How much of a cueball is useable normally?

[BC21]

It doesn't, which is why I don't understand why instructional aids don't simply use X,Y. I've seen it in _SOME_ aids (not many at all).

This is a 14 by 14, but it probably should be a 10 by 10. People can visual smaller sections like 5 to the the left 5 to the right, thus 20% steps. So if you were using 20% steps, instead of -2, 2 like in the picture, you could use -2, 2.3 and the 2.3 could easily be visualized between 2 and 3 (which would then be 46% whichever direction from 0% or 0,0... center).

Yeh I know, you're wondering how long it took me to get my P.H.D. in graphic arts... about 12 years.

Nice. I like this. I would like to have one marked in 3.1mm increments, matching the quarter tip measurement of a 12mm to 13mm tip size. Then the tip could be used in fairly precise quarter increments, making it easy to visualize and easy to determine exactly how much a certain fractional tip offset affects the shot, as far as spin, diamond movements, etc... The Rempe training cb is similar to your image. Not sure what the distance is between marked increments. In your illustration they are 3.8mm increments with 1.9mm smaller increments in between.

 

[Bob Jewett]

... or "Bob", you can name anything Bob....

You'll be getting a call from my legal team. They resemble rabid weasels.

I think the angle the side spin causes off the cushion is the best way to talk about it since it is easy to describe and measure. Also, you are typically using side for the effect on the cushion so it makes sense to define it that way.

 

[Cron]

Nice. I like this. I would like to have one marked in 3.1mm increments, matching the quarter tip measurement of a 12mm to 13mm tip size. Then the tip could be used in fairly precise quarter increments, making it easy to visualize and easy to determine exactly how much a certain fractional tip offset affects the shot, as far as spin, diamond movements, etc... The Rempe training cb is similar to your image. Not sure what the distance is between marked increments.

It's how it's done world wide by hundreds of millions of people, just not strictly with cue balls.

I describe points to my son in this manner, which is where my opinion of a problem is, the length of the word "negative". We shortened the fractional stuff by just using 2 digits to describe everything. ie. 1.2, 1.6 is "twelve sixteen" 0.5, 0.5, 1 is "oh five oh 5" ("zero" is too long). It's very quick to say, until you have to say "negative". "Dash" works better, but it still is a little.... eehhhh.

But he asked me once how much percentage of the ball is usable typically, which now I know (in both a 2D and by area). _IF_ I finish this little WASM app, I'll link the page that has an interactive simulation. It's like many web pages you can already find that can demonstrate it, but I wanted to make 1 that incorporated "throw" (none of them incorporate throw... it's weird).

 

[pt109]

I’m a visual guy....can’t play with those calculations going through my head.....
...in this picture, the edge of the stripe is the ‘miscue zone’....
...turn the pic any way you need to....depending on what spin you’re going to use.

Pretty sure I got this idea from PJ...a few years ago...he does up with nice stuff.

 

[Bob Jewett]

View attachment 544675

I’m a visual guy....can’t play with those calculations going through my head.....
...in this picture, the edge of the stripe is the ‘miscue zone’....
...turn the pic any way you need to....depending on what spin you’re going to use.

Pretty sure I got this idea from PJ...a few years ago...he does up with nice stuff.

The idea is from George Onoda who wrote an intermittent series of articles for Billiards Digest from 1989 to 1992. The article in which he discusses using the stripe as a "safe area" indicator appeared in August 1991. All of his articles are available on the SFBA website.

Some stripes are wider than others.

 

[pt109]

The idea is from George Onoda who wrote an intermittent series of articles for Billiards Digest from 1989 to 1992. The article in which he discusses using the stripe as a "safe area" indicator appeared in August 1991. All of his articles are available on the SFBA website.

Some stripes are wider than others.

Ah, I was wondering about the consistency of the width of the stripes.

 

[pt109]

The idea is from George Onoda who wrote an intermittent series of articles for Billiards Digest from 1989 to 1992. The article in which he discusses using the stripe as a "safe area" indicator appeared in August 1991. All of his articles are available on the SFBA website.

Some stripes are wider than others.

Ah, I was wondering about the consistency of the width of the stripes.
...I recall PJ saying the stripe was 50% of the ball surface.

 

[Bob Jewett]

Ah, I was wondering about the consistency of the width of the stripes.
...I recall PJ saying the stripe was 50% of the ball surface.

Many designs have them as half the total height when horizontal. I think the Centennial design has wider stripes because the number is in the stripe and it looks more balanced to have a slightly wider stripe.

(I thought that the 1/2 area in the caps idea was wrong with far more area in the stripe, but it turns out to be correct. Each one-mm-thick slice of ball -- if you were to slice it horizontally -- has exactly the same fraction of the surface of the sphere. Unless I forgot my freshman calculus, which I took as a senior.:grin

 

[BC21]

Many designs have them as half the total height when horizontal. I think the Centennial design has wider stripes because the number is in the stripe and it looks more balanced to have a slightly wider stripe.

(I thought that the 1/2 area in the caps idea was wrong with far more area in the stripe, but it turns out to be correct. Each one-mm-thick slice of ball -- if you were to slice it horizontally -- has exactly the same fraction of the surface of the sphere. Unless I forgot my freshman calculus, which I took as a senior.:grin

You must have done well in that class, because you are 100% correct!

 

[Cron]

(I thought that the 1/2 area in the caps idea was wrong with far more area in the stripe, but it turns out to be correct. Each one-mm-thick slice of ball -- if you were to slice it horizontally -- has exactly the same fraction of the surface of the sphere. Unless I forgot my freshman calculus, which I took as a senior.:grin

I don't understand the proof from slicing :-/ I can see the area of a 2.25" cue ball is ~10260mm (using 4π(r*r)), but how do you know the stripe is 50% of the area, or did you use a compass or something?

 

[Bob Jewett]

I don't understand the proof from slicing :-/ I can see the area of a 2.25" cue ball is ~10260mm (using 4π(r*r)), but how do you know the stripe is 50% of the area, or did you use a compass or something?

It's integral calculus. The slicing is a standard way to describe (in simple terms) how an integral is performed if you integrate versus height (dy). Instead it is easier (for me) to integrate the area as circumference(phi)*dphi where phi is the latitude (or polar angle) to find the area. The circumference is proportional to cos(phi) and the height is sin(phi). The result is that the area from the equator up is proportional to how far you go up, or each horizontal slice of a particular thickness has the same area.

Since the result is so neat I imagine I've seen this exact problem before but it was probably in the aforementioned class in 1965.

 

[BC21]

I don't understand the proof from slicing :-/ I can see the area of a 2.25" cue ball is ~10260mm (using 4π(r*r)), but how do you know the stripe is 50% of the area, or did you use a compass or something?

The end caps (white portions of the ball) each have a surface area around 2,565 sq-mm. Add these together and you have about 5,130 sq-mm, 50% of the ball's total surface area.

End cap surface area = 2 * 3.142 * 28.575 * 14.287 = 2,565 sq mm

28.575mm is the ball's radius

14.287mm is the cap height, which is a quarter of the ball, fractionally.

That's what Bob was talking about when he said you can slice the ball into horizontal pieces, based on width of the ball, and each piece would be the same fractional portion of the circumference of the ball.

 

[Bob Jewett]

... That's what Bob was talking about when he said you can slice the ball into horizontal pieces, based on width of the ball, and each piece would be the same fractional portion of the circumference of the ball.

Actually, I was taking equal thickness horizontal slices. Each such slice has the same amount of surface from the original ball's spherical surface. The 1-mm slice off the top of the ball has the same area (not counting the flat surface) as a 1-mm slice at the equator.

Or maybe that's what you meant?

 

[BC21]

Actually, I was taking equal thickness horizontal slices. Each such slice has the same amount of surface from the original ball's spherical surface. The 1-mm slice off the top of the ball has the same area (not counting the flat surface) as a 1-mm slice at the equator.

Or maybe that's what you meant?

I was thinking in terms of the width of each slice vs the surface arc lenth of each slice, how a 1mm thick slice is about 1/57 of the ball's width, and so the surface arc lenth of each slice is 1/57 of the ball's circumference across the hemisphere you're looking at. I realize now that's not what you were talking about when you mentioned fractionally equal.

 

[Patrick Johnson]

Each one-mm-thick slice of ball -- if you were to slice it horizontally -- has exactly the same fraction of the surface of the sphere.

Very interesting - is it useful for knowing how much of the CB is "usable", or is that a 2D question?

pj
chgo

 

[BC21]

Very interesting - is it useful for knowing how much of the CB is "usable", or is that a 2D question?

pj
chgo

The usable area if calculated via 2D, a simple circle, is 25% of the ball (circle). If calculated using the spherical 3D method, the usable area is 13.4% of the half sphere (hemisphere) you're looking at, even though it doesn't look like it, because we don't truly see in 3D. So using the properties of a simple circle work great for aiming, or for calculating the amount of usable cb area for tip placement.

 

[3kushn]

It's integral calculus. The slicing is a standard way to describe (in simple terms) how an integral is performed if you integrate versus height (dy). Instead it is easier (for me) to integrate the area as circumference(phi)*dphi where phi is the latitude (or polar angle) to find the area. The circumference is proportional to cos(phi) and the height is sin(phi). The result is that the area from the equator up is proportional to how far you go up, or each horizontal slice of a particular thickness has the same area.

Since the result is so neat I imagine I've seen this exact problem before but it was probably in the aforementioned class in 1965.

And my solution was too complicated and confusing?

 

[Patrick Johnson]

The usable area if calculated via 2D, a simple circle, is 25% of the ball (circle). If calculated using the spherical 3D method, the usable area is 13.4% of the half sphere (hemisphere) your're looking at, even though it doesn't like it, because we don't truly see in 3D. So using the properties of a simple circle work great for aiming, or for calculating the amount of usable cb area for tip placement.

OK. Thanks.

pj
chgo

 

[garczar]

How do you guys ever make a ball with all this s&*t bouncin' around in your dome? Wow.

 

[Bob Jewett]

How do you guys ever make a ball with all this s&*t bouncin' around in your dome? Wow.

I've already explained that. I guess you missed it.
Try to keep up.