Swinging indeed like smoke simulation! :)

i was just playing with this for fun. you can truly sweep 1 segment and then array it.

edit: i think i might have done that with 'flat' sweep anyway. d'oh. :)

Yes it's the trick as show above ;)

Works pretty good with the extrude-path. Here is sin wave "amp=4 length=20 cycle=10 points=5"

Sorry. I just noticed your talkin about your "particular" curves. My bad.

Ack, this one broke flat sweep. Extrude path worked. Better stop now. :)

In fact seems nature of curves, & orientation are very sensitive!
this one works fine with Network! (5 seconds on a very old comput)
A small change and all works fine or not!
So a big training is necessary :)