Is the thickness always the same regardless of the cueing method?
The thickness depends on the cueing method.
The thickness depends on the cue speed and the cue point of the vertical and horizontal lines.
This is because there is friction between the ball and the cue.
Keep this in mind when cueing!
Do you think that the thickness of the ball is constant and independent of the way you hit it?
If so, you are mistaken!
If you think that the thickness is constant and does not change with cueing, you are wrong!
The result is that the thickness you should realistically aim for will vary depending on the combination of these factors.
Why is this?
It is because of the force of friction.
The cue ball, the target ball, and the rasha all interact with each other due to the force of friction.
However, since the rasha is heavier in mass (it is spread over the entire table and is fixed to the table), the frictional force apparently affects only the cue ball and the target ball.
In the long run, we can see that the rasha was also affected by frictional forces, as the rasha is worn out or has holes in it.
Both vertical and horizontal rotations of the cue ball are transmitted like gears because of the frictional force between the cue ball and the target ball.
However, it is the friction between the cue ball and the target ball that greatly affects the movement of the target ball after the rotation is transmitted from the cue ball to the target ball.
Friction with the rasha will affect the direction in which the target ball runs, and this must be taken into account in advance.
The thickness of the target ball is determined by taking into account the empirical information from the input side (cue speed, twist, etc.), since it is impossible to know the friction with the rasha in reality.
The reason why a slower cue speed results in a stronger throw is that the target ball is moving slower towards the pocket, and therefore has more contact time with the rasher and is more affected by the friction of the rasher.
In addition, when you add moderate rotation to the cue ball, the target ball also gets moderate rotation, which allows the target ball to run on the rasha with a constant direction of rotation, thus reducing the effect of the throw.
For example, if you try to move a mobile cart with the wheels locked, you will have a hard time because of the strong friction between the wheels and the floor.
On the other hand, when the wheels are unlocked, the wheels are free to rotate, so the wheels can rotate moderately before receiving excessive friction from the floor, and as a result, the load can be carried with ease.
Thus, if the rotation of the wheel can be taken as the rotation of the target ball, the more rotation there is in the target ball, the less friction there is with the rasha, and the thicker the aim can be with less influence from the throw.
If you think about this, a table that slides well and a table that is heavy will have a different degree of friction from the rasha, so strictly speaking, the thickness of the target will be different.
The same is true for a dry table on a sunny day and a damp, heavy table on a rainy day.
It is also impossible to ignore the effect of the side spin (twist) of the cue ball on the target ball.
This is because the twist of the cue ball causes the target ball to flip sideways.
Therefore, when you do a forward twist, intentionally make it a little thicker.
This is because the thickness is made in anticipation of the target ball being flipped sideways by the twist.
Usually, the forward twist cancels out the throw, which stabilizes the trajectory of the target ball.
Try cueing the ball with this in mind!