Tilt and Rotation in ball motion
In previous discussions of ball motion, the ball could not be in the roll phase without axis rotation and axis tilt equalling zero.
Also, tilt could not be greater than rotation at any point on the lane.
As discussed in the "Interesting finding on Blueprint" discussion on the forum:
- As far as Powerhouse Blueprint is concerned, axis tilt angle can exceed axis rotation angle.
- Axis rotation angle and axis tilt angle are the two parameters that allow us to represent the ball's angular velocity as a 3D vector (with X, Y, and Z components) that is relative to the ball's direction of travel. So, for use as an aid in this discussion, we should first define this coordinate system...this is done in figure 1 (right).
- Using this notation, here are some examples of how certain balls' angular velocity vectors are oriented: a ball with no side roll and no tilt has its angular velocity vector oriented in the +Y direction; a ball with pure side roll and no tilt has its angular velocity vector oriented in the -X direction; a ball that is spinning like a top has its angular velocity vector oriented in the +Z direction. This coordinate system discussion really doesn't become too important until much later (if/when we discuss why axis rotation angle decays to zero, but axis tilt angle does not), but I thought it would be best to mention it early so we're all on the same page.
- Blueprint treats axis rotation angle and axis tilt angle as the two angles of a spherical coordinate system. An example of a spherical coordinate system is the one used to describe points on the surface of the Earth, where each point is uniquely described by its longitude and latitude. The situation of describing a ball's angular velocity vector (which is oriented along its axis of rotation) is quite similar, except we use the terms "axis rotation angle" and "axis tilt angle" instead of "longitude" and "latitude". The convention used by Blueprint for these two angles is shown in Figure 2 (right).
- In Blueprint, the axis rotation angle is always measured with respect to the ball's instantaneous direction of travel. It is possible that this is one of the causes of the discrepancy, since empirical studies of axis rotation / tilt decay during the shot would probably involve observation of the ball from a fixed position behind the foul line.
- The ball enters the roll phase when axis rotation angle equals zero.
Conclusion by Mo
Blueprint has done a great service here. the difference is instantaneous direction as opposed to a fixed point rotation is measured against. Since the bulk of my research is from a fixed camera position, this difference can occur. Very educational!
Axis tilt is in relation to the horizon, so it's the same in either system. True "roll out" occurs when the ball has 0* instantaneous axis rotation and 0* of axis tilt. Using Blueprint's system of measuring axis rotation, a ball stops hooking when the instantaneous axis rotation is 0*, the second transition! The ball will have effective hitting power as long as it still has axis tilt. The ball stops hitting when axis tilt reaches 0*.
More information on Tilt and Rotation by Blueprint: http://www.blueprintbowling.com/Blog/Posts/axis-rotation-and-axis-tilt-explained.aspx