Hard Banks Curve Short - Why?

[Jal]

...I take it "spin vector" is what I would call the axis of spin?

Pretty much. That is, it's represented as an arrow aligned with the spin axis, whose magnitude (length) is proportional to the rate of spin. Each spin component, then, has its own axis of spin, although we see the combination (vector sum) as one. (Maybe it should be mentioned that analyzing what appears to be a single vector, such as spin, into components, is, mathematically speaking, arbitrary and done for convenience. That is, it's easier to relate particular causes to effects on particular components, then later combine the components into a "resultant" final sum. Typically, the components are chosen such that they are perpendicular to one another, such as an x-component, y-component, and z-component, for instance. When numerically re-combining these 'orthogonal' components, they sum according to the Pythagorean Theorem (square root of the sum of the squares)). Okay Jim, enough.

As for whether (2) or (3) would be considered "draw spin", I think it would be both (the sum of them), since they would each, if acting alone, "masse" the ball off its rebound path in the direction of draw spin.

Very true - I was being stupid or facetious, not sure which.

They each produce spin that increases as its masse effectiveness decreases (due to the changing bank angles), so I'm guessing the maximum combined masse effect is achieved at about the middle of the range of angles, or about 45 degrees. Does that sound right?

That's a standard math problem, but to arrive at an accurate answer you would have to know how they vary with incoming angle. I think the third component I listed is the most troublesome to estimate. Also, bed friction during impact, while smallish, is not insignificant. And there are additional complications from the cushion's "parallel springiness" (tangential coefficient of restitution, which Dr. Dave sometimes calls "cushion throwback"). That said, 45 degrees sounds like a very good estimate to me, but I wouldn't be too married to it. I would be surprised if it were grossly wrong though.

Jim

 

[Jal]

I think the object ball slides on the rail abefore the rebound & the object balls picks up spin. Then the object curves on the rebound trajectory line like a slight masse'...

I think we'd all agree...at least most of us. Nice insight.

Jim

 

[Jal]

The only way to evaluate the effects of compression is to change the compressibility of the cushion, while holding constant other factors, such as cloth friction, tension, speed and angle of impact, ect.

The stated experiment seems to fix everything except velocity, and is therefore designed to evaluate that parameter.

Yes, but following up on Patrick's post, speed does change the depth of the OB's penetration into the cushion. That's what Bob's setup was designed for: to show that the shortening of the re-bound angle has very little to do with the amount of cushion compression, but that it's really a function of acquired topspin (or lack of it) on the way to it. It wasn't designed to relate that shortening to the properties of a particular cushion. I got very similar results on the Gold Crowns where I play.

Sure, it would be nice to do more testing, but the generic result is very useful to know in order to organize one's experience with rebound angles. No?

Jim

 

[Dead Crab]

Yes, but following up on Patrick's post, speed does change the depth of the OB's penetration into the cushion. That's what Bob's setup was designed for: to show that the shortening of the re-bound angle has very little to do with the amount of cushion compression, but that it's really a function of acquired topspin (or lack of it) on the way to it. It wasn't designed to relate that shortening to the properties of a particular cushion. I got very similar results on the Gold Crowns where I play.

Sure, it would be nice to do more testing, but the generic result is very useful to know in order to organize one's experience with rebound angles. No?

Jim

From a science point of view, it does not resolve anything because the state of "roll" and compression are confounding variables, and therefore the conclusion drawn regarding this can't be substantiated (although I do not exclude the possibility it is correct).

From a practical point of view, the results are useful as they form the basis for why good bankers tend to shoot firmly (eliminate forward roll), and the fact that banking is more robust with respect to velocity than is generally thought.

I will add, however, that I've mapped the pushback variation (at multiple incidence angles) of a number of tables with Simonis covered cushions and find it difficult to explain the results without acknowledging potential variation in compression effects.

This would be a good Masters thesis project for someone, but the experimental controls and equipment needed to control for confounding is beyond the reach of this amateur scientist.

 

[dr_dave]

From a practical point of view, the results are useful as they form the basis for why good bankers tend to shoot firmly (eliminate forward roll), and the fact that banking is more robust with respect to velocity than is generally thought.

There are several advantages for shooting banks firmly.

I will add, however, that I've mapped the pushback variation (at multiple incidence angles) of a number of tables with Simonis covered cushions and find it difficult to explain the results without acknowledging potential variation in compression effects.

This would be a good Masters thesis project for someone, but the experimental controls and equipment needed to control for confounding is beyond the reach of this amateur scientist.

Agreed. This is not an easy problem to solve. I've personally thought about it for many years, and have done some experiments; but, as you point out, there are many important physical parameters (cushion normal and transverse COR, cushion nose COF, rail-groove COR and COF, and table-cloth rolling resistance and COF) and all of them can change with speed, incidence angle, cushion nose height, cushion cloth tightness and condition, and/or ball/table-cloth conditions.

Marlow takes a basic look at some of these effects in his book, but I think a lot more can be done to improve understanding; although, I honestly doubt the study would result in any truly practical revelations. Most practical kick and bank effects are already fairly well know and understood.

Regards,
Dave

 

[dr_dave]

Why do hard-hit bank shots curve short after rebounding from the rail?
...

2. the rail cloth's friction shortening the rebound angle
...

I mean the OB's rebound path starts out straight but then curves short as if it had draw on it (like a kick shot with draw),

I'm thinking it's cross-table topspin caused by the cushion nose being higher than centerball (as if the OB was hit above center by a cue aimed across the table perpendicular to the rail). Topspin in this direction would be across the "natural" rebound path and would act like backspin put on a CB for a kick shot, causing the ball to masse short off its straight rebound path.

Anybody know for sure or have a reasoned opinion?

I certainly agree with you and the other posters who attribute it to the nose of the cushion being above the "equator" of the OB. But just a slight note.

Ultimately, it is friction with the cushion that generates the spin. The ball and cushion interaction takes place at their surfaces. Normal forces (perpendicular) to the surface of the OB, generated by cushion compression, act through the OB's center. Thus, no torque is produced, and no spin can be generated by them.

The friction forces, however, act tangentially to the surface, and thereby create the torque - the moment arm is equal to the radius of the ball. In the case of a stun shot (no sidespin either) you can picture two masse type of spin components being produced by them, and three spin components in all:

1) A perfectly vertical spin component which does not contribute to subsequent masse action. Here the spin vector (arrow) is pointing straight up.

2) A spin vector perpendicular to the cushion and parallel to the table bed. This arises in tandem with (1) above, as the ball rubs against the cushion due to its parallel (to the cushion) translational velocity, and the cushion's nose overhang. In effect, this spin is equivalent to the ball being struck below center and driven parallel to the cushion.

3) A spin vector component parallel to the cushion, due to rubbing of the cushion as the ball "penetrates" the rubber. You can see this in Dr. Daves high-speed video on kick losses, HSV B15 (stun section, normal conditions). The examples are for perpendicular approach angles, but I would think it still applies at other ones too, to some extent. This spin is equivalent to being struck below center and driven perpendicular to the cushion.

I suspect that (3) would be dominant at approach angles not too far from perpendicular to the cushion, while (2) would dominate at more shallow approaches. As indicated, though, that is a speculation. Both (2) and (3) should generate these "backspin" components, but they happen to be at 90 degrees to one another. I guess it's optional as to which one might be considered acquired "draw spin."

Just some pedantic blathering, which you probably already knew.

Jim,

Good explanation!

I agree with you that "3" is the primary factor explaning the effect PJ describes. When I filmed HSV B.15 - Straight-on kick shot rebound losses and spin changes for roll, stun, and draw shots, I was honestly a little surprised that the stunned ball came off the rail with as much topspin as it did in the "slick conditions" test (creating the draw shortening effect). I thought the reduction in friction (from Silicone spray) would dramatically reduce the effect, but it didn't. In fact, there seemed to be even more spin (certainly not less) with slick conditions. This might be because the spin is created mostly while the ball is in contact with the compressed cushion nose; and with less friction, less of the created spin is lost due to sliding friction. So friction is needed to create the spin, but friction also reduces the amount of created spin while the ball is still in contact with the cushion. Does that make sense?

Regardless, as shown by HSV B.15, a ball stunned into a rail (as is the case with a fast-speed bank) will pick up topspin (with a spin axis parallel to the rail) to make the rebounding ball curve shorter (for both slick and sticky conditions).

Regards,
Dave

 

[Jal]

... When I filmed HSV B.15 - Straight-on kick shot rebound losses and spin changes for roll, stun, and draw shots, I was honestly a little surprised that the stunned ball came off the rail with as much topspin as it did in the "slick conditions" test (creating the draw shortening effect). I thought the reduction in friction (from Silicone spray) would dramatically reduce the effect, but it didn't. In fact, there seemed to be even more spin (certainly not less) with slick conditions. This might be because the spin is created mostly while the ball is in contact with the compressed cushion nose; and with less friction, less of the created spin is lost due to sliding friction. So friction is needed to create the spin, but friction also reduces the amount of created spin while the ball is still in contact with the cushion. Does that make sense?

I just watched the video again several times (normal and slippery conditions), with the playback slowed way down. All I can tell is that the spin is induced at around maximum cushion compression, and seems to be essentially fully developed by the time the ball has acquired any rebound velocity. So it doesn't seem to be bed friction that's generating the torque. Other than that, it's hard to see what's going on, particularly why the slick conditions produce so much spin. It seems (perhaps) as if the cushion wants to flex upward at maximum compression, then takes the ball's surface with it. Maybe static friction is holding throughout? But why isn't this reversed (canceled) as the ball begins its rebound motion?

Regardless, as shown by HSV B.15, a ball stunned into a rail (as is the case with a fast-speed bank) will pick up topspin (with a spin axis parallel to the rail) to make the rebounding ball curve shorter (for both slick and sticky conditions).

My guess would have been that the spin brought about by the ball rolling along the cushion (item (2) in my post), was the main cause when approach angles are well off of perpendicular. But given your comments, and having looked at the video again, I'm not so sure. That is quite a bit of spin induced by whatever mechanism is at play in your video.

Jim

 

[Jal]

From a science point of view, it does not resolve anything because the state of "roll" and compression are confounding variables, and therefore the conclusion drawn regarding this can't be substantiated (although I do not exclude the possibility it is correct).

But do you agreee that in Bob's test, the state of roll is not a confounding variable. (Setting up the balls very close to the cushion pretty much eliminates this, doesn't it?)

I will add, however, that I've mapped the pushback variation (at multiple incidence angles) of a number of tables with Simonis covered cushions and find it difficult to explain the results without acknowledging potential variation in compression effects.

If the data is in transmissible form, would it be possible to share it with us? I'm not saying I'm going to do anything with it, but if it's all the same to you....

Jim

 

[Dead Crab]

*********
But do you agreee that in Bob's test, the state of roll is not a confounding variable. (Setting up the balls very close to the cushion pretty much eliminates this, doesn't it?)
*********

The way the experiment was explained, the OBs get moved back, so that the degree of roll is variable. If they were strictly stunned into the rail, then it would remove "roll" as a confounding variable.

**************
If the data is in transmissible form, would it be possible to share it with us? I'm not saying I'm going to do anything with it, but if it's all the same to you....
*************

Transmissable? It isn't that high tech. Every time I go to a pool hall to play I map out the pushback at key sites and write it on an index card. Unfortunately, I tend to lose the cards, but here is some sample data on a couple of GC V's. For table #9, I used a wooden collimator (covered with felt) to make sure the balls stay on target.

I use 10 units per diamond, so a 20-10 bank is targeted to the first diamond.

Table #9:
10-5: 0 degrees
15-7.5: 2.8 degrees
20-10: 4.5 degrees
30-15: 6 degrees
40-20: 8.5 degrees
50-25: 8.5 degrees
60-30: 7.5 degrees

Table #12:

10-5: 3.5 degrees
20-10 5.5 degrees
30-15: 8 degrees
40-20: 8.5 degrees
50-25: 10.5 degrees
60-30: 8.5 degrees

Table 3:
20-10: 6 degrees
40-20: 10 degrees
Can't recall others

Home table:
20-10: 5 degrees
30-15: 7 degrees
40-20: 8 degrees
50-25: 8 degrees
60-30: 8 degrees

I've got some other data around. I've played on a couple of tables with really soft cushions where the max pushback has been around 12 degrees. You really need to check them on the day of play, as they can vary a couple of degrees.

Note: I use the diamond position projections on the rails (not shooting thru diamonds).

 

[Bob Jewett]

... The way the experiment was explained, the OBs get moved back, so that the degree of roll is variable. If they were strictly stunned into the rail, then it would remove "roll" as a confounding variable. ...

Well, you can place the three object balls with the last almost touching the cushion and then you can do stun at all speeds. The article suggests exactly this as the first part of the test.

The result for stunning at different speeds into the cushion is very, very different from what most people expect. The most surprising wrinkle for me was the discovery that on a snooker table (standard British L-shaped rubber, BCE steel-block rails), the harder stun shots bank longer than the softer shots.

 

[Jal]

*********
But do you agreee that in Bob's test, the state of roll is not a confounding variable. (Setting up the balls very close to the cushion pretty much eliminates this, doesn't it?)
*********

The way the experiment was explained, the OBs get moved back, so that the degree of roll is variable. If they were strictly stunned into the rail, then it would remove "roll" as a confounding variable.

**************
If the data is in transmissible form, would it be possible to share it with us? I'm not saying I'm going to do anything with it, but if it's all the same to you....
*************

Transmissable? It isn't that high tech. Every time I go to a pool hall to play I map out the pushback at key sites and write it on an index card. Unfortunately, I tend to lose the cards, but here is some sample data on a couple of GC V's. For table #9, I used a wooden collimator (covered with felt) to make sure the balls stay on target.

I use 10 units per diamond, so a 20-10 bank is targeted to the first diamond.

Table #9:
10-5: 0 degrees
15-7.5: 2.8 degrees
20-10: 4.5 degrees
30-15: 6 degrees
40-20: 8.5 degrees
50-25: 8.5 degrees
60-30: 7.5 degrees

Table #12:

10-5: 3.5 degrees
20-10 5.5 degrees
30-15: 8 degrees
40-20: 8.5 degrees
50-25: 10.5 degrees
60-30: 8.5 degrees

Table 3:
20-10: 6 degrees
40-20: 10 degrees
Can't recall others

Home table:
20-10: 5 degrees
30-15: 7 degrees
40-20: 8 degrees
50-25: 8 degrees
60-30: 8 degrees

I've got some other data around. I've played on a couple of tables with really soft cushions where the max pushback has been around 12 degrees. You really need to check them on the day of play, as they can vary a couple of degrees.

Note: I use the diamond position projections on the rails (not shooting thru diamonds).

Thanks for taking the time to type that out.

If I understand, 20-10, for instance, means a path from the second diamond across table to the first diamond, measuring from the cushion noses. Assuming that's right (or not), a couple of further questions if you will. Where does the ball start from along that line, or maybe more to the point, are you always attempting to stun into the cushion? How are the "pushback" values calculated (i.e., what exactly do they mean)?

Jim

 

[book collector]

Hard Banks curve short

Is the object ball sliding when it comes off the rail and then grabs to shorten up?

 

[Bob Jewett]

Is the object ball sliding when it comes off the rail and then grabs to shorten up?

If the object ball is sliding when it comes off the cushion, it will travel in a straight line. The object ball must have the equivalent of masse as it comes off the rail or it will not curve. That means it must be spinning at least partly on an axis parallel to its motion.

 

[Dead Crab]

Thanks for taking the time to type that out.

If I understand, 20-10, for instance, means a path from the second diamond across table to the first diamond, measuring from the cushion noses. Assuming that's right (or not), a couple of further questions if you will. Where does the ball start from along that line, or maybe more to the point, are you always attempting to stun into the cushion? How are the "pushback" values calculated (i.e., what exactly do they mean)?

Jim

Yes, for example a 50-25 bank would be from the nose at the 5th diamond away from the target pocket to nose location midway between the 2nd and 3rd diamonds on the banking rail.

I usually have the OB one diamond away from the cushion. As you get into the shallow banks, it has to be moved a bit farther back to avoid the double kiss or hitting the collimator.

The reason I do this is practical. I'm not gathering data for science. I want to know how to play the table on that day. Example:

During warm up I place the OB on the 20-10 line about a diamond off the cushion and bank it with a firm stroke. It banks short, hitting the cushion about 5" away from the effective pocket center. I place a coin on the top of the cushion where it hit and repeat. If I hit the same spot, I have confirmed the bank is 5" short. With a little trig, this is about 5.5 degrees, which I will round to 6 degrees.

Knowing that, I want to test my result. So I put the OB back on the 20-10 line, about 1 diamond out, and put the CB on the 20-10 line, maybe 18" away. To correct my aim, I take the 6 degrees of expected pushback and multiply by 0.8 (because the OB is one diamond off the rail) and see that I need to cut the ball about 5 degrees. So my aim point on the OB will be about 5mm off center. I will then shoot, with a tiny amount of outside english (to offset CIT), and the bank should go.

Another example: 20-10 bank, OB two diamonds off banking rail where there is a 20 degree cut needed to send the OB along the 20-10 line. In this case:
pushback correction = 6 degrees x 0.66 = 4 degrees

aim point on OB = 20mm (cut) + 4mm (pushback correction) = 24mm off OB center

I will shoot this shot aiming 24mm off OB center, with about 5mm of outside backhand english. This should send the OB along the modified bank line without sidespin, and hopefully, it goes in.
***************

I came up with some of this independently, but Jack Koehler had the same basic approach described in his book. Some of what he has is over-complicated (I look only at the total pushback, not how much is related to specific components), and his chart for angle correction multipliers is not very accurate. But, the basic approach is sound.

 

[Patrick Johnson]

Well, you can place the three object balls with the last almost touching the cushion and then you can do stun at all speeds. The article suggests exactly this as the first part of the test.

The result for stunning at different speeds into the cushion is very, very different from what most people expect. The most surprising wrinkle for me was the discovery that on a snooker table (standard British L-shaped rubber, BCE steel-block rails), the harder stun shots bank longer than the softer shots.

My first theory about this would be that the thinner profile of the snooker rubber allows the ball to sink farther into it, which causes it to follow a larger curve while in contact so that it exits the cushion farther along (the same effect you produced on your video test with pool cushions, only bigger).

pj
chgo

 

[Patrick Johnson]

Dead Crab:
I will shoot this shot aiming 24mm off OB center, with about 5mm of outside backhand english. This should send the OB along the modified bank line without sidespin, and hopefully, it goes in.

I take it this outside spin is how you attempt to eliminate rail friction as the shortening culprit? Doesn't it confound the results with aiming uncertainties?

pj
chgo

 

[Dead Crab]

I take it this outside spin is how you attempt to eliminate rail friction as the shortening culprit? Doesn't it confound the results with aiming uncertainties?

pj
chgo

The outside english is for "gearing". I want the OB to hit the rail without sidespin.

 

[Patrick Johnson]

book collector:
Is the object ball sliding when it comes off the rail and then grabs to shorten up?

Bob:
If the object ball is sliding when it comes off the cushion, it will travel in a straight line. The object ball must have the equivalent of masse as it comes off the rail or it will not curve. That means it must be spinning at least partly on an axis parallel to its motion.

I think there might be a confusion of terms here. If the OB is "sliding" in the sense that it has no spin whatsoever, then it will not curve. But it can also be "sliding" in the sense that any spin on it has not yet produced visible results ("grabbed"). For the latter definition, the answer to the question is yes - the OB appears to go straight for a distance before the curve "grabs" (although it's actually just curving more gradually until then).

pj
chgo

 

[Patrick Johnson]

Me:
I take it this outside spin is how you attempt to eliminate rail friction as the shortening culprit? Doesn't it confound the results with aiming uncertainties?

Dead Crab:
The outside english is for "gearing". I want the OB to hit the rail without sidespin.

Yes, that's what I meant. Do you shoot every shot with the same sidespin and from the same CB/OB distance? I'm trying to imagine how you control for aiming discrepancies.

pj
chgo

 

[Dead Crab]

Yes, that's what I meant. Do you shoot every shot with the same sidespin and from the same CB/OB distance? I'm trying to imagine how you control for aiming discrepancies.

pj
chgo

For gearing english, I use 1 mm of BHE for every 5 degrees of cut as my rule of thumb. So if I am cutting the OB ball right 30 degrees, I'm going to use (or try to use) 6mm of left (outside) english.

In terms of aiming, I use whatever cut angle presents itself in the course of play. For shots with long CB-OB distance, the usual pitfalls are there regarding the effects of english and aiming.