How do you use cosine error to beat a radar or laser speeding ticket?

Answer 1

The below information is incorrect. The cosine error does in fact cause a lower reading than the actual speed, but if the target speed is correct and the patrol car speed is in error due to the cosine effect, it will make the radar system "think" that it is moving slower than it actually is. Therefore when you take the measured speed minus the errored patrol car speed you will get a higher number than your actual speed. Example. I am driving 45mph and the patrol car is traveling at 45mph toward me. Without accounting for the patrol cars speed the radar detector would tag me at 90mph. The radar in the patrol car, however, takes a measurement of the patrol car relative to the ground in front of it, if that measurement is correct it will read the patrol car speed at 45mph and subtract that from the 90mph reading to get a correct measurement of my speed at 45mph. Now what if the patrol car speed is miscalculated due to the cosine effect. If the radar that is measuring the patrol car speed tags an object at a large angle, the cosine effect would cause the patrol car reading to be much lower than anticipated. if that reading make the patrol car believe it is traveling 35 mph, then when you subtract the 35 from 90, the radar will think I am moving at 55mph. causing a higher reading due to the cosine error on the patrol car speed (not the target)

(ORIGINAL POST BELOW)

You can't. Cosine error actually works <i>in your favor</i> in incidents of the use of traffic radar or laser speed detection.

The hand-held units law enforcement types use are pointed at vehicles that are basically coming "head on" at the officer and the unit. (Sometimes moving away.) These units detect Doppler shift in the electromagnetic signal that is returned from the target. The returned signal is compared to the one sent out. The greater the difference in frequency, the higher your speed. It's like being trackside in the middle of a long straight at an F1 event. The cars coming at you sound "higher" in pitch than when they are in front of you, and the ones moving away sound "lower" in pitch than the ones in front of you. That's Doppler shift. It works with electromagnetics as well as the mechanical energy of sound.

Let's take a "worst case" instance and look at that. Imagine you are moving at a right angle to the line of sight of the officer and his unit. You will be seen to be moving "across" his field of vision, but how fast? If a laser is used, the light leaves the unit, touches your vehicle and gets back to the unit <i>really fast</i>. Speed of light. But in the instant the laser does this, your car has hardly moved. It's the same with the microwave signal of the radar gun. But that's not the point.

The point is, you are moving <i>across</i> the field of vision. Your actual motion <i>toward</i> or <i>away</i> from the officer and his unit is zero. As regards the radar gun, the frequency of the returned signal matches the frequency of the transmitted one - there is <i>no</i> Doppler shift. You could be going a hundred miles an hour and the laser (or in this case the microwave beam) would not see you as moving toward or away from it at all. Your speed (zero mph) is "cloaked" by cosine error. You got away clean.

You won't be making your case with cosine error. You will have to find another method to beat the ticket. Say, "look past" error. But consider that the cops have been down this road before. A lot. So has the court. Good luck.

The only possible way to use cosine error would be in questioning the officer on the stand. Provide some introductory questions...what was the weather like, what was your position on the road, were you preoccupied with any additional tasks, etc. Then move into a few tougher questions about radar and slip in, "Was there any error in the measurement you took of my vehicle?" The cop either has to say 'yes' and admit there were errors - which sounds pretty good in your favor or he has to say 'no'. If he said 'yes' run through the list of the dozen or so errors which can affect radar to find out which ones were involved with the reading (the more the better for you). If he said 'no' you can bring up cosine error (and others which may apply). But, unless he was directly in your path of travel at the same elevation, there would be cosine error.

So now the cop has either admitted there were errors which is a good thing to use in closing arguments. Or he said no errors and there was a 99.999% chance there was 'some' error, so you may be able to make a point that he is not competent to run the radar or fully aware of all errors involved.

In reality, you probably still won't win the ticket, but at least you can make the cop look silly on the stand and gobble up an hour or so of his and the court's time. In which case you 'technically' still win by showing them that you are not a little lamb who will simply stand around and fork over ticket money without challenge. Plus, they have likely spent more to defend the case than the cost of your ticket, so they didn't have anything to gain by preying on you.