I've done some searching on catenary curves, and I'm wondering if anybody could explain, or link to a good explanation of how to set up a proper curve on a cat tarp?

Any help you could provide would be much appreciated.

Thanks!!

let's say the ridgeline of your tarp is 10 feet long.
you'll want to take both of your tarp pieces, before sewing together at ridge obviously, and hang it on a wall (garage?) with push pins. you want to make sure that both sides of your hung tarp are even and level. for this you'll maybe need a line level, and string, as your floor is certainly not perfect and measuring up from there could be off by a bit.
this does not have to be precise, and only takes a few minutes. now, get 11' of ball chain from your pocket that you've previously purchased from Ace hardware and hang it even on the tarp ridgeline ends, so that the chain hangs about 1.5-2 inches below the straight ridgeline edge.
this is the only hard part. you have to trace the ball chain (without moving it too much) with a sharpie.

now take both pieces down to the machine and while holding each edge together, sew along your sharpie mark.

that is the ghetto way. it works tho.. as the definition of a catenary curve is the sag in a chain hung from two points.

Edited by mikeinfhaz on 05/21/2011 11:38:33 MDT.

I agree with your method . I've used it in carpentry to lay out arches. I use spray paint to get the outline. If you could use a tempera paint in a sprayer it would probably wash out.

Edited by Meander on 05/21/2011 12:01:02 MDT.

Hi Mike:

Thanks for your instructions.

First, I'd like to apologize for the long subject line on this thread ... don't know how that happened.

Your instructions sound good ... but I'm still concerned about one thing. When you sew the two sides together, and open the tarp, the curve will be changed. Opening the two sides changes it.

Here's something I thought of after reading your instructions:

How about if we marked a cat curve directly on a wall, following your ball-chain method. Then run a series of height measurements every horizontal inch along the (level) floorline. Then we'll know how high the tarp needs to be at each spot, and we'll know how wide the "floor" of the tarp needs to be. The floor and height of the tarp are at right angles to eachother. So ... we can then run right-angle calculations to give us the measurement of the "roof" fabric coming off the catenary curve. This would give you a series of measurements for each inch of your fabric. From those measurements, you could then construct a curve on some paper to create a pattern for your fabric.

This could easily be automated in Excel or something like that.

Here is an image to show what I'm talking about:

What do you think?

yes, the curve will be changed.. it will be deeper. as you know, adding 1.5-2" per side can give you up to a 4" deep curve, if both sides pulled out on full horizontal plane - you can even play with the "tilt" of the curve, my simple directions were for a flat tarp, rectangular. but with a tarp say tapering from 7' at front to 5' in rear, you can tilt the ridgline downward so that the back half of the tarp gets a steeper curve than the front half. this is visible and observable on many of the tapered cat tarps (see pics of tarptent, mld, and spinntwin, et al.)

one thing to note: once i'd sew the ridgline i would then cut the tag fabric within a 1/4 inch and then fold it over, to sew again. zpacks uses this method.. however a felled seam might be stronger - this method worked for me for many tarps and is holding up on my big hammock tarp just fine.

Thanks for the additional info. I think the thing to do is get some grid paper ... past it to the wall, use the ball chain to get your cat curve on that, and get your measurements every inch along the length of the curve. Then, run the calculations to get the measurements for the fabric, and lay that out on another piece of grid paper to use as a pattern.

Again, thanks for your help ... the "ball chain" thing is perfect.

I wonder ... is there some computer program that can do all of this?

Edited by TheNewGuy on 05/21/2011 12:44:52 MDT.

You can use formula - (cosh((2 * x / ridge) - 1) - cosh (1)) * deflection * 1.8413

where x is the distance along the ridge
ridge is the ridgeline distance for example 100 inches
deflection is the deflection at the midpoint for example 2 inches

this gives you the deflection for any point along the ridgeline
for example, it's zero at each end, 2 inches at the middle

there's a downloadable spreadsheet in Roger's article but I think you have to be a member to get it, sorry, that's just the business model for this website, I've noticed many websites are doing that these days

you don't have to worry about correcting for right angle. Just lay the curve out on each piece of fabric and it will look good

I've done a 2 inch deflection on a 100 inch ridgeline and thought maybe a little more would be better, maybe 3 inches

I think any reasonably smooth curve would be just as good

Another thing you could do is to take a springy board and bend it in the middle with the desired deflection and trace along it

You'de probably want to make a pattern on a stiff board or cardboard and use that to lay out on each piece of fabric

-----------
The URL for the BPL article is http://www.backpackinglight.com/cgi-bin/backpackinglight/myog_tech_note_catenary_curves.html
Yes, subscribers only: we have to pay the bills for the server. But the maths is simple.
Cheers
Roger Caffin

Edited by rcaffin on 05/21/2011 17:13:12 MDT.

Computer program:

There's a number of people here who have set up spreadsheets to calculate cat curves. I like something more visual and intuitive, and use the modeling program SketchUp for designing a lot of things (there's a free version available). There are several free SU plugins that help with shelter design, including one that draws cat curves. Details in this thread:

http://www.backpackinglight.com/cgi-bin/backpackinglight/forums/thread_display.html?forum_thread_id=46175&skip_to_post=394300#394300

The idea above with beaded chain + spray paint is a good one, I think. You could use paper or cardboard to make a template, rather than spray painting directly on your fabric. In fact, I bet this method would be quicker than computer layout + piecing together a bunch of sheets of print-out.

Edited by DavidDrake on 05/21/2011 13:12:38 MDT.

David,

FYI take a look at Lance Marshall's Catenary Curve Spreadsheet.

Follow the link and click on Catenary Curve Spreadsheet, the second item in the menu. If you are using Google Chrome it may show up in the bottom of your monitor as a "box" that needs to be clicked to get the spreadsheet to come up on your monitor.

Use lines 7, 8 & 9. Enter your seam length in the box on line 7. Choose and enter your degree of severity in the box on line 8. Your deflection in inches will appear in the box on line 9.

In columns A, B and C starting on line 14 you will see a set of measurements that you can use to plot out a pattern for a catenary curved seam. You can use that pattern to mark your material if you are interested in doing curved seams.

I hope this is what you were looking for.

Party On,

Newton

I posted the spray painting tip. Some other thoughts. You don't have to use ball chain i.e. brass chain for pull-chains although it is useful if you have pull-chain light fixtures. I used cheap decorative chain and window sash chain which is useful around older houses. In decorative carpentry the creation of such curves pre-CAD got you into expensive drafting tools and most are only good for scale models. What is still compelling about the chain method is that it gives you a full size curve cheaply. In addition you can make an asymmetric curve good enough to make a wooden template for replication. Cheap and fast is good. In my work , doing free form curved designs I ended up using colored chalks and jigsaws to produce what I wanted. Math is great , but sometimes it's in the way. Old books on circular forms in English woodworking are somewhat helpful in visualizing how to mock this stuff up. But for one-offs, cardboard, plywood, string , whatever can be much more like it. Does chalk for a snap-line stick to fabric? Another way to maybe get that line.