Is there any way to determine cut angle in degrees?

[Bob Jewett]

... If you want to actually calculate the angle, you need precise measurements and a calculator.

Having that information will in no way help you as a player because you won't have it when you need it. ...

This may be true for some people but not for all. A very good player around here bought a programmable HP calculator when they first came out and had me program it so he could put in diamond counts for a particular line and get out degrees. He then memorized the relative angles to the rails for a whole bunch of positions. For example, if the object ball is 4 and a half diamonds from the corner pocket and off the cushion far enough (about 8 inches) that the line to the pocket "comes from" a spot 1 1/8 diamonds out on the end rail, he knows that the path of the object ball forms an angle of 8 degrees relative to the long rail. He then looks at the line of the cue ball to the object ball and knows (for example) that it forms an angle of 43 degrees with that same rail. He just subtracts those two numbers (in this case) and knows that the cut is 35 degrees.

To answer the original question: if you put your tip at the center of the ghost ball and your stick in line with the path of the object ball and then swing the cue around keeping the tip in place until your cue is over the cue ball, each inch of movement of the cue's bumper is one degree of cut. This is exactly true if your cue is 57.2957795 inches long.

The distance the bumper moves is called an "arc length" and since it is curved it is a little tricky to measure. The approximation above from Dead Crab (with a 15-inch mark) is close but not exact except (I think) for 0 and 60 degrees. At other angles (not too large) it is correct within about a degree, which is close enough for nearly all purposes.

I think the benefits of knowing the angles of shots include forcing the player to pay attention to the shot and having the shot in a framework that has been used during practice.

 

[dr_dave]

This may be true for some people but not for all. A very good player around here bought a programmable HP calculator when they first came out and had me program it so he could put in diamond counts for a particular line and get out degrees. He then memorized the relative angles to the rails for a whole bunch of positions. For example, if the object ball is 4 and a half diamonds from the corner pocket and off the cushion far enough (about 8 inches) that the line to the pocket "comes from" a spot 1 1/8 diamonds out on the end rail, he knows that the path of the object ball forms an angle of 8 degrees relative to the long rail. He then looks at the line of the cue ball to the object ball and knows (for example) that it forms an angle of 43 degrees with that same rail. He just subtracts those two numbers (in this case) and knows that the cut is 35 degrees.

To answer the original question: if you put your tip at the center of the ghost ball and your stick in line with the path of the object ball and then swing the cue around keeping the tip in place until your cue is over the cue ball, each inch of movement of the cue's bumper is one degree of cut. This is exactly true if your cue is 57.2957795 inches long.

The distance the bumper moves is called an "arc length" and since it is curved it is a little tricky to measure. The approximation above from Dead Crab (with a 15-inch mark) is close but not exact except (I think) for 0 and 60 degrees. At other angles (not too large) it is correct within about a degree, which is close enough for nearly all purposes.

Thanks Bob. I also like Steve's post about using an analog watch on your wrist (or just visualize a clock face) to approximate a cut angle.

Would it be illegal to have a miniature protractor as a design on a wristwatch or printed on (or inlayed into) the butt of the cue? Then any angle could be measured easily and quite accurately; and if one knows what cut angle values correspond to each ball-hit fraction, one could fairly accurately estimate a line of aim with fractional-ball aiming. On VEPS-I, we show how to use the 30-degree peace-sign and variations to estimate ball-hit fraction fairly reliably; although, I still like DAM better.

I think the benefits of knowing the angles of shots include forcing the player to pay attention to the shot and having the shot in a framework that has been used during practice.

Agreed. The primary benefits of "aiming systems" include focus and routine. However, I still think knowing the exact numerical value of a cut angle is of little practical use to most people, but I'm still interested to know how others think this number is useful for aiming.

Regards,
Dave

 

[CocoboloCowboy]

Pretty much anything over 90 DEGREES is not a makable shot.

 

[dr_dave]

Pretty much anything over 90 DEGREES is not a makable shot.

You make a good point. :grin:

However, cuts beyond 90 degrees are possible. See:

NV B.92 - "Impossible" cut shots, from VEPS V​

Regards,
Dave

 

[CocoboloCowboy]

You make a good point. :grin:

However, cuts beyond 90 degrees are possible. See:

NV B.92 - "Impossible" cut shots, from VEPS V​

Regards,
Dave

Good link Dave requiring a whole lot of skill!

 

[dr_dave]

Actually, cuts of 90deg are impossible.

The amount of speed that the cueball imparts to the object ball upon contact can be figured by the formula:
Vo=Vc*cosine (Theta).

Where Vo is velocity of the object ball, Vc is velocity of the cueball, theta is the angle of the desired path of the object ball compared to the path of the cue. If you use a theta of 90deg (cos (90)=0), the velocity of the object ball will be 0.

Good point. Maybe I should have used "effective cut angle due to throw" instead of "cut angle." All that really matters at the table is where the CB is and where the OB goes, regardless of what terminology and math you use.

Regards,
Dave

 

[duckie]

Actually, I (and my students) can do better and measure any shot with 1 degree accuracy with hardly more than a glance. It can be very helpful in all kinds of ways beyond simple precision aiming, especially if you also play other games like 3-cushion that require precise caroms and spin control when hitting different amounts of object ball. The method I developed (and will soon be publishing) was originally developed for billiards to avoid kisses and play position, but I soon found that it directly translates to pool as well since the physics is identical.



Exactly. But the more precisely you know the degree of cut, the more precisely you know just what that trade-off is and can make better predictions at the table. Of course, the human mind is a powerful thing, and you can learn this through thousands of hours of trial and error. But there are definitely ways to shortcut the process if you have a good model to work from and don't mind incorporating a little analysis into your game.

Robert

There are no shortcuts in pool. I repeat there are no shortcuts in pool.

Once again , the actual degree of the cut in useless, meaningless and anyone that tries to figure out if a cut is 30 degrees or 29 degrees are wasting their energy. Knowing that difference of 1 degree is meaningless.

Knowing that 1 degree of difference does not tell you anything about how to stroke the CB to make the shot and get position.

One of the places I play have 6 3 cushion tables and I can tell they don't care about degrees either. Just how to manage the energy needed based on how much they hit a ball. They are either diamond system player or HAMB players.

Thats it in a nutshell. Learning how the different cuts shots affects the transfer of energy from the CB and OB. The difference of 1 degree in a cut shot is not greatly gonna affect the transfer of energy between the CB and OB unlike going from a straight in shot to a high cut shot where it there is a great difference in transfer in energy.

Knowing the degree of cut does nothing to help you adjust for different balls, tables, clothes, lights, weather, things that affect play from day to day.

There are no shortcuts in pool and the up and coming serious player needs to realizes that getting really good at pool takes quality table time over a long period of time. You can read all you want, watch all the DVD, you want, but its quality time at the table that is the heart and soul of becoming a top player. Reading and watching ain't the same as doing something.

There are no shortcuts.

 

[Robert Raiford]

The approximation above from Dead Crab (with a 15-inch mark) is close but not exact except (I think) for 0 and 60 degrees. At other angles (not too large) it is correct within about a degree, which is close enough for nearly all purposes.

Dead Crab's method as stated measures using the line from the cue ball through the center of the object ball, not the ghost ball as you describe when measuring cuts, so his error depends on CB-OB distance (which he doesn't account for).

Even if it did use the ghost ball line, wouldn't you be comparing ASIN(d/15) with 4*d? That's only within a degree up to cuts around 1/2-ball, then gets progressively worse beyond that: it's 8 degrees off at 60, and it would consider a 90 degree cut 60 degrees (4*15)! Thinner cuts would be where you need better approximations since the margin of error is less, right?

What's worse is how sensitive to measurement error it is. Every inch is roughly 4 degrees in the linear region, so that's 1 degree of error for every 1/4 inch you're measurement is off. Also, you're measurement is off even more however many degrees you're not exactly parallel with the target line to begin with.

I think the benefits of knowing the angles of shots include forcing the player to pay attention to the shot and having the shot in a framework that has been used during practice.

Absolutely, but I also agree with your hedge "include" that there are other benefits as well.

Robert

 

[dr_dave]

I think the benefits of knowing the angles of shots include forcing the player to pay attention to the shot and having the shot in a framework that has been used during practice.

Absolutely, but I also agree with your hedge "include" that there are other benefits as well.

All aiming systems "include" many benefits, many of which are listed here:

http://billiards.colostate.edu/threads/aiming.html#benefits​

Regards,
Dave

 

[Robert Raiford]

[deleted argumentative post]

 

[Robert Raiford]

A very good player around here bought a programmable HP calculator when they first came out and had me program it so he could put in diamond counts for a particular line and get out degrees.

I assume the HP calculator already had a tangent function, so what did the programming involve beyond that?

Robert

 

[Dead Crab]

Dead Crab's method as stated measures using the line from the cue ball through the center of the object ball, not the ghost ball as you describe when measuring cuts, so his error depends on CB-OB distance (which he doesn't account for).

Even if it did use the ghost ball line, wouldn't you be comparing ASIN(d/15) with 4*d? That's only within a degree up to cuts around 1/2-ball, then gets progressively worse beyond that: it's 8 degrees off at 60, and it would consider a 90 degree cut 60 degrees (4*15)! Thinner cuts would be where you need better approximations since the margin of error is less, right?

What's worse is how sensitive to measurement error it is. Every inch is roughly 4 degrees in the linear region, so that's 1 degree of error for every 1/4 inch you're measurement is off. Also, you're measurement is off even more however many degrees you're not exactly parallel with the target line to begin with.


Absolutely, but I also agree with your hedge "include" that there are other benefits as well.

Robert

Normally I value your opinion, and I certainly am impressed by your impressive billiards credentials. However, I do think you've been somewhat shortsighted in your assessment of my method. Recall that earlier in this thread I did make it clear that I was not presenting a complete version.

As you are well aware, there is convergence of the CB-GB and CB-OB lines near the CB. Most shots that require use of any aiming method in pool are relatively long. Because of this, using the easily identifiable CB-OB line as a reference to place the tip does not result in a significant error. For example, a 6 foot CB-OB distance 30° cut shot will have the distance between these two lines less than 0.2 inches 15 inches from the cue ball. As the CB-OB distances get shorter, it would be prudent to place the tip on a best approximation of the CB-GB line. In my opinion, this can usually be done within a couple of tenths of inches, and the errors associated with this are not nearly as severe as you state.

You are correct that there is a breakdown of the method at higher angles, mainly above 40°. Hoverver, it is generally accurate to around .5 degree up to that point. Since I mainly play banks, I tend to shy away from cuts above this magnitude. But, it is an acknowledged weakness.

Finally, perhaps there is something wrong with me, but I do believe that I can accurately estimate the perpendicular distance to within about a quarter of an inch. In billiards, this is a substantial piece of real estate, and I would have to question as to whether anyone who lacks the visual spatial skills to do this (after some practice) will not encounter substantial difficulties in other areas of the game.

I do look forward to learning your method of estimation "at a glance" to within 1°. This would certainly simplify my life and probably improve my game. However, so far you haven't put forth anything that substantiates this. If you are ever in the Midwest (IL), let me know, and I would gladly pay you typical instructor fees for an hour lesson in how to estimate angles. First, though, we will play a quick low stakes game of "guess the angle", and I will expect you will deliver me a first-class whoopin' to justify my paying for your instruction time.

 

[Dead Crab]

***************
Agreed. The primary benefits of "aiming systems" include focus and routine. However, I still think knowing the exact numerical value of a cut angle is of little practical use to most people, but I'm still interested to know how others think this number is useful for aiming.

Regards,
Dave
*****************************
Example:

20 degree cut shot to be shot with stun. You know that this will produce about 3 degrees of throw with your equipment. Therefore, you aim this as a 23 degree shot (about 3mm wider).

There are other situations, particularly involving cushions, where knowing the cut angle is valuable.

 

[cuesmith]

Is there a reliable way to determine the actual cut angle of a shot, say within five degrees? Years ago, I vaguely recall a system where one would draw a line from the pocket though the object ball and extend it into the rail. Then do the same for the cue ball...from the pocket to the rail; then there was a formula one could apply. However, I know there is an easier way to get within +/- five degrees. Any thoughts? Yes, I'm aware that a peace sign with your fingers is approximately 30 degrees, but frankly for me it's of limited use. Thanks in advance for your help.

I don't understand why you'd want to know this? Or how you think it would be of help. Do yourself a favor and forget about the degrees and just get out there and hit balls. Be observant of the results of each shot and learn to correct when you miss. When you try to compute a bunch of data in order to make a shot, you're handicapping yourself. You want your mind free of those thoughts and just shoot where you know you have to to make the ball. If you miss, pay attention to where the OB went and adjust to make it go. You want a clear mind when you're down on the ball, not a head full of angles and degrees. Hope this helps!

 

[dr_dave]

I do look forward to learning your method of estimation "at a glance" to within 1°.

How do you personally use knowledge of the cut angle value to help you aim a shot. Are you using it to estimate the required ball-hit fraction?

Are you willing to describe your method, or must we wait for the book or DVD to come out?

Thanks,
Dave

 

[3andstop]

:deadhorse::deadhorse::deadhorse: So .... honestly, I'm truly curious with all this angle figuring, isn't it much easier to envision a straight line to a tangable target, than some arbitrary degree to an estimated point on the OB?

What's the point of all this? :shrug:

 

[Dead Crab]

How do you personally use knowledge of the cut angle value to help you aim a shot. Are you using it to estimate the required ball-hit fraction?

Are you willing to describe your method, or must we wait for the book or DVD to come out?

Thanks,
Dave

No, I've been public with it before.

If you know the cut angle, you know where to aim from the CB center.

1mm per degree up to 30 degrees and above that, 0.8mm/degree off ball edge over 30 degrees covers it pretty well.

Ball landmarks come in handy. A visible gap becomes apparent between cloth and ball at about 10mm off center (napped), 7-8 mm worsted.

A 20 degree cut can be aimed at 7:30 or 4:30 on the clockface, a 25 degree shot at 8:00 or 4:00. A 23 degree cut is 2mm shy of a 25 and 3mm more than a 20.

That sort of thing ... which ain't for everybody.

 

[dr_dave]

Thank you for posting that again. I didn't remember the details from your past postings.

Now I remembered why I didn't remember it ... that method is not very attractive to me. You must be a savant at being able to estimate and visualize millimeter distances. I'm not. I prefer DAM (a combination of ghost-ball, contact-point-to-contact-point, and "just seeing the angle").

Regardless, thanks again for sharing your approach. I suspect some people might relate to it better than I do.

Regards,
Dave

No, I've been public with it before.

If you know the cut angle, you know where to aim from the CB center.

1mm per degree up to 30 degrees and above that, 0.8mm/degree off ball edge over 30 degrees covers it pretty well.

Ball landmarks come in handy. A visible gap becomes apparent between cloth and ball at about 10mm off center (napped), 7-8 mm worsted.

A 20 degree cut can be aimed at 7:30 or 4:30 on the clockface, a 25 degree shot at 8:00 or 4:00. A 23 degree cut is 2mm shy of a 25 and 3mm more than a 20.

That sort of thing ... which ain't for everybody.

 

[Slide Rule]

A Proposed Method to estimate angles.

No, I've been public with it before.

If you know the cut angle, you know where to aim from the CB center.

1mm per degree up to 30 degrees and above that, 0.8mm/degree off ball edge over 30 degrees covers it pretty well.

Ball landmarks come in handy. A visible gap becomes apparent between cloth and ball at about 10mm off center (napped), 7-8 mm worsted.

A 20 degree cut can be aimed at 7:30 or 4:30 on the clockface, a 25 degree shot at 8:00 or 4:00. A 23 degree cut is 2mm shy of a 25 and 3mm more than a 20.

That sort of thing ... which ain't for everybody.

Finally a metric. Something odd and possibly useful for a guy with a math background.

Your cue tip is a known dimension say 12mm. This gives the cut angles for 0 through 12.

A mark on the cue tip would help measure the value at the OB. The horizontal distance would be the offset needed at the OB. Just align the offset value at the CB directly at the OB point. That is the near OB point through OB to the pocket.

Something to investigate in the morning at the table.

I will also look at the angles you mentioned above.
20 degree 7:30,
25 degree 8:00,
and the interpolation with the mm/degree.

I hope the following helps in your angle estimating and in making balls. I do have a second, slightly easier method which is an offshoot of that below, but it hasn't been confirmed.


A METHOD FOR ANGLE ESTIMATES.
Say you wish to estimate cut angle for a side rail bank shot.

Sight through the OB on the desired angle and note the intersections with the near and far rails. Now sight through the CB on the line you wish to hit the OB and note the intersections. Determine the differences to a 0.1 degree basis for both rails. Add the two values and divide by 2. This is the average basis.

From the far rail to a selected diamond and the next diamond is about 14 degrees. You can use 14 degrees/diamond or approximate this for 15 degrees/diamond to simplify at the table calculations.

Each 0.1 diamond on the average distance is about 1.5 degrees.

So, take the difference in tenths of a diamond, and add half this value and come up with a close estimate for degrees.

I have used this value to improve slow speed bank shot accuracy.

You can also use 3.5 degrees/quarter diamond and this works well up to a difference on the rails of 1.5 diamonds. After that the numbers start to diverge.

Values shown for quarter diamond multiples up to 4 diamonds.
3.5
Multiple--Angle
0,-------0
3.5------3.6
7,-------7.1
10.5,----10.6
14,------14
17.5,----17.4
21,------20.6 Still quite good

24.5,----23.6 Starting to diverge
28,------26.6
31.5,----29.4
35,------32
38.5,----34.5
42, -----36.9
45.5,----39.1
49,------41.2
52.5,----43.2
56,------45 Not even close

 

[Robert Raiford]

However, I do think you've been somewhat shortsighted in your assessment of my method. Recall that earlier in this thread I did make it clear that I was not presenting a complete version.

You're right, my mistake! I was analyzing it as posted in terms of all shots without considering your mention that it was incomplete. There was obviously enough thought and technical understanding behind it that I should've assumed you'd account for further details in a longer exposition. I think, for your criteria - long distances and fuller hits - it's a clever method that is simple and accurate.

My concerns are obviously with closer and/or thinner shots, which we weigh differently. I don't doubt your ability to estimate the distances accurately for the fuller hits you reference. Since 1/4" is a bigger percentage of the smaller distances, it's more obvious. Personally, I would find longer distances difficult to eye with confidence (distinguish 9.5" and 10", for example).

I think we can agree that whatever method you use, it's important to understand its inherent limitations due to whatever assumptions/approximations you're making.

Robert

p.s. Playing "guess the angle" LOL! As if the people here don't think we're crazy enough as it is