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in order for the analogy to work properly the tape needs to be
*carefully* laid down on the surface locally straight/even with no
bunching/wrinkling or stretching/tearing of the tape material as it
is laid down. If the surface has significant curvature over a
length scale comparable to the width of the tape and the tape *can't*
be laid down without local distortion, then the tape needs to be
laid down in a way that any unavoidable stretching or binding is
laterally symmetric across the centerline of the tape.
(But maybe this caveat is included in one of JD's lurid details.)