LOP plotting question

[BigBill]

When you plot your TOWARD or AWAY distance, do you account for the change in distance between degrees of longitude? For instance, if you were plotting T or A of  10' east to west, do you plot it at the full 10 nautical miles or would you compensate for the narrowing of longitude lines away from the equator? Whereas when plotting T or A north to south you would plot 10' as 10 NM.

I have been using full values when the azimuth is within about 25 ° of E or W and compensating for greater angles. Not sure if it's helping or hurting or even makes a difference.    

I hope the question makes sense, I've had a couple of glasses of wine. :)

[CarlosPindle]

BigBill,

No, I don't. However, I was reading last night in Pub. No. 229 vol 1. page xv (pdf page 16) and found "C. Special Techniques" and section "1. Adjustment of Straight Line of Position."

Section "2. Interpolation for Latitude and Local Hour Angle."

Those techniques may be able to help.

See here in volume 1- https://thenauticalalmanac.com/Pub229Vol1.pdf#page=18

Carlos

[pabrides]

When you plot your TOWARD or AWAY distance, do you account for the change in distance between degrees of longitude? 

Darn-it, Bigbill... you just made me doubt my own work - great question.  I have been using great circle distance and use latitude to ascertain distance. (Using distance from right or left margin.)  In other words I use full nautical miles without compensation for divergence (or convergence) of latitude. But then again I live at 10 degrees north and do all my observations here where there is not much difference between true Nautical miles and max seconds of longitude in meters which vary with latitude..

[Rumata]

When you plot your TOWARD or AWAY distance, do you account for the change in distance between degrees of longitude? 

Darn-it, Bigbill... you just made me doubt my own work - great question.  I have been using great circle distance and use latitude to ascertain distance. (Using distance from right or left margin.)  In other words I use full nautical miles without compensation for divergence (or convergence) of latitude.  But then again I live at 10 degrees north and do all my observations here.  There is not much difference between true Nautical miles and max seconds of longitude in meters which vary with latitude..

I found the technique described in Mixter, 1942, article 195, how to make your own plotting sheet helpful. In particular, on page 108, it says "...the diagonal gives the scale of latitude OR DISTANCE FOR USE ANYWHERE ON THE PLOTTING SHEET." On the UPS lattitude scale looks reasonable.

[Fred_B]

Rumata,

Can you explain what that means?

Thanks,

Fred

[pabrides]

Fred_BRumata,
Can you explain what that means?  
Thanks,
Fred

I think what he means, Fred, is that if you take a compass rose and make (for example) the radius one degree at the equator, then draw a diagonal (hypotenuse) to any degree up from 90 (say 45 degrees) from the rose center to the circumference edge, and then draw a vertical line down from that point to the 90 horizontal line where it and the line you just drew (side opposite) form a right triangle, the line length along the side adjacent (90 degree line) then represents the scale of longitude (one degree) at 45 degrees north or south latitude on the globe....  For me it is more entertaining to use this method to scale longitude than to use the curved lat/long scale associated with all printed work sheets where the scale is drawn for you.  You may then also take any length in minutes (and seconds if the scale is sufficiently large) .   I did my best... :) 

I always assumed that if a measurement in nautical miles or knots (say boat speed) is required, I use full knots as measured along any great circle line of longitude irregardless of latitude; but if a measurement is called for in degrees, minutes, and seconds (such as in the trig) I then use the method described above to ascertain the length of degrees of longitude at higher latitudes. I hope this made sense.
joe

[BigBill]

Diagrams would sure help in a discussion like this. :)

[Rumata]

Rumata,

Can you explain what that means?  

Thanks,

Fred

Gentlemen, below is the long citation from Mixter which explains , I hope, the method

"...Place the paper with the ruled lines vertical. Near the lower edge draw a horizontal line to represent the parallel of lattitude (let's make a plotting sheet for a small area  north and west of 35 deg. N, and 70 deg. West) 35 deg N. Near the right-end of this selecta point where it intersects a vertical line and label the point  35 deg N and 70 deg. W. Westward, to the left, label each 10' of longitude and blacken the vertical lines which represents the meridians through these points. The ruling of the paper may indicate that the space between the vertical lines should represent 2' or 3' of longitude. Avoid a scale of less than 1/8" per 1' of longitude.

To complete a plotting sheet, parallels of lattitude must be drawn. As it is a Mercator projection, the lattitude scale will be greater than the longitude scale, the increase depending on the lattitude. To locate the 10' parallel, draw a line from a point on the parrallel already drawn, such as 70deg30' W, with the line making an angle with the horizontal equal to the latitude, or 35 deg.N in this instance. The length of this line between the vertical lines labeled 30' and 20' is the required space between the 0' and 10' parallel and the 10' parallel is drawn accordingly.

For practical purposes the same spacing may be used to draw the parallels of 20' and 30', or any other 10' interval within 1 deg of the lattitude used as the angle for drawing the diagonal line. When marked at the points where it intersects each vertical line, the diagonal gives the scale of latitude or distance for use anywhere on the plotting sheet. ..."

---

Fred_BRumata,
Can you explain what that means?  
Thanks,
Fred

I think what he means, Fred, is that if you take a compass rose and make (for example) the radius one degree at the equator, then draw a diagonal  (hypotenuse) to any degree up from 90 (say 45 degrees) from the rose center to the circumference edge, and then draw a vertical line down from that point to the 90 horizontal line where it and the line you just drew (side opposite) form a right triangle, the line length along the side adjacent (90 degree line) then represents the scale of longitude (one degree) at 45 degrees north or south latitude on the globe....  For me it is more entertaining to use this method to scale longitude than to use the curved lat/long scale associated with all printed work sheets where the scale is drawn for you.  You may then also take any length in minutes (and seconds if the scale is sufficiently large) .   I did my best... :) 

I always assumed that if a measurement in nautical miles or knots (say boat speed) is required, I use full knots as measured along any great circle line of longitude irregardless of latitude; but if a measurement is called for in degrees, minutes, and seconds (such as in the trig) I then use the method described above to ascertain the length of degrees of longitude at higher latitudes.  I hope this made sense.
joe

Gentlemen, below is the long citation from Mixter which explains , I hope, the method

"...Place the paper with the ruled lines vertical. Near the lower edge draw a horizontal line to represent the parallel of lattitude (let's make a plotting sheet for a small area  north and west of 35 deg. N, and 70 deg. West) 35 deg N. Near the right-end of this selecta point where it intersects a vertical line and label the point  35 deg N and 70 deg. W. Westward, to the left, label each 10' of longitude and blacken the vertical lines which represents the meridians through these points. The ruling of the paper may indicate that the space between the vertical lines should represent 2' or 3' of longitude. Avoid a scale of less than 1/8" per 1' of longitude.

To complete a plotting sheet, parallels of lattitude must be drawn. As it is a Mercator projection, the lattitude scale will be greater than the longitude scale, the increase depending on the lattitude. To locate the 10' parallel, draw a line from a point on the parrallel already drawn, such as 70deg30' W, with the line making an angle with the horizontal equal to the latitude, or 35 deg.N in this instance. The length of this line between the vertical lines labeled 30' and 20' is the required space between the 0' and 10' parallel and the 10' parallel is drawn accordingly.

For practical purposes the same spacing may be used to draw the parallels of 20' and 30', or any other 10' interval within 1 deg of the lattitude used as the angle for drawing the diagonal line. When marked at the points where it intersects each vertical line, the diagonal gives the scale of latitude or distance for use anywhere on the plotting sheet. ..."

[pabrides]

Diagrams would sure help in a discussion like this. :)

https://en.wikisource.org/wiki/File:APN2...e2603b.png

This example is 40 north or south (from American Practical Navigator), however, i always start with drawing the center horizontal and vertical lines at the center of the page - it gives me a better frame of reference, then the circle is added with the aid of a circle drawing tool (adjustable compass), but the following directions are good too.

Step one: At the center of the sheet draw a circle with a radius equal to 1° (or any other convenient unit) of latitude at the desired scale. If a sheet with a compass rose is available, as in Figure 2603b, the compass rose can be used as the circle and will prove useful for measuring directions. It need not limit the scale of the chart, as an additional concentric circle can be drawn, and desired graduations extended to it.

Step two: Draw horizontal lines through the center of the circle and tangent at the top and bottom. These are parallels of latitude; label them accordingly, at the selected interval (as every 1°, 30', etc.).

Step three: From the center of the circle draw a line making an angle with the horizontal equal to the mid-latitude. In Figure 2603b this angle is 40°.

Step four: Draw in and label the meridians. The first is a vertical line through the center of the circle. The second is a vertical line through the intersection of the oblique line and the circle. Additional meridians are drawn the same distance apart as the first two.

Step five: Graduate the oblique line into convenient units. If 1' is selected, this scale serves as a latitude and mile scale. It can also be used as a longitude scale by measuring horizontally from a meridian, instead of obliquely along the line.

(Steps four and five also apply to printed plotting sheets)

[Rumata]

Diagrams would sure help in a discussion like this. :)

Big Bill, just attached the scan

[Rumata]

Diagrams would sure help in a discussion like this. :)

Big Bill, just attached the scan

That was Pabrides who attached the scan and instructions..... :)

I attached the scan but unfortunately its size was more than permitted by the site, and it didn't show up.  Pabrides instructions are from Practical NAvigator.  I provided the long citation from Mixter "Primer of NAvigation." With the help of Sysadmin ( big thanks to him) the photo is attached  and you can see it.

[BigBill]

Excellent. Thanks.