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Author
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Topic: Plotting Sheet Errors?
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engsolnorm
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posted June 02, 2006 10:52 AM
The course manual suggests finding the +40 and
-40 points on the center degree wheel,
then drawing a short line North and South to creat a (short) longitude line to the right of the
center longitude line.
I've never had much luck extending a short line into a long one with much accuracy
using a straight-edge.
My procedure (unless there's a reason I shouldn't do this) is to use a straight-edge to line up
the +40 and -40 points on the center degree wheel, and mark where the straight-edge
crosses the center Latitude line. Then I set a pencil compass to the distance between that
mark and the center Longitude line.
Then I go to the top of the plotting sheet (to the top-most Latitude line), and place the
compass needle point on the intersection of the top-most Latitude line and the center Longitude line,
and swing an arc both left and right, crossing the top-most Latitude line, (42 N(twice, actually))
The, without changing the pencil compass setting, I do the same thing at the bottom of
the plotting sheet, but using the lower-most Latitude line, (38 N)
Then I use the straight-edge to draw a vertical line from the top-most point to its
corresponding lower-most point, and I have my Longitude lines.
In short, I've transfered the distance found in step 1 to the top and bottom of the plotting sheet.
Is this accurate? Yes, and no. The course text suggests that this is close enough. But to be more
exact the spacing between the Longitude lines at the top (and bottom) should be cos Lat * 60.
Given the example in the book, this works out to be
Top Lat line = 42 degrees North. cos 42 = .74314, times 60 equals 44.59 nautical miles, between lines of Longitude at this Latitude.
Bottom Lat line = 38 degrees North. cos 38 = .7880, times 60 equals 47.28 nautical miles,
a difference between top and bottom of about 2.69 nautical miles.
Clearly showing that the lines of Longitude are not parallel, and should be drawn slightly
converging at the top of the plotting sheet.
Even at the center Latitude, 40 degrees North in this case, setting the dividers to 30 mintutes,
using the funny little chart in the lower right corner of the plotting sheet, the distance between
123 W and 122W (as well as 123W and 124W)is something less than two hops of the dividers.
If I'm assured that these apparent errors are not significant in the "real world", I'll
ignore them. Or did I totally FUBAR the concept?
Thanks,
Norm
From: Oregon
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David Burch
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posted June 03, 2006 02:05 PM
This is an interesting observation. Thanks for working out the details and posting them. A first guess from this might be that fixes could be off some 2.7 miles or so using this plot, but i do not think that is the case.
we have a spacing at 40°N of 60xcos40 = 45.96 miles. At the top or bottom of the page this differs by about 1.35 miles. Thus relative to the center, the top or bottom of the page has a longitude scale that is in error by 1.35/45.96 = 2.9%.
We will always be measuring our fix longitude relative to the nearest meridian, and so the largest line segment we would measure is less than 30' of longitude, and 2.9% of 30 = 0.87'.... but this is the worst possible case.... ie at the very top of the page, getting a fix exactly in the middle of two meridians.
If your fix was just halfway up the page, you have 1.4% and if the fix were within 15' of the nearest meridian (statistically the most likely case) then you have a scale error of 0.2' of longitude which is within the plotting errors in general.
So i think we are OK with this scheme.
Does this logic make sense? I must admit to not having thought on this issue before. Thanks again for bringing up the point.
=======
Your plot method, by the way, is a good way to do it and likely safer than just extending the center segment, but once you have the ruler lined up with top mark and bottom mark, you could just draw in the full line if the ruler is long enough.... partly why we recommend the W77 Ruler in our suggested tools pak.
From: Starpath, Seattle, WA
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