Knot for Joining the ropes of different thicknesses
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 are swimming in a lake nearby. Having said this, We are not entirely relying on this as well.
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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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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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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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