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Visual Speed Measurements
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Visual Speed Measurements
Some courts (Ohio Supreme Court June 2010) have accepted an officer's visual observation (visual estimate) as good enough -- weak subjective evidence. Most police departments have no or minimal training practicing visual speed measuring. Training typically consist of maybe a half of a day guessing speeds and comparing to someone else running radar. Apparently training from a moving patrol vehicle is not even attempted. The author cannot find any empirical data for visual speed measurement accuracy, or angles, minimum observation times and distances required.If the officer claims the visual observation is accurate ask;
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Be prepared to compare the officer's distance/time numbers to the speed the numbers add up to (really divide by). Speed equals distance divided by time -- speed in feet (or meters) per second, distance in feet (or meters), and time in seconds. A small time error can easily introduce a large speed error. See Chapter 1.2 -- Timing Systems (Clocking) / Stop Watch for speed=distance/time equations and conversions.
It is extremely difficult to judge the speed of any object traveling directly or nearly directly at (or away) from an observer. At long ranges vehicles appear to be stationary or almost stationary. The vehicle angle and profile changes are extremely small and hard to see let alone judge (guess) speed. At 855 feet (260 meters) a 6 inch (15.24 centimeter) high license plate is just barely visible to someone with 20/20 vision. The greater the distance the observer off the road, the faster the angle changes and the easier (if only a little) it is to judge (guess) speed. Radar and lidar are just the opposite, the closer to the road the more accurate the measured speed.VEHICLE ANGLE AND RATE
Vehicle angle to an observer depends on the distance an observer is from vehicle lane (d) and vehicle range (R). The angle rate of change (angular rate) is a function of (d) and (R) and vehicle speed (Vo) and time (t) to even with observer.
ANGLE
| alpha = tan-1(d/R) |
ANGULAR RATE (Rad/sec)
| d(alpha)/dt |
| = d / (Vot2 + d2/Vo) |
| = d/(R2/Vo+d2/Vo) = Vod / (R2 + d2) |
Vo = Speed
R = Range
t = Time to Even with Observer
alpha= Vehicle Angle to Observer
d = Observer Distance to (Vehicle) Lane
d(alpha)/dt = Vehicle Angular Rate to Observer (radians/second)VEHICLE PROFILE
Vehicle change in profile can be estimated from vehicle dimensions and a reference or comparison distance -- distance from eye (reference) profile would appear if projected onto a screen or looking through glass (lidar HUD for example).
Resolution is the ability to resolve (distinguish) 2 objects. The maximum theoretical highest angular resolution for the human eye is 1.2 arc minutes (0.02° = 0.35 mR). Actual resolution varies with person from about 1.7 - 3 arc minutes (0.028° - 0.05°). Someone with 20/20 vision has a resolution of about 2 arc minutes or (1/30)°. Angular resolution can be converted to linear resolution as shown above, also see examples below.
z = Linear Resolution
ß = Angular Resolution
Rr = Distance
| Distance (feet) | 5.6 ft | 36 ft | 72 ft | 145 ft | 860 ft | 1720 ft | 3440 ft | 5160 ft |
| Linear Resolution (z) | 0.04 in 0.1 mm |
0.25 in 6 mm |
0.5 in 13 mm |
1.0 in 26 mm |
6 in 153 mm |
1 ft 305 mm |
2 ft 610 mm |
3 ft 915 mm |
| Distance (meters) | 0.86 m | 1.8 m | 17.2 m | 43 m | 258 m | 516 m | 1032 m | 2062 m |
| Linear Resolution (z) | 0.5 mm | 1 mm | 10 mm | 25 mm | 15 cm | 30 cm | 60 cm | 1.2 m |
Vehicle profile does not change much until the vehicle is very close, typically a second or two from even with an observer. Profile and change in angle (rate) depends on vehicle speed and observer distance from vehicle lane.
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alpha2 = tan-1 [ (d + w) / R ] alpha1 = tan-1 [ d / (R + L) ] alphaw = alpha2 - alpha1 |
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| x = 2 Rr tan(alphaw / 2) | y = h Rr / R |
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R = Vehicle Range Rr = Distance from Eye to Profile Projected (at Rr) d = Distance from Observer to Vehicle Lane (Vehicle closest edge) |
w = Vehicle Width L = Vehicle Length h = Vehicle Height |
Calculator -- Vehicle Angle, Angular Rate, and Profile
Given observer Distance (d) from lane, a starting range or time, range or time interval (data point spacing) calculates angle and rate for various times and ranges. Also estimates profile given vehicle dimensions and a visual reference distance.
