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Thread: The Carolina Bays are conic sections

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    The Carolina Bays are conic sections

    If you create an ellipse with axes proportional to the length and width of a Carolina Bay, the ellipse will fit exactly.

    img-bowmore-nc.jpg

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    Closed pending clarification.

    Clarified: this thread is intended to discuss the geomorphology and geometry of the Carolina Bays and Nebraska rainwater basins. Related discussion about their origins must be consistent with currently accepted mainstream model(s).
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    Quote Originally Posted by citpeks View Post
    If you create an ellipse with axes proportional to the length and width of a Carolina Bay, the ellipse will fit exactly.

    img-bowmore-nc.jpg
    Exactly? For tens of thousands of bays? It doesn't even fit exactly the ones in your illustration??

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    I don't get the hoopla. They are elliptical, so I would expect them to be ellipses? Are you saying they all have the same proportions? That's not true across the whole breadth of the bays... for example, the ones in north Florida are nearly circular, I believe.

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    So, is there some meaning to this "miraculous" geometry? Aliens? Gods? Or just coincidence? As Grapes points out, not even all of the ones in your picture are anywhere near eliptical.
    Lots of geometry occurs naturally. Beehive cells are hexagonal. Planets are spherical, or nearly so. So are soap bubbles. Crystals form lots of lovely geometric shapes. What's your point? Sounds a bit ATM, to me.
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    The bays that have well defined margins can be fitted with ellipses. Here is another example from around Fayetteville, NC.

    img-carolina34.850-79.205.jpg

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    Quote Originally Posted by Trebuchet View Post
    So, is there some meaning to this "miraculous" geometry? Aliens? Gods? Or just coincidence? As Grapes points out, not even all of the ones in your picture are anywhere near eliptical.
    Lots of geometry occurs naturally. Beehive cells are hexagonal. Planets are spherical, or nearly so. So are soap bubbles. Crystals form lots of lovely geometric shapes. What's your point? Sounds a bit ATM, to me.
    I already had my say at an ATM Topic. This is strictly about the morphology. Planets are spherical for a reason, maybe the bays are elliptical for a reason also?

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    Yes. Because they are elliptical. So? There are any number of natural processes that can do this. I happen to think water and wind erosion/sediment transport fit best with the evidence. Have you read the research on the bays? I'm not an expert, but I'm at least a little familiar with it, so the fact that some are nearly "perfect" ellipses isn't really a big thing.

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    Quote Originally Posted by citpeks View Post
    The bays that have well defined margins can be fitted with ellipses. Here is another example from around Fayetteville, NC.

    img-carolina34.850-79.205.jpg
    Even the ones in that picture don't look like they could be fitted "exactly."

    Some look more like superellipses than ellipses.

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    Quote Originally Posted by grapes View Post
    Even the ones in that picture don't look like they could be fitted "exactly."

    Some look more like superellipses than ellipses.
    Working only in two dimensions, I am getting the images of the ellipses from Math Open Reference, which has an ellipse that can be adjusted:
    http://www.mathopenref.com/coordgeneralellipse.html

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    Quote Originally Posted by citpeks View Post
    This is strictly about the morphology.
    What about it?
    I see they are elliptical, but "exactly"? How do you define the exact location of the edges?


    I found this image which is an unmodified section of your picture.

    Looking at the craters that you obscured with your shading, we see that the lower (southern) edges of the craters have a gentle slope. How can you determine exactly where that edge lies?

    Quote Originally Posted by citpeks View Post
    Planets are spherical for a reason, maybe the bays are elliptical for a reason also?
    For vastly different reasons.
    What shapes would you expect from a crater?

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    Quote Originally Posted by citpeks View Post
    Working only in two dimensions, I am getting the images of the ellipses from Math Open Reference, which has an ellipse that can be adjusted:
    http://www.mathopenref.com/coordgeneralellipse.html
    I think most of us on this board know what an ellipse and conic sections are.

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    In areas where the bays are relatively unaffected by human activity, are they expanding or shrinking, becoming more round or more oval, more defined or less defined? Are new ones appearing where they did not exist before?
    Depending on whom you ask, everything is relative.

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    Quote Originally Posted by NEOWatcher View Post
    What about it?
    I see they are elliptical, but "exactly"? How do you define the exact location of the edges?

    I found this image which is an unmodified section of your picture.

    Looking at the craters that you obscured with your shading, we see that the lower (southern) edges of the craters have a gentle slope. How can you determine exactly where that edge lies?
    Determining the edge of a figure, whether done by algorithms or by humans, is always difficult. Determining the borders of the Carolina Bays will have the same problems that are encountered in determining the borders of Moon craters. It would be necessary to use consistent criteria. For the Carolina Bays, I would define the edge as the line just inside the sandy rim. I would not include the sandy rim.

    Quote Originally Posted by NEOWatcher View Post
    For vastly different reasons.
    What shapes would you expect from a crater?
    I suppose this is a test question. For an impact crater, the shape would depend on many factors, including the type of target and velocity and composition of the projectile, see for example Melosh 1989. For a volcanic crater, there is a lot of variability. In general, craters have circular shapes, but not always. If you had a crater in the form of tilted cone, the crater edge would be an ellipse. http://en.wikipedia.org/wiki/Ellipse

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    Quote Originally Posted by citpeks View Post
    For the Carolina Bays, I would define the edge as the line just inside the sandy rim. I would not include the sandy rim.
    But you didn't do that. You interpolated the it in some areas.

    Let's take your 16x24 ellipse for example.
    The rim area to the direct left of the intersection of your axis flows farther into the crater than your circle.
    The rim area immediately clockwise from that flow, there is a large flat area level with the floor of the crater that extends past the rim.

    So; how can you say "exactly"?




    Quote Originally Posted by citpeks View Post
    I suppose this is a test question. For an impact crater, the shape would depend on many factors, including the type of target and velocity and composition of the projectile, see for example Melosh 1989. For a volcanic crater, there is a lot of variability. In general, craters have circular shapes, but not always. If you had a crater in the form of tilted cone, the crater edge would be an ellipse. http://en.wikipedia.org/wiki/Ellipse
    You don't have to explain conic sections to me. My question is why is this formation worth discussing if an ellipse is a valid shape?

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    Quote Originally Posted by citpeks View Post
    Quote Originally Posted by grapes
    Even the ones in that picture don't look like they could be fitted "exactly."

    Some look more like superellipses than ellipses.
    Working only in two dimensions, I am getting the images of the ellipses from Math Open Reference, which has an ellipse that can be adjusted:
    http://www.mathopenref.com/coordgeneralellipse.html
    So, instead of "exact", did you mean "approximately"?

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    Quote Originally Posted by NEOWatcher View Post
    But you didn't do that. You interpolated the it in some areas.

    Let's take your 16x24 ellipse for example.
    The rim area to the direct left of the intersection of your axis flows farther into the crater than your circle.
    The rim area immediately clockwise from that flow, there is a large flat area level with the floor of the crater that extends past the rim.

    So; how can you say "exactly"?
    You have to take into consideration the illumination. The top edge is black, but the bottom edge is lighter in color making it appear to extend further. Is there anything in real life that is "exactly"? All actual measurements have their plus or minus uncertainty.


    Quote Originally Posted by NEOWatcher View Post
    You don't have to explain conic sections to me. My question is why is this formation worth discussing if an ellipse is a valid shape?
    Structures that are 99% elliptical are not encountered frequently in nature. The orbits of the planets, the Carolina Bays, ballistic trajectories, and maybe a few others. I think that the elliptical shape is significant compared to the shape of other terrestrial features such as the Alaskan lakes:
    alaska-lakes.jpg

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    So, it's clearly true that while not perfect ellipses, the Carolina Bays are pretty close to elliptical. And they're all aligned in pretty much the same direction, with the long axis northwest to southeast. It's a fascinating land formation.

    Rather than quibble about how precisely elliptical they are or are not, my question is, what significance are you ascribing to this, citpeks? Why are you bringing it up here?
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    Quote Originally Posted by mkline55 View Post
    In areas where the bays are relatively unaffected by human activity, are they expanding or shrinking, becoming more round or more oval, more defined or less defined? Are new ones appearing where they did not exist before?
    Wind and water are mostly eroding the bays rather than crating new ones. In Nebraska, only the largest ones are still visible. Here is a LiDAR image of some bays in Nebraska. Without LiDAR they are almost impossible to see:
    nebraska-bays.jpg

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    Quote Originally Posted by Grey View Post
    So, it's clearly true that while not perfect ellipses, the Carolina Bays are pretty close to elliptical. And they're all aligned in pretty much the same direction, with the long axis northwest to southeast. It's a fascinating land formation.

    Rather than quibble about how precisely elliptical they are or are not, my question is, what significance are you ascribing to this, citpeks? Why are you bringing it up here?
    The reason for my starting this thread in the Geology and Planetary Surfaces section is that the Carolina Bays do not receive much attention in geology courses. Many geologists are not familiar with the regular geometry and alignment of the bays.

    My own opinion is that the elliptical structures could have resulted from geological remodeling of oblique conical cavities. However, the mainstream hypothesis is that they were created by wind and water processes because the dates of the terrain span millennia (See for example Brooks 2010). So, I ask myself, how do the wind and water processes create almost perfect ellipses?

    ==
    Brooks, M. J.; B. E. Taylor; and A. H. Ivester, 2010, Carolina bays: time capsules of culture and climate change. Southeastern Archaeology. vol. 29, pp. 146163

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    That's because the bays are not so geological as geomorphological. And there have been extensive studies of the bays and their age, origins and how they might be changing. The orientations seem to correlate with prevailing wind patterns (or reconstructed wind patterns during and just after the last glaciation). Round ponds are actually fairly common - kettle ponds are a good example, though they tend to be smaller than the bays. These features become circular due to erosion and deposition along the shoreline or inner edge - small headlands or lumps are eroded away and any inlets or depressions are filled in, smoothing and circularizing the feature. It's the same process and smooths beaches and bays (proper bays). It's not mysterious or unusual.

    Now, I agree, the bays themselves are fascinating. There are theories on how they initially formed, but there is still much to learn about them. The comet fragment hypothesis is not well supported by the current evidence, but you'll still see serious work being done on that front.

    the elliptical structures could have resulted from geological remodeling of oblique conical cavities.

    ??? What does this even mean?

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    Quote Originally Posted by citpeks View Post
    If you create an ellipse with axes proportional to the length and width of a Carolina Bay, the ellipse will fit exactly.
    Given that all of the Carolina Bays are roughly circular or elliptical then of course they are conic sections by definition.
    The reason would be that the mechanism of formation created them as roughly circular or elliptical: Carolina Bays: Theories of origin.
    The wide range of measured ages of the bays suggests that they were not created in one event. So an impact event is not that viable.
    The orientation of the bays being consistent with wind patterns suggests a mechanism that created roughly circular depressions that were then sculpted by wind. Maybe currents when the area was under the sea. Movement of ground water can also create circular depressions.

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    Quote Originally Posted by citpeks View Post
    So, I ask myself, how do the wind and water processes create almost perfect ellipses?
    Why do you ask yourself, citpeks - why do you not ask a geologist or geomorphologist ? Apparently they are comfortable with various wind and water processes creating almost perfect ellipses (the Bays).

    One reasonable scenario:
    • Carolina is covered with a sea.
    • The sea drains away - suddenly in some areas.
    • We know that receding water can create kettles. So it is reasonable to expect Carolina to have roughly circular depressions.
    • Wind could remodel the rims into approximate eclipses.


    Once formed by wind and water processes they could retain their shapes and orientations:
    Conference Paper: RAPID SCOUR, SAND RIM CONSTRUCTION, AND BASIN MIGRATION OF A CAROLINA BAY IN SOUTHEASTERN NORTH CAROLINA, Moore et. at. Jun 30, 2014
    The fact that these landforms can migrate, yet maintain their characteristic oval shape, orientation, and rim sequences demonstrate that Carolina bays are oriented lakes shaped by lacustrine processes. Clear evidence of basin scour into the underlying Tertiary marine sandy clays reveal that Carolina bay are capable of creating, shaping, and migrating through their own basins while backfilling remnant basins with a regressive sequence of paleoshorelines.
    N.B. This conference paper may hint that Bays start as ovals however no date of formation of the bay is stated and the oldest date (32 ka) seems well after the date of Bay formations.

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    Quote Originally Posted by CJSF View Post
    That's because the bays are not so geological as geomorphological. And there have been extensive studies of the bays and their age, origins and how they might be changing. The orientations seem to correlate with prevailing wind patterns (or reconstructed wind patterns during and just after the last glaciation). Round ponds are actually fairly common - kettle ponds are a good example, though they tend to be smaller than the bays. These features become circular due to erosion and deposition along the shoreline or inner edge - small headlands or lumps are eroded away and any inlets or depressions are filled in, smoothing and circularizing the feature. It's the same process and smooths beaches and bays (proper bays). It's not mysterious or unusual.

    Now, I agree, the bays themselves are fascinating. There are theories on how they initially formed, but there is still much to learn about them. The comet fragment hypothesis is not well supported by the current evidence, but you'll still see serious work being done on that front.


    the elliptical structures could have resulted from geological remodeling of oblique conical cavities.

    ??? What does this even mean?

    CJSF
    The remodeling of oblique conical cavities into shallow ellipses was discussed and illustrated in another thread. I will not discuss it here because it is not mainstream.

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    Quote Originally Posted by Reality Check View Post
    Why do you ask yourself, citpeks - why do you not ask a geologist or geomorphologist ? Apparently they are comfortable with various wind and water processes creating almost perfect ellipses (the Bays).

    One reasonable scenario:
    • Carolina is covered with a sea.
    • The sea drains away - suddenly in some areas.
    • We know that receding water can create kettles. So it is reasonable to expect Carolina to have roughly circular depressions.
    • Wind could remodel the rims into approximate eclipses.


    Once formed by wind and water processes they could retain their shapes and orientations:
    Conference Paper: RAPID SCOUR, SAND RIM CONSTRUCTION, AND BASIN MIGRATION OF A CAROLINA BAY IN SOUTHEASTERN NORTH CAROLINA, Moore et. at. Jun 30, 2014

    N.B. This conference paper may hint that Bays start as ovals however no date of formation of the bay is stated and the oldest date (32 ka) seems well after the date of Bay formations.
    My reason for posting on this forum is not to answer my own question, but to ask the help of geologists or geomorphologists for references to the fluid mechanics calculations or numerical models that show how the elliptical or quasi-elliptical structures of the Carolina Bays are formed.

    Thus far, I have not come across a bay formation paper that specifies exactly the motion of the currents, or the motion of the wind, or whatever geological process is needed for the formation of precise ellipses. I don't demand 100% elliptical, I would settle for at least 98% elliptical.

    The scenario that you propose is similar to what I have read in many articles. Some depression is altered by water, wind and shifting sand and, voila!, you get elliptical bays. That is a very rough sketch for something that should be very precise.

    So it is reasonable to expect Carolina to have roughly circular depressions.
    It is reasonable, but I am not satisfied with "roughly".

    Wind could remodel the rims into approximate eclipses.
    I know that you intended to say ellipses, so I will not dwell on that, but I do not like the word "approximate". I would prefer 98% elliptical, or something like that.

    I have many questions, like how are the currents or wind regulated so that they stop when the ellipse shape is achieved? Why doesn't (or didn't) this happen with the kettle lakes in Alaska or Russia? What prevents the wind and water from deforming a perfect ellipse once it has been formed?

    All I would like is a reference to a paper that is not wishy-washy with information about prevailing winds or ocean currents. I would like something that has a numerical model that I could plug into my computer and shows me step-by-step how the precisely elliptical bays were formed, and how the overlapping bays managed to retain their elliptical shapes. By the way, the Carolina Bay ellipses are neither too elongated nor too circular. Why do they have a width-to-length ratio around 0.6?

    I know that these are hard questions, but a mainstream theory should have the answers.

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    Quote Originally Posted by citpeks View Post
    My reason for posting on this forum is not to answer my own question, but to ask the help of geologists or geomorphologists for references to the fluid mechanics calculations or numerical models that show how the elliptical or quasi-elliptical structures of the Carolina Bays are formed.
    You are welcome to ask, but you may have more luck on a geology forum.
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    Quote Originally Posted by citpeks View Post
    I don't demand 100% elliptical, I would settle for at least 98% elliptical.
    [...]
    It is reasonable, but I am not satisfied with "roughly".
    [...]
    but I do not like the word "approximate". I would prefer 98% elliptical, or something like that.
    That's what I have a problem with.
    I don't agree with your approximations of the shapes.
    To illustrate, I took my picture and used them as insets to yours. 1 is unaltered, the other has a rough blue outline of where I see the bottom of the rim of one of the craters.
    img-bowmore-nc2.jpg
    Even if I strayed a few pixels, it goes nearly 20 pixels off of an ellipse for a 100 pixel wide shape. No where near 98%, exact, perfect or whatever you want to say.
    On top of that, you only marked out 3 out of about 10 (depending if you want to count concentric ones).
    What about the one to the left of the 31x19 crater? The top of it is quite round while the bottom left is quite flat.

    Quote Originally Posted by citpeks View Post
    Why do they have a width-to-length ratio around 0.6?

    Even among the 3 you marked there is a 10% variation in ratios.

    Besides, why would you expect a large deviation in a fairly uniform soil anyway?

    I, myself, would love to see some experimental re-creations, or simulations for it too. But; your issue about using the word "roughly" seems unfounded.

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    Quote Originally Posted by Swift View Post
    You are welcome to ask, but you may have more luck on a geology forum.
    Thanks, I may do that.

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    Quote Originally Posted by NEOWatcher View Post
    That's what I have a problem with.
    I don't agree with your approximations of the shapes.
    To illustrate, I took my picture and used them as insets to yours. 1 is unaltered, the other has a rough blue outline of where I see the bottom of the rim of one of the craters.
    img-bowmore-nc2.jpg
    Even if I strayed a few pixels, it goes nearly 20 pixels off of an ellipse for a 100 pixel wide shape. No where near 98%, exact, perfect or whatever you want to say.
    On top of that, you only marked out 3 out of about 10 (depending if you want to count concentric ones).
    What about the one to the left of the 31x19 crater? The top of it is quite round while the bottom left is quite flat.
    I agree with you that finding the edges of the bays is difficult. My main point is that compared to the Alaskan lakes or the lakes in the Yamal peninsula, the Carolina Bays have remarkably elliptical shapes.

    Quote Originally Posted by NEOWatcher View Post
    Even among the 3 you marked there is a 10% variation in ratios.

    Besides, why would you expect a large deviation in a fairly uniform soil anyway?

    I, myself, would love to see some experimental re-creations, or simulations for it too. But; your issue about using the word "roughly" seems unfounded.
    [/COLOR]
    The variation from the elliptical shape is one thing. This is a curve-fitting matter.

    The variation in the ratios of the conic sections is another thing. This is a variation in the angles of the corresponding cones. If the angle of the cone corresponds to sin(θ) = width/length, then we have:
    a ratio of 16/24 corresponds to a cone inclined at an angle of 41.8
    a ratio of 22/32 corresponds to a cone inclined at an angle of 43.4
    a ratio of 19/31 corresponds to a cone inclined at an angle of 37.8

    There should be some meaning in that.

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    Quote Originally Posted by citpeks View Post
    So it is reasonable to expect Carolina to have roughly circular depressions.
    It is reasonable, but I am not satisfied with "roughly"
    But, even the limited amount of examples that you yourself have provided show that the Carolina Bays are only roughly elliptical.

    Quote Originally Posted by citpeks View Post
    I agree with you that finding the edges of the bays is difficult. My main point is that compared to the Alaskan lakes or the lakes in the Yamal peninsula, the Carolina Bays have remarkably elliptical shapes.



    The variation from the elliptical shape is one thing. This is a curve-fitting matter.

    The variation in the ratios of the conic sections is another thing. This is a variation in the angles of the corresponding cones. If the angle of the cone corresponds to sin(θ) = width/length, then we have:
    a ratio of 16/24 corresponds to a cone inclined at an angle of 41.8
    a ratio of 22/32 corresponds to a cone inclined at an angle of 43.4
    a ratio of 19/31 corresponds to a cone inclined at an angle of 37.8

    There should be some meaning in that.
    The calculations you make using width-to-length ratios to calculate the angle of the cone depend upon them being perfect ellipses. That's clearly a false assumption.

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