# Doppler effect, or the issue of accuracy of speed determination by traffic police radars

When people talk about the Doppler effect, I always remember the old Soviet joke.

*Once, a scientist drove a red traffic light and was stopped by an inspector.
– Are you breaking? – the Inspector asked
The resourceful scientist decided to show off his knowledge.
“Not at all, Comrade Inspector.”
– Why did you go to the red traffic light?
– You see, it seemed to me green due to the Doppler effect
The inspector was also with a technical education and deprived the scientist of a driver’s license for astronomical speeding.*

### The essence of the phenomenon

In fact, the Doppler effect – the phenomenon of changes in the frequency of waves recorded from moving objects or moving objects – is observed everywhere. This is true both for sound and for electromagnetic waves (of course, with certain corrections).

We constantly encounter the Doppler effect in life, for example, when we hear the sound of an approaching siren and then of a departing one. At first the sound seems higher, and then – on the contrary, lower in tone. Theoretically, it was justified by an Austrian physicist back in 1842, and today this effect is applied in many fields of science and technology – from space research … to writing fines to drivers.

The Doppler effect can be briefly described as follows: the movement of one object relative to another leads to the fact that the wave peaks arrive from the source to the receiver late (or ahead), and this causes the signal frequency to change.

Therefore, the wavelength for the detected radiation is determined by the formula (all calculations can be found in Wikipediabut if you are too lazy, we also moved them here).

And the frequency that the fixed receiver registers is determined by the formula

### Police radar

In the case of police radars, we are talking about radio waves, therefore, the calculation formulas do not take into account the parameter C – the signal propagation speed in the physical environment. Instead, a special theory of relativity is used, and the formula takes the form:

In this formula, C is the speed of light, and V is the speed of the source relative to the receiver. The cosine of Theta reflects the angle between the direction to the source and the velocity vector in the reference frame of the receiver.

Police radar is both a signal source and a receiver that records the frequency of the reflected radio frequency radiation.

Most modern radars operate in the K band, which means they emit radiation at a frequency of about 24.15 GHz. The signal reflected from a moving object has a different frequency. And to determine the speed of the car, the difference is halved, and the relative radial speed is calculated according to the formulas above.

Manufacturers of modern radars, such as ARROW, declare an error of no more than 1 km / h, and the error of the KRIS-P is 1 km / h. Older radar models may have an error of up to 2 km / h. Radars with greater accuracy are no longer used

Thus, it turns out that if the radar speed of your car gets into the radar field of view, in most cases it will be determined with an accuracy of 2 km / h. In this case, the radar will not take into account that component of the velocity, which is directed perpendicularly. That is, when driving in a turn, as well as on hilly terrain, the recorded speed of the car will be the lower, the greater the component of the direction of movement, perpendicular to the line connecting the radar and the car.

If the movement occurs in a straight line, without changes in elevation and turns, it can be considered. that the radar registers your speed and, in the worst case, +2 or +5 km / h, given the “reinsurance” factor.

However, you should not think that these units of kilometers per hour can be determined by the speedometer of the car. Today, manufacturers specifically overestimate speedometers to increase traffic safety. And even if you think that you are traveling at a speed of 100 km / h, in practice it may turn out that the actual speed does not exceed 90 km / h.

That is why devices with a built-in GPS receiver, such as DVRs with GPS informers, for example, Playme Sigma, radar detectors, such as Playme Silent 2 or Playme Hard 3, or combo devices, for example, Playme P570, are used to effectively determine speed. According to satellite data, you can determine your real speed and move as quickly as possible, but in the allowed mode.

### Laws and fines

Today, in the Russian Federation, the law defines a threshold of non-fines of 20 km / h (which in the near future can be reduced to 10 km / h), which allows you to avoid a fine if you exceed speed in this limit. That is, you can not be afraid of fines if you are traveling at a speed of 15-18 km / h more (and soon – 5-8 km / h more) allowed. Otherwise, the camera error may not be in your favor.

In Europe, there is a slightly different scheme for the formation of fines. Different countries set different thresholds for speed violation. At these thresholds, instrument errors are already “protected”. For example, in Austria this parameter is 3 km / h for a stationary laser radar, 5 km / h for a stationary radio radar, and 7 km / h for a mobile radar. In Belgium, France and Italy – 5 km / h for all types of radars. In Finland, violations of 7 km / h + radar error are taken into account, and in Serbia they are fined even for an excess of 1 km / h, without taking into account the error of radars. That’s where it is not necessary to overclock too much.