A system for computer-implemented golf shot analysis includes a tracking device and a computing device. The computing device accesses ball flight data generated by the tracking device in view of a predetermined gradient map and associated functionality to derive a performance metric that penalizes shots deemed to be offline.

A golf ball is disclosed herein that includes at least one radar detectable mark such that a projected pattern is formed when the at least one radar detectable mark is radially projected onto an outer surface of the golf ball. The projected pattern can have a first wave profile mapped along a path defined by a first spherical arc on the outer surface of the golf ball. The projected pattern can comprise at least one first crest and at least one first trough. The projected pattern can have a periodic function selected from: a sine wave, a sawtooth wave, a triangle wave, or a square wave.

A launch monitor for golf training includes both a continuous wave radar transmitter and a frequency modulated continuous wave radar transmitter. A first set of golf ball trajectory parameters are estimated with the continuous wave radar transmitter and a second, different set of golf ball trajectory parameters are estimated with the frequency modulated continuous wave radar transmitter. The array of transmitters and receivers may be non-uniform.

Methods and apparatus relating to predicting outcome in a sporting environment are described. The methods and apparatus are used to relate trajectory performance of an object to body motions and body orientation associated with a generating the trajectory of the object. When equipment is utilized to generate the trajectory of an object, than the effects of equipment motions and equipment orientation can be also related to trajectory performance. The method and apparatus can be used to predict body motions and body orientations that increase the likelihood of achieving a desired outcome including specifying optimum motions and orientations for a particular individual. The method and apparatus may be used in training, coaching and broadcasting environments.

A golf ball can have a relatively large number of dimples on a surface thereof. A trajectory of the golf ball calculated under conditions of an initial speed of 260 ft/s, a launch angle of 15.0 degrees, and an initial backspin rate of 3000 rpm can satisfy the following mathematical formula:

Amin≥−5.0*Vave−38.98,

wherein A min represents a minimum value (degree) of a vector angle A in the trajectory, and Vave represents an average volume (mm.sup.3) of the dimples. The vector angle A can be calculated by the following mathematical formula:

A=ATAN(Vy/Vx),

wherein Vx represents a horizontal component of a speed of the golf ball, and Vy represents a vertical component of the speed of the golf ball.

A golf ball can have a large number of dimples on a surface thereof. A trajectory of the golf ball can be calculated under conditions of an initial speed of 260 ft/s, a launch angle of 15.0 degrees, and an initial backspin rate of 3000 rpm satisfying the following mathematical formula,

[00001]$\text{Amax}\ge \text{4}\text{.0}\text{*}\text{Vave + 13}\text{.10,}$

wherein Amax represents a maximum value (degree) of a vector angle A in the trajectory, and Vave represents an average volume (mm.sup.3) of the dimples. The vector angle A can be calculated by the mathematical formula

[00002]$\text{A}\text{=}\text{ATAN}\left(\text{Vy}/\text{Vx}\right),$

wherein Vx represents a horizontal component of a speed of the golf ball, and Vy represents a vertical component of the speed of the golf ball.

The invention relates to a method for the analysis of movement of a piece of sports equipment of a type of ball sport, in particular a racket, preferably a golf club, or a ball, preferably a golf ball, wherein a first virtual trajectory model is reproduced in a display device in a way that said first virtual trajectory model is displayed as a first line on the display device in superimposition with at least one, in particular in reality, visible section of the environment, particularly when a field of view is directed on the at least one section of the environment which is visible in reality.

The disclosure is directed to systems and methods for providing a user with key performance indicators of a basketball player relating to accuracy, precision and improvement. Specifically, the disclosure is directed to a system of sensors coupled to a basketball backboard adapted to provide an accurate tracking of a shot in a given three-dimensional space and extract features manipulated to yield key performance indicators based on establishing whether, how often and where the ball center passes the rim plane at a sub-cm resolution over a period of no more than 200 msec.

Embodiments provided herein measure metrics of an athletic action and an object associated therewith, and more particularly, to measuring the metrics and characteristics of a baseball during the wind-up, release, flight, and catch of a pitch sequence. Methods may include: receiving, from at least one motion sensor associated with an object, acceleration data and angular velocity data of the object in response to an athletic action performed on the object; processing the acceleration data to establish vector rotation data between a frame of reference of the object and an Earth frame of reference; applying the vector rotation data to the acceleration data to obtain acceleration of the object in the Earth frame of reference; applying the vector rotation data to the angular velocity data to obtain angular velocity of the object in the Earth frame of reference.

Systems for assisting a user with programming of a custom basketball shots made in a row practice arrangement includes a control system which receives data from a user interface indicating a user selection of a number of shots to be made in a row at each of a subset of pass receipt locations in the custom basketball shots made in a row practice arrangement and command a ball ejector to launch basketballs to a particular one of the pass receipt locations in the subset until data is received indicating that the number of shots is made in a row is made, and instead begin launching basketballs to a second particular one of the plurality of pass receipt locations in the subset. The control system also generates data for a report indicating performance feedback for the user during the custom basketball shots made in a row practice arrangement.