Fractional aim points and their cut angles

[7stud]

I'm surprised that I couldn't find this anywhere. What are the cut angles for all the main fractional aiming points:

1/8 = 61 degrees
1/4 = 49 degrees
3/8 = 39 degrees
1/2 = 30 degrees
5/8 = 22 degrees
3/4 = 15 degrees
7/8 =  7 degrees

I tried using Dr. Dave's formulas here:

fraction = 1 - sin(angle)
angle = asin(1 - fraction)

but for a 5/8 cut, I get:

angle = asin(3/8)

which gives me:

0.38

which is wrong: the angle should be between 30 and 15 degrees. What am I doing wrong?

Edit: Ahhh...0.38 is in radians rather than degrees. I will fill in the chart myself.

 

[heater451]

For a visual representation, our very own Bob Jewett has a PDF on his sfbilliards page, #16 - "GRAPH". The fractions of the cueball have to be in decimal form--for example, 5/8 = 0.625, which is about 22.5 deg on the chart.

I would screencap, resize, and post it here, but didn't know if that was okay. Also, I was actually remembering there was a scan of an old Billiards Digest article he wrote when I found the PDF. It might be in the misc docs, but you'd need to search or ask Bob.

 

[Bob Jewett]

,,, or ask Bob.

 

[straightline]

I just wanna say CPG...

 

[garczar]

if i had to think about that shit while playing i'd never make a ball. so easy to overthink/over-complicate this game.

 

[Mensabum]

if i had to think about that shit while playing i'd never make a ball. so easy to overthink/over-complicate this game.

if i had to think about that shit while playing i'd never make a ball. so easy to overthink/over-complicate this game.

Kiss

 

[Patrick Johnson]

if i had to think about that shit while playing i'd never make a ball. so easy to overthink/over-complicate this game.

The "clock system" shown below is, to me, an easier way to connect visual cut angles to CB/OB overlap fractions.

pj
chgo

 

[Patrick Johnson]

And, since we're on the subject, here's another way to simplify visualizing fractional cut angles - I hope it's self explanatory.

pj
chgo

Full disclosures:
1. 1:4 = 14.0°
2. 1:2 = 26.6°
3. 1:1 = 30.0°
4. I don't use fractional aiming.

 

[Bob Jewett]

And here is a diagram of fractional aiming from about 110 years ago

 

[Patrick Johnson]

And here is a diagram of fractional aiming from about 110 years ago.

Back when players could see 1/16ths.

pj
chgo

 

[Bob Jewett]

Back when players could see 1/16ths. ...

A local player knew all the angles down to 64ths. Seriously. He was one of the top local players. He did things his own way.

 

[gregcantrall]

I seriously don't understand numbering the angles of the shots. I name mine If it goes in the pocket, I call it sweetheart. In the event of a miss there are numerous names for how much it missed by. A near miss starts with Shit Head.

 

[book collector]

I seriously don't understand numbering the angles of the shots. I name mine If it goes in the pocket, I call it sweetheart. In the event of a miss there are numerous names for how much it missed by. A near miss starts with Shit Head.

Some people just start out right , or find the correct way to pocket balls faster and easier than others, everyones brain works a little different. A fractional aiming system helped me tremendously.
You are actually using a fractional system , it is just reward or beratement, in varying degrees.

 

[straightline]

I seriously don't understand numbering the angles of the shots. I name mine If it goes in the pocket, I call it sweetheart. In the event of a miss there are numerous names for how much it missed by. A near miss starts with Shit Head.

Fractions afford the neurotic player repeatability. If a shithead is desired it will come with a specific number. It's all high tech out there.

 

[Mensabum]

The "clock system" shown below is, to me, an easier way to connect visual cut angles to CB/OB overlap fractions.

pj
chgo

View attachment 806140

I can see your avg league player jumping all over that!!

 

[Mensabum]

And here is a diagram of fractional aiming from about 110 years ago

View attachment 806060

People way back then had smarts too??

 

[straightline]

I can see your avg league player jumping all over that!!

Can you see the coach/player arguments?

 

[bbb]

I'm surprised that I couldn't find this anywhere. What are the cut angles for all the main fractional aiming points:

1/8 = 61 degrees
1/4 = 49 degrees
3/8 = 39 degrees
1/2 = 30 degrees
5/8 = 22 degrees
3/4 = 15 degrees
7/8 =  7 degrees

I tried using Dr. Dave's formulas here:

fraction = 1 - sin(angle)
angle = asin(1 - fraction)

but for a 5/8 cut, I get:

angle = asin(3/8)

which gives me:

0.38

which is wrong: the angle should be between 30 and 15 degrees. What am I doing wrong?

Edit: Ahhh...0.38 is in radians rather than degrees. I will fill in the chart myself.

this diagram from dr dave did not answer your question?

 

[gregcantrall]

My aiming method would be contact point to contact point. Must be Ghost ball. I don't play against the ghost, I play With the ghost. The only time numbers are involved is counting the money. Kinda like Grandma cooked. No measuring spoons just a littleof this or a touch of that. A bland diet is prefered on the pool table. Center ball strikes make the equation much simpler.

 

[nataddrho]

if i had to think about that shit while playing i'd never make a ball. so easy to overthink/over-complicate this game.

You still don't understand. Nobody is expected to, or should be, thinking about or doing math while playing pool. All of this stuff is simply an external exercise to come to conclusions with clarity.

For example, a player can spend their entire career playing beautifully and winning tournaments and cash, without ever being aware that they can not generate more top spin by hitting the ball higher then 40% above center. They can hit the ball harder, but going 50% or 55% doesn't add to the amount of spin generated. Maybe the way they play top spin shots is that they try to get their tip as close as possible to the miscue limit near the top of the ball, but they never know that this is unnecessary or why.

Doing the math, at a desk in your house away from pool, quickly shows that the center of percussion of the ball is 2/5R, or 40% from center, on straight top shots. Because of the downward component contributing to friction, a top spin ball hit above 2/5R can never slide. It only rolls.

This calculation is done once in a lifetime, or read once in a lifetime. The player then goes back to the pool hall, only with a distilled piece of knowledge about a simple thing, and maybe it helps them relieve a little pressure on top shots.

For the case of the fractional aiming vs angle plot, the take away is that it is mostly linear except near the end where the angles become very sensitive to the amount of ball hit. That's it. No protractors or measuring tapes or numbers. We all still have to learn contact-points and ghost-balls like everyone else and be able to recognize them from appearance only. Maybe the plot will help some people learn.

Again, math isn't done in anyone's head when they are playing, it is only an alternative exercise in insight that is sometimes useful.

Does that make sense now?