What happens in a bowline if, intentionally or by accident, one of its two essential elements, the collar, cease to exist altogether ? Will this half-bowline still be capable to hold some loading ?
In the standard, common bowline, without the presence of the collar, the nipping loop will open up, and it will degenerate, from a closed loop to an open helix, in no time. However, there are some double bowlines where this will not happen - at least not immediately - because the two nipping loops are stabilized, to a large degree, by the the continuation of the tensioned eye-leg-of-the-bight ( the "first" leg of the collar) that penetrates both of them, the one after the other. I believe that the Water bowline and the Girth-hitched bowline are utilizing the stabilizing action of the collar only a little bit, so they will be capable to bear some loading indeed, even if the bight of their collar is cut in two.
I have tried to figure out a bowline which, at the moment the brave knot experimentalist will dare to cut the bight of the collar with a razor, when the loop is still under load, NOTHING will happen - or, at least, nothing really catastrophic. I have started from a very stable double nipping loop, where the two coils are crossed - and I weaved the working end through this knot along a path that will ensure that two ccrossed oils will remain crossed, under any circumstances ( so the advantage of their mutual self-stabilizing entanglement will remain at all times) . The result is shown at the attached pictures. Under loading, the two crossed nipping loops do not run the danger to open up, because they encircle and stabilize the one the other, without much help from the collar. The situation is similar with the cases of the Water bowline and the Girth-hitched bowline, only this time the two nipping loops are interlocked, and so they can not move apart from each other.
( Note : To form the collar, the working end can go around the standing end passing from the one or the other side - following a clockwise or a counter-clockwise path. ( If we watch the loop from " above" , the one shown here is the clockwise path. In relation to the direction the working end itself is heading to, it is the counter-clockwise path). As far as all the rest of the route is the same, this makes no difference - either path is O.K, so we do not have to remember or to pay any attention which one we should trace with the working end.)