How do radar guns work?

SDStaff Q.E.D. replies:

In its simplest form, radar (really, it should properly be RADAR, since the term is an acronym for RAdio Detection And Ranging, but it has long since entered the lexicon as a word in its own right, so “radar” it is) is a directed radio-frequency transmission that can bounce off an object and return information about it. This information can include the shape, size, location, distance, velocity and even the composition of the object, measured either directly or indirectly. Radar was developed during World War II to locate enemy aircraft and ships and has found its way even into mundane activities such as shopping: Many supermarkets use low-power radar to detect the motion of a person or shopping cart and automatically open the doors.

Speed radar was first used in the U.S. in 1947. Early units used vacuum tubes and were extremely bulky. They transmitted in the S-band at around 2.455 gigahertz (GHz), very close to today’s microwave ovens, which operate at 2.45 GHz. Radars using the X-band at about 10.525 GHz were introduced in the mid 1960s. Around 1976, radars began using the K-band on two channels, 24.125 and 24.150 GHz. The problem with K-band is that it’s close to a band of frequencies readily absorbed by water, which is centered around 22.24 GHz. As a result, K-band radar is strongly diminished by high atmospheric moisture such as fog and heavy rain. Modern traffic radars almost always use the Ka-band nowadays, on one of 13 channels from 33.4 to 36.0 GHz in either narrow band or wideband mode. Higher frequencies are preferred because, all things being equal, they have a narrower beamwidth than lower frequencies, which improves range and accuracy.

There are three main modes of traffic radar operation. Continuous, or CW, radars are always on and are mostly used nowadays for unattended operation, such as in those roadside trailers with big LED speed displays that tell you how fast you’re going. They’re also used in automated speed traps. Pulsed-mode radars emit a brief pulse every few seconds, with the timing being variable by the operator. The intermittent pulse provides a level of countermeasure against radar detectors. Pulsed radars are most often used for continuous, light-duty traffic monitoring while the police cruiser is in motion, and are also frequently used in unattended operation. Instant-on radar is manually triggered by an officer parked at the roadside, and is often in the form of a gun-type device that can be carried virtually anywhere. Radar detectors are rendered virtually useless by instant-on radar, unless you’re fortunate enough to catch a radar reflection from a car being targeted ahead of you.

Instead of directly measuring the time it takes for a pulse to bounce back as you might expect, police radars make use of the frequency shift caused by the Doppler effect. The Doppler effect is caused by the motion of the wave source or an object the waves bounce off of. You’ve probably noticed the pitch of a train whistle rise as it approaches, then fall once it passes. You’re hearing the Doppler effect. Let’s examine briefly why it happens.

First, let’s start out with some assumptions. Number one is the speed of sound. We’ll call it 344 meters per second (m/s) — the actual speed can vary considerably, depending primarily on temperature, air pressure and humidity. Number two is the natural frequency of the train horn. For simplicity, we’ll say it’s 1 kilohertz (kHz) or 1000 cycles per second. The third is the speed of the train — again, for simplicity, we’ll call it 10 m/s, or about 22.3 MPH. Now let’s examine what happens when the train, moving towards us at 10 m/s, sounds its 1 kHz horn. The clock starts when the first pressure wave reaches our ears. We’ll pretend that happens exactly at a wave peak. The next peak is due exactly 1/1000th of a second after that, but because of the motion of the train towards us, the next peak arrives slightly sooner than expected. How much sooner? Well, in that .001 second, the train, at 10 m/s, has moved 1 centimeter, which means that the second peak had to travel 1 centimeter less distance than the first peak. If the speed of sound is 344 m/s, then the wavelength of a 1 kHz sound is 34.4 centimeters. A sound with a wavelength 1 centimeter less, or 33.4 cm, would therefore have a frequency of 34.4/33.4 x 1 kHz, or 1.029 kHz.

Police radar uses this same principle to measure vehicle speed, only it uses microwaves instead of sound. The radar is aimed at traffic, and the control unit measures the difference between the frequency of the emitted signal and the frequency of the return signal. It figures in the speed of the police car and displays the result on the front panel as the speed of the car being targeted. It makes no difference with most typical speed radars if the car is moving towards or away from the radar — the system merely needs to know the difference in frequency between the transmitted and received signals plus the speed of the police cruiser in order to calculate the target’s speed.

Various errors can affect the accuracy of the reading. The most prominent, called cosine error, is caused by the radar beam striking at an angle to the path of the target vehicle — the greater the angle, the larger the error. The effect is to measure a lower speed than the target is actually traveling. Some radars can be programmed to compensate for this error by inputting the angle. Another source of error is frequency drift due to temperature change, voltage fluctuation, etc. This can be minimized through compensating circuitry.

Police officers are specially trained and certified to operate these units, and must be periodically recertified. Part of the training includes learning how to ensure that the vehicle the officer thinks is being targeted is actually the one the radar is measuring. The radar units themselves can help in this regard by displaying information such as the speed of the strongest return target and the speed of the fastest target. The strongest return is usually from the nearest vehicle, all else being equal. Larger vehicles, such as tractor trailers, will return a stronger signal as well, but these can also be readily identified visually. Visual cues are important in other ways, such as noticing that one vehicle is obviously traveling faster than the others on the road. Using visual information, displayed readings and other techniques, the officer can establish with high confidence that the intended target is the one actually measured.

Radar units must be periodically calibrated and recertified. Certifications for both the unit and the operator may need to be presented in court if a motorist contests a speeding ticket. In short, a number of safeguards and checks are in place to ensure the radars are used properly and effectively, and that the information they return is accurate and interpreted correctly.

SDStaff Q.E.D., Straight Dope Science Advisory Board

Send questions to Cecil via cecil@straightdope.com.

STAFF REPORTS ARE WRITTEN BY THE STRAIGHT DOPE SCIENCE ADVISORY BOARD, CECIL’S ONLINE AUXILIARY. THOUGH THE SDSAB DOES ITS BEST, THESE COLUMNS ARE EDITED BY ED ZOTTI, NOT CECIL, SO ACCURACYWISE YOU’D BETTER KEEP YOUR FINGERS CROSSED.