What affects how well a cue delivers speed to the cue ball?

The amount of energy a cue delivers to the CB is called “hit efficiency” or “energy transfer” or coefficient of restitution (COR or e). A heavier cue with a harder tip will generally create more CB speed for a given cue speed. For more info, see cue weight and:

From the experiment in the video, the range of CORs were between 0.71 to 0.75 for playing cues with medium-hardness tips and 0.81 to 0.87 for jump and break cues with phenolic tips. The analysis at the bottom of TP A.30 shows the effect this has on break power (where cue weight is also an important variable). A phenolic tip can add about 17% more power or energy to a break as compared to a medium-hardness leather tip. TP B.22 shows how peak tip contact force and contact patch size vary with shot speed. It also shows how to simulate different CB speeds with cue drop tests.

For other effects related to tip hardness, see cue tip hardness effects.

Cue construction (ferrule, joint, butt, and bumper) can also have an effect on both a cue’s efficiency and hit/feel/feedback/playability. Also, whether or not the joint fastens and stays tight also effects these things. Be sure to keep the joint tight while playing, especially before any power shots.

A shaft that is very flexible (not very stiff), will tend to deform and vibrate more during (and mostly after) a hit. This vibration represents lost energy because that energy remains in the cue and is not delivered to the CB. For more info and demonstrations, see the cue vibration resource page.

Concerning tips, it is elasticity that affects COR and hit efficiency, but harder tips are generally more elastic than softer tips.

Isn’t a more efficient cue worse on fast cloth since small changes in cue speed have bigger effects on CB speed, potentially resulting in less CB distance control?

No, in general, since efficiencies don’t vary that much from one playing cue to the next and from one tip to the next, and a player can learn to easily adjust their stroke in this typical range (just as a player makes adjustment for cloth speed). Also, with a less efficient cue, the CB gains less speed and the cue loses less speed as a result of a hit, potentially resulting in bad hits at large tip offsets. If anything a lighter cue, instead of a less efficient tip, is a better choice for dealing with distance control on fast cloth.

Form more info, see:

from Mike Page (in FaceBook post):

There is general consensus that hard tips are more efficient (give more cueball speed for a given stick speed) than soft tips. Dave Alciatore (Dr-Dave) and Bob Jewett have done an experiment with clever apparatus they call Cue Stick Efficiency Tester with high-speed video for which this is a conclusion. It is well known that we use hard leather and phenolic tips on break cues. I question that Dave & Bob’s experiment is sufficient to conclude that hard tips are more efficient. I explain here the background, what I think is wrong with the measurements.

I’ve brought up in the past a potential issue for cue tip efficiency with very hard tips. When we talk about cue tip efficiency, we are really talking about the efficiency of the tip AND STICK hitting a 6oz ball. For maximum speed, the ball needs to “feel” the full weight of the cue. The tip-ball contact time for phenolic tips is less that 0.001s and may be as short as 0.0005s (half a millisecond). The speed of sound in maple is about 4 meters per millisecond, and therefore the time it takes for the ball to even begin to know about the back of the cue (disturbance travels two stick lengths, about 3m) is about 0.75ms–the contact time with a phenolic tip. So there is reason to believe that all else being equal a longer contact time might be better.

Dave and Bob use as empirical evidence this is not a concern and as a demonstration showing hard tips are more efficient an experiment in which they drop cues with different tips onto a steel plate and measure how high they bounce. Phenolic tips bounce higher than leather tips, and this, in essence, is the basis of their conclusion.

Here is the problem: A stick dropped on steel does not have the same contact time as a stick hitting a ball. In fact, I estimate the tip-steel contact time to be about twice as long as the tip-ball contact time. So for cues with phenolic tips dropped on steel, the disturbance has time to travel about four cue lengths during contact rather than just two. This is a critical difference.

The compression and relaxation of the tip during a collision can be approximately modeled as a harmonic spring, at least for the purpose to determining the effect of mass on the contact time. A mass M on a spring with spring constant K connected to a rigid wall has a frequency proportional to sqrt(K/M), and the period (for us the contact time) is proportional to the inverse of this, i.e., varies as sqrt(M).

What is M for a stick-ball collision? Two massés and a spring (that of the stick and the ball) act the same as a single mass and a spring provided you use what is called the “reduced mass.” The reduced mass is M1*M2/(M1+M2). For a 6oz ball and 18 oz stick, the reduced mass is about three quarters the mass of a ball, 4.5 oz. For an 18 oz stick hitting a rigid steel plate (large mass), the reduced mass is the mass of the stick, 18 oz. This is four times the reduced mass of the stick-ball combination. Because the contact time goes as the square root of the reduced mass, the contact for the drop test is expected to be twice that of a stick-ball collision.

dr_dave’s reply:

You bring up some good points. I would be curious to see some test results that demonstrate these effects. Maybe you can come up with a simple test that will simulate a ball strike. The efficiency depends on many things: tip restitution, friction between the tip and CB during deformation, shaft vibration, elastic wave propagation, cue construction, etc., so it is difficult to offer confident theories without physical testing.

In general, over a range of speeds, I think harder tips are more efficient (see HSV B.42 – tip and cue efficiency, with Bob Jewett). Concerning the effects of shot speed and tip hardness on tip contact time, see the tip contact time resource page.

from Mike Page (in AZB post):

A softer tip might take almost twice as long to compress and decompress against the ball than a hard tip. And this, by itself, doesn’t affect energy transfer at all. But there is some empirical evidence hard tips tend to be a little more elastic (have less energy loss). Also, this is going to be a tip-to-tip thing. It is not like here is anything automatic about softer tips that make them less elastic.

For the cueball to “feel” the entire weight of the cue, the tip-ball collision has to last long enough for the signal the collision is in progress to travel back and forth across the stick a sufficient number of times. So at some point as we get harder and harder tips, the cueball might not feel the full weight of the cue.

This is a little like a fast-moving train hitting a car that is on the tracks. The car will be launched with a speed characteristic of being hit by just the engine or the engine plus the first couple of cars. The collision time would have to be longer for the car to feel the weight of the rest of the train cars as they crush across the couplings.

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