Please turn on javascript in your browser to play chess.
Posers and Puzzles

Posers and Puzzles

  1. Subscriber sonhouse
    Fast and Curious
    01 Mar '13 18:44 / 1 edit
    I am using a nice new LED stroboscope to measure water flow on a flow switch made by Proteus.

    It has 6 paddles arranged every 60 degrees around the circle, symmetrically arranged, and water forces it to move in response to the flow. There are several flow models in this line.

    You can measure the actual flow with a stroboscope.

    So I find the lowest PPM setting at 387 pulses per minute, which if the same paddle is shown in the same position, that would be the same as the RPM'.

    So you can get other numbers to stop the paddles,
    like this: (all in Pulses per minute)

    387, 450, 538,677,904,1361,2696.

    I see two problems here. One is why don't they go up linearly, these numbers are anything but linear.

    The second problem I see here is there are 7 numbers, not 6. Since the paddles are arrange in a hex pattern and are exactly 60 degrees apart, how does a strobe manage to stop the image on the last one, 2696 ? All the other numbers from 60 PPM to 10000 or so do not stop the paddles, hold them steady.

    Only those 7. But why 7 and not 6? And why are they not a time sequence more in line with the paddles being 60 degrees apart? I think it safe to say the lowest frequency that gives a steady paddle image would be the actual RPM's and the other numbers stopping them would be 60 degrees shy of the paddle reaching top dead center and here are the numbers I calculated should be showing if things were linear: (rounded off)
    At 387 RPM there should be about 0.025 seconds between paddle wheels (each 60 degree jump) so subtracting .025 from the original, inverting and multiplying by 60 for each one gives numbers I think they should be reading:

    387, 461, 571, 750, 1090, 2000. Notice how the entire spread is smaller than the list I gave at the beginning. Why aren't I reading #'s more like those?
  2. 01 Mar '13 22:24 / 1 edit
    I think 387 (60/387 = 0.15503876 seconds) is probably the time for 7/6 ths of a revolution, meaning the time between paddles is about 0.022148 seconds, which predicts flash rates rounded to the nearest integer of:

    387, 452, 542, 677, 903, 1355 and 2709

    Those are very close to your measurements, so the wheel is rotating at about 451.5 rpm
  3. 02 Mar '13 00:53
    Take 60/x for each of your strobe rates, and put them in reverse order, when plotted on an x/y chart you should see that they lie in a nice straight line intercepting 0,0
  4. Subscriber coquette
    Already mated
    07 Mar '13 16:53
    Originally posted by iamatiger
    Take 60/x for each of your strobe rates, and put them in reverse order, when plotted on an x/y chart you should see that they lie in a nice straight line intercepting 0,0
    you are amazing! my head was swimming in garbage theory. this is the same as try plugging it in!
  5. 07 Mar '13 22:07 / 1 edit
    Reworked my best guess with a line fit setting intercept to 0,0. I now think it is 450.6044207 rpm, giving a time for 1 rotation of 0.0221924143254389. This fits the measurements quite well with a rms of 4.78

    The full set of predictions are:

    Measured Predicted
    387 386.2324
    450 450.6044
    538 540.7253
    677 675.9066
    904 901.2088
    1361 1351.813
    2696 2703.627

    predicted is x*n/60
    where x is 0.0221924143254389, the "time for 1 paddle"
    and n varies from 7 to 1 representing the number of paddles that go past between flashes.

    I would have thought you should see stationary paddles with many lower flash rates too, e.g:
    338, 300, 270, 246, 225, 207...
  6. Subscriber sonhouse
    Fast and Curious
    11 Mar '13 01:03 / 2 edits
    Originally posted by iamatiger
    Reworked my best guess with a line fit setting intercept to 0,0. I now think it is 450.6044207 rpm, giving a time for 1 rotation of 0.0221924143254389. This fits the measurements quite well with a rms of 4.78

    The full set of predictions are:

    Measured Predicted
    387 386.2324
    450 450.6044
    538 540.7253
    677 675.9066
    904 901.2088
    1361 1351.813
    2696 see stationary paddles with many lower flash rates too, e.g:
    338, 300, 270, 246, 225, 207...
    I have hit the paddles with numbers lower than 338 but haven't found them yet. Thanks for the work!

    When I find #'s above 2700's, I get still images but the paddles are very narrow, not sure why, but at least I verified it was going about 450 RPM.

    But why are there 7 numbers and not 6? There are only 6 paddles.
  7. 11 Mar '13 05:21
    Hi sonhouse, apparently cinema film can be run as slow as 16Hz and still be perceived as stationary by the human eye/ brain. So above about 60*16 = 960 flashes per minute, your eyes will try to average up multiple flashes into one picture and you quite literally cannot trust the evidence of your own eyes. At very high flash rates you will hit a frequency where the the brain can only process one in n of the flashes so you will see false stationary paddles which are fainter (and perhaps thinner?) than they should be because they were only "there" for 1 of the n flashes integrated up by the brain/eye.

    As for 7 and not 6, as I said above, it looks as if you got 7/6ths of a rotation during the slowest strobe rate, which also brings a paddles back to the same position as another paddle and looks stationary.
  8. Subscriber sonhouse
    Fast and Curious
    11 Mar '13 07:46
    Originally posted by iamatiger
    Hi sonhouse, apparently cinema film can be run as slow as 16Hz and still be perceived as stationary by the human eye/ brain. So above about 60*16 = 960 flashes per minute, your eyes will try to average up multiple flashes into one picture and you quite literally cannot trust the evidence of your own eyes. At very high flash rates you will hit a frequency w ...[text shortened]... which also brings a paddles back to the same position as another paddle and looks stationary.
    I will remedy that situation the next time I have to clean the flow switch, it comes apart, so you just turn off the cooling water and take the front cover off and clean it and while I am doing that, dob something like white out on one of the paddles and then I will have only one strobe # that will show the paddle in the same position each time. The cooling water is not as clean as we would like it to be even though it is filtered, eventually rust browns out the water and requires us to change the water in the chiller, we use distilled water which we get by the pallet full, it takes 20 gallons to fill.
  9. 15 Mar '13 23:08 / 1 edit
    That sound a fine idea, let me know what rotation rate you get then.

    By the way, I found a guide to using stroboscopes to measure rotation rate, and it says that below 300 fpm the human eye isn't tricked into seeing a stationary image by the flashes, which is probably why you can't find any stationary paddles below that.

    see:
    http://www.monarchinstrument.com/pdfs/Strobe%20for%20RPM.pdf