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  1. #41
    Senior Member blackbishop351's Avatar
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    The easy answer is that I prefer to be precise when precision doesn't cost me anything. Using an approximation when the physically supported data are so easy to obtain just rubs me the wrong way.

    The slightly harder answer is that, if memory serves, the greatest variation in functional form occurs at the ends of the curved cut. Which, on a tarp, corresponds to the corners. Small differences at a corner can add wrinkles and wind-dams across the whole body of the tarp. Again, I'm not sitting here doing the math, so this is back-of-the-napkin. And relying on 10 year old memory.
    "Physics is the only true science. All else is stamp collecting." - J. J. Thompson

  2. #42
    Senior Member blackbishop351's Avatar
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    Quote Originally Posted by Kroma View Post
    Does this have anything to do with the parable of the cat and the canary?
    Yes, absolutely.
    "Physics is the only true science. All else is stamp collecting." - J. J. Thompson

  3. #43
    Senior Member kitsapcowboy's Avatar
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    Quote Originally Posted by blackbishop351 View Post
    The easy answer is that I prefer to be precise when precision doesn't cost me anything. Using an approximation when the physically supported data are so easy to obtain just rubs me the wrong way.
    And that's what makes you a legend. See?

    Honestly, I appreciate the response.

    Quote Originally Posted by blackbishop351 View Post
    The slightly harder answer is that, if memory serves, the greatest variation in functional form occurs at the ends of the curved cut. Which, on a tarp, corresponds to the corners. Small differences at a corner can add wrinkles and wind-dams across the whole body of the tarp. Again, I'm not sitting here doing the math, so this is back-of-the-napkin. And relying on 10 year old memory.
    I think the reason we disagree stems less from the numbers and more from a matter of perspective, on which I hope you'll grant me latitude in the spirit of HYOH.

    I believe you are exactly correct; the greatest deviation between these two curves would occur at extremes furthest from the line of symmetry.

    However, just as you prefer to be precise with numbers, I prefer to be precise with words, which is why I qualified my original statements exactly as I did...

    Quote Originally Posted by kitsapcowboy View Post
    ...for certain common aspect ratios in those same applications a parabola is usually a sufficient approximation to the appropriate catenary curve to provide some of the same engineering benefits and has the virtue of being easier to describe and compute mathematically...
    The ends of these curves would vary more greatly across a different span, but for long, flat curved edges such we find on tarps and bridge hammocks the biggest differences are proportionately pretty darn small...

    Also, for me, the latter point is likewise important, if you have the same appreciation of the difference between accuracy and precision that I do. The calculated values using the catenary curve may be more precise and model more closely the true relationships at work in the physical world, but if the variance introduced when rendering a set of precise theoretical coordinates as a practical application in the real world -- with small errors introduced during successive steps of rounding, measuring, templating, transferring, cutting, and sewing -- puts the final result of using the precise method and the final result using a quick-and-dirty approximation within the same bounds, then the approximation is a valid one, and in this case it seems to be not only sufficiently precise but also sufficiently accurate, as well as being something one could calculate quite easily with nothing more than a pencil and a cocktail napkin, given nothing more than the correct parabolic equation -- no spreadsheets or laptops needed. (Newton's laws of motion were rendered technically "incorrect" by Einstein's work, but Newtonian kinematics were sufficient to put a man on the moon and still work well in virtually every day-to-day situation involving bodies in motion that we encounter because the errors remain so small.) To me, avoiding anything "analytically intractable" in the calculation of the curve has practical value at virtually no cost, making the parabolic curve used in this application a logical alternative. I understand if your priorities and criteria for evaluation may differ, but I don't think mine were in error, unreasonable, or misleading to anyone else.

    Thanks for furthering the discussion.
    Last edited by kitsapcowboy; 02-12-2017 at 09:49.
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  4. #44
    Senior Member blackbishop351's Avatar
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    I think at the end of the day, HYOH is the operative idea. You recognize that there are differences in the two curves (some wouldn't), so if you can live with those differences on your kit, great. You may well be correct with regard to the scope of those differences; in a real-world application, using one over the other may offer exactly zero advantage. I'll stick with what I'm doing though, it just feels more..... right.
    "Physics is the only true science. All else is stamp collecting." - J. J. Thompson

  5. #45
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    The calculator maxes out at 160 Is that because most tarps are less than that? I'm making a group tarp that's 15 feet long. Would I be better to have two curves and a middle tie out? Or can I trick the calculator into giving me a longer curve?

    Thanks
    Steve

  6. #46
    Senior Member blackbishop351's Avatar
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    Quote Originally Posted by Duncanslam View Post
    The calculator maxes out at 160 Is that because most tarps are less than that? I'm making a group tarp that's 15 feet long. Would I be better to have two curves and a middle tie out? Or can I trick the calculator into giving me a longer curve?

    Thanks
    Steve
    For a tarp that long, you might be better off using three tie-outs per side. And in that case, yes you'd have two cat cuts per side too.
    "Physics is the only true science. All else is stamp collecting." - J. J. Thompson

  7. #47

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    Catenary idea, Is the big gap required?

    I know this is an old thread, but.... Question. The height of the curve seems to be somewhat arbitrary. And the rule of thumb is that it's 1" of height for each running foot (width) of the span, so a 12' wide tarp would need a 12" depth. The calculator allows height to be an independent variable.
    Seems to me that this curve should be based on the stretch of the fabric and the width, so a very stretchy fabric would need more height of curve.... But I'm really just guessing at this.
    Second thought: What if instead of cutting and hemming the catenary, instead you just ran a raised gather(?) using very sturdy series of stitches, following the catenary curve. Then you wouldn't have to cut the fabric. These 'gathers' would be wider near the corners and wouldn't have to meet in the middle. This would stretch the fabric out more along the baseline, to match the tension along the catenary.... I'll include my sketch. (My sketch has two catenary gathered seams because Xtrekker's cool calculator makes it easy to calculate.)

    Keep in mind the 'gaps' (white areas) along the catenary lines are to be pulled together and stitched. The top drawing was my original idea, using different panels, but then I realized you could probably just gather together fabric and stitch it. The 'gaps' at the bottom would be bast on the specific stretch of the particular fabric, so polyester would have a smaller gather than nylon (because nylon stretches more).

    It seems to me that the issues with a flapping tarp are 1. the bottom edge, and 2. an general area in the tarp where tension seems to drop because it's spread out. It's an interesting puzzle that once sorted should allow for tarps of any shape. (and likely this has already been figured out and I've been googling the wrong terms while trying to reinvent the wheel.....)
    Will

    Catenary Conjecture.pdf

  8. #48
    jellyfish's Avatar
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    Catenary / Parabola Curve Calculator

    Quote Originally Posted by WillUpnDown View Post
    I know this is an old thread, but.... Question. The height of the curve seems to be somewhat arbitrary. And the rule of thumb is that it's 1" of height for each running foot (width) of the span, so a 12' wide tarp would need a 12" depth. The calculator allows height to be an independent variable.
    Seems to me that this curve should be based on the stretch of the fabric and the width, so a very stretchy fabric would need more height of curve.... But I'm really just guessing at this.
    Second thought: What if instead of cutting and hemming the catenary, instead you just ran a raised gather(?) using very sturdy series of stitches, following the catenary curve. Then you wouldn't have to cut the fabric. These 'gathers' would be wider near the corners and wouldn't have to meet in the middle. This would stretch the fabric out more along the baseline, to match the tension along the catenary.... I'll include my sketch. (My sketch has two catenary gathered seams because Xtrekker's cool calculator makes it easy to calculate.)

    Keep in mind the 'gaps' (white areas) along the catenary lines are to be pulled together and stitched. The top drawing was my original idea, using different panels, but then I realized you could probably just gather together fabric and stitch it. The 'gaps' at the bottom would be bast on the specific stretch of the particular fabric, so polyester would have a smaller gather than nylon (because nylon stretches more).

    It seems to me that the issues with a flapping tarp are 1. the bottom edge, and 2. an general area in the tarp where tension seems to drop because it's spread out. It's an interesting puzzle that once sorted should allow for tarps of any shape. (and likely this has already been figured out and I've been googling the wrong terms while trying to reinvent the wheel.....)
    Will

    Catenary Conjecture.pdf
    I am not sure that I understand your diagram. Is the ridgeline at the top?

    I like a 1:12 cat cut, but the curve is not 12í long. It is in segments with tie outs. It is windy here and the luffing is minimum. If I ever get a problem it is because a gust has pulled a stake, lol. I like the added coverage of 1:12.

    I think Black Bishop likes a 1.5:12 and his tarps look nice and pitch tight. His tarps are 12í ridgeline, which is too long for my hammock stand, so Iím using an 11í ridgeline and then I get the extra coverage I need with a more shallow cat cut.

    If you did some gathering or rouching, that would transfer the strain from the fabric to the thread. Iím not sure you would need much to start popping stitches.
    I sew things on youtube.
    I donít sew on commission, so please donít ask. Thanks.

  9. #49

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    Hi Jellyfish,
    This would be one side of a four sided fly, the dotted line is the ridge between side panels. I'm just puzzling this out. It's an interesting problem. Yes the stitches would be under a lot of tension.
    There are two things that interest me. First I think the underlying idea is probably sound and second the mentions that some tent/fly makers make non-flapping full panel tents and flys--without any information how they do it. I'm heading up to camp in snow, I have a Warbonnet SuperFly, I thought maybe I'll stretch some thin line between the attachment points and see how changing the tension on it affects things.

    There is more than enough going on in just hammocks, flys and tents to make it a field of engineering.

  10. #50
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    Quote Originally Posted by WillUpnDown View Post
    Hi Jellyfish,
    This would be one side of a four sided fly, the dotted line is the ridge between side panels. I'm just puzzling this out. It's an interesting problem. Yes the stitches would be under a lot of tension.
    There are two things that interest me. First I think the underlying idea is probably sound and second the mentions that some tent/fly makers make non-flapping full panel tents and flys--without any information how they do it. I'm heading up to camp in snow, I have a Warbonnet SuperFly, I thought maybe I'll stretch some thin line between the attachment points and see how changing the tension on it affects things.

    There is more than enough going on in just hammocks, flys and tents to make it a field of engineering.
    What holds up the center? Will you have a center pole? How will a hammock suspension fit inside?
    I sew things on youtube.
    I donít sew on commission, so please donít ask. Thanks.

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