I was playing with my six year old daughter the other day with her toy airplanes (I’m a pilot and she’s very interested in aviation now). I took the little F16 toy and flew it passed her as quickly as I could. It moved fast enough that we couldn’t make it out until my hand was on the other side of my body. She asked, “Daddy, how fast would that be if I was in the cockpit?” That really got me thinking. How fast was I able to move my hand and make the toy jet move, and what would that speed be in a larger scale if it were the real sized thing, scale speed.
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$\begingroup$ You could try recording yourself spinning and swinging your hand the same way, and count the seconds/milliseconds it takes to perform a whole/half turn of your arm in a circle. After that find out the radius of your arm to your axis of rotation (middle of your body) and you can use some circular motion formulas to get a rough idea of your hands speed. $\endgroup$– CraigCommented Jun 22, 2023 at 14:42
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2$\begingroup$ I don't think the title and body really match each other, to me they ask different questions. The title seems to be asking what is the max speed a human hand could ever hope to move, while the body seems interested in how fast your specific hand movement was, which as Craig mentioned you can actually calculate with video footage. $\endgroup$– TriatticusCommented Jun 22, 2023 at 15:22
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1 Answer
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This question is asked rather vaguely. However, I try to come up with an answer that hopefully satisfies you. First of all, here are some specifications of the F16 (the large one of course) found on German wikipedia:
- Top Speed at optimal altitude: $V = 2142 \, \mathrm{km/h} \approx 2 \times 10^{3} \, \mathrm{km/h}$
- Length: $L = 14.52 \, \mathrm{m} \approx 15 \, \mathrm{m}$
If we just naively scale the speed by a factor that is the ratio of the toy's length $\ell$ and the real F16 lengths $L$, then the top speed $v$ of the toy model would be
$$v = V \cdot \frac{\ell}{L}$$
Since I do not know how large your toy is, but it obviously fits in your hand, I just assume it is about the same length. My own hand is eyeballed about $15 \, \mathrm{cm} = 0.15 \, \mathrm{m}$ long (how convenient the numbers) and so setting $\ell = 0.15 \, \mathrm{m}$ gives
$$\frac{\ell}{L} \approx 10^{-2} \quad \Longrightarrow \quad v \approx 20 \, \mathrm{km/h}$$
and so the scaled down top speed of the toy would be
- Top speed of toy F16: $v \approx 20 \, \mathrm{km/h}$.
I assume a human hand/arm may easily attain such a speed, although I did not measure nor extensively google it. I, however, found this SE post as a comparison, where it is stated that some baseball player threw his ball with record-speed of approximately $160 \, \mathrm{km/h}$. Since his hand must have been moving this fast, this should provide an upper bound of how fast your hand was. But in conclusion, it should be humanily possible to provide speeds to the toy model that exceeds the top speed of the scaled down F16.
