use the latitude scale to determine minutes and seconds of distance and then convert that to nm.

Or maybe we're all saying the same thing and something is getting lost in the translation...

[secrabtree]

Thank you StuM. Yes I would like to refraise.
By convention a minute of latitude or longitude, or any minute along a great circle, any great circle is considered a nautical mile.
And, of course because of the irregular shape of the earth, the conventional nautical mile does vary. The amount of variation is not really significant for navigation of small boats. But because humans don't seem to like unknowns, we humans have defined the nautical mile as a certain number of meters.

[Blue Stocking]

The answer is Creamy Peanut Butter, but Chunky is close enough.

[secrabtree]

Originally Posted by Blue Stocking

The answer is Creamy Peanut Butter, but Chunky is close enough.

That's the answer, but what is the question?

[StuM]

Originally Posted by secrabtree

Thank you StuM. Yes I would like to refraise.
By convention a minute of latitude or longitude, or any minute along a great circle, any great circle is considered a nautical mile.
And, of course because of the irregular shape of the earth, the conventional nautical mile does vary. The amount of variation is not really significant for navigation of small boats. But because humans don't seem to like unknowns, we humans have defined the nautical mile as a certain number of meters.

Aaaaah!

Delete the two words in red and you are correct. A minute of Longitude is NOT a nautical mile by convention unless it is at the equator since in all other cases it is a measurement around a line of latitude (a parallel) which is not a great circle.

[StuM]

Originally Posted by monte

These links may be worth a quick browse to clarify the above comments
Mercator projection - Wikipedia, the free encyclopedia
How to use dividers and a nautical chart

Thank you for the second link in particular. Well worth reading for those who still think that a minute of longitude is a nautical mile and/or that tehy use the Longitude scale on a chart for dsitance.

"Using dividers and the latitude scale on your nautical chart, you are able to measure distance in nautical miles. (Remember, do not use longitudes to measure distance. Longitude lines converge at the poles and the distance between them changes relative to your position on the earth.)"

[secrabtree]

StuM - Please note that I said "along a great circle". With that provision, a minute of longitude if measured along a great circle alsi fits the conventional definition of a nautical mile - since the only great circle upon which one can measure a minute of longitude just happens to be the equator. So my statement is true. But, since most charts do not include the equater, it is probably best to exclude any reference to longitude.

[StuM]

Originally Posted by secrabtree

StuM - Please note that I said "along a great circle". With that provision, a minute of longitude if measured along a great circle alsi fits the conventional definition of a nautical mile - since the only great circle upon which one can measure a minute of longitude just happens to be the equator. So my statement is true. But, since most charts do not include the equater, it is probably best to exclude any reference to longitude.

My apologies. I see what you meant now. Compound sentences with multiple commas can sometimes make it difficult to determine the writers real intention.

I interpreted this as three separate cases, not two cases with the second one qualified by a subordinate phrase.
"a minute of latitude or longitude, or any minute along a great circle"