Two balls in one shot (same pocket)

Two balls in one shot (same pocket)

Howdy-

Consider the following situation, applicable to most any pocket game:

=========
Ball A is in the jaws of the corner pocket.  An additional constraint:
suppose it is 8-ball, and this ball is my opponent's ball.

Ball B (the object ball) is situated well for a shot into that same corner
pocket, but Ball A is directly in the way, with no room to carom or
squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
A.  The question is:  How?
=========

I've successfully done this occasionally, but I just can't figure out the
key;  intuition might suggest that a lot of draw  could convey some
forward roll to the object ball, but draw has NEVER worked for me.

My copy of Byrne's Std. Billiards is no help in this regard [a rare phrase
out of my mouth]

Can anyone offer me a rule of thumb they might have developed to deal with
this shot?

thanks
rob worman

Two balls in one shot (same pocket)

Quote:

>Howdy-

>Consider the following situation, applicable to most any pocket game:

>=========
>Ball A is in the jaws of the corner pocket.  An additional constraint:
>suppose it is 8-ball, and this ball is my opponent's ball.

>Ball B (the object ball) is situated well for a shot into that same corner
>pocket, but Ball A is directly in the way, with no room to carom or
>squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
>A.  The question is:  How?
>=========

>I've successfully done this occasionally, but I just can't figure out the
>key;  intuition might suggest that a lot of draw  could convey some
>forward roll to the object ball, but draw has NEVER worked for me.

>My copy of Byrne's Std. Billiards is no help in this regard [a rare phrase
>out of my mouth]

>Can anyone offer me a rule of thumb they might have developed to deal with
>this shot?

Draw is what you should use for these types of shots.    Draw does
place some forward on the object ball.  I've been able to make some of
these shots using draw.  If the two object balls aren't in a straight
line to the pocket, you would have to figure out how the first ball is
thrown to make sure that it is thrown into the pocket.

Gary

Two balls in one shot (same pocket)

Quote:

>>Ball A is in the jaws of the corner pocket.  An additional constraint:
>>suppose it is 8-ball, and this ball is my opponent's ball.
>>Ball B (the object ball) is situated well for a shot into that same corner
>>pocket, but Ball A is directly in the way, with no room to carom or
>>squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
>>A.  The question is:  How?

>      Draw is what you should use for these types of shots.    Draw does
>place some forward on the object ball.  I've been able to make some of
>these shots using draw.  If the two object balls aren't in a straight
>line to the pocket, you would have to figure out how the first ball is
>thrown to make sure that it is thrown into the pocket.

I've had the same situation many times as well.  I've been pretty consistent
by making sure the connection between ball A and B is pretty straight-in and
shooting _slow_ or soft, however you want to call it.  The concept of
inducing follow on an object ball, to me, is ridiculous... I believe the % of
actual spin transferred between balls is like 8% or less, so the amount of
follow actually transferred through draw on the cue ball would be nearly
nonexistent, unless the blocking ball and object ball were a couple of inches
apart, if that.

My idea is that if you shoot softly, you get object ball B to roll smoothly,
without any side or back spin or any knuckle-ball action (forward motion
without forward rotation), then it tends to hit the blocking ball and roll
right in after it, assuming a slightly less than perfect contact, but
certainly close enough that the deflection doesn't send the object ball off
and out of the pocket.

If balls A and B are very close to each other, I often like to masse the B
ball into the A (blocking) ball, such that the cue ball strikes, then returns
back and forces the B ball back into the pocket.  It's more dramatic, but
less controlled.  ;-)

The Panther!
--
[)---->  "What proof can they exhibit that may show it's not too late?
[)---->   It's time to feed the dragon, but our lives' are on the plate."

Two balls in one shot (same pocket)

Quote:
Rob Worman writes:
>Ball B (the object ball) is situated well for a shot into that same corner
>pocket, but Ball A is directly in the way, with no room to carom or
>squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
>A.  The question is:  How?

I may be completely off-base on this, but the only way I've been able to do
this is with draw, which, as you said, imparts some forward roll to the first
of the object balls.  I've noticed that this only works if the balls are
directly lined up, straight into the pocket; otherwise, the 'follow' won't go
in the right direction.

Patrick

Two balls in one shot (same pocket)

Quote:
Rob Worman writes:
> =========
> Ball A is in the jaws of the corner pocket.  An additional constraint:
> suppose it is 8-ball, and this ball is my opponent's ball.

> Ball B (the object ball) is situated well for a shot into that same corner
> pocket, but Ball A is directly in the way, with no room to carom or
> squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
> A.  The question is:  How?
> =========

> I've successfully done this occasionally, but I just can't figure out the
> key;  intuition might suggest that a lot of draw  could convey some
> forward roll to the object ball, but draw has NEVER worked for me.

I haven't tried it but it should work if ball B is not too close to the
pocket:  Try to shoot with low speed, so that B2 will travel slowly
enough to collect some rolling due to friction, but fast enough to be
able to use this rolling to drive it into the pocket after colliding
with ball A.

I don't think that a lot of draw would help. If you use hard
cueball-ball B contact to transfer some forward rolling to ball B, the
speed of ball B is implied to be very high so that it won't be able to
collect spin from friction with the cloth.

of the cueball ;-)

Csaba

.---------,----------------.----------------------------.
\  Csaba Markus            | Ericsson Technika Hungary  /

`--------------------------^----------------------------'

Two balls in one shot (same pocket)

Quote:

>The obvious conclusion:  Ball B needs to go "through" Ball
>A.  The question is:  How?

No, the question should be why?

Bank your ball.  Unless it's a really short shot, why risk the loss?
Make sure to leave yourself long and force your opponent to avoid
dropping the eight, if you should miss.

If the balls aren't really jawed and it's a short shot, then follow
is what you're looking for....

Remember -- a ball is an even smaller target than a pocket.  You're
now shooting at a ball, since you need to send your ball into another
one and past the obstruction ball and into the pocket.  There isn't
very much room for error there.

Safeties are a legal and honorable way out of situations like this
as well....

Jim
--
***********************************************************************
--- Jim Ortlieb          -- aka... Head Junkie of the CrackHouse

Today you will win big, pick a fight with a four year old...

Two balls in one shot (same pocket)

: Howdy-

: Consider the following situation, applicable to most any pocket game:

: =========
: Ball A is in the jaws of the corner pocket.  An additional constraint:
: suppose it is 8-ball, and this ball is my opponent's ball.

: Ball B (the object ball) is situated well for a shot into that same corner
: pocket, but Ball A is directly in the way, with no room to carom or
: squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
: A.  The question is:  How?
: =========

: I've successfully done this occasionally, but I just can't figure out the
: key;  intuition might suggest that a lot of draw  could convey some
: forward roll to the object ball, but draw has NEVER worked for me.

: My copy of Byrne's Std. Billiards is no help in this regard [a rare phrase
: out of my mouth]

: Can anyone offer me a rule of thumb they might have developed to deal with
: this shot?

: thanks
: rob worman

My response has no base in physics or logic...only personal
experience.  I have done this several times and every time this
situation comes up i think "top-medium" the cue ball hits the object
ball, the object ball rolls forward, gaining rotational momentum,
clips the "blocking" ball into the corner and continues to roll into
the pocket.  If you don't believe me, thats ok...but just try it.  It
works for me.  The trick is to impart just enough velocity into the
object ball so that it doesn't careem off the "blocking" ball; but it
must have enough speed so that its rotation carries it into the
pocket.

Another suggestion, if the three are lined up somewhat close is
to give the cue extreme top, pop the object ball semi-solidly into the
"blocking ball and make the objest ball with a double kiss with the
cue ball.  If you play call your shot then this will be particularly
impressive.  I don't think i've tried this but I will thursday and
I'll get back with the results (I work in recreation therapy and I
don't work again until thurs).

willy

Two balls in one shot (same pocket)

Quote:
> Howdy-

> Consider the following situation, applicable to most any pocket game:

> =========
> Ball A is in the jaws of the corner pocket.  An additional constraint:
> suppose it is 8-ball, and this ball is my opponent's ball.

> Ball B (the object ball) is situated well for a shot into that same corner
> pocket, but Ball A is directly in the way, with no room to carom or
> squeeze by it.  The obvious conclusion:  Ball B needs to go "through" Ball
> A.  The question is:  How?
> =========

> I've successfully done this occasionally, but I just can't figure out the
> key;  intuition might suggest that a lot of draw  could convey some
> forward roll to the object ball, but draw has NEVER worked for me.

> My copy of Byrne's Std. Billiards is no help in this regard [a rare phrase
> out of my mouth]

> Can anyone offer me a rule of thumb they might have developed to deal with
> this shot?

> thanks
> rob worman

>So many factors may cause the english that's applied to the cue ball to
>affect the object balls reaction not to work.  The one I come across alot
>is the faster the cue ball is spinning the less transfer of english occurs.
>Try to use less draw, therefore, allowing some friction on contact. I
>suggest that you experiement with the speed of the draw that you apply
>to the cue ball and get that feel to stick in your stroke.

Two balls in one shot (same pocket)

Quote:
> Consider the following situation, applicable to most any pocket game:

A picture would help:
___________  ____________
a  b    q
|                         |
|                         |
|                         |
|                         |
|                         |
___________  ____________

Pocket ball b in the pocket where a is sitting.  Balls a and b are not
touching.

Draw on the cue ball transfers negligible follow to ball b.  Far more
follow is acquired from ball b rolling on the cloth.  The ball needs
time to get that roll.  Shoot just hard enough that ball b is rolling
smoothly when it hits ball a.  If they are too close, it is not possible
to get enough follow from the cloth.

If you are using a large (bar) cue ball, it is possible to shoot hard
with draw and the cue ball will slide forward hitting ball b a second
time.  The cue ball must be heavy, and you must have all three balls in
a straight line for this to work.  It is easier the closer b is to a.

If b is rolling smoothly on the cloth when it hits a (as opposed to partly
sliding into a) you can figure the accuracy required by the "small cut
angle follow rule":  "If a ball is cut a small angle to the left, a
rolling cue ball will deflect three times that much to the right."  (The
theoretical number is not quite three.)  This means that you have to put
ball a into the middle third of the effective pocket, roughly.

Bob Jewett

Two balls in one shot (same pocket)

Quote:
>> Consider the following situation, applicable to most any pocket game:

>A picture would help:
>  ___________  ____________
> a  b    q
> |                         |
> |                         |
> |                         |
> |                         |
> |                         |
>  ___________  ____________

>Pocket ball b in the pocket where a is sitting.  Balls a and b are not
>touching.

>Draw on the cue ball transfers negligible follow to ball b.

Depending on how sticky are the balls, you can get "b" to follow only
3"-4" by transfering draw.  So "a" must be within about a balls width of
the lip for this approach.  And even then, the cue ball is going to suck
back to the other end of the table; not always what you need.

However, I've noticed that when the cue ball is jumped, then it can
sometimes impart extra follow to the ball it contacts.  I doubt that it is
as much as natural roll, but it seems more than what you would expect from
transfering draw.  My jump shot isn't consistent enough to depend on this,
but it might be worth practicing for those out there who can jump well.
You want to jump the cue so that it rolls back off of "b", forcing "b"
forward into "a".  This would be useful when the distance between "a" and
"b" is too close to allow "b" to pick up enough roll from the cloth.  It
also works when "a" and "b" are frozen together.

BTW, another reasonable shot here is a safety.  Say you're playing 8-ball
and "a" is your opponents ball and "b" is your ball.  You can often
concede "a", leave "b" near the pocket, and freeze the cue ball against
the pocket side of"b" by hitting soft with extreme 1:30 or 10:30
(depending on the positions of "a" and "b").  Even if you can't get the
balls to freeze, you can often get a snooker from this position, depending
on the positions of the rest of the balls.

[...]

Quote:
>If b is rolling smoothly on the cloth when it hits a (as opposed to partly
>sliding into a) you can figure the accuracy required by the "small cut
>angle follow rule":  "If a ball is cut a small angle to the left, a
>rolling cue ball will deflect three times that much to the right."  (The
>theoretical number is not quite three.)  This means that you have to put
>ball a into the middle third of the effective pocket, roughly.

Bob, can you post the derivation for this?

\$.02 -Ron Shepard

Two balls in one shot (same pocket)

Quote:
> >Draw on the cue ball transfers negligible follow to ball b.

> Depending on how sticky are the balls, you can get "b" to follow only
> 3"-4" by transfering draw.

I don't believe the effect is that large, except maybe at very high
speeds.  Let's try an experiment.  Place the two object balls 5mm apart.
Place a third object ball near the first two to act as a marker, or use
some other method of measurement.  Place the cue ball in the same line
as the first two balls.  Shoot straight at the two balls with draw.
Take notes.  Report results.

Note that since the balls are only 5mm apart, if the cue ball is heavy,
it will certainly hit the first ball a second time.  If you have no cue
ball of the correct weight, substitute an object ball.

Quote:
> And even then, the cue ball is going to suck back to the other end
> of the table; not always what you need.

Well, the theory says that as long as the cue ball has more draw than
the object ball has acquired follow, the surface of the cue ball is
still slipping on the surface of the object ball and it makes no
difference whether the excess rotation on the cue ball is 1RPM or
10000RPM.  Therefore, the cue ball need draw no further than you want the
object ball to follow, neglecting whatever follow rubs off on the second
object ball.

Quote:
> However, I've noticed that when the cue ball is jumped, then it can
> sometimes impart extra follow to the ball it contacts.

I haven't noticed this.  Could it be that the object ball is jumping which
can give the illusion of follow?

Quote:
> It also works when "a" and "b" are frozen together.

When the two object balls are touching, neither draw nor jumping is
required.  For example, the double spot shot can be made with a stop
shot or even follow.

(A double spot shot is when two balls are spotted on the foot spot, and
the cue ball is in hand behind the line.  The common method of making
the head ball straight into one of the corner pockets is to put the cue
ball six inches from the centerline of the table and draw it perfectly
straight back from the head object ball.  Draw is not required on the
shot, which can be demonstrated by placing a third object ball 5mm from
the head ball and in the line of the cue ball's path.)

Quote:
>> the "small cut angle follow rule":  "If a ball is cut a small angle to
>> the left, a rolling cue ball will deflect three times that much to the
>> right."
>Bob, can you post the derivation for this?

I'll start the outline of a derivation, and leave the details as an
exercise for the reader.  The following assumes that the balls are
ideal.

First the notion of velocity vectors.  To study a particular shot, it is
useful to draw out the velocity vectors of the balls involved.  A
velocity vector has both length and direction, showing the speed and
direction of travel of the cue ball.  If the cue ball with a speed of V0
hits an object ball with a cut angle of alpha, the initial velocity (V1)
of the object ball will be V0*cos(alpha) while the initial velocity of
the cue ball (V2) will be V0*sin(alpha).  Note that V0^2=V1^2+V2^2,
which is just conservation of energy, while the fact that the vectors
sum (V0-> = V1-> + V2->) is conservation of momentum.

It is also useful to draw on the same diagram the "spin" (follow or
draw) vectors of the balls.  By way of informal definition, the spin
vector of a smoothly rolling cue ball is coincident with the velocity
vector.  The spin vector of a cue ball with maximum draw is in a
direction opposite to the velocity vector and about the same length.

When the spin and velocity vectors are not coincident, the bottom of the
ball must be slipping on the cloth, and the two vectors are changing at
a rate determined by the ball-to-cloth friction.  How they change is the
critical item in the analysis.  The end of each vector moves towards the
other, but at different rates because spin is "less effective" than
speed.  For each two units that the velocity vector moves, the spin
vector moves by five units.  (The two and five come from the analysis of
angular momentum for a sphere.)  The two vectors move uniformly towards
each other along the line joining them until they are coincident and
smooth rolling is achieved.  At the instant the cue ball hits an object
ball, its spin vector doesn't change, but the velocity vector changes as
above.

(It is possible to actually solve for the curved path of the cue ball
graphically by taking successive velocity vectors and putting them end to
end.)

First result:  A cue ball hit with maximum draw (assumed to be the
opposite of smooth rolling) will slow to 3/7 of its initial velocity
when smooth rolling is achieved.

Second result: The curved part of the cue ball's path is a parabola.

Third result: The follow angle theta for a cut angle of alpha for a
smoothly rolling cue ball is given by:

theta = atan(7*tan(alpha)/2)-alpha

This is the fairly simple result that should have accompanied diagram
5-5 in Koehler.  The plotted curve there is clearly not the theoretical
curve.  The follow angle has a maximum value for about a half ball cut.
Question: what is the theortical cut angle for maximum follow angle?

Fourth result (which is what Ron asked for):  From trig, for small
angles, the tangent of the angle is nearly equal to the angle, so for
small cut angles, the follow angle is 2.5 times the cut angle (7/2-1).
(This ignores friction and such.  Actual measurements seem to show
something nearer 3.)

Bob Jewett

Two balls in one shot (same pocket)

Quote:
>> >Draw on the cue ball transfers negligible follow to ball b.

>> Depending on how sticky are the balls, you can get "b" to follow only
>> 3"-4" by transfering draw.

>I don't believe the effect is that large, except maybe at very high
>speeds.  Let's try an experiment.  Place the two object balls 5mm apart.
>Place a third object ball near the first two to act as a marker, or use
>some other method of measurement.  Place the cue ball in the same line
>as the first two balls.  Shoot straight at the two balls with draw.
>Take notes.  Report results.

I was demonstrating this very shot last week to some of our league
players.  The ball separation might have been more like 1/2" rather than
1/4", but still too close for the cloth friction to impart the roll.  The
balls are sticky where we play, so 3"-4" of follow is typical there.  That
is, it usually rolls more than one ball but less than two balls forward.
The cue ball does not hit twice; this is just due to transfer of spin.

Quote:
>Well, the theory says that as long as the cue ball has more draw than
>the object ball has acquired follow, the surface of the cue ball is
>still slipping on the surface of the object ball and it makes no
>difference whether the excess rotation on the cue ball is 1RPM or
>10000RPM.  Therefore, the cue ball need draw no further than you want the
>object ball to follow, neglecting whatever follow rubs off on the second
>object ball.

This is an aspect that I hadn't considered, but I think your argument is
correct.  I did this two ways, firm with center ball, and soft with draw,
in order to demonstrate that it is the spin that does the trick and not
the force.  I was using enough draw to get the cue from the center to the
end of the table.

Quote:
>> However, I've noticed that when the cue ball is jumped, then it can
>> sometimes impart extra follow to the ball it contacts.

>I haven't noticed this.  Could it be that the object ball is jumping which
>can give the illusion of follow?

with a shot that you (BJ that is) don't know!  ;-)  I don't know why this
shot works.  Yes, it could be that the first object ball is airborne when
it contacts the second ball.  Another possibility is that the cue ball
hits the first object ball more than once -- that is it bounces on the
ball as it rolls off.  Perhaps the last bounces occur after impact between
"a" and "b"?  However, this effect is obvious when it occurs; the ball can
roll forward a couple of feet!  BTW, the cue ball need not be jumped with
much force.  This is still a soft shot.

Quote:
>> It also works when "a" and "b" are frozen together.

>When the two object balls are touching, neither draw nor jumping is
>required.  For example, the double spot shot can be made with a stop
>shot or even follow.

>(A double spot shot is when two balls are spotted on the foot spot, and
>the cue ball is in hand behind the line.  The common method of making
>the head ball straight into one of the corner pockets is to put the cue
>ball six inches from the centerline of the table and draw it perfectly
>straight back from the head object ball.  Draw is not required on the
>shot, which can be demonstrated by placing a third object ball 5mm from
>the head ball and in the line of the cue ball's path.)

I've seen a variation of this in one-pocket.  If a second spotted ball is
placed just a tad to side of the spotted ball in front of it (yes, this is
illegal), then the first spotted ball can be made in the corner without
doing anything special by hitting it head on from the center of the
balls, is a rotation of this one, but requires, I believe, a bit more
accuracy at that sharper throw angle.  When you play one-pocket, you
should always casually check that balls are spotted properly; it can make
a big difference.

Quote:
>>> the "small cut angle follow rule":  "If a ball is cut a small angle to
>>> the left, a rolling cue ball will deflect three times that much to the
>>> right."

>>Bob, can you post the derivation for this?

>I'll start the outline of a derivation, and leave the details as an
>exercise for the reader.  The following assumes that the balls are
>ideal.
[...]
>First result:  A cue ball hit with maximum draw (assumed to be the
>opposite of smooth rolling) will slow to 3/7 of its initial velocity
>when smooth rolling is achieved.

This is something that you've posted before.  5/7 for a center ball hit,
3/7 for maximal draw, right?

[...]

Quote:
>Third result: The follow angle theta for a cut angle of alpha for a
>smoothly rolling cue ball is given by:

>    theta = atan(7*tan(alpha)/2)-alpha

>This is the fairly simple result that should have accompanied diagram
>5-5 in Koehler.  The plotted curve there is clearly not the theoretical
>curve.  The follow angle has a maximum value for about a half ball cut.
>Question: what is the theortical cut angle for maximum follow angle?

expression is correct, then the maximum occurs at a cut angle of
(1/2)acos(5/9), or about 28.1255 degrees, right?  This is the zero of the
expression

-1 + 28 / (53 - 45 * cos(2*alpha))

which I got by differentiating and simplifying the trig.  As you say, this
is close to a half ball hit, which would be 30 degrees.  This corresponds
what happens when friction between the balls is included?  I would assume
that this changes slightly both the cue ball and the object ball paths.

\$.02 -Ron Shepard

Two balls in one shot (same pocket)

: >> >Draw on the cue ball transfers negligible follow to ball b.
: >>
: >> Depending on how sticky are the balls, you can get "b" to follow only
: >> 3"-4" by transfering draw.
: >
: >I don't believe the effect is that large, except maybe at very high

Gosh I must be nuts.

Shooting an object ball through another is not a shot I hesitate to
shoot when it comes up. I don't think 6" with new balls is all that
hard. or a foot with scratched/old balls.

I'll check it out tonight and post.

Whit
--
o      \       Torn Between                    /|\
~  _ <<_     / 'All who wander are not lost'  /     / | \
~   /.\>/.\    \ & 'f/8 and be there'           \    /0 |  \

Two balls in one shot (same pocket)

Quote:
> Let's try an experiment.  Place the two object balls 5mm apart.  Place a
> third object ball near the first two to act as a marker, or use some
> other method of measurement.  Place the cue ball in the same line as the
> first two balls.  Shoot straight at the two balls with draw.  Take
> notes.  Report results.

I tried the experiment.  For soft draw where the cue ball comes back two
diamonds, the first object ball rolled forward two to two and a half ball
diameters from where it contacted the other object ball.

When the shot was played at much higher speed (also with two diamonds or
so of draw) the object ball followed forward twelve inches or so.

I attempted to separate out the effects of transferred follow and
inelasticity (both of which will tend to make the first object ball
follow through the second) by placing a third object ball in front,
thus eliminating transfer of follow.  At high speed, the object ball
(now the middle one) went forward about six inches.  My conclusion is
in the high speed case.

The hardest part of the experimental set up was making sure that the cue
ball didn't get involved more than once on the shot, especially if it
was hopping a little.  This was partly insured by blocker balls placed
to each side of the first object ball and almost touching the cue ball
at the moment of impact.

Bob Jewett

Two balls in one shot (same pocket)

[...]

Quote:
>Shooting an object ball through another is not a shot I hesitate to
>shoot when it comes up. I don't think 6" with new balls is all that
>hard. or a foot with scratched/old balls.

>I'll check it out tonight and post.

This was posted last week, but my newsreader seems to have missed some
messages (I'm seeing several replies without seeing the originals).  Did
you have a chance to verify this yet?

\$.02 -Ron Shepard