Cosine effect - always in favour of the motorist ?
Discussion
I've read in a number of places, incl ACPO guidelines, that the off-axis effect on measured speed is always in favour of the motorist.
This is sometimes referred-to as the cosine effect.
Off-axis being when, say, a scamera van is on an overpass or in a layby where the direction of travel of your vehice is at some angle to the laser beam.
I think this is probably true for radar because the beam is very wide. Does it hold true for laser ?
My schoolboy geometry suggests that the laser beam would measure along the hypotenuse of a triangle. If one assumes that the angle betweeen laser and direction of travel is constant for the 1/3 of a sec (ie the operator doesn't 'pan' the beam) then surely the measured speed is always slightly greater than the actual speed ?
i.e. speed = 60 mph (10.36 m/s)
Operator distance = 100 m and 6m off-axis.
Off-axis angle = 3.43 degrees
Actual distance travelled in 1 second = 10.36m
Measured distance travelled in 1 second = 10.38m
Measured speed = 60.12 mph
Admittedly, the difference is negligible in this example and, i suspect, in most real life examples. However, this suggests that the cosine effect is NEVER in favour of the motorist.
Get your calculators out !
Am I talking thro' my hat ? Does it matter in the slightest ?
This is sometimes referred-to as the cosine effect.
Off-axis being when, say, a scamera van is on an overpass or in a layby where the direction of travel of your vehice is at some angle to the laser beam.
I think this is probably true for radar because the beam is very wide. Does it hold true for laser ?
My schoolboy geometry suggests that the laser beam would measure along the hypotenuse of a triangle. If one assumes that the angle betweeen laser and direction of travel is constant for the 1/3 of a sec (ie the operator doesn't 'pan' the beam) then surely the measured speed is always slightly greater than the actual speed ?
i.e. speed = 60 mph (10.36 m/s)
Operator distance = 100 m and 6m off-axis.
Off-axis angle = 3.43 degrees
Actual distance travelled in 1 second = 10.36m
Measured distance travelled in 1 second = 10.38m
Measured speed = 60.12 mph
Admittedly, the difference is negligible in this example and, i suspect, in most real life examples. However, this suggests that the cosine effect is NEVER in favour of the motorist.
Get your calculators out !
Am I talking thro' my hat ? Does it matter in the slightest ?
Through the hat I'm afraid. The cosine rule is applied to radar guns which measure the speed of approach of your vehicle using doppler shift. So, unless the car is driving straight at the radar gun (and I'm not necessarily recommending this), the speed recorded by the device is the actual speed multiplied by the cosing of the angle between the angle of travel of the car and the straight line between the gun and the car. Cosine of an angle is less than or equal to 1 so it's in favour of the car driver.
I'm not very up on laser devices but I seem to recall that they take two accurate measures of distance over a known time and use that to calculate the speed. WIthout doing too much geometry, I'm pretty sure they will underread by a tiny amount if there is an angle between the direction of travel and the straightline twixt gun and car.
I'm not very up on laser devices but I seem to recall that they take two accurate measures of distance over a known time and use that to calculate the speed. WIthout doing too much geometry, I'm pretty sure they will underread by a tiny amount if there is an angle between the direction of travel and the straightline twixt gun and car.
Hmm. Not so sure SC.
Radar is more reliable as it measures dopplar shift, and as all parts of the car body are travelling at the same speed they all generate the same shift.
Laser measures range, and calculates the change in range directly into speed. However, all parts of the car are NOT at the same distance to the gun, eg the windscreen may be 1.5 meters behind the number plate.
1 MPH roughly equates to 13cm, so sweeping the spot from the windscreen to the bumber could add 1.5 meters or approx 11MPH to the reading. 41MPH from a 30MPH car?
Tried this with a laser gun and manages to get 7MPH from a stationary car.
the LTI2020 has algorithms to try to stop this happening, but who knows if it has?. No log, no records, nothing. You just have to take it as gospel that it has read right.
Scary? you bet.
Video helps this, and you can usually see that the officer (or scam chav) is trying to aim at the numberplate.
Cosing error hardly has any effect at all until you get to large angles, but as quoted, is always in favour of the motorist.
A lot is in favour when you think. Speedos overread (my golf by about 3MPH), and ACPO guidelines are 10% plus 2, plus the cosine error (minimal)
so in a 30MPH you've got 10% plus 2 which is 35, and the speedo overreads by 3, so you're looking at 38 - 39MPH on the speedo before you get pinged.
Hmm.
Radar is more reliable as it measures dopplar shift, and as all parts of the car body are travelling at the same speed they all generate the same shift.
Laser measures range, and calculates the change in range directly into speed. However, all parts of the car are NOT at the same distance to the gun, eg the windscreen may be 1.5 meters behind the number plate.
1 MPH roughly equates to 13cm, so sweeping the spot from the windscreen to the bumber could add 1.5 meters or approx 11MPH to the reading. 41MPH from a 30MPH car?
Tried this with a laser gun and manages to get 7MPH from a stationary car.
the LTI2020 has algorithms to try to stop this happening, but who knows if it has?. No log, no records, nothing. You just have to take it as gospel that it has read right.
Scary? you bet.
Video helps this, and you can usually see that the officer (or scam chav) is trying to aim at the numberplate.
Cosing error hardly has any effect at all until you get to large angles, but as quoted, is always in favour of the motorist.
A lot is in favour when you think. Speedos overread (my golf by about 3MPH), and ACPO guidelines are 10% plus 2, plus the cosine error (minimal)
so in a 30MPH you've got 10% plus 2 which is 35, and the speedo overreads by 3, so you're looking at 38 - 39MPH on the speedo before you get pinged.
Hmm.
Just done some back of the envelope stuff, and it looks to me that, because it deals in ranging rather than doppler effects, off axis laser will return a higher speed than is actually being done. Effect will mostly be negligible though, and certainly below the noise level when you include panning and bad aim inaccuravies.
Thanks guys but can you show this using geometry ? I understand the accepted wisdom bu this is what I want to challenge / explore.
I accept radar will under-read owing to it's wide beam pattern. But laser ? Not so sure.
Have posted a diagram at http://public.fotki.com/PaulPa/cosine/cosine.html
If you accept a negligible beam width for laser (often cited) and no panning then I believe it will always over-read albeit by a small amount.
Paul
I accept radar will under-read owing to it's wide beam pattern. But laser ? Not so sure.
Have posted a diagram at http://public.fotki.com/PaulPa/cosine/cosine.html
If you accept a negligible beam width for laser (often cited) and no panning then I believe it will always over-read albeit by a small amount.
Paul
paul_355 said:
Thanks guys but can you show this using geometry ? I understand the accepted wisdom bu this is what I want to challenge / explore.
I accept radar will under-read owing to it's wide beam pattern. But laser ? Not so sure.
Have posted a diagram at http://public.fotki.com/PaulPa/cosine/cosine.html
If you accept a negligible beam width for laser (often cited) and no panning then I believe it will always over-read albeit by a small amount.
Paul
As posted above, a bit of pythagoras shows this to be correct, unless you're driving straight at them
, and assuming the target point for the laser is constant on the approaching vehicle.einion yrth said:
As posted above, a bit of pythagoras shows this to be correct, unless you're driving straight at them
Which then begs the question.. "What if the target point is not constant?"
i.e. starts off on the windscreen, and "slips" down to the front number plate. That would be an "extra" 3 feet or so your car has "travelled", just by the difference in the distance between the two points.
Ok, so it may be negligible in the speed calculation stakes, but I can't be ar$ed getting a calculator out at this time of night....
I would have thought that the results from the radar gun and the laser are identical. Correct me if I'm wrong;
The light/radio wave leaves the gun, hit's your car and bounces back. The return signal is mixed with the outgoing signal, and according to normal hetrodyne principals, the mixing process yields four components.
The first component is the outgoing signal, the second the return signal the third the sum and the fourth the difference.
We are only interested in either the sum or the difference signal (since the transmit frequency is known), so signals at or above the transmit frequency are filtered out, as are negative frequencies.
In the radar the beat associated with the changing path length is filtered.
Examining the difference signal yields the doppler frequency, which is a function of the wavelength compression associated with the moving vehicle. Convieniently this frequency is low enough that it can be filtered an measured with cheap electronics.
In the laser gun, due to the optical technologies involved, it is difficult to measure the the doppler frequency, and the beat from the changing path length is the means by which the speed is measured, probably in a linear CCD. (un)Fortunately electronics have improved to the point where this is possible.
Irrespective of all this, the rate of change in doppler shift is directly proportional to the rate of change in path length, irrespective of where you stand relative to the vehicle.
I don't think it makes a jot of difference.
The light/radio wave leaves the gun, hit's your car and bounces back. The return signal is mixed with the outgoing signal, and according to normal hetrodyne principals, the mixing process yields four components.
The first component is the outgoing signal, the second the return signal the third the sum and the fourth the difference.
We are only interested in either the sum or the difference signal (since the transmit frequency is known), so signals at or above the transmit frequency are filtered out, as are negative frequencies.
In the radar the beat associated with the changing path length is filtered.
Examining the difference signal yields the doppler frequency, which is a function of the wavelength compression associated with the moving vehicle. Convieniently this frequency is low enough that it can be filtered an measured with cheap electronics.
In the laser gun, due to the optical technologies involved, it is difficult to measure the the doppler frequency, and the beat from the changing path length is the means by which the speed is measured, probably in a linear CCD. (un)Fortunately electronics have improved to the point where this is possible.
Irrespective of all this, the rate of change in doppler shift is directly proportional to the rate of change in path length, irrespective of where you stand relative to the vehicle.
I don't think it makes a jot of difference.
Gassing Station | Speed, Plod & the Law | Top of Page | What's New | My Stuff