Easy way to measure an angle in degrees

[Bob Jewett]

Maybe finally....

In any analysis of a system or method or estimation, it's good to see how much error is built in. Here is a table of the actual angle of the cut and then the inches between cue bumper locations, the inches for the "anti-cut" measurement described above for cuts over 45 degrees, and the anti-cut measured cut angle.

This is calculated for a cue stick that is 58 inches long which is a more common length than the ideal 57 and a little bit.

The last column is the error which is just the difference between the angle and the inches (using the anti-cut after 45 degrees).

The maximum error is only a fraction of a degree. I think that's pretty good for a method that requires little math. Of course the ability of the player to estimate distances is very likely to give larger errors than this angle-measuring method, so the method itself is probably not going to be a limiting factor.

 

[AimPro Billiards]

Math?

Respectfully, my excel spreadsheet shows different numbers (bigger errors)? What equation did you use?

 

[Bob Jewett]

Respectfully, my excel spreadsheet shows different numbers (bigger errors)? What equation did you use?

The distance I use is shown in the diagram in post 2 in this thread. Also note that I'm using 58 inches for the cue stick which will tend to reduce the error for the larger angles although it slightly increases the error for small angles. Still, there's always the possibility of an equation error somewhere.

For a 45-degree cut, the distance in inches between the two bumper positions will be 58*sin(45/2)*2. By my calculation, that comes out as 44.391278 inches.

 

[AimPro Billiards]

Math 2

I use this excel formula:
=+$A$2*SIN(C10*PI()/180)

With $A$2 being 58
C10 holding the angle in degrees

For 40°, I get 37.3".

If I compute the arc, for 40°, I get 40.5". Neither match your numbers. I'm confused.

 

[Bob Jewett]

I use this excel formula:
=+$A$2*SIN(C10*PI()/180)

With $A$2 being 58
C10 holding the angle in degrees

For 40°, I get 37.3".

If I compute the arc, for 40°, I get 40.5". Neither match your numbers. I'm confused.

I use the base of an equilateral triangle for the length. That's where the two factors of 2 come from. Evidently you are using a perpendicular dropped from one of the bumper positions to the other line. My distance will have about a quarter of the error of your method.

 

[AimPro Billiards]

yes, you are right. I see that now. My mistake. Thanks for the explanation.

 

[Bob Jewett]

yes, you are right. I see that now. My mistake. Thanks for the explanation.

BTW, I used to take the perpendicular as in your calculation but many years ago someone (here? RSB?) pointed out that the base of the isosceles triangle has less error -- and is easier to use on the table.

 

[AimPro Billiards]

I'm embarrassed to remember that I learned how to do this exact problem correctly in high school math -- and apparently forgot! I also forgot the basic approach of drawing a diagram before writing any equations, thinking it was too simple a problem to need that.

But I'm intrigued by your comment that the correct method is easier to do on the table. Could you explain that. To me, it's just estimating the distance between the two endpoints. [Put finger down to mark starting position; move cue to other position and estimate the distance.] You are suggesting to estimate half the distance and doubling it is somehow easier as well as more accurate?

 

[Bob Jewett]

... You are suggesting to estimate half the distance and doubling it is somehow easier as well as more accurate?

No. The division into two separate distances is only in the analysis. The measurement is of the base of an equilateral triangle for which the two sides are your cue stick. Just like in the original diagram. Only the entire distance is measured. From the position of the bumper to the new position of the bumper. That distance is the number of degrees directly. No division or multiplication. Just take the distance.

(For angles over 45 degrees, you measure the complement and subtract, as described above. But that is only for such thin cuts.)

 

[AimPro Billiards]

OK, thanks. I get it.

I'll comment that in the past, I've tried measuring the complement angle for thin cuts. It's the obvious approach. But it didn't work for me generally, because I found that estimating the line of the complement (the tangent) was not easy for me to do accurately enough (within one degree). Do you have any suggestions of an easy way to get the tangent direction accurately?

My only method is using "Table Geometry" (see my video https://www.youtube.com/watch?v=4PGSQiq5b9g&t=186s) and getting the "Object ball angle", to which I can add 90 degrees. But at that point, I'd rather just get the "Cue ball angle" and compute the cut angle.

 

[Bob Jewett]

O ... Do you have any suggestions of an easy way to get the tangent direction accurately?
...

The best I know of, other than to use a fixture is to place my cue stick as in response 28.

 

[Imac007]

Dr. Dave and Bob J to the rescue

OK, thanks. I get it.

I'll comment that in the past, I've tried measuring the complement angle for thin cuts. It's the obvious approach. But it didn't work for me generally, because I found that estimating the line of the complement (the tangent) was not easy for me to do accurately enough (within one degree). Do you have any suggestions of an easy way to get the tangent direction accurately?

My only method is using "Table Geometry" (see my video https://www.youtube.com/watch?v=4PGSQiq5b9g&t=186s) and getting the "Object ball angle", to which I can add 90 degrees. But at that point, I'd rather just get the "Cue ball angle" and compute the cut angle.

One comment stuck in my mind. It had to do with why would a player want to know an angle to pocket a ball? None of the aiming systems I know are based on a way to target based on degrees. But there is one area of the game where knowing the angle is beneficial, position. The benefit of knowing the cb path in degrees after contact tells us how to avoid scratches, whether the cb will miss or hit a ball off contact or If the path into a rail will result in position.

“Rolling Cue Ball Deflection Angle Approximations” ILLUSTRATED PRINCIPLES David Alciatore, PhD (“Dr. Dave”) https://billiards.colostate.edu/bd_articles/2011/nov11.pdf is a great place to start. While Dr. Dave’s peace sign can be used from the cue ball side of the collision to estimate where the rolling ball will deflect after contact, the fact that it is known to approximate 30° can be used from the opposite side of the shot. Line the ghost ball centre to the cb centre with the cue. My shaft on my cue is 29 inches. Pivoting my cue joint, from the gb centre through ~15 inches equals about 30°. That applies on the ¼ through ¾ ball cuts. On thinner cuts the formula used is about 70% of the angle from cue line to tangent line. This allows a player at the table to simply use the cue to find the natural rolling path off contact on these thin shots.

 

[Patrick Johnson]

Pivoting my cue joint, from the gb centre through ~15 inches equals about 30°.

This is equivalent to Bob’s technique of moving the butt 30 inches.

pj
chgo

 

[Imac007]

This is equivalent to Bob’s technique of moving the butt 30 inches.

pj
chgo

Exactly the point of the perceptual move to the joint, especially when the surroundings make it easier. The cue can be used at the table to measure both 58” and half that amount 29”. Thinking inside the box, working with what’s there.

Paths into a rail also remain the same regardless of which end you look at them. A good example, I teach, has to do with spot on the wall. The concept is explained here. https://billiards.colostate.edu/bd_articles/2011/feb11.pdf

It can be combined with another concept called Magic Spot. The 3 cushion diagram 1 in the Dr. Dave spot on the wall pdf goes over the spot, for that table. The idea is explained here. https://billiards.colostate.edu/resource_files/Marcel_magic_spot_mirror_image_kick.pdf

Once the mirror contact point is decided, the line from the starting point through the magic spot tracks to the mirror. Of course, the cb is seldom in the reflective position at the table. By extending the original cue line, as in the spot on the wall idea, a new spot on the wall is established.

But there is almost never a convenient wall. The trick is for the player to become the spot. From the spot, the player can pivot to the cb location. Where that line crosses the rail becomes the new cue line. The point is the line crosses the rail at the same location regardless of which end of the line you look from.

Sometimes you need to calibrate for the magic spot. Tables are different. The method is quite simple. Starting from the corner, discover the line to the first rail that ends up, using running side, as 3 to the corner (the mirror). Once that track is known the trick is to find another mirror track to the third cushion. A good place to begin is from the second diamond up the long rail from the original corner start. Pick a starting point on the rail. The contact point on the opposite rail off 3 cushions through the magic spot with running follow should mirror the starting position. For the table you are calibrating, the magic spot must lie somewhere along that line or the table won’t work.

Where the two mirror image shot lines cross is the calibrated magic spot for the table.

 

[AimPro Billiards]

------------------------------------------------------------------------------------------------
One comment stuck in my mind. It had to do with why would a player want to know an angle to pocket a ball? None of the aiming systems I know are based on a way to target based on degrees. But there is one area of the game where knowing the angle is beneficial, position. The benefit of knowing the cb path in degrees after contact tells us how to avoid scratches, whether the cb will miss or hit a ball off contact or If the path into a rail will result in position.
---------------------------------------------------------------------------------------------------------
Let me start by saying that to learn to have consistency and to learn to aim, I believe in setting up repeatable shots that you know EXACTLY how to aim. So, I insist on an aiming system with an exact answer for my practice shooting drills. So, when I miss, I know exactly who is to blame and what (my mechanics)!

I aim by using the cut angle all the time. But I don't have a separate aim for each degree; I do it in increments -- usually ~4 degrees, although evolving towards 2 degrees. Consider it 'digital' aiming. My method is derived from double the distance aiming and appears to be, but is just closely related to fractional aiming. See https://www.youtube.com/watch?v=gCvaLS37FDo&t=21s

And position play is definitely an area where knowing the cut angle helps. For cue ball angle: watch https://www.youtube.com/watch?v=7ywxQhG7JW0 which illustrates this using follow at both slow and fast speeds at a full spread of cut angles, and the same concept goes for draw, and for rebound off a cushion following the hit, but there are complicating factors off a cushion.

But knowing the cut angle also helps with position distance, since the cut angle affects the remaining cue ball energy, and thus, distance traveled. For example, with normal roll and playing a safety, cutting the OB 34 degrees means equal travel distance for both, after the hit. And with a 22° cut, the OB will travel twice the distance as the cue ball. Is this useful to know (intuitively or numerically)? You decide. Note: these are angles I know EXACTLY how to aim. So recognizing the angle is very important to me.

And knowing the cut angle allows one to know exactly how much sidespin to use if you want to exactly cancel cut-induced throw. For example, with a 18.2° cut (11/16 hit), use 25% of maximum sidespin.

This data is all available from me in tables for 16 cut angles. Dr. Dave and others have graphs and equations. But the information is imprecise, if not useless, if you don't know the cut angle at least somewhat accurately.

Now, I'm talking in terms of cut angle, but there's a direct equivalent to ball fraction which must be an aiming method you've heard of.

Most people do not want to be thinking such numbers when they are playing a game, but I find it very useful for efficient training (drills) and quickly developing the intuition we want to use when playing.

 

[duckie]

------------------------------------------------------------------------------------------------
One comment stuck in my mind. It had to do with why would a player want to know an angle to pocket a ball? None of the aiming systems I know are based on a way to target based on degrees. But there is one area of the game where knowing the angle is beneficial, position. The benefit of knowing the cb path in degrees after contact tells us how to avoid scratches, whether the cb will miss or hit a ball off contact or If the path into a rail will result in position.
---------------------------------------------------------------------------------------------------------
Let me start by saying that to learn to have consistency and to learn to aim, I believe in setting up repeatable shots that you know EXACTLY how to aim. So, I insist on an aiming system with an exact answer for my practice shooting drills. So, when I miss, I know exactly who is to blame and what (my mechanics)!

I aim by using the cut angle all the time. But I don't have a separate aim for each degree; I do it in increments -- usually ~4 degrees, although evolving towards 2 degrees. Consider it 'digital' aiming. My method is derived from double the distance aiming and appears to be, but is just closely related to fractional aiming. See https://www.youtube.com/watch?v=gCvaLS37FDo&t=21s

And position play is definitely an area where knowing the cut angle helps. For cue ball angle: watch https://www.youtube.com/watch?v=7ywxQhG7JW0 which illustrates this using follow at both slow and fast speeds at a full spread of cut angles, and the same concept goes for draw, and for rebound off a cushion following the hit, but there are complicating factors off a cushion.

But knowing the cut angle also helps with position distance, since the cut angle affects the remaining cue ball energy, and thus, distance traveled. For example, with normal roll and playing a safety, cutting the OB 34 degrees means equal travel distance for both, after the hit. And with a 22° cut, the OB will travel twice the distance as the cue ball. Is this useful to know (intuitively or numerically)? You decide. Note: these are angles I know EXACTLY how to aim. So recognizing the angle is very important to me.

And knowing the cut angle allows one to know exactly how much sidespin to use if you want to exactly cancel cut-induced throw. For example, with a 18.2° cut (11/16 hit), use 25% of maximum sidespin.

This data is all available from me in tables for 16 cut angles. Dr. Dave and others have graphs and equations. But the information is imprecise, if not useless, if you don't know the cut angle at least somewhat accurately.

Now, I'm talking in terms of cut angle, but there's a direct equivalent to ball fraction which must be an aiming method you've heard of.

Most people do not want to be thinking such numbers when they are playing a game, but I find it very useful for efficient training (drills) and quickly developing the intuition we want to use when playing.

There is no benefit, other than in ones mind, of trying to estimate the cut angle. It is a useless step in ball placement.

I have never estimated a cut angle or angle off the OB, yet I’m real good at putting balls where I need them.

Estimating a cut angle is not a fundamental of aiming. It’s not needed at all. Trying to do so just adds a unnecessary step to something that is already pretty complicated.

Y’all just think it is needed.

 

[Bob Jewett]

There is no benefit, ...

Duckie, I am absolutely certain that nothing I have to say will ever be of any benefit to you. I'm just letting you know so you don't have to waste your time in the future pointing out to me that what I have to say is worthless to you.

 

[AimPro Billiards]

There is no benefit, other than in ones mind, of trying to estimate the cut angle. It is a useless step in ball placement.

I have never estimated a cut angle or angle off the OB, yet I’m real good at putting balls where I need them.

Estimating a cut angle is not a fundamental of aiming. It’s not needed at all. Trying to do so just adds a unnecessary step to something that is already pretty complicated.

Y’all just think it is needed.

I'm sure you miss shots and position, just like the rest of us. How can you be sure that knowing the angle and the things that go with it might not have helped you in those cases?

In any event, to make that claim, you have to have considered all players, beginners included; not just yourself. You also have to consider that things evolve and while some things work well, some newer things might work better -- at least for some and for some of the time (like while learning) or certain situations. While I estimate cut angles all the time, my goal is to be able to shoot like you: intuitively. I'm just not there yet.

 

[AimPro Billiards]

I'm just not there yet.

Let me amplify on a personal level. I had been an APA 7 (8 ball in Colorado). Then in Arizona, I was an Arizona 7. Around the early days of the AimRight development and my starting to practice with a prototype and starting to think about cuts in degrees (which I'd never done before), my AZ rating went up to an 8. Then I got a FargoRate of about 545 and recently it went up to 570 and would have gone higher except for some personal factors and covid-19. This is all from my AimRight practice drills and estimating angles during games.

Specifically, I am much better now 1) at several categories of shots; and 2) at different speeds and spins (better overall mechanics from shooting known cut angles). The easiest shots to describe are back cuts, but there are others. I ALWAYS misjudged them (generally over cut them). Now, I know how to estimate the angle accurately and I shoot to make that cut angle and I do much better. There are many side pocket shots I would only attempt in desperation in the past; now that I can estimate the cut angle, I have little hesitation if it's the right shot for strategy.

When covid abates, I hope to get back to playing again and continuing my quest to improve. I think FargoRate of 600 is in reach. Beyond that, I probably need more work on other things -- and making the aiming and position play more unconscious.

So, my point is that using angles consciously has helped me. So I'm certain it can help others. Maybe not you. And if your FargoRate is above 600, then it's likely you should focus on other areas -- although I see even pros having trouble with backcuts.

 

[dr_dave]

Good thread Bob. FYI, I've added some quotes to the how to estimate a cut angle resource page, adding to all the other methods already there.

Those interested should check it out,
Dave

In case you want to measure an angle for any reason and happen to have a cue stick in your hand....

A one-degree angle has a spread of one inch in 57 inches. If you place your tip at the center of the ghost ball and pivot around it from the line to the pocket to the line of the shot (over the cue ball), the number of inches the bumper on the cue travels is the number of degrees of the cut angle.

To be precise, you should measure the distance around the arc of the travel of the bumper, but for cut angles up to 30 degrees the straight-line distance between the two positions of the bumper is pretty close.

If you're working on your aiming you might try measuring the angle for each cut by this quick and simple method. Of course you need to be able to see how many inches a distance is. A couple of useful references: A proper-sized hand has a span of nine inches. A dollar bill is six inches.

Another point on accuracy: The perfect cue length to get one degree per inch is 57.2958 inches. A 58 inch cue or even a 60 inch cue is not going to be off very much and if you always measure with the same cue, you will get used to "degrees" that are a little large or small.