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I've got an anemometer to measure wind speed.

Its ratio is $50Hz = 15.5m/s$, so my Arduino counts pulses in 3100ms, which should give a count of $100 = 10m/s$.

I can display this on a dashboard on the wall, but I'm more interested in an average.

(I'm just using this for fun, I'm not controlling the traffic on a bridge or in an airport)

But what makes more sense? I can count pulses for $(19*3.1) = 59.8 \text{seconds}$ and divide by 190 to get an average for 1 minute. Or the same for 10 minutes.

Or I could have a memory of the last p samples so I add the sample to a register, and divide with p, then at Tp subtract it from the register again, so I get a running average over the last minutes.

I could also take a weighted average of the current value and the current average as the next current average, which would emulate the charging and discharging of a capacitor. Something like

$$\overline{V} = \frac{V + (n-1)\overline{V}prev}{n}$$

Or should I take into the account that energy of the wind is proportional to the speed cubed?

So 1 minute of 10m/s and 1 minute of 20 m/s have the same energy of

$$ \sqrt[3]\frac{10^{3} + 20^{3}}{2} \approx 16.5 $$

Lenne
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    The energy of the wind is proportional to the speed squared. The power of the wind is proportional to the speed cubed. – Acccumulation Jan 04 '19 at 22:56
  • So would it give more sense to calculate the RMS than the average? – Lenne Jan 04 '19 at 23:57
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    It depends on why you want an average. If you want to know how far a free-floating balloon might drift in an hour, you want average velocity. If you want to know how much electricity a wind turbine might generate in an hour, you want average power (I think--anyway not just average speed). – David K Jan 05 '19 at 00:03
  • What kind of average would be the right to determine if it was safe to cross a bridge in a storm? – Lenne Jan 05 '19 at 00:08
  • You might experiment with "exponential smoothing". It's easy to compute, flexible, and is often used to smooth time series. https://en.wikipedia.org/wiki/Exponential_smoothing – awkward Jan 05 '19 at 13:32
  • @awkward, that's my second-last formula. I did invent that myself without knowing it was already invented ;-) – Lenne Jan 05 '19 at 14:41
  • To determine if it is safe to cross a bridge, you do not want an average, but rather max speed. It matters not if most of the crossing was a "breeze" if one gust pushes you over the edge! – Paul Sinclair Jan 05 '19 at 15:40

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