> The problem with the basic bowline is that it can work loose with time.
POINT ! This needs to be understood well: it CAN do this, somewhat YMMV on many factors. It is NOT a reason to forego "the bowline" in general, but a reason to take a precaution --and there are many ways to do so-- against such loosening; one can still have the good benefits of the knot (easy tying AFTER sizing the eye (nothing to "pre-tie" like a Fig.8), easy untying after heavy loading).
> The options for increasing the security of the knot are:
>1) Add a stopper knot with a long enough tail
>2) Tie a double loop variant eg double bowline, water bowline, to make the knot less likely to slip
Here, your words can confuse: "double loop" = (/=) "double EYE" ?
Your examples manifest /=. *Slippage*, per se, isn't so much the problem as here as a sort of *expanding* of the knot into a (too) loose form. As much loosening can occur with the "Dbl.Bowline" (rabbit hole doubled), but a given amount of opening of this double turn requires now twice the external, back-into-knot material and so resists opening as much.
(NB: this bowline was shown just *flowing* eye material out of the knot by slow rotation of the double loop, in pure, 12-strand HMPE rope !!! amazing (eye collapses to nil)!)
There is, as noted above, the variation of putting in a 2nd eye, making a fully redundant finish to the knot (one could e.g. bring the tail up into the knot on the 2nd eye and then go directly above the knot and tie off with the Strangle ("half a Dbl.Fish") knot).
> 3) Pass the free end in some way through part of the knot in an attempt to secure it eg Yosemite, Edwards, numerous others...
What the Water Bowline, and its similar-themed "mirrored" extension & Mirrored Bowline do is keep the eye leg that comes directly from the mainline reasonably snug to the knot body and this greatly inhibits loosening. The so-called (because it's like placing a mirror immediately across a bowline's eye legs facing the knot boty) "Mirrored Bowline" has is a Larkshead ("foot" for the wrong-headed
/ girth hitch at its center, tail making those "around the tree & back into the hole" wraps at both ends (around mainline & its corresponding eye leg)
> 4) A combination of these eg double bowline with yosemite finish. You can even add a stopper as well if you are of a nervous disposition!!
Or if you just have that much tail to tie up out of the way. Using various knots will move the folding/compressing of this "live end" of the rope across a broader area and so distribute the wear over using the same tie-in repeatedly. --some small benefit?
> ... meaningful strength testing ...
A fair question is how meaningful strength is at all -- assuming, quite reasonably, that ANY knot will break in dynamic rope only well beyond forces that will wreck your body!?
Moreover, the sort of testing best fitting rockclimbing is dynamic loading (drop testing), and not the usual sort of slow-pull testing that is commonly done. Dave Merchant (author of _Life on a Line_ knots booklet) asserts that his testing found that e.g. an Overhand eyeknot had fairly consistent strength between slow-pull & dynamic loading whereas the Fig.8 and more so the Fig.9 showed lesser strength on dynamic loading; he conjectures that greater rope movement in the more bulky knots leads to more movement and frictional heat. For slow-pull testing, though, confer Dave Richards's information (nb: the top two bar graphs are flipped -- that labeled for "12.5 Static" is with the 10.5 dynamic data and vice versa). Note that one does NOT know how the Fig.8 was loaded (which "end" was "tail"/"live", i.e.).
[Knot Break Strength vs Rope Break Strength,
by Dave Richards, Technical Director, Cordage Institute]
www.caves.org/section/vertical/nh/50/knotrope.html
Note other things, too: the variance of a given knot across this trio of cordage; the different Std.Dev.s; the curiosity of testing the "Fig.8" got by TWO tying methods (which if "dressed & set properly" one should think would yield identical knots, but ... ?!) --his "end" & "bight".
And I note that in all cordage the Grapevine (aka "Dbl.Fisherman's") bend is slightly stronger than the Fig.8 eyeknots; but I recall some fellow who did some home-brew testing of end-2-end knots in small cordage (1/4", 3/8") using Fig.8 eyeknots (again, of some unknown geometry) to anchor all test specimens and NEVER did the eyeknots fail ! Richards's data would suggest otherwise, and it might be so, for the different cordage.
.:. One cannot so simply give attributes of strength, etc., to a particular knot form irrespective of material.
*kN*