As the reader would have understood by now, I think that the "nipped tail" is exactly what characterizes the "hitch component". It is the ONLY mechanism that can transform a "single wrap" component into a "hitch" component. So, it is the only geometric characteristic that is different between the "single turn" component and the "hitch" component - the other characteristic, that is not shown in the pictorial representations of those two quite different things - is, of course, the asymmetry in the loading of the legs. ( With the provisional term "single wrap" component" I mean something like the "single turn" component, but where only the one leg is loaded. I repeat, in a 'single turn" component, both legs are loaded, to the same , more or less, degree. In a :"hitch" component, only the one leg is loaded, the other has been transformed into a more or less free end. (Derek Smith will probably figure out a more appropriate name for this " single wrap" element, I guess.)
I can not see how a " turn" , in general, could function as a "hitch" , without incorporating this 'nipping tail" characteristic. This is exactly how the one leg can "absorb", in a sense, the load that would otherwise have been transported throughout the other leg. So, it is the only
geometrical transformation required, with the help of which a "single turn" component to be turned into into a " hitch" component - the
mechanical transformation required is the loading of only the one, not the two ends.
Now, of course there are more complex hitches that do not use this " nipping tail" trick... but another way to prevent the slippage of the second leg through the knot s nub, at a first stage, and off the object, at a final stage. I was only considering the most simple case, of the most simple rope path, able to hitch/be hitched around an object, and so be able to remain stationary even if only one of its two leg is loaded.
(2012-6-3 P.S.) I have edited my previous posts, by removing anything that had to do with an analogy / joke I have made about the very large friction forces on a very long rope, laid upon a flat (or warped around a round) Earth !
The fact that - as the " capstan equation" and Derek Smith show-, even the very light load of the weight of short segment of a chord one the one leg can withstand any very heavy load on the other leg - provided that the rope is warped around a round object a sufficiently large number of "single turns"- does not, in my view, forces us to call a multi-warp system by the generic name of
"a hitch". The mere accumulation of friction forces by the repetition of many turns can serve to attach a line on a pole or rope, indeed, it can
serve to attach a line on an object, it can
play the role of a hitch - but, at least according to my view of what is a knot (1), it is not a knot - so it is not a hitch, therefore and we should not call it "a hitch". Why it is not a knot ? Because it can be untied, without any obstacles imposed by the topology, the friction, or the mere bulk of the rope. What is prevented by friction ( by the capstan equation and by Derek Smith
) is its motion/rotation, as a whole, around the encircled object - or the motion/rotation of the encircled object around it . The multi-warp system is not entangled within itself in a way that would allow us to call it " a knot" .
However, we could well call a single wrap as a " hitch component" ( when it is loaded only from the one leg ), just as we call a 360 degree bight around an object "a single turn component" ( when it is loaded by both legs ) - although nor the " single wrap" nor the " single turn" are genuine knots, in the sense described above. They are
elements of knots, and when the knots do have a certain name, these elements can well shear the same name.
Then, why I do not wish to call this " single wrap" element/component, a " hitch" element/component ? Because I think that it is better, and more convenient, to reserve the use of this name for the case where we have a riding turn over a tail - the first one ( the loaded) leg going over the other, and squeezing it in between the riding turn and the surface of the encircled object.. Out of this embrace, this second leg walks out as a free end - well, more or less, this is but a simplified, general, abstract picture. In this picture, there is a
geometrical characteristic that distinguishes it from a "single warp", this asymmetric position of the two legs relatively to each other, which is the cause of the difference in the loadings - the one leg is loaded ( and remains loaded), while the other is not ( because it does not) .
I believe that, if we keep in our mind those simple distinctions, we can analyse a certain knot in a more useful way, in order to reach a point where we acquire a deeper understanding of how this knot works, in particular, and how knots work, in general. A " single warp component", a " hitch component" , a " single turn component" - after all, it is not rocket science!
1)
http://igkt.net/sm/index.php?topic=3610.msg20611#msg20611