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There is a well known video of a helicopter with 5 evenly spaced rotor blades where the rotor is synced with a digital camera's frame rate.

Assuming the camera is at 60 hertz (60 frames per second), the rotor must be spinning at x/5 * 60. Where it seems like x could be any integer. However, let's say x is 1. So the rotor is spinning at 12 hertz. It's quite possible that in actuality, it's spinning slower than that, so my equation of rotor rate = x/5*60 seems to be incorrect.

The reason is that given the footage, it's impossible to say if a single rotor is spinning all the way around, or just 1/5, or 3/5 around, etc. Or 8/5 around.

What is the description/name of the relationship between x and 60? It's not a factor is it?

Here's the original vid: https://www.youtube.com/watch?v=yr3ngmRuGUc

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  • $\begingroup$ why not describe x as a multiple of 12? $\endgroup$ – David Diaz Jul 2 '18 at 1:32
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    $\begingroup$ "The rotor must be spinning at either 60 hertz or $\frac{x}{5}\cdot 60$ hertz where $x$ is an integer"... the first case is covered by the second case by letting $x=5$, so there is no reason to mention it. Further, the second case can be simplified to say "the rotor must be spinning at $x\cdot 12$ hertz where $x$ is an integer." Here, I would call $x$ a factor of the total hertz, but certainly not necessarily one of $60$. $\endgroup$ – JMoravitz Jul 2 '18 at 1:32
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    $\begingroup$ Not to nitpick, but I suppose $x$ needs to be, more specifically, a nonnegative integer. If $x$ were allowed to be $0$ then it would no longer be an illusion but it would actually be hovering. $\endgroup$ – WaveX Jul 2 '18 at 1:35
  • $\begingroup$ @DavidDiaz here is where it gets confusing. The rotor can obviously be spinning slower than 12 hertz, so I guess x does not need to be an integer. I am not sure how to explain it that's why I brought forth the question. $\endgroup$ – Alexander Mills Jul 2 '18 at 1:49
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What you seem to be describing here is aliasing or folding where your system's frequency cannot be distinguished from another frequency that's reflected across the Nyquist Frequency.

But that's not $1/x$: if your sampling rate is, say, $60\text{Hz}$, your Nyquist frequency is $30 \text{Hz}$, and phenomena running at $25 \text{Hz}$ will have aliases at $60k - 25 = (35 + 60k)\text{Hz}$ and $(25 + 60k)\text{Hz}$.

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  • $\begingroup$ Honestly this doesn't make that much sense to me, where the heck did you get 30hz from, 60hz/2? $\endgroup$ – Alexander Mills Jul 2 '18 at 1:50

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