I’ve heard that a speed gun uses the Doppler effect to do some calculation and get the speed of a car, but can it work on multiple vehicles at the same time? How is it possible?
In: Physics
There are two main types of speed measurement devices used by law enforcement:
**Radar (Radio Wave)**
This type of device shines a beam of radio waves like a flashlight shines visible light. If you’ve ever shopped for flashlights, you know they come in varieties that can shine a very focused beam in the center, with a broader cone that is less bright.
Handheld radar speed detection devices do something similar. So the officer can point the device at a car and “focus” on a single target. This is only so effective though, and if there is a tight group of cars, there’s no guarantee that it’s getting only one car. The device will typically report back the strongest signal it receives. Some units have the ability to report the fastest vehicle detected, provided it is within a reasonable signal strength. It depends on the unit.
Dash mount radar speed detection devices can often report the speed of multiple vehicles in a group. Typically they will report the fastest and second fastest in a group. They disperse a beam of radar in a somewhat broad pattern, then look for signal reflections that are the shifted the most.
The way radar guns do all of this uses a fascinating math algorithm called Fast Fourier Transform, often shortened to FFT. This algorithm can convert single waveform into the signal strength (amplitude) at each frequency. [3Blue1Brown has a great FFT video](https://www.youtube.com/watch?v=spUNpyF58BY). You should definitely watch the first few minutes of that video before reading further, because it will make a lot more sense. It might seem complicated at first, but give it a few minutes.
So we know that the Doppler effect causes the radar waves bouncing off of a car to be shifted, and we know the frequency of the waves transmitted from the gun. The gun also has a sensor that records the radar wave being reflected back, sends it through a FFT, then looks at the amplitude peaks at various frequencies.
The thing is, the radio waves being bounced back to the gun come from everything in front of it. Objects at the transmitting frequency aren’t moving, so we can ignore those. Any radio waves shifted so that the object’s velocity would be greater than speeds cars are capable of can be ignored. So the analysis of the FFT plot can be focused on frequencies that are within the range of what we’d expect for vehicles traveling at automotive speeds.
Then we can look at the amplitude of various peaks. A car will reflect back radar at an amplitude that fits within a typical range. Any *really* strong signal can be ignored. The gun transmits at a specific amplitude, so we’d expect the signal to be less than that. On the lower end, we need a certain signal strength in order to make a reliable assessment, so we ignore anything below a certain strength.
What we’re left with are a series of peaks that represent the speed of objects in front of the device. Knowing how much each peak varies from the base frequency means we can tell how fast it is going. We could, theoretically, produce the speed of 10 objects if we wanted, but the signals processing required make this more-and-ore expensive.
**LIDAR (Laser light)**
Pretty much everything we learned about measuring speed with radar applies here as well. The key difference is that the laser light used by LIDAR equipment shines in a *very* focused beam. At 1,000 feet away, the LIDAR beam is only 3 feet across. That makes it suitable only for targeting specific vehicles.
The same FFT technique is used for processing the light that returns. We’re only looking for one peak though, and typically the strongest. Law enforcement are trained to aim for the car’s front bumper, which will produce a clear, strong peak.
**Use in Enforcement**
It’s probably worth mentioning that, in many jurisdictions, the use of speed detection equipment in traffic enforcement is only a used for verification. Also, the specific citation written will determine the role of detection equipment in the prosecution of the citation.
In many jurisdictions, traffic courts are operated in a way that doesn’t follow traditional court procedures. This is because most citations are not criminal in nature. Driving is considered a privilege, not a right. Constitutional protections still apply for any criminal charges, but the ability to suspend or revoke your license is much broader.
For example, an officer may choose to cite you for exceeding the speed limit (which typically requires a valid measurement) as well as other citations such as failure to use due care (which typically does not). Both will have penalties, but you can’t get the latter thrown out because of a technicality.
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