My last speculation on the rippling of a waving flag (September 25 posting) was at the end of the summer when windy days were rare. We have had plenty since, and these have given me new insights.
As anyone can see from close observation, the ripples do not radiate evenly from the inner edge, but start at the bottom, inner corner and radiate out and up on an angle to the far top corner. The top edge, at least in moderate winds, does not actually ripple, but flops side-to-side on a more-or-less straight line, out of sync with the bottom edge, and this produces the satisfying, inspiring snap. Why does it do this?
My earlier theory was that the angled ripples are somehow related to the attachment of the flag: the top inner corner is held tightly to the flag pole by the pulley, but the bottom corner is free to flop loosely on the halyard. So, on a breezy day, I climbed on the roof and observed the motion as I held the bottom of the flag tightly to the pole. (I am a bit concerned that none of the neighbors saw fit to call the police on seeing a 74-year-old man standing on the roof of his house holding onto a flag pole with the flag flapping in his face. What if I really became senile? Would they notice?) There was no change. The flag rippled as before, disproving this theory.
My other piece of data came while waiting at the Marcus Hook SEPTA train station one breezy morning. The station faces the Sunoco oil refinery and I could watch the flag high up on the main distillation tower where the wind coming off of the Delaware River is very strong. The ripples were coming rapidly and evenly straight from the flag’s inner edge, something I had not seen on mine. The wind speed is obviously a factor.
The center of gravity of the flag is at the physical center, and this weight is supported entirely by the upper corner. With no wind, the center of gravity hangs straight down from the pulley. As the wind picks up, the center of gravity is pulled up and out on an arc from the top pulley, and this determines the angle of the ripple. According to my current theory, that is.
In very strong winds, the force of gravity becomes insignificant. The ripples then come straight out, as in the Marcus Hook flag.
Apropos of nothing, while the leaves are down, I can see from my window a flag on Concord Pike as well as my own. Could life be sweeter? Also, Philadelphia’s 30th Street
train station has twenty flags! A group of four on each side of both front and back entrances (16 right there) plus one on each corner of the roof. A great sight on a sunny day What lucky person gets to raise them each morning?