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The Physics of Bowling BallsThe Physics of Bowling Balls

Jim TalamoJim Talamo

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Physics and BowlingPhysics and Bowling

Many ideas from basic mechanics occur inMany ideas from basic mechanics occur int he world of bowling.t he world of bowling.

These ideas explain why bowlers t hrowThese ideas explain why bowlers t hrowt he ball t he way t hey do, why balls hookt he ball t he way t hey do, why balls hookt he way t hey do, and ultimately howt he way t hey do, and ultimately how

bowling balls are made.bowling balls are made.

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Preliminary QuestionsPreliminary Questions

Why do good bowlers make a bowling ballWhy do good bowlers make a bowling ballhook?hook?

What are lane conditions, and how doWhat are lane conditions, and how dot hey affect how a bowling ball hooks?t hey affect how a bowling ball hooks?

Why are t here so many different bowlingWhy are t here so many different bowling

balls on t he market today?balls on t he market today?

What is a bowling ball made out of?What is a bowling ball made out of?

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Why make a ball hook?Why make a ball hook?

This above all else is a great example of This above all else is a great example of t he importance of momentum in bowling!t he importance of momentum in bowling!

First, pin numbering:First, pin numbering:

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In order to maximize score, bowlers try toIn order to maximize score, bowlers try to

bowl as many strikes as possible. This is bowl as many strikes as possible. This is achieved by t hrowing a ball t hat hooks,achieved by t hrowing a ball t hat hooks,and having t hat bin hit t he pins betweenand having t hat bin hit t he pins between

t he 1 and t he 3 pin for right hander, andt he 1 and t he 3 pin for right hander, andt he 1 and 2 pin for left handers.t he 1 and 2 pin for left handers.

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Why a ball should hookWhy a ball should hook

When a ball t hat is t hrown straight hit s t heWhen a ball t hat is t hrown straight hit s t hepocket, it deflect s (conservation of momentum),pocket, it deflect s (conservation of momentum),

often times leaving a 5 pin or strange split soften times leaving a 5 pin or strange split s When a ball hooks into t he pocket, it does not When a ball hooks into t he pocket, it does not 

deflect as much, and carries t he 5 pin. Wit h adeflect as much, and carries t he 5 pin. Wit h ahooking ball, t he pins also mix much morehooking ball, t he pins also mix much more

SPLITSPLIT!!!!!!

STRIKE!!!STRIKE!!!

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Momentum and Pin CarryMomentum and Pin Carry

A bowling ball has bot h linear and A bowling ball has bot h linear androtational momentum. When t he ball hit s rotational momentum. When t he ball hit s t he pins, t his momentum is transferred tot he pins, t his momentum is transferred tot he pins.t he pins.

The harder t he ball is t hrown, and t heThe harder t he ball is t hrown, and t he

more it hooks, t he more likely you are tomore it hooks, t he more likely you are tot hrow a strike.t hrow a strike.

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What makes a ball hook?What makes a ball hook?

There is OIL on bowling lanes. WhileThere is OIL on bowling lanes. Whileinvisible to t he naked eye, oil dramatically invisible to t he naked eye, oil dramatically 

affect s t he way a ball hooks.affect s t he way a ball hooks.

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How Oil  Affect s a BallHow Oil  Affect s a Ball

In order for a ball to hook, t here must beIn order for a ball to hook, t here must befriction between it and t he lane.friction between it and t he lane.

Oil affect s t he amount of friction.Oil affect s t he amount of friction.

The ball slides out over oil, and hooks The ball slides out over oil, and hooks when it sees friction.when it sees friction.

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Typical Lane PatternTypical Lane Pattern

When a right handedWhen a right handedbowler throws the ball toobowler throws the ball toofar to the right, there isfar to the right, there is

less oil, causing the ball toless oil, causing the ball tohook earlier (and thushook earlier (and thushook more). This allowshook more). This allowsthe ball to hit the pocket.the ball to hit the pocket.

When a left handedWhen a left handedbowler throws the ball toobowler throws the ball too

far to the left, there isfar to the left, there ismore oil, causing the ballmore oil, causing the ballto hook later (and thusto hook later (and thushook less). This allowshook less). This allowsthe ball to hit the pocket.the ball to hit the pocket.

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 Amount of Oil Amount of Oil

The amount of oil affect s t he way t he ballThe amount of oil affect s t he way t he ballhooks.hooks.

If t he oil pattern is longer, t he ball hooks lessIf t he oil pattern is longer, t he ball hooks less

If t he oil isnt as t hick, t he ball hooks more.If t he oil isnt as t hick, t he ball hooks more.

As a bowler bowls, t he oil on t he lane changes. As a bowler bowls, t he oil on t he lane changes.In t ypical leagues, t here is significantly less oilIn t ypical leagues, t here is significantly less oilafter a few games of bowling t han t here was after a few games of bowling t han t here was 

initially.initially.

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Balls, balls, ballsBalls, balls, balls

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Why are t here so many balls on t heWhy are t here so many balls on t he

market?market? As a result of various different oil patterns, As a result of various different oil patterns,

bowling ball companies have designed abowling ball companies have designed a

number of balls t hat each hook differently.number of balls t hat each hook differently. This is achieved t hrough t heThis is achieved t hrough t he

COVERSTOCK and t he CORE of t heCOVERSTOCK and t he CORE of t hebowling ball.bowling ball.

=> Bowling Balls arent just a lump of => Bowling Balls arent just a lump of stuff!!!stuff!!!

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Bowling Balls:  An Inside LookBowling Balls:  An Inside Look

There are two mainThere are two maint ypes of cores:t ypes of cores:

symmetric andsymmetric andasymmetric cores.asymmetric cores.

Each t ype affect s t heEach t ype affect s t heMoment of Inertia of Moment of Inertia of 

t he ball, and t hus t he ball, and t hus affect s how t he ballaffect s how t he balltends to hooktends to hook

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Finding t he Moment of Inertia andFinding t he Moment of Inertia and

Radius of Gyration of a Given BallRadius of Gyration of a Given Ball Scope: This met hod is for determining t he principal

moment s of inertia of a bowling ball passing t hrough t hegeometric center of t he ball.

Definitions: The moment of inertia is a measure of and is defined as 

t he opposition which a body offers to having it s state of rotation changed.

The radius of gyration is a numerical value equal to t heradius of a t hin hoop of t he same mass, having t he same

moment of inertia as t he bowling ball. The moment of inertia will be expressed as pound

(mass) inches squared. The radius of gyration will beexpressed as inches.

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Test Met hod: EquationsTest Met hod: Equations

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 Apparatus Apparatus

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ClaibrationClaibration

Calibration: The apparatus must be calibrated before use to determine t he

torsional constant. Each device will have it s own constant due

to differences in t he wire. At least two known moment s of inertia are required. The suggested

masses are a sphere of uniform densit y (ie. made of only onematerial) and a steel cylinder of uniform densit y, bot h weighingbetween 10 and 16 pounds (a steel cylinder approximately 2 1/2diameter and 9 long will weigh around 12 pounds and a solidpolyuret hane sphere wit h t he same diameter as a bowling ball will

also weigh around 12 pounds). Accurately weigh t he masses and measure t he radius of t he sphere

and t he radius and lengt h of t he cylinder. From t hesemeasurement s, calculate t he moment of inertia as follows:

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ProcedureProcedure

Calibration Procedure: Determine t he period of oscillation of t he cradle by setting it in

motion oscillating on a horizontal plane t hrough an included angleof 15 degrees or less. Using a stopwatch or ot her timing device,determine t he time for 10 complete oscillations.

Calculate t he time for one complete oscillation by dividing by 10.This value is Tc.

Place t he sphere in t he cradle and determine t he period as above.This value is T.

Repeat t his procedure wit h t he cylinder. The cylinder should be

tested two different ways. Place t he cylinder vertically in t heapparatus and measure t he period. Then place t he cylinderhorizontally in t he cradle so t hat it is centered and again measuret he period. These values are also T.

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Some Moment s of InertiaSome Moment s of Inertia

Sphere : I= 2/5 MR^2

cylinder on axis (standing upright) : I= ½ MR^2

cylinder on central diameter: I= ¼ MR^2 +1/12 ML^2

where I = moment of inertia (lbm-in2)

M= mass of sphere or cylinder (lbm) R = radius of sphere or cylinder (in)

L = lengt h of cylinder (in)

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Torsional Constant Torsional Constant 

For each measurement, solve for t he torsionalconstant as follows:

K 1= (4 pi ^2 I)/(T^2-Tc^2) NOTE: The moment of inertia of two object s is 

equal to t he sum of t he individual moment s of inertia. However, since t he moment of inertia of t he cradle is not known, t he above equationuses t he relationship t hat t he moment of inertiais proportional to t he square of t he period.

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Bowling Ball Test Procedure: The formula for moment of inertia is as follows: I= k1*T^2/(4 Pi^2) First calculate t he moment of inertia of t he cradle by substituting Tc into t he above

equation. This value is Icradle* A minimum of two separate measurement s of t he moment of inertia are to be taken

for each ball. The maximum and minimum moment s of inertia are required. The minimum moment of inertia occurs 

when t he heaviest portion of a ball is located on t he axis (vertically in t he test apparatus). The maximum moment of inertia

will occur when t he heaviest portion of  a ball is located furt hest from t he axis (900from vertical in t he test apparatus). For existing bowling balls, t he minimum moment of inertia usually occurs when t he

weight block (on 3 piece balls) or pin (on 2 piece balls) is aligned at t he top of t he ball when it is placed in t he test apparatus.

This will be called Imin* For existing bowling balls, t he maximum moment of inertia usually occurs when t he

weight block (on 3 piece balls) or pin (on 2 piece balls) is aligned horizontally when it 

is placed in t he test apparatus. This axis will be located 900 from t heImin* axis.

It may be necessary to test at several locations which are all 900from Imin todetermine t he axis of maximum moment of inertia.

This will be called Imax* Place t he ball in t he cradle wit h each axis directed upward and measure t he period of 

oscillation as in t he calibration procedure. Calculate t he moment s of inertia using t he above equation where T is t he period of 

t he ball and cradle in seconds.

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Radius of GyrationRadius of Gyration

The principal moment s of inertia are calculated as follows:

Imin = Imin&cradleImin = Imin&cradle  

IcradleIcradle Imax = Imax&cradleImax = Imax&cradle  

IcradleIcradle

The radius of gyration of each axis may be calculatedby t he following equation:

K ̂ 2 = I /MK ̂ 2 = I /M

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What does t his all mean?What does t his all mean?

Each bowling ball has a unique core designed forEach bowling ball has a unique core designed fora specific ball reaction. This ball reaction is a specific ball reaction. This ball reaction is determined by t he moment of inertia and radius determined by t he moment of inertia and radius of gyration of t he ball, as well as t he RGof gyration of t he ball, as well as t he RGdifferential (Imaxdifferential (Imax--Imin)Imin)

The moment of inertia tells when t he ball willThe moment of inertia tells when t he ball willstart hookingstart hooking

The radius of gyration tells how much t he ballThe radius of gyration tells how much t he ball

will hookwill hook The RG Differential tells t he shpae of t he ballThe RG Differential tells t he shpae of t he ball

reactionreaction

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The Exciting World of CoverstocksThe Exciting World of Coverstocks

Anot her factor t hat determines t he way a ball Anot her factor t hat determines t he way a ballhooks is t he coverstock of t he ballhooks is t he coverstock of t he ball

The coverstock is what you see on t he surfaceThe coverstock is what you see on t he surfaceof a bowling ball.of a bowling ball.

This affect s t he amount of friction between t heThis affect s t he amount of friction between t heball and t he lane.ball and t he lane.

One can alter existing coverstocks via sanding orOne can alter existing coverstocks via sanding orpolishing to affect t he amount of frictionpolishing to affect t he amount of frictionbetween t he ball and t he lane.between t he ball and t he lane.

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Types of CoverstocksTypes of Coverstocks

Four major coverstocks:Four major coverstocks: 1) Plastic/Polyester1) Plastic/Polyester   This provides t he smallest amount This provides t he smallest amount 

of friction between t he ball and t he lane.of friction between t he ball and t he lane. 2) Uret hane2) Uret hane-- Implemented in t he 1970 s; provides moreImplemented in t he 1970 s; provides more

friction t han plasticfriction t han plastic

3) Reactive Resin3) Reactive Resin-- Implemented in t he 1990 s; provides Implemented in t he 1990 s; provides t he most amount of friction between t he ball and t het he most amount of friction between t he ball and t helane.lane.

4) Particle4) Particle-- Implemented in t he late 1990 s early 2000 s.Implemented in t he late 1990 s early 2000 s.This t ype of ball is made by adding small particles of This t ype of ball is made by adding small particles of 

ceramics or glass to uret hane balls. This provides aceramics or glass to uret hane balls. This provides asmoot her reaction, while still providing a large amount of smoot her reaction, while still providing a large amount of friction between t he ball and t he lane. Today s friction between t he ball and t he lane. Today s manufacturers tinker wit h t his st yle of ball to make balls manufacturers tinker wit h t his st yle of ball to make balls for all lane conditions.for all lane conditions.

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Some Different BallsSome Different Balls

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Technical Stuff Technical Stuff 

Scope: This met hod is for determining t he coefficient of friction

of a bowling ball using a sled and a standard lane

surface. Definitions: Coefficient of friction is defined as t he ratio of t he force

opposing t he relative motion of two surfaces to t henormal force

acting perpendicular to t he opposing force. Test Method: The test met hod will be to measure t he force needed to

slide a bowling ball mounted in a sled across a lanesurface at a speed

of approximately 0.5 feet per second.

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Test  ApparatusTest  Apparatus

Test Apparatus:

The equipment necessary for t he determination of bowling ball coefficient of friction includes t he following:

 A standard lane surface sample at least 24 inches by 36 inches.

 A sled wit h t he abilit y to secure t he ball and prevent any rotation.

 A means of moving t he ball at a constant speed, in asliding motion across t he standard lane surface.

 A means of measuring t he force needed to move t heball and sled as a unit.

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ProcedureProcedure

Procedure The standard lane sample is cleaned t horoughly wit h 

isopropyl alcohol and allowed to dry completely. The bowling ball is mounted and secured in t he sled. The sled is pulled at a constant speed of 0.5 feet per

second and t he average force needed to move t he sledis recorded. This procedure is repeated for a total of 8separate test s.

The eight readings are t hen each divided by t he totalweight of t he ball and sled to calculate 8 separatecoefficient of friction values. These 8 values are t henaveraged to determine t he coefficient of friction.

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 Altering t he Coverstock Altering t he Coverstock

In order to adjust to different lane conditions,In order to adjust to different lane conditions,bowlers will alter t he coverstock on t heir balls bowlers will alter t he coverstock on t heir balls 

via sanding or polishingvia sanding or polishing Sanding creates a rougher surface, t hus Sanding creates a rougher surface, t hus 

enabling t he ball to hook moreenabling t he ball to hook more

Polishing creates a smoot h surface, making t hePolishing creates a smoot h surface, making t heball hook later. This is very helpful for dry lanes ball hook later. This is very helpful for dry lanes or for t he end of tournament s when t he oil is or for t he end of tournament s when t he oil is very t hin.very t hin.

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Examples of different shot sExamples of different shot s

Plastic Ball StrikePlastic Ball Strike

Resin StrikeResin Strike

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ReferencesReferences

http://www.bowl.com/Downloads /pdf/USBCequihttp://www.bowl.com/Downloads /pdf/USBCequipmanual2005_appendix.pdf#search=%22radiuspmanual2005_appendix.pdf#search=%22radius

%20of%20gyration%20average%20definition%%20of%20gyration%20average%20definition%20bowling%20%2220bowling%20%22

http://www.mrfizzix.com/bowling/index2.htmlhttp://www.mrfizzix.com/bowling/index2.html

http://www.topendsport s.com/sport/tenpin/physhttp://www.topendsport s.com/sport/tenpin/phys

ics.htmics.htm http://www.madsci.org/post s /archives /dec99/94http://www.madsci.org/post s /archives /dec99/94

4266601.Ph.r.html4266601.Ph.r.html