i'd like to know... the solid angle that is "covered" by the ultrasonic sensor of NXT kit and which is the maximum distance from an object the sensor can perceive it
The short answer is "it depends". Rather unsatisfying, I know. But it varies greatly depending on the shape and surface of the object (soft or round objects like balls reflect only a little sound energy back towards the sensor, so are hard to detect), the floor (hard floors tend to extend the range), and even keeping all those things constant the field of view angle varies with range (very close to the sensor it has a narrow field of view, while near the limits of detection the sensor only gets enough of a return if the object is centered in front of it; somewhere in between those two there's a wider cone of detection). And it's not remotely uniform over the solid angle, as you might expect from the sensor itself not being uniform (it is not a point source with the receiver at the source point).
Do some tests and see - there are too many variables to trust a simple short answer here. I can detect some objects at a range of 1.5 meters... but others are invisible just 30 cm away. YMMV.
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Brian Davis