The purpose of this study was to determine the optimum release conditions for the free throw in men's basketball. The study used hundreds of thousands of three-dimensional simulations of basketball trajectories. Five release variables were studied: release height, release speed, launch angle, side angle, and back spin. The free throw shooter was assumed to shoot at 70% and to release the ball 2.134 m (7 ft) above the ground. We found that the shooter should place up to 3 Hz of back spin on the ball, should aim the ball towards the back of the ring, and should launch the ball at 52 degrees to the horizontal. We also found that it is desirable to release the ball as high above the ground as possible, as long as this does not adversely affect the player's launch consistency.

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Navigation and guidance systems are a critical part of any autonomous vehicle. In this paper, a novel sensor grid using 40 KHz ultrasonic transmitters is presented for adoption in indoor 3D positioning applications. In the proposed technique, a vehicle measures the arrival time of incoming ultrasonic signals and calculates the position without broadcasting to the grid. This system allows for conducting silent or covert operations and can also be used for the simultaneous navigation of a large number of vehicles. The transmitters and receivers employed are first described. Transmission lobe patterns and receiver directionality determine the geometry of transmitter clusters. Range and accuracy of measurements dictate the number of sensors required to navigate in a given volume. Laboratory experiments were performed in which a small array of transmitters was set up and the sensor system was tested for position accuracy. The prototype system is shown to have a 1-sigma position error of about 16 cm, with errors between 7 and 11 cm in the local horizontal coordinates. This research work provides foundations for the future development of ultrasonic navigation sensors for a variety of autonomous vehicle applications.

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