billiards-devel
[Top][All Lists]

## [Billiards-devel] Jumping the cue ball

 From: Dimitris Papavasiliou Subject: [Billiards-devel] Jumping the cue ball Date: Thu, 25 Mar 2010 18:31:00 +0200

```Hello all,

due to popular interest (popular here can be quantified to as many as
one or two users which I'm inclined to consider as large given the
total interest in Billiards so far), due to this popular interest
therefore I'm forced to bring up the matter of cue ball jumps.

A couple of versions back I considered these not possible at all, but
it seems now that they are.  This is the situation as far as I have
pondered on it:  as pointed out by Fracois Gaumond the "proper" way
(that is the one that won't be considered a foul) to jump the cuball
is with the stick positioned as in 2 in this diagram:

What happens is that the cue stick drives the cue ball into the ground
forcing it to bounce away from it and take off.  You can see what
actually happens in more detail in the following high-speed camera
video clips:

http://www.billiards.colostate.edu/high_speed_videos/HSV7-23.htm
http://www.billiards.colostate.edu/high_speed_videos/HSV7-24.htm
http://www.billiards.colostate.edu/high_speed_videos/HSV7-25.htm

In a simulation I can think of two things that are important for this to work:

a)  The collision between the tip and the ball must not be considered
as instantaneous.  At the moment the elevated cue tip strikes the ball
it does indeed give it some downward velocity which should make it
rebound off the floor and fly into the air but at that particular
instant the cue tip is still on top of the cue ball.  If it was to
take off it would have to go through the tip.  The cue in Billiards
does indeed disappear as soon as you strike the ball but it actually
goes away once the collision is completed.  At the moment when the
collision takes place it is in fact still there although the joint
that's supposed to simulate your hand and keep it moving in a straight
line is removed.  This allows interesting effects such as cue ball
squirt and miscues to happen but this is another story.

b)  There is some elasticity both in the cue tip and in the playing
surface and cue ball.  What I think happens is that as the cue drives
the ball down, it compresses and so does the playing surface.  This
energy is then released when the cue tip is no longer in the way and
the ball rebounds upwards.

The problem is that I have no clue as to how important each of these
aspects is and whether there might be other ones worth considering.
Now a couple of months ago I implemented elasticity in the contact
between the cue ball and the surface.  In ODE this elasticity is
simulated as a spring more or less with some given stiffness and
damping characteristics.  I fiddled around with these numbers a bit
and observed that jump balls were possible to some degree.  You could
also control them.  The elevation of the cue determines the height the
ball will jump to as is logical and you can control its forward speed
and whether it will jump at all with the amount of backspin you apply
and also with the force of the hit.  The problem is that, since I
couldn't find any papers studying the phenomenon of a jump ball in any
detail I have no way of determining whether this behavior is realistic
at all and to what degree.

My take on the subject is that both of the points above are important
and, although they can't be accurately simulated with ODE , it might
be possible to simulate them to some degree, maybe enough for
realistic results to be achieved.  Unfortunately I'm having problems
with the right button of my mouse so elevating the cue is a bit
difficult which doesn't allow me to perform experiments right now
(this has to be the lamest excuse ever).  If someone with interest in
pool physics and preferably with access to some good textbooks on the
matter feels like trying to implement and finetune this aspect of the
simulation let me know.  Of course any theoretical contributions in
the form of  comments on my points are welcome as well.

Dimitris

```

reply via email to