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#1
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No. Straight lines on Lambert Conformal maps are not great circles.
It's my understanding that the Lambert Conformal is better than any other flat surface at representing the curved surface of the earth in such a way that a straight line on the chart comes very close to being a Great Circle. Any straight line through the exact center of a chart, regardless of direction, will be precisely a Great Circle. A line across a corner of the chart will be the poorest representation of a Great Circle, but still "good enough for government work." Probably as close as the average GA pilot can hold a course, anyway. vince norris |
#2
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Are sectional paths correct across "long" distances?
Awhile ago I pointed out in rec.aviation.piloting that one of my
tools will generate a map using stitched sectionals for a given route. http://groups.google.com/groups?hl=e....edu.au#link10 Ben Jackson mentioned that it didn't look correct to just draw a straight line between two points so far away (across multiple sectionals). I have looked into it a few times but I haven't come up with a definitive answer. So...anyone know the answer? Pilots are certainly accustomed to drawing straight lines on a sectional to find the shortest path between two points, and I've never been taught to do anything other than align sectionals by sight to plan multi-sectional flights. Does this not work over long distances? One path I know fairly well is LAF-MER. The Great Circle path happens to go right near Denver (where I usually stop). If that path is plotted as a straight line on the sectionals https://aviationtoolbox.org/Members/...selected.x=411 it appears to follow the path I'd expect. https://aviationtoolbox.org/Members/...selected.x=427 Also, there's an easily-identified area on that path where Iowa, Illinois, and Missouri meet. Take a look at the Great Circle route. http://gc.kls2.com/cgi-bin/gcmap?PAT....380N+120.568W Again, this seems to match the area on the straight-line path drawn on the sectional. https://aviationtoolbox.org/members/...selected.y=324 Anyone know for sure whether or not this is an accurate way of depicting Great Circle paths in the conUS? Thank you. --kyler |
#3
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In a previous article, Kyler Laird said:
Anyone know for sure whether or not this is an accurate way of depicting Great Circle paths in the conUS? No. Straight lines on Lambert Conformal maps are not great circles. We use it normally because within one section it doesn't make a huge difference, but if you're crossing several, the errors add up. -- Paul Tomblin http://xcski.com/blogs/pt/ "Pilots are reminded to ensure that all surly bonds are slipped before attempting taxi or take-off" |
#4
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vincent p. norris writes:
Any straight line through the exact center of a chart, regardless of direction, will be precisely a Great Circle. A line across a corner of the chart will be the poorest representation of a Great Circle, but still "good enough for government work." Probably as close as the average GA pilot can hold a course, anyway. I decided to finally test this. I drew Great Circle segments on top of the straight line path. The difference is small but significant. https://aviationtoolbox.org/Members/...=1453666.76955 (The yellow line is straight. The red is made of ten GC segments.) Time to start using GC calculations... --kyler |
#5
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"Kyler Laird" wrote in message news:h2sei1- So...anyone know the answer? Pilots are certainly accustomed to drawing straight lines on a sectional to find the shortest path As a technical matter, the only chart projection on which a drawn straight line is a great circle is a gnomonic. These are rarely used, particularly over large areas, as they show about as much distortion as the standard Mercator we all grew up with (remember thinking that Greenland was about twice the size of the US?). The Lambert Conformal projection, however, is made such that a straight line, while not precisely a great circle, is so close that the differences are inconsequential. Oceanic plotting charts used in aviation to monitor navigation progress are Lamberts. The standard oceanic enroute chart is a Mercator, but the plotting chart is Lambert. Sectional charts are also Lamberts,iirc. So, the short answer to your question is, just lay out the line, and go. Note, though, that the straight line on your patched sectionals will require you to alter heading periodically. JG |
#6
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"John Gaquin" wrote in message ... "Kyler Laird" wrote in message news:h2sei1- So...anyone know the answer? Pilots are certainly accustomed to drawing straight lines on a sectional to find the shortest path As a technical matter, the only chart projection on which a drawn straight line is a great circle is a gnomonic. These are rarely used, particularly over large areas, as they show about as much distortion as the standard Mercator we all grew up with (remember thinking that Greenland was about twice the size of the US?). The Lambert Conformal projection, however, is made such that a straight line, while not precisely a great circle, is so close that the differences are inconsequential. Oceanic plotting charts used in aviation to monitor navigation progress are Lamberts. The standard oceanic enroute chart is a Mercator, but the plotting chart is Lambert. Sectional charts are also Lamberts,iirc. So, the short answer to your question is, just lay out the line, and go. Note, though, that the straight line on your patched sectionals will require you to alter heading periodically. JG "the straight line on your patched sectionals will require you to alter heading periodically" precisely because you will be flying close to a great circle route, which requires a constantly changing heading. Harvey |
#7
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"John Gaquin" wrote in message ... As a technical matter, the only chart projection on which a drawn straight line is a great circle is a gnomonic. A straight north-south line is a great circle on all the common chart projections. |
#8
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Any straight line through the exact center of a chart, regardless of
direction, will be precisely a Great Circle. A line across a corner of the chart will be the poorest representation of a Great Circle, but still "good enough for government work." Probably as close as the average GA pilot can hold a course, anyway. I decided to finally test this. I drew Great Circle segments on top of the straight line path. The difference is small but significant. That's a very interesting chart, Kyler. I can't see the red GC line very well except against the dark brown of the higher elevations; but it seems as if the two lines are only about a line-width apart. I wouldn't consider that "significant," but of course that's a personal judgment. My reaction is the opposite of yours: I'm impressed by how well the straight line follows a Great Circle. Can you tell me how many nautical miles separate the two lines, at the point of widest divergence? Thanks. vince norris |
#9
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"Steven P. McNicoll" wrote in message A straight north-south line is a great circle on all the common chart projections. Correct. Those are the two [possibly rare] exceptions to my post -- if you happen to be flying a course of true north or south anywhere, or a course of true east or west on the equator, then your course will layout as a straight line and will be a great circle on any chart projection. I probably should have mentioned it, lest someone get lost and run out of fuel. |
#10
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In article ,
(Paul Tomblin) wrote: In a previous article, Kyler Laird said: Anyone know for sure whether or not this is an accurate way of depicting Great Circle paths in the conUS? No. Straight lines on Lambert Conformal maps are not great circles. We use it normally because within one section it doesn't make a huge difference, but if you're crossing several, the errors add up. You've got to go pretty big distances before GC errors start to become significant. For example, to go from 38N/77W to 38N/122W (roughly Washington, DC to San Francisco, CA), the rhumbline is 270 and the GC is 284. 14 degrees on a coast to coast trip. If you're flying it nonstop in a jet, it makes sense to take that into account. For most of us flying spam cans, we just can't fly long enough legs for it to become significant. I just tried another one. From 38N/77W to 38N/100W is just under 1100 nm, or about the limit for the longest legged GA airplane I know of. Again, a rhumbline of 270, CG of 277 (7 degrees correction). For most of us, CG routes are just not something to worry about. |
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