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Catenary cut for tarp ridgeline

June 09, 2021 — BarryK

After constructing the TH1P tarp Mark-1 and erecting in my lounge room, then eye-balling it, I realised that it would be better if the ridgeline is joined in a catenary-cut. Previous post, showing photos erected in lounge room:

It is not apparent from those photos, but the fabric either side of the ridgeline is loose, not taut. even though I pulled the cords fairly firmly at each end. The problem is, the ridgeline is never going to be a straight line, no matter how firmly you attempt to tie each end. It will sag.

This photo shows the sag in a straight-cut ridgeline. OK, it is a bit exaggerated, because the ends have not been pulled firmly, but the shadow does show you the effect of the sag:


This sloppiness can be mitigated by having extra tie-outs on the sides of the tarp, but I would prefer not to have more stakes to hammer in.

There is a fix for this problem, to join the ridgeline in a curved shape, so when erected, the fabric either side of the ridgeline will be taut. This photo shows a tent which has such a curve:

img2 can see, a reasonably firm tension applied each end, the ridgeline has a sag, but the fabric each side is taut.

My apologies to whoever posted the above photos, for not acknowledging you. I downloaded them and don't recall the URLs. Ah ha, found one URL, but he also has "borrowed" the photo from somewhere else.

The curve shape is known as a "catenary". The Wikipedia defines a catenary as:

A catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.

So, it would be good to join the two halves of the tarp so that the ridgeline has this natural hanging shape. As I have already created a straight ridgeline, I decided to modify it to be a catenary.

Firstly, I need a formula for calculating the points along the catenary. Fortunately, 'XTrekker' has done it: can run the formula online, or download the Excel spreadsheet  -- which runs great in LibreOffice.

I have uploaded the Excel spreadsheet here.

Note, XTrekker's formula is for both ends of the tarp to be at the same height. My tarp is lower at the foot-end, but I don't think it matters if the cut is not to an exact catenary mathematical formula.

Back in an early post of these tarp construction instructions, I gave the dimensions of each side of the tarp, and the ridgeline was 222.2cm. After folding the hems, the final ridgeline length on my tarp is 215cm.

But the big question, how much "sag" to put into that formula? After a bit of reading other people's experiences of a minimal catenary, I chose 4cm. Tabulating the results from the spreadsheet:

Offset "b"
0 (centre)
107 (end)

I have modified my tarp, by cutting along the ridgeline, then re-glueing.

For someone constructing the tarp from scratch and wanting the catenary curve on the ridgeline, I would like to theorize on a couple of ways it can be done. Let's call them "method-1" and "method-2"....

Method-1: variable overlap

This sketch explains theoretically how I think it could be done:


The top sketch shows the two tarp ridgelines placed together, and the red dashed line is the pencilled catenary shape. There has to be some overlap at the ends, named "a", and in the centre there will be an overlap of "a" + "b", where "b" is from the above table.

One thing that I think you will need to be careful about, is not just to pull #2 side up to the pencil line, as the ridgeline will be slightly wonky. #1 and #2 edges need to be pulled equally. I think that a way to achieve a nice non-wonky join, is to do what I suggest in the bottom sketch.

I have indicated a sequence, 1, 2, 3, but you might find it better to do 2 first. That is, anchor each end firmly with weights, then pull the two edges so that they overlap and follow the pencil line. Then put in pins to hold the overlap in place.

Then step-3, glue. Tarp #2 will be sitting on top of #1, and you can glue it down. Usual procedure: dribble a line of silicone adhesive, then run your finger along to spread it, then press down. The only thing to be concerned about is that the spread of glue as you run your finger down, reaches the edge, so edge #2 is glued down all the way along.

Take out the pins, leave overnight. Next day, flip over and glue the other edge.  It is then wise to leave for several days, to fully cure.

Method-1 is wasteful of fabric and glue, and the tarp will be unnecessarily heavy, as the "b" value gets bigger. Plus, I am not sure how the ridgeline will hang with a large centre overlap.

I came up with that 4cm sag figure from reading forum posts, but those people were using method-2. So, "b" should be doubled for method-1, but 8cm fabric overlap is, I think, not the way to go. I am describing method-1 in this blog post, for consideration if you only want a tiny sag value.

The alternative is the traditional way, cut a catenary shape on the ridgeline edges of both tarps, and then join them with a constant overlap the entire length. This is Method-2...

Method-2: Catenary cut

Another sketch to show this:


With this method, you mark catenary lines on both edges, then cut. This is shown by the pink dashed lines. If you used a "b" value of 4cm, as per the above table, then you are going to get twice the catenary effect than for method-1.

On side #1, mark another line for the overlap. I suggest the orange dashed line to be 3cm from the pink dashed line.

To glue the two sides, I think that you could still use the pins. So you would pull side #2 over side #1, pull each end and put weights, then pin, then glue.

Leave overnight, then flip over and glue the other edge.

I used method-2 on my tarp, and used pins. To make it easier to insert the pins, I hung the two tarp-sides near vertically, using a plank. The plank is dressed pine, 184x19x2400mm. Use a large crocodile clip at one end, to hold the two pieces of tarp together, with 3cm overlap, onto the end of the board. At the bottom end, you could use another crocodile clip to hold the tarp pieces together, again 3cm overlap.

Haven't got a photo of that, but it should be easy enough to visualize. That made it very easy to insert the pins.

I then laid it horizontal and glued. I left the pins in, but that is OK, next day flipped the tarp over and glued the other flap.

I had removed the tie-outs at each end of the tarp. Need to reconstruct those, then will take a photo of the erected tarp, and will update the tarp construction details here:

This time, will use some heavier-duty webbing for the ridgeline tie-outs.

EDIT: TH1P tarp mark-1 with catenary-cut

I cut along the ridgeline, cut the catenary curves, re-glued, sewed new webbing tie-outs. Unfortunately, all this messing around has resulted in a lot more glue and some extra reinforcing bumping the weight from 178g to 218g, a jump of 40g. That is unnecessary extra weight, would have been less if had done the catenary-cut from the start.

Here is a photo:


I am really not convinced that the catenary-cut is worth the effort. Yes, it does take up some of the slackness along the ridgeline. The tautness will also have an advantage when wind hits the side of the tarp, it will more readily flow over the tarp, instead of trying to push it over. Some people cut even deeper catenary, but then they are going to be loosing more height inside.

A straight-cut is probably preferable if you want to erect the tarp in other ways, not just as a V ridgeline.

For the tie-outs on the ridgeline, I have gone for a thicker webbing. This, 12mm wide by about 1mm thick: is only available in black.       

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