Do frozen balls throw more than non-frozen balls?
In the case of combinations, frozen balls will always throw more than non-frozen balls (especially with a larger gap between the OBs) because the 1st OB will pick up some forward roll, which reduces throw. Also, if faster speed is used to help prevent this, throw will be reduced by the speed.
In the case of a cut shot, the OB can be thrown very nearly as much as with a frozen combo, as long as slow speed and stun are used, where throw is maximum (see maximum throw for more info). One reason some people might think frozen balls throw more than a stun shot is that frozen balls can be hit softly, easily creating maximum throw. With frozen balls, stun is guaranteed. However with a non-frozen cut shot, where there is distance between the CB and OB, it is very difficult to ensure stun with a soft shot. Therefore, it is rare to get maximum throw with a cut shot. Although, if you do hit a true stun shot at soft speed, the OB will throw very close to the same amount as a frozen ball would. For information and demonstrations concerning how to compensate for throw when aiming combination shots (including frozen combos), see combination shot aiming.
To answer the question above more scientifically, I did a careful experiment to attempt to measure the difference between throw with a frozen-combination and throw with a stunned ball at the same speed.
I used two new and clean Aramith measles balls as OBs, and wiped them after every shot, along with the CB which was another Aramith measles ball. I firmly tapped the two OBs into place (frozen, but not leaning against one another) with one OB on the head spot and the other on the head-rail side of the first with the line of centers along the table centerline or “long string.” I also marked the tapped positions with little white donuts to help further ensure consistent ball placement, shot after shot. I then hit the 1st OB squarely with another CB placed between the balls and the head rail to locate and mark on the far rail the line of centers direction (which was pretty much exactly along the table “long string” with every shot). I then tapped and marked the CB position about 6 inches on the head-rail side of the near OB along the center-to-edge line of the frozen-ball combo to ensure a consistent cut angle (with a square hit on the 1st ball) very close to 30°. I then hit this shot (after checking that the OB were in fact frozen) about 20 times at as consistent a speed as I could and marked on the far rail where the thrown OB hit (by placing a piece of chalk on the rail with one edge pointing along the line of the thrown OB). I only checked shots where the CB stopped dead and the 2nd OB bounced off the foot rail and came back to within a 1/2-diamond of the head rail to ensure consistent speed. All of the target-speed shots threw the OB very consistently to the same position on the rail.
I then removed the donut for the lead OB, replaced and carefully tilted the lead OB back toward the CB along the CTE line a very small amount and firmly re-tapped the ball into the cloth until the OB sat about 1mm (a very small gap) away from the 2nd OB. When I was confident with the placement, I put down another donut in the new location and tapped the ball in place even more firmly. I then hit about 20 shots with this new position (resulting in a non-frozen stunned hit of the lead OB into the 2nd), with everything else the same. Again, the direction the ball headed was very consistent for the shots at the target speed.
Here are the results after measuring the distances between the head spot and rail marks carefully and doing the throw angle calculations:
throw angle for frozen balls = 5.16°
throw angle for non-frozen stun shot of same speed and cut angle = 4.95°
Therefore, my experiment suggests frozen balls might throw a very small percentage more (about 4% more) than a stunned ball. However, this difference is not very significant, and could be partly due to experimental error. It could also be due to the fact that when there is a gap between the balls, the 1st OB has full speed before contacting the 2nd OB. This would result is less friction during the initial part of the collision, which could delay gearing (or prevent it from happening). This could explain the difference between frozen and non-frozen throw, especially at different cut angles and shot speeds. It is also possible that with non-frozen balls, the air between the balls being compressed before the collision might help create a slight cushioning effect (especially with higher-speed shots), which could reduce the amount of throw. Another difference between frozen and non-frozen collisions is that with the frozen case, there is simultaneous impact among three balls, and the physics for this is slightly different than with two separate collisions of two balls at a time (see the Q&A below).
The following video documents a more recent experiment that has mixed results, but the conclusion is clear: a frozen combo throws about the same amount as a stun shot of the same speed.
The following video explores throw effects related to “nearly frozen” combinations with various gap sizes between the balls (supported by TP B.21):
For more information, see small-gap combination shot aiming.
During a frozen-ball combo, does the CB still apply force on the 1st OB while it is in contact with the 2nd OB, and wouldn’t this change the amount of throw?
There are delays in the ball interactions due to the time it takes for elastic waves to travel between the contact areas (between the CB and 1st OB, and between the 1st and 2nd OBs), but this happens very quickly. From speed of sound data, the elastic wave speed in pool balls is probably close to 4000 m/s. From Marlow’s experiments, ball contact times are probably close to 0.0003 seconds. During that time, the waves have time to travel back and forth across the 1st OB at least 20 times. From these rough calculations, it is clear that forces developed between the CB and 1st OB can certainly have an effect while the 1st OB is interacting with the 2nd OB.
The CB interaction would tend to slow the induced spin that develops in the 1st OB as it interacts with the 2nd OB. This would tend to increase the relative sliding speed between the OBs, which would reduce the dynamic friction COR (since friction is less at faster sliding speeds with pool balls). This would tend to decrease the amount of throw. However, gearing between the 1st OB and the 2nd OB will be hampered some, and more throwing force can develop before the balls gear together, creating more throw. The experiment described above did show a small increase in throw, possibly due to this effect.