How fast am I going?

RADAR determined speed.

GPS speedometers are absolutely more accurate than speedometers using an algorythm based on timing the rotations of a wheel. But radar units are thought to be equal or better than GPS. Also more expensive.

In a car, the number of rotations of a wheel can be ascertained by attaching a cable to an axle, a differential, or even a transmission. The most accurate data collected is the data gathered at the wheel or axle as wearing of gears can affect accuracy over time.

Knowing how long it takes for a wheel to complete a revolution is the most accurate of mechanical methods of ascertaining speed, but the diameter of the wheel can be affected by tire wear, inflation pressure, even temperature.

Other inaccuracies can include friction in the cable housings of speedometers that use a magnet drive.

If known, the diameter of a wheel can be easily converted to its circumference, which can be converted to distance travelled per revolution. RPM's can be converted to MPH with simple math.

So determining speed is not reliably accurate just by looking at your speedo, yet it's more than accurate enough for you to avoid tickets.

Car manufacturers have also given you a little help there, In the US, auto makers calibrate their products by an "over read" of 10% plus 4, meaning if you are traveling at 20 mph, your speedo will read 10% higher (22), plus 4 mph for a total of 26 mph.

The 10% is to allow for the difference in wheel circumfrence in case you change tires from the manufacturer-installed ones to a different brand of the recommended size, and for the difference in tire pressure that is inherent with pneumatic tires as air molecules do escape from tires over time, which is why we need to check tire pressure every few weeks. Tire wear also causes decreased circumfrence which means more revolutions per minute per mph, all still figured into that 10% over read. The 4 mph is just more insurance.

So, if we never buy bigger tires than our car manufacturer recommends, and barring any mechanical failures, we can rest assured that we are always travelling at a speed less than that shown on our speedo.

Cops have another, more accurate means of determining your speed...radar. Radar measures your speed with algorythms applied to "doppler shift". I went to radar school as a California Highway Patrolman and served as the resident radar expert in San Juan Capistrano and in North Sacramento.

Part of my job in Sacramento was to calibrate all the speedometers in all the patrol cars and motorcycles used in speed enforcement periodically. One thing I found was that the more miles a car had on it, the less accurate its speedometer became, usually reading lower compared to true speed as it aged. Another thing I noticed was that speedos that were highly accurate at normal speed ranges of 25 mph to 95 mph became less accurate at high speeds, so it was sometimes difficult to get an accurate speed at 140 mph, but most often it was all still within that 10% + 4 inaccuracy window described above.

Of course, the radar units have the potential for inaccuracy, too. Each unit is tested when an officer begins his or her shift, by an internal calibration (testing the computer that applies the algorythm), and by a low speed (35 mph) and high speed (65 mph) "tuning fork" test. Enterprising officers would also test it against the vehicle speedo at various speeds of 100+ mph. Really enterprising officer would test it over a measured mile with a stopwatch. Being a math and science oriented individual, and a really enterprising officer, I tested my radar and car speedos daily and frequently performed measurements of various distances by using speed and time calculations.

You may wonder how I can measure the distance between 2 points with a stopwatch and a radar unit or speedometer and I will explain that shortly. But first I want to explain what Doppler shift is.

As you probably know, sound is transmitted by "waves", as are radio signals, cell phone signals, and teevee signals. These waves have a frequency that is measurable by receivers, which are also capable of presenting the data represented by the waves into something you can interpret.

For instance, your ears and brain are capable of receiving and interpreting sound waves so you can communicate audibly, enjoy music, etc.
Your radio can be tuned into different frequencies and translate radio waves into sound for you. A radar device sends out a signal then receives it back after it bouces off something.

This is how our defense can detect things like approaching nuclear missiles and is how an airport knows what is flying around it, departing, approaching, etc. The items it bounces off of have a "signature" that enable the receiver to ascertain what it bounced off of. Radar devices can determine the difference between a 747 and Cessna, and even the more subtle difference between a MIG 29 and a MIG 21.

But in speed determination, radar offers the critical component known as "Doppler shift". Doppler is the name of a person who discovered the Doppler effect in radar applications we use to determine speed. To explain it briefly, it is the change in frequency of radar (or other) waves in reflected waves by the receiver compared to the transmitted wave frequency.

To make it easier to "visualize" Doppler shift, imagine you are standing along side a train track and there is a train coming toward you. Trains are noisy so it is emitting sound waves that are easily received by your ears and your brain interprets these waves and identifies them as train sounds for you. As the train gets closer these sound waves change and the train sounds you hear change too. As it passes you, there is a significant change in the sound as the sounds are no longer being affected by the train approaching you and they change even more as the train moves away from you.

The sound wave changes are due to the speed and angle of the train in relation to your ears. This is the doppler effect. It can be measured.

Radar waves transmitted from a radar speed unit, bounce off everything they hit and reflect back toward the receiver. The change in frequency of objects moving toward or away from the unit increases (toward) or decreases (away from) the unit.

Faster moving objects create a greater change and neaerer or larger objects create a stronger signal. The radar units need very accurate and complex algorythms to determine speed, and the units can mis-identify your speed even when the cop has his radar gun pointed right at you. If there is a faster moving car within the beam, or a car nearer to the unit, or a larger vehicle in the vicinity, the speed of the faster, nearer or larger vehicle could be what shows on the receiver's display.

If I were to ever get a radar ticket, I would be sure to note any vehicles nearer to the cop's position, cars moving faster than me, or cars larger than me. I would immediately make a written notation with as much detail as possible as to the description of such vehicles, their position, direction and estimated speed. I would also ask the cop to identify the make and model of his radar unit and to show me the log book where he recorded the results of the required tests he made at the beginning of his shift. Take a picture of the log. Ask when he received radar training, where, and with what make and model of radar unit.

With the CHP, there were few radar units available but the ones that were available could be checked out by any officer, whether trained or not and most untrained guys never followed any of the rules for testing the equipment, had no knowledge of how they worked and could not explain tthe Doppler effect if queried. They wrote tickets and most of the time they wrote them to drivers who were speeding and never contested them, so they cheated and mostly got away with it. When I was the radar expert and an untrained user was called to court to testify on a radar ticket, I always urged them to ask the court to dismiss the case. Some just didn't show at court, I suppose.

Radar officers usually have to take a test to show they can estimate vehicle speeds by observing cars travelling at different angles away or toward them as well as perpendicular to their orientation. They should be able to qualify in court to enforce speed without their radar gun by estimate only. Officers should know when they were tested on estimating speeds, what speed ranges they were certified at, and the name of the person who tested them.

There is a lot to testify to in a court case involving radar speeding tickets.

I hope to be able to cover GPS speedometers in the future. They are getting quite cheap these days and might be something that interests people who are interested in accurate speed information. They are more accurate than the speedo on your car, can be a cheap replacement for a broken speedo, and are cheaper and about as accurate as radar.

How to measure the distance between 2 points with a stop watch and a speedometer or radar unit:

1) zero the stopwatch and drive past point a, starting the stopwatch as you pass point a heading toward point b.

2) maintain a contant speed until you pass point b, stopping the stop watch as you pass point b.

Convert your speed to feet per second. Feet per second is 1.47 times the MPH, so 30 mph turns out to be 44 feet per second. Multiply feet per second times the number of seconds it took to traverserse the distance, and your result is the number of feet between point a and point b.

Example: It took you 11.15 seconds to transerse your distance at 15 mph. 15 mph = 22 fps, thereforse 11.15 times 22=245.3 feet