# Math Questions For Pool Players:

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
How much surface area of a ball touches the billiard table when flat and not near a rail?

#### boogieman

##### It don't mean a thing if it ain't got that ping.
A little bit. If we're talking theoretically and on a solid, non clothed perfect surface, it's basically an infinitely small point.

How much surface area of a ball touches in a perfectly tight and frozen rack? This is a different answer as gravity isn't flattening the bottom.

Edit: in reality it will depend on the material of the pool ball and how perfectly flat the surface is. When you're setting on cloth the sphere is cradled by the cloth, and how much surface area entirely depends on the cloth and it's properties.

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#### HNTFSH

##### Birds, Bass & Bottoms
Gold Member
Silver Member
Is it a 7 or 9 foot table?

#### pt109

##### WO double hemlock
Gold Member
Silver Member
It varies with the quality of the balls.
It also varies greatly with speed....the contact area would be far greater for the head ball on a rotation rack at 25 MPH than for the balls sitting in a perfect rack. Balls have elasticity to some degree.

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#### ChrisinNC

##### AzB Silver Member
Silver Member
How much surface area of a ball touches the billiard table when flat and not near a rail?
I would guess in the neighborhood of 1 / 10,000th, but it wouldn’t surprise me if it was considerably less than that.

#### pvc lou

##### AzB Silver Member
Silver Member
How much surface area of a ball touches the billiard table when flat and not near a rail?
when what is flat?

#### Island Drive

##### AzB Silver Member
Silver Member
Mind numbing question..............

#### pwd72s

##### recreational banger
Silver Member
paging Dr. Dave....

#### PoolBum

##### Ace in the side.
Silver Member
How much surface area of a ball touches the billiard table when flat and not near a rail?
Enough.

#### Johnny Rosato

##### AzB Silver Member
Silver Member
How much surface area of a ball touches the billiard table when flat and not near a rail?
two much

#### MitchAlsup

##### AzB Silver Member
Silver Member
A perfectly round polished hard pool ball on the hard slate has a contact point on the order of 2 dozen square microns.

A perfectly round polished hard pool ball on the hard slate covered by cloth has a contact point on the order of 1 square millimetre.

#### Banger

##### AzB Silver Member
Silver Member
In a perfect world, it only touches the table (let's say, a flat surface) at one point. But the world isn't perfect, and the ball is sitting on cloth. So.....

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
I am not sure if this is possible or not, but its possible a curve would twist onto itself, but why?
I have heard about DrDave and his so called swerve theory.

I think it has to do with the amount of surface area contacting the cloth on the table.
I've done some experiments adjusting the frictional coefficient of the surface and here are some observations.

DrDave's sense of physics is broken. This stuff can happen. But why only left turns?
Is there some type of one dimensional parameter than translates into a two dimensional shift?

Silver Member

#### logical

##### apart of their 'semi public'
Silver Member
If only there was a competent math instructor around...they would know.

Sent from my SM-G960U using Tapatalk

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
If only there was a competent math instructor around...they would know.

Sent from my SM-G960U using Tapatalk

I was hoping anyone that got access to the Physics 401 Lab or Engineering disciplines would know.
Computer simulations are pretty good and accessible now, however table mechanics are more rare than a physicist.

Imagine all the lost knowledge of table mechanics because its not a college major. Has anyone been documenting the current practices?

#### eddieindetroit

##### AzB Silver Member
Silver Member
Ouch. Not a point. Almost impossible to model f(x). Really tough equation because most of the components of the equation that would determine the surface area of contact are likely exponential functions and not linear. A few of the variables that come to mind.

1. The resilience of the material the ball is made of as it undergoes deformation. (Not linear function and depends on other variables.)
2. The resilience of the material the slate is made of as it undergoes deformation. (Not linear function and would depend on many of the other variables.)
3. The resilience of the cloth under the ball as it undergoes deformation. (Not linear function.)
4. The mass of the ball.
5. The diameter of the ball.
6. The smoothness of the ball.
7. The thickness of the slate under the ball. (The slates gravity acts upon the ball
8. The mass of the materials between the ball and the center of the earth as the gravitation of the matter under the ball acts upon the ball. (Slate, cloth, wood, etc.)
9. The deformation of the cloth under the balls weight (mass) as the cloth conforms to the shape of the ball. (Not a linear function AND depends on the other variables)
10. The mass of the cloth under the ball. (Not a linear function as the area under the ball increases AND it depends on all the other variables.)
11. The distance of the ball from the center of the planet earth. (Greater distance equals less earth gravity acting upon the ball)
12. The distance of the ball from the sun, and the moon and any other sources of gravitation acting upon the ball. (many more exponential equations.)
13. Is the ball in motion or at rest?
14. How level is the slate?
Now I’m just numb. What other variables would affect the surface area of contact between the ball and the cloth?

#### Pin

##### Registered
1. The distance of the ball from the sun, and the moon and any other sources of gravitation acting upon the ball. (many more exponential equations.)
Now if someone could invent a game that was affected by the gravity of the moon at the time of playing...
I suppose anything sea-based is. But that spoils the idea! A table game that behaved differently with different 'tides'...

#### Cuedup

##### Active member
1. The distance of the ball from the center of the planet earth. (Greater distance equals less earth gravity acting upon the ball)
2. The distance of the ball from the sun, and the moon and any other sources of gravitation acting upon the ball. (many more exponential equations.
Now I’m just numb. What other variables would affect the surface area of contact between the ball and the cloth?