Radar speed gun

Radar speed guns use Doppler radar to perform speed measurements.

Radar speed guns, like other types of radar, consist of a radio transmitter and receiver. They send out a radio signal in a narrow beam, then receive the same signal back after it bounces off the target object. Due to a phenomenon called the Doppler effect, if the object is moving toward or away from the gun, the frequency of the reflected radio waves when they come back is different from the transmitted waves. When the object is approaching the radar, the frequency of the return waves is higher than the transmitted waves; when the object is moving away, the frequency is lower. From that difference, the radar speed gun can calculate the speed of the object from which the waves have been bounced. This speed is given by the following equation:

${\displaystyle {v}={\frac {\Delta f}{f}}\times {\frac {c}{2}}}$

where ${\displaystyle c}$ is the speed of light, ${\displaystyle f}$ is the emitted frequency of the radio waves, and ${\displaystyle \Delta f}$ is the difference in frequency between the radio waves that are emitted and those received back by the gun. This equation holds precisely only when object speeds are low compared to that of light, but in everyday situations, this is the case and the velocity of an object is directly proportional to this difference in frequency.

After the returning waves are received, a signal with a frequency equal to this difference is created by mixing the received radio signal with a little of the transmitted signal. Just as two different musical notes played together create a beat note at the difference in frequency between them, so when these two radio signals are mixed they create a "beat" signal (called a heterodyne). An electrical circuit then measures this frequency using a digital counter to count the number of cycles in a fixed time period, and displays the number on a digital display as the object's speed.

Since this type of speed gun measures the difference in speed between a target and the gun itself, the gun must be stationary in order to give a correct reading. If a measurement is made from a moving car, it will give the difference in speed between the two vehicles, not the speed of the target relative to the road, so a different system has been designed to work from moving vehicles.

In so-called "moving radar", the radar antenna receives reflected signals from both the target vehicle and stationary background objects such as the road surface, nearby road signs, guard rails and streetlight poles. Instead of comparing the frequency of the signal reflected from the target with the transmitted signal, it compares the target signal with this background signal. The frequency difference between these two signals gives the true speed of the target vehicle.

Modern radar speed guns normally operate at X, K, K_a, and (in Europe) K_u bands.

Radar guns that operate using the X band (8 to 12 GHz) frequency range are becoming less common because they produce a strong and easily detectable beam. Also, most automatic doors utilize radio waves in the X band range and can possibly affect the readings of police radar. As a result, K band (18 to 27 GHz) and K_a band (27 to 40 GHz) are most commonly used by police agencies.

Some motorists install radar detectors which can alert them to the presence of a speed trap ahead, and the microwave signals from radar may also change the quality of reception of AM and FM radio signals when tuned to a weak station. For these reasons, hand-held radar typically includes an on-off trigger and the radar is only turned on when the operator is about to make a measurement. Radar detectors are illegal in some areas.[7][8]

The primary limitation of hand held and mobile radar devices is size. An antenna diameter of less than several feet limits directionality, which can only partly be compensated for by increasing the frequency of the wave. Size limitations can cause hand-held and mobile radar devices to produce measurements from multiple objects within the field of view of the user.

The antenna on some of the most common hand-held devices is only 2 inches (5.1 cm) in diameter. The beam of energy produced by an antenna of this size using X-band frequencies occupies a cone that extends about 22 degrees surrounding the line of sight, 44 degrees in total width. This beam is called the main lobe. There is also a side lobe extending from 22 to 66 degrees away from the line of sight, and other lobes as well, but side lobes are about 20 times (13 dB) less sensitive than the main lobe, although they will detect moving objects close by. The primary field of view is about 130 degrees wide. K-band reduces this field of view to about 65 degrees by increasing the frequency of the wave. Ka-band reduces this further to about 40 degrees. Side lobe detections can be eliminated using side lobe blanking which narrows the field of view, but the additional antennas and complex circuitry impose size and price constraints that limit this to applications for the military, air traffic control, and weather agencies. Mobile weather radar is mounted on semi-trailer trucks in order to narrow the beam.

A second limitation for hand-held devices is that they have to use continuous-wave radar to make them light enough to be mobile. Speed measurements are only reliable when the distance at which a specific measurement has been recorded is known. Distance measurements require pulsed operation or cameras when more than one moving object is within the field of view. Continuous-wave radar may be aimed directly at a vehicle 100 yards away but produce a speed measurement from a second vehicle 1 mile away when pointed down a straight roadway. Once again falling back on the training and certification requirement for consistent and accurate visual estimation so that operators can be certain which object's speed the device has measured without distance information, which is unavailable with continuous wave radar.

Some sophisticated devices may produce different speed measurements from multiple objects within the field of view. This is used to allow the speed-gun to be used from a moving vehicle, where a moving and a stationary object must be targeted simultaneously, and some of the most sophisticated units are capable of displaying up to four separate target speeds while operating in moving mode once again emphasizing the importance of the operators' ability to consistently and accurately visually estimate speed.

The environment and locality in which a measurement is taken can also play a role. Using a hand-held radar to scan traffic on an empty road while standing in the shade of a large tree, for example, might risk detecting the motion of the leaves and branches if the wind is blowing hard (side lobe detection). There may be an unnoticed airplane overhead, particularly if there is an airport nearby, which again emphasizes the importance of proper operator training.