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I'm trying to build a DIY tool to measure the speed of something moving very fast in a straight line, e.g. a bullet exiting the barrel of a rifle, based on the Doppler effect.

I've looked for several Doppler radar modules online, but most of them state a maximum speed detection of 150-350 mph (that is ~67 to ~156 m/s), which is way under your typical rifle bullet moving at 700-1000 m/s.

Commercial products built specifically for that purpose (measuring the speed of a bullet) state a frequency of ~120 GHz. I'd like to understand why such a high frequency is needed.

I can understand why a "too low" frequency, let's say 100 Hz, would be an issue:

  • The bullet is moving at 1000 m/s
  • To detect the waves bouncing back, the bullet must not be too far from the radar, let's say 1 m at most
  • So if the frequency is 100 Hz, we'll probably miss the bullet because in 0.01s (1 / 100 Hz) the bullet could already be 10 m away (1000 * 0.01 / 1), exceeding our given 1 m detection range.

However, with the same reasoning, a few KHz would be more than enough to measure the speed of the bullet.

Why, in reality, do we need much higher frequencies such as 120 GHz to measure the speed of a bullet? Is there a formula to calculate the required frequency?

ocrdu
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GuiTeK
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  • The electric field is continuous, so it's not possible to "miss" it; there are no gaps. The problem with a very low frequency is going to be how accurately you'd be able to measure the (tiny) frequency shift. If you try a very low frequency you will have larger uncertainty in frequency shift and so less accurate measurement of velocity. – user1850479 Feb 15 '24 at 00:19
  • Do you really have to use Doppler radar for this? Optical detection would be so much simpler if you can use it. – TooTea Feb 15 '24 at 11:30
  • This is the same reason you can see through your microwave oven door - the frequencies in the oven are low enough that those little holes are as if they aren't there. It's the same with your bullet. If the wavelength of the RF is much larger than the thing you're trying to measure. it's almost like it's not there (the bullet). – Steve Feb 15 '24 at 15:56

2 Answers2

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Why, in reality, do we need much higher frequencies such as 120 GHz to measure the speed of a bullet?

For such a small object, you need a very high frequency with a very short wavelength (roughly about the same size as the bullet) in order to get a decent reflection. So, say the bullet is 10 mm long, that means an RF operating frequency of at least 30 GHz.

120 GHz easily fits the bill and, for other reasons (such as detecting a lot of reflected cycles in a high-level of background noise) might be imperative.

Andy aka
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You’re right. We don’t need super high frequencies, it just is cheapest that way. With lower frequencies you need bigger antennas, very low noise (potentially cryogenically cooled) preamplifiers to get enough sensitivity to detect the very weak signal, and/or high transmitter output (needs licensing or an anechoic chamber), and so on.

If you had a little X-band transmitter somewhere near the NRAO dish and shot a bullet away from the transmitter, they’d have no trouble plotting the Doppler shift for you. The hourly operating cost for that place is a wee high for personal budgets though :)

Kuba hasn't forgotten Monica
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