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As, I have been using a Double Fisherman's knot to join the two ropes. With some physics that I know, in Double Fisherman's knot the same amount of pressure (stress) is applied over the two turns of each rope, so making sure there is no significant damage done to any of the rope.
However I believe that if the two ropes are not of equal thickness, or may be say if the difference between the thicknesses is a considerably huge, Double Fisherman's would(?) do some damage to the thinner rope.

In that case how trustworthy are Sheet Bend and Zappelin Bend?

Edit: I am Not going to use this for rappelling at all. I intend to use that as a holding line when me and friends a re swimming in a lake nearby. Having said this, We are not entirely relying on this as well.

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What thickness of ropes are you trying to join? Is this for rappelling? A "sheet bend" will join 2 ropes, but I've never seen it recommended for rappelling. If you're trying to join a pair of climbing ropes (i.e., a single rope and a halfrope, or a single rope and a twin rope) there's probably a more specific recommendation –  DavidR Sep 21 '13 at 13:12
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I assumed op was not referring to Climbing or Rappelling since there were no tags mentioning these. Perhaps WedaPashi could clarify this for us. –  Dopeybob435 Sep 21 '13 at 16:07
    
@DavidR: Yes Sir, I am Not going to use this for rappelling at all. I intend to use that as a holding line when me and friends a re swimming in a lake nearby. Having said this, We are not entirely relying on this as well. –  WedaPashi Sep 23 '13 at 4:55
    
@WedaPashi you're going to use it to tie yourselves together while swimming? –  Dopeybob435 Sep 24 '13 at 12:41
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3 Answers

up vote 11 down vote accepted

A Sheet Bend is designed for joining two lines of different size. If you need additional security use the Double Sheet Bend

http://www.animatedknots.com/sheetbend/

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Thanks for the link –  WedaPashi Sep 24 '13 at 4:46
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Anyone reading this should note that this knot is absolutely not safe for climbing. –  Felix Sep 27 '13 at 14:36
    
@Felix The question never referenced climbing and includes the statement that 'I am Not going to use this for rappelling' –  Dopeybob435 Sep 27 '13 at 19:25
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What is your intended use for those joined ropes? If your life depends on it (you tagged your question with "safety"), I would not recommend using drastically different sized ropes in the first place and I would recommend something that has been well tested by the rock-climbing community. Most rock climbers either join their ropes with the double fisherman's (without any damage, as far as I know,) or, when the profile of the knot needs to be small, the overhand knot with lots of tail.

I have not heard of the double fisherman's damaging ropes, where did you hear that?

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yeah, I am NOT going to use it for Rappelling at all. I intend to use that as a holding line when me and friends a re swimming in a lake nearby. Having said this, We are not entirely relying on this as well. –  WedaPashi Sep 23 '13 at 4:54
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VERY IMPORTANT: The overhand knot must be tied on a bend. Because it looks scary (yet is perfectly safe), climbers call this the European Death Knot, or EDK: animatedknots.com/flatoverhand/index.php –  Lagerbaer Sep 23 '13 at 16:26
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@Lagerbaer Are you saying overhand on a bend for drastically differently sized lines? I don't see that knot working in the scenario described so clarity helps. –  Dopeybob435 Sep 24 '13 at 12:39
    
My scenario is intended for equally sized ropes, which is the scenario where rock climbers use the overhand knot. But again, it has to be the correct version of the overhand (EDK). –  Lagerbaer Sep 24 '13 at 17:24
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@BenCrowell: For activities related to rappelling (where the profile of the knot matters) I do advocate using the overhand with ropes that are commonly used for climbing. There is an interesting blog article based on some test-data the author linked to at the end of the article. I haven't heard of anything going wrong with ropes that have sensible differences in diameter, but if you know of any incidences or testing that show the contrary, please share! –  DudeOnRock Sep 27 '13 at 23:02
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If I was going to rappel on it, and the bulk of the knot wasn't an issue, I would tie a figure-eight in a bight of one piece of rope, then attach the other rope to it using a rewoven figure-eight. This way the knots that had to hold in order to keep me from getting killed would be two almost independent knots, each of which was tied in a single type of rope, and each of which was a standard type of knot (figure-eight) that is widely used in climbing and known to be safe.

As Dopeybob435 has pointed out, this is really a classic application of a sheet bend, but for a life-critical application I would prefer to use something based on a knot that was totally standard for climbing, both so I could be sure of tying it correctly and so that my climbing partner could check my knot.

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Sorry, but this is incorrect and unsafe. The double fisherman's or flat overhand are much better knots that do not have ropes rubbing on each other. –  Felix Sep 27 '13 at 14:37
    
@Felix: I think you're incorrect, and in fact your suggestion would be the unsafe one. The knots you're suggesting are not intended for ropes of very unequal thickness and there's no reason to think they'd be secure in such a situation. Rubbing would only be an issue if one rope was to travel through a loop in another rope while under load. That's not the case here, where the two loops are like the links of a chain. –  Ben Crowell Sep 27 '13 at 16:13
    
As discussed in the comments under DudeOnRock's answer, we may not be visualizing the same ratio of diameters. My answer is describing what I'd do if the ropes' diameters differed by a factor of 2, and in that situation I stand by my statement that your recommendations would be extremely dangerous. –  Ben Crowell Sep 28 '13 at 0:33
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