Spin Analysis for a Projectile in Flight

A computing apparatus with non-transitory machine-readable media programmed to:

• collect a user magnetometer frame of reference vector from a user magnetometer;
• collect a user accelerometer frame of reference vector from a user accelerometer;
• collect a ball magnetometer frame of reference vector from a ball magnetometer on a golf ball at rest;
• collect a ball accelerometer frame of reference vector from a ball accelerometer on the golf ball at rest;
• calculate frame of rotation coefficients from the user magnetometer frame of reference vector, the user accelerometer frame of reference vector, the ball magnetometer frame of reference vector, and the ball accelerometer frame of reference vector using a Kabsch Algorithm;
• collect a ball magnetometer time series matrix from the ball magnetometer as the ball is in flight;
• process the ball magnetometer time series through a Rodrigues Rotation Formula using the frame rotation coefficients to create a rotation vector;
• calculate a prior vector difference and a second prior vector difference;
• calculate a spin axes by multiplying the prior vector difference by the second prior vector difference;
• calculate a Theta vector by taking an arccosine of a dividend of a product of the prior vector difference multiplied by the second prior vector difference divided by a product of an absolute value of the prior vector difference multiplied by an absolute value of the second prior vector difference;
• calculate a spin rate by dividing a change in Theta by the change in time;
• and
• display the spin rate and the spin axes on a display device connected to the computing apparatus.

A system comprising:

• artificial grass including a launch location for a golf ball, a user magnetometer, and a user accelerometer;
• the golf ball including a wireless interface, a ball magnetometer, and a ball accelerometer;
• a central processing unit connected to the user magnetometer and the user accelerometer, the central processing unit further comprising a wireless transceiver wirelessly connected to the wireless interface, wherein the central processing unit creates frame rotation coefficients from data collected from the ball magnetometer, the ball accelerometer, the user magnetometer, and the user accelerometer using a Kabsch Algorithm;
• where the central processing unit uses a Rodrigues Rotation Formula on the frame rotation coefficients and ball magnetometer data after the golf ball is hit by a golf club, to produce a prior vector difference vector and a second prior vector difference vector;
• where the central processing unit uses the prior vector difference vector and the second prior vector difference vector to determine a spin axes and a spin rate;
• and
• a display device connected to the central processing unit, the display device receives the spin axes and the spin rate from the central processing unit, and displays the spin axes and the spin rate.

A system comprising:

• artificial grass including a launch location for a golf ball, a user magnetometer, and a user accelerometer;
• the golf ball including a wireless interface, a ball magnetometer, and a ball accelerometer;
• a central processing unit connected to the user magnetometer and the user accelerometer, the central processing unit further comprising a wireless transceiver wirelessly connected to the wireless interface, wherein the central processing unit includes a means for creating frame rotation coefficients from data collected from the ball magnetometer, the ball accelerometer, the user magnetometer, and the user accelerometer;
• where the central processing unit includes a means for producing a prior vector difference vector and a second prior vector difference vector from the frame rotation coefficients and ball magnetometer data after the golf ball is hit by a golf club;
• where the central processing unit includes a means for determining a spin axes and a spin rate from the prior vector difference vector and the second prior vector difference vector;
• and
• a display device connected to the central processing unit, the display device receives the spin axes and the spin rate from the central processing unit, and displays the spin axes and the spin rate.