From: Doctor Nisith Bairagi Subject: Vanishing of Rotating Fan Blades at Critical Speed::Ension Phenomenon (sci.math.independent) Date: May 7, 2013 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Dear Readers, I am presenting an interesting common observation through a proposed phenomenon of of Ension. Please comment on this new concept, for betterment. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (A) Observation:: [Replaced Medium, Ension] : At a high speed, the rotating blades of a fan appear to vanish, creating a sense that, as if there are no blades at all. But the Replaced Medium, which apparently replaces the rotating blades, allows the light from the other side to pass directly through it, showing light of reduced intensity. The phenomenon of apparent vanishing of rotating disc, having cut-outs intermittently (i.e., holes and no-holes alternatively arranged in regular pattern at a certain radial distance from the centre), transmitting light of reduced intensity from the other side, is identified as ENSION, and the critical speed at which Ension occurs, is identified as En-speed. Starting from the centre (r = 0) towards the outer most periphery of the blades (r = max), the transparency varies linearly from zero (dark) to maximum (maximum clarity). At Ension, it is possible to read a write-up clearly held behind the rotating blades with sufficient clarity.
(B) Question is:: [Vanishing of rotating blades-where?] : Question 1: Where have the opaque blades vanished totally as a result of the effect of rotating of the blades at some critical angular speed? Question 2: On the contrary, since every moment, the clear space is getting covered by the opaque blades, the observer could as well see the entire circular portion as dark, all the time, instead.
(C) The phenomenon of Ension can also be described in a number of different ways:
(a) Experiment 1:: [Ension, En-speed] : Take an opaque disc of radius R and punch a small hole, H at a radial distance r, (r < R). Place a source of light at the eye level through the single hole, H. At lower speed, blinking (or twinkle) effect will reach the eye. At En-speed, the observer will see a continuous circular ring of light at the radial distance r, containing the single hole, H.
If, I<0> = intensity of the original light source at a distance d from the eye I<1> = intensity of light at Ension through the ring of light, (I<1> is less than I<0>) and, I<1> / I<0> = U<1N>, [suffixes 1N::1 = one hole, N = En-speed] = refractive index of the Ensioned medium wrt air [1 = one hole, N = En-speed]. = velocity (or intensity) of light through 1 hole at Ension / velocity (or intensity) of light in air Instead of one, if there are, n number or of concentric holes, En-speed required for Ension will be far less than that for one hole. Then En-speed (required) for n number of holes = En-speed (required) for 1hole / n I<n> = [n.U<1N>].I<0>
(b) Experiment 2:: [Single intensity] : Take an opaque card board of rectangular size (length = L, Width = B), and fix an axis along the width at mid-length of L, so that both sides of the axis, there are equal rectangular , A<2> = (L/2) x B, so that the arrangement appears as two equal vanes fixed on either side of the axis, diametrically opposite to each other.
At poison 0 deg [full view of 2 number of (L/2 x B)], no light from the other side will be visible through the card board. For further rotation of 90 deg, full light will be visible, since the card position now is just a vertical line (of width = B). This way, further 90 deg, and another 90 deg, the positions of the card board will give similar situations as that of 0 deg and 90 deg, respectively. That is, for one complete 360 deg turn, two full view of light and two full no-view of light coming from the other side of the card board, can be viewed, creating similar situation as that of the rotating disc with two holes placed diametrically opposite two each other. In between the positions, the variation of the reduced intensity of light through the replaced medium, shows repeated cycle from zero to reach maximum, again from it to reach zero, and so on.
At Ension, the intensity of light through the zone covering the portion, (L/2) x B, will be termed as Single intensity.
(c) Experiment 3:: [Differential Vane System, Double intensity] : In Experiment 2, take the axis not at the symmetry line, but shifted parallel to it, so that, for the card board: the length of the right side = a, and that of the left side = b, (a > b, a + b = L). Area of the left side, A<1> = b x B, and that of the right side = a x B. Thus, the right side gets an area, A<2> = (a-b) x B, more than that of the left side. This arrangement of the vane system is to be termed as: Differential Vane System.
For every one complete 360 deg turn, viewed from either right or left side of the axis of rotation, the area A<2> will give two full views and two no-views, but the area A<1> will show views double to that as shown by the area A<2>. Zone A<2> (towards the outer periphery of the vanes) will show much more clarity than that by zone A<1> (near and adjacent to the axis of rotation). This is because, Ension at zone A<2> occurs at much earlier at lower En-speed, and that at zone A<1> requires much higher En-speed.
At Ension, the reduced intensity will not show continuous variation from the tip (r = a) to the axis (r = 0). A sudden vertical jump in the intensity of reduced light through the replaced medium, will be noticed at r = b, (at the common boundary of A<1> and A<2>).
(D) Application :: Utilising the simple behaviour of the differential vane system at Ension, light intensity of intense nature can be converted /reduced to a comfortable one, instantly. This system has a good resemblance to the principle of the step-down transformer, where a high voltage is required to reduce to a smaller one. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Thanks to All.
Doctor Nisith bairagi Uttarpara, West Bengal, India ^^^^^^^^^^^^^^^^^^^^^^^^^^