Every now and then a pool player in a match calls for someone to “watch the hit”. What are they doing? Typically they are concerned with detecting a double hit or making sure the proper ball is struck first. By far, the most controversial of these is the double hit. A double hit occurs when the cue stick's tip strikes the cue ball twice in the same stroke. This can occur when the cue ball is close to the target object ball.

The APA rule concerning double hits is:

10g “Causing even the slightest movement or altering the course of the cue ball, even accidentally, is a foul. …” ⁱ

The question is, “How do you judge a double hit when the cue ball is extremely close to an object ball?”

Of course, if you can see or hear the double hit; it is easy to make the call. What do you do when the balls are close together and things happen too fast to see or hear? Basically, you watch what happens after the hit. The cue ball and the struck object ball(s) give clues. We’ll look at two scenarios; close full hits and close cut shots.

There are a few things to remember about the physics of ball collisions.

In a full hit (not a cut with an angle) with no spin, the cue ball will stop. It will not continue on with the object ball.

Full Hit Sliding

Everyone has seen one of the Newton's Cradle table top toys with 5 hanging balls where one ball hits the others and the first ball stops dead while the ball on the end then bounces out of the line of balls. It actually demonstrates the same principle of momentum that two billiard balls colliding operate under.

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Newtons Cradle

When a sliding ball hits another full on, the first ball stops just like the swinging ball in a Newton's Cradle. When balls are real close together the Cue Ball does not have time to start rolling. It slides into the object ball. It should stop just like the balls in a Newton's Cradle.

In a full hit with topspin (follow or roll) applied, the cue ball will stop momentarily, spinning in place (due to the collision), and then accelerate as the topspin gains traction with the felt. The cue ball movement will be much slower and for less distance than the object ball movement.

Full Hit with Topspin

CLOSE FULL HITS

So, where’s the problem? The problem is when the cue stick hits the cue ball a second time. This occurs when the cue ball stops (like it is supposed to do) and the cue stick doesn’t. The cue stick strikes the cue ball again. This is called a “double hit” and clearly violates the rule by causing movement or altering the course of the cue ball.

Double Hit Full

For full hits, if the cue ball follows the object ball with close to the same speed (as the object ball) after the collision, you can be pretty sure the cue tip hit it a second time. Remember the physics. The cue ball should stop after a full hit.

Many double hits occur when the cue ball and object ball are close and the cue ball is hit with topspin (follow). As the cue ball strikes the object ball, it pauses, spinning in place, and the cue tip strikes the cue ball a second time. It is virtually impossible to put a tremendous amount of topspin on a cue ball without an exaggerated, long, follow-through of the cue stick. When the balls are close, this practically guarantees a double hit. The speed of the stroke sometimes masks this second hit. You need to watch where the cue ball goes and its speed to detect a double hit.

CLOSE CUT SHOTS

In a collision where the balls do not hit full (but are cut at an angle), the cue ball will rebound at a right angle (90 degrees) to the centers of the balls. This is known as the “90 degree rule.”ⁱⁱ After a little time/distance, any follow or draw will take hold on the felt and cause the cue ball to curve from this 90 degree rebound. In the long term, a ¼ ball to ¾ ball cut ⁱⁱⁱ with normal roll will usually diverge about 28 to 34 degrees from the initial cue ball path. This is known as the “30 degree rule”.^iv You won't see this very often when a double hit is a possibility since the cue ball usually slides initially and doesn't have enough time to start rolling. Most close shots with any travel for the cue ball after the collision should exhibit a 90 degree rebound off the object ball.

90 Degree Rule

How about when the cue ball and object ball are close but the object ball is not hit full? Here it is sometimes tricky, but several things can happen that are dead giveaways. Remember the physics. If the cue ball does not rebound at a 90 degree angle, but instead takes off immediately in the direction the cue is stroking, you have a clear indication the cue tip struck it a second time. There should be some displacement (and delay) along the 90 degree rebound angle before the follow (topspin) takes hold of the felt and drives the cue ball in the direction of the stroke.

Double Hit While Cutting Ball

Note that for collision angles (cuts) of less than 45 degrees, the object ball will receive the larger amount of energy and move faster/farther than the cue ball. If the cue ball goes as far or further/faster than the object ball, you can be sure the tip hit the cue ball a second time.

If the cut angle is greater than about 45 degrees, the cue ball usually is not slowed enough for the cue to hit it a second time (and no foul occurs). This is not an absolute though. Watch the rebound angle.

Another scenario where a double hit occurs is when the cue ball and object ball are close and an attempt to "throw" the object ball with outside English is undertaken.^v The cue ball is “trapped” by the cue stick as it rebounds off the object ball. Again, the primary symptoms of a double hit are the lack of a 90 degree rebound and excess energy in the direction of the cue stroke by the cue ball. Here, the cue ball rebounds off the object ball back into the cue stick. The only way to really insure a double hit doesn't occur on real close cut shots is to put inside English on the cue ball. This way, the rebound is away from the cue stick.

Double Hit Trapping Cue Ball with Outside English

There are two common approaches to avoiding double hits on close shots. The first is to elevate the cue to a 45 degree angle. This reduces the cue tip travel in the direction of the stroke toward the collision and rebound zone. The other common approach is the "nip" stroke where the follow-through of the cue is kept as short as possible. Still, in both of these approaches, the follow-through of the cue stick must be controlled with care to avoid the double hit.

A 45 degree elevation on the cue stick when hitting full into a ball that is practically frozen but not actually touching can still result in a double hit. Remember the physics. The cue ball should stop as soon as it contacts the object ball. During a normal stroke the cue tip usually remains in contact with a cue ball for about 1 millisecond. At 5 mph, this is less than 0.09 inches of distance. You’ll have to get out your feeler gauges I guess. At 45 degrees, the cue ball travels 0.062” (~1/16 of an inch) along the direction of travel with the tip in contact (for 1ms) with the cue ball. You can argue that the tip is still in contact with the cue ball when it hits the object ball if they are closer than this (0.09”). Most leagues (BCA, WPBA) rule it a foul if the cue stick is in contact with the cue ball when it strikes an object ball^vi. Alas the APA is not clear about this. Regardless, time-lapse photography^vii shows the cue stick bends and the tip bounces off the cue ball at normal stroke speeds and the tip does not stay in contact with the cue ball long enough to displace the cue ball without a second hit. In a normal hit the cue ball leaves the collision (of the tip) with 133% of the original cue speed while the cue stick slows to 60% of the original cue speed^viii. The cue stick does not keep up with the cue ball. For a full stroke (to the felt) at 45 degrees, the cue tip travels 1.92 inches through the cue ball in the direction of travel. Clearly, a double hit is going to occur if the cue ball cannot move out of the way. Even with a 45 degree elevation, a full stroke will produce a double hit. You still need to perform a “nip” stroke when the cue stick is elevated at 45 degrees.

Craig Watson