Swing analysis method using a sweet spot trajectory
A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.
1. A swing analysis method using a sweet spot trajectory, comprising:
obtaining a time series of sensor data from a sensor coupled to a piece of equipment during a swing of said piece of equipment, wherein said sensor comprises
a three-axis accelerometer that generates acceleration data; and,
a three-axis gyroscope that generates angular velocity data;
such that said sensor data comprises said acceleration data and said velocity data;
determining a time of impact of said swing from said time series of said sensor data;
obtaining a location of a sweet spot of said piece of equipment,
wherein said sweet spot comprises a location on said piece of equipment, a range of location on said piece of equipment or a shape of an area on said piece of equipment where an impact occurs that produces a maximum energy transfer of said swing at a predefined threshold or value;
defining a reference frame from said sensor data;
calculating a trajectory of said sweet spot relative to said reference frame based on said sensor data; and,
calculating one or more swing metrics based on said trajectory of said sweet spot and on said time of impact.
2. The method of claim 1 wherein said piece of equipment comprises a bat.
3. The method of claim 1 wherein said reference frame comprises
an origin at a position of said sweet spot at said time of impact;
a z-axis pointing vertically upward from said origin in a direction opposite to a gravity vector;
an x-axis perpendicular to said z-axis and oriented so that a longitudinal axis of said piece of equipment lies in a plane defined by said z-axis and said x-axis at said time of impact; and,
a y-axis perpendicular to said x-axis and to said z-axis.
4. The method of claim 3 wherein said determining said time of impact comprises
determining whether said swing is a valid air swing; and,
when said swing is said valid air swing, setting said time of impact to a time when a magnitude of said angular velocity data projected onto an xy-plane defined by said x-axis and said y-axis in said reference frame equals a peak value of said magnitude of said angular velocity data projected onto said xy-plane during said swing.
5. The method of claim 4 wherein said determining whether said swing is said valid air swing comprises
determining whether said peak value of said magnitude of said angular velocity data projected onto said xy-plane exceeds a first threshold;
calculating a peak value of a magnitude of said acceleration data projected onto said z-axis during said swing; and,
determining whether said peak value of said magnitude of said acceleration data projected onto said z-axis exceeds a second threshold.
6. The method of claim 1 wherein said determining said time of impact comprises
searching said time series of said sensor data for a change in said angular velocity data exceeding a first threshold; and,
searching said time series of said sensor data for a change in said acceleration data exceeding a second threshold.
7. The method of claim 1 further comprising:
determining a time of start of downswing of said swing; and,
calculating a time to contact metric as a difference between said time of impact and said time of start of downswing.
8. The method of claim 1 further comprising:
calculating a trajectory of a hand position on said piece of equipment relative to said reference frame based on said sensor data.
9. The method of claim 8 further comprising:
calculating a center of rotation of said swing relative to said reference frame based on said sensor data.
10. The method of claim 9 , wherein said calculating said center of rotation of said swing comprises
calculating said center of rotation as a point that is equidistant from said hand position at three different points of said trajectory of said hand position.
11. The method of claim 10 , further comprising:
calculating an axis of rotation as an axis perpendicular to a plane through said three different points of said trajectory of said hand position.
12. The method of claim 11 , wherein said one or more swing metrics comprises
a body tilt angle, wherein said body tilt angle comprises an angle between said axis of rotation and a vertical axis.
13. The method of claim 9 further comprising:
calculating a two-lever model of said swing based on
said trajectory of said sweet spot;
said trajectory of said hand position; and,
said center of rotation; and,
wherein said calculating said one or more swing metrics is based on said two-lever model.
14. The method of claim 13 wherein said piece of equipment comprises a bat, and wherein said two-lever model comprises
a body lever extending from said center of rotation to said hand position; and
a bat lever extending from said hand position to said sweet spot.
15. The method of claim 14 wherein said one or more swing metrics comprise
a body ratio, wherein said body ratio comprises a ratio of a rotation of said body lever during said swing to a rotation of said bat lever during said swing.
16. The method of claim 14 wherein said one or more swing metrics comprise
a hinge angle based on a relative orientation between said bat lever and said body lever, at one or more points in time during said swing.
17. The method of claim 16 wherein said one or more swing metrics comprise
a hinge angle at impact, wherein said hinge angle at impact comprises said hinge angle at said time of impact.
18. The method of claim 16 wherein said one or more swing metrics comprise
a time of commit, wherein said time of commit is a point in time wherein a rate of change of said hinge angle exceeds a threshold.
19. The method of claim 18 wherein said one or more swing metrics comprise
a hinge angle at commit, wherein said hinge angle at commit comprises said hinge angle at said time of commit.
20. The method of claim 16 wherein said one or more swing metrics comprise
a hinge angle at impact, wherein said hinge angle at impact comprises said hinge angle at said time of impact;
a time of commit, wherein said time of commit is a point in time wherein a rate of change of said hinge angle exceeds a threshold;
a hinge angle at commit, wherein said hinge angle at commit comprises said hinge angle at said time of commit; and,
a hinge release, wherein said hinge release comprises a difference between said hinge angle at impact and said hinge angle at commit.
21. The method of claim 1 wherein said piece of equipment comprises a bat, and further comprising
determining a bat impact velocity vector as a velocity of said sweet spot at said time of impact; and,
determining a swing plane as a plane through said sweet spot at said time of impact and spanned by said bat impact velocity vector and by a longitudinal axis of said piece of equipment at said time of impact.
22. The method of claim 21 further comprising
calculating an off-plane distance as a distance between said sweet spot and said swing plane, at one or more points in time during said swing.
23. The method of claim 22 further comprising
calculating a time on plane as an earliest time in said swing when said off-plane distance is below a threshold and remains below said threshold until said time of impact.
24. The method of claim 23 wherein said one or more swing metrics comprise
an on-plane metric, wherein said on-plane metric comprises an angular range of motion between said time on plane and said time of impact.
25. The method of claim 1 wherein said piece of equipment comprises a bat, and further comprising
determining a forward bat velocity as a velocity of said sweet spot projected onto a plane perpendicular to a longitudinal axis of said bat, at one or more points in time during said swing.
26. The method of claim 25 wherein said piece of equipment comprises a bat, and wherein said one or more swing metrics comprise
a bat speed, wherein said bat speed comprises a magnitude of said forward bat velocity at said time of impact.
27. The method of claim 26 wherein said one or more swing metrics comprise a swing power, wherein said swing power comprises a product of
said bat speed, and
a mass of said piece of equipment, and
an average acceleration of said sweet spot during said swing.
28. The method of claim 25 wherein said one or more swing metrics comprise
a peak bat speed, wherein said peak bat speed comprises a maximum magnitude of said forward bat velocity during said swing.
29. The method of claim 1 wherein said one or more swing metrics comprise
a swing plane tilt angle, wherein said swing plane tilt angle comprises an angle of a longitudinal axis of said piece of equipment with respect to horizontal at said time of impact, or
an attack angle, wherein said attack angle comprises an angle of a velocity vector of said sweet spot with respect to horizontal at said time of impact, or
both said swing plane tilt angle and said attack angle.
30. The method of claim 1 further comprising:
providing sound or image data based on said time series of sensor data, or providing metrics derived from said time series of sensor data.