The point of aim is expressed as a
percent. Multiplying
that percent by the radius of the
ball gives one the distance from the center of object ball to
the point of
aim. Thus, if the
value is 100%, the
point of aim is one radius from the center of the object ball –
that is, the
outside edge of the object ball.
The decimal can range from 0%, for a
direct hit, to
200%, for the thinnest possible hit.
1.
The BASIC, GEOMETRIC RULE
The
point of aim, if there were no friction, (and if the cue ball
was very far from
the object ball) would be (2 x Sin A) radii from the center of
the object ball,
converted to a percentage, where A is the angle between the line through the centers of the object ball and
the cue ball,
and the line through the
object ball and
the pocket.
Sin
A is equal, then, to the following two ratios:
(1) The perpendicular
distance of the pocket
from the line
through the centers of the cue ball and the object ball,
divided by the
distance from the object ball to the
pocket.
(2) The
perpendicular distance of the cue ball
from the line through the center of the object ball and the
pocket, divided by
the distance from the object ball to the
cue ball.
Sometimes
the first calculation is easier, and sometimes the second is.
Estimating
the distances between the object ball and the pocket, or between
the object
ball and the cue ball, is not too difficult.
Estimating the relevant perpendicular distance is
sometimes trickier. So
here are some ideas.
Using Ratio 1:
How can one measure the perpendicular
distance from the pocket to the line through the centers of the
cue ball and
the object ball?
One can go down to the
vicinity of the pocket,
place the cue on the line passing through the
center of the cue ball and the center of the object ball,
and then estimate
the distance between the cue and the pocket.
Using Ratio 2:
How can one measure the perpendicular
distance from the cue ball to the line through the center of the
object ball
and the pocket?
Looking towards
the pocket,
place the cue on the line passing through the
center of the object ball and the pocket, and then
estimate the distance
between the cue and the cue ball.
A third
method involves a ratio that is defined using the line
that runs down the
center of the table through the head spot and foot spot.
Using the Center Line Ratio:
Find the point
where the line
through the object ball and the cue ball intersects the centerline that runs through the spots on the
table. Estimate the
distance, first, from that point
to the object ball, and then secondly, the perpendicular
distance from that
point to the line through the pocket and the object ball, and
then divide the
latter distance by the former.
(Placing
one’s cue on the table along the line from the object ball to
the pocket should
help one estimate the relevant perpendicular distance.
A final
method can be used in cases where the line through the cue
ball and the
object ball is nearly
parallel to
one of the cushions. This
method can be
used in two ways.
(1)
When the line through the cue ball and the object ball is nearly parallel to one of the cushions, the
perpendicular distance
between that line and the pocket will be virtually equally to
the distance
between the pocked and the point on the rail through which the
line through the
centers of the cue ball and the object ball passes. So divide the latter
distance by the distance
from the object ball to the pocket.
(2) Alternatively, one can make a
parallel calculation
from the cue ball side. Looking
towards
the pocket, determine the distance between the following two
points: (a) the
point where a line from the object ball to the cue ball
intersects the near
rail, and
(b) the point where a line from the pocket to the object ball
intersects the
near rail. That
distance is the relevant
“perpendicular distance”. Then
divide
that distance by the distance from the object ball to the same
rail along the
line from object ball through the cue ball.
2.
The DISTANCE CORRECTION RULES
(1) If 2 x Sin A ≥ 100%, add
2/distance
between the edges of the balls measured in ‘basic units’
where a basic
unit is equal to one tenth of the distance between adjacent
diamonds.
(2) If 2 x Sin A < 100%, multiply
(2 x Sin
A) by 2/distance between the edges of the balls measured
in basic units as
just defined.
3.
The THROW FACTOR ADDITION RULES
For
this correction, use one of the following two rules:
Medium or hard shots: 20% of (2 x Sin
A), or 11%, whichever is
less.
Soft shots:
20% of (2 x Sin A), or 16%, whichever is
less.
This factor represents the 'throw'
effect due to
friction between the cue ball and object ball at contact. This force of friction
acts in a direction
perpendicular to the line joining the center of the object ball
and the cue
ball at the point of contact and reduces the angle at which the
object ball
sets off towards the pocket.
Moving the
point of aim further from the center of the object ball corrects
for the effect
of this force.
Note: Shots on the rail cannot
be hit at the proper
impact point because of the rail.
To
compensate for this, using running English.
AN APPROXIMATE METHOD
A
simpler method, which is quite good provided that the cue ball
and object ball
are at least two diamonds apart, is as follows:
(1) Calculate Sin A.
(2) Double that value.
(3) Add 20%.
The
rationale for the approximate method is as follows:
1.
The value
of the increase associated with the distance from the object
ball to the cue
ball is between 3% and 10%, as long as the distance from the
object ball to the
cue ball is at least two diamonds.
2. The value of the increase
associated with the
throw effect is between 11% and 20%.
3.
So the
increase associated with the two factors together ranges from a
minimum of 14%
to a maximum of 30%, as long as the distance from the object
ball to the cue
ball is at least two diamonds.
4.
So the
approximation method will never be in error by more than 10%, as
long as the
distance from the object ball to the cue ball is at least two
diamonds.