What's the sight of the ultrasonic sensor according to the distance of the object? Hey I'm programming a sumobot for a first-year university Civil Engineering project. We should need the sight of the ultrasonic sensor according tot the distance of an object. 
For example, the sensor can detect an object that is located 30 cm away 55° to the right of the sensor, but an object 50 cm away from the sensor can only be detected to 45° to the right of the sensor (approximately). Does anyone know the relationship (maybe a function?) between the sight and the distance? Thanks!
ETH Zurich faculty/students conducted some experiments on exactly this back in 2006.  The relevant parts of their results have been reproduced below.  For more information, visit their website: http://www.tik.ee.ethz.ch/mindstorms/sa_nxt/index.php?page=tests_us.

The chart below shows accuracy of the sensor at detecting a 14.5 cm x 9.5 cm x 6 cm block at various distances and angles from the sensor.



Distanz is Distance in CM, Winkel is Angle in degrees, and Relative Fehler is relative error.  

According to the researchers:


  The results show that the ultrasonic sensor should always be placed in horizontal position, other positions decrease as well the field of vision as the sighting distance of the sensor. The sensor seems to be a bit 'blind' on the left eye, which can be explained by the fact that the left eye is actually the receiver of the ultrasonic wave while the right eye is the sender.