TP 4.1 Distance required for stun and normal roll to …

1 TP required for stun and normal roll to developsupporting: The illustrated principles of Pool and billiards David G. Alciatore, PhD, PE ("Dr. Dave")originally posted: 7/10/2003last revision: 2/26/2014: time for stun to develop over Distance tsdsm: ball mass: time for sliding to stop over Distance dtd : ball angular speed < 0: bottom spin > 0: topspin = 0: stunThe direction of the friction force is as shown when the CB has "overspin" (where > v/R). Therefore, the constant linear acceleration (negative implies deceleration) of the ball can be expressed as: a sign vR Fm sign vR g gwith no overspin ( < v/R):with overspin ( > v/R): sign vR 1 : + sign vR 1 : - a g a gNon-Commercial Use OnlyLinear speeds at stun () and when sliding stops (v'):vs vs+v ats v gts v' v gtdConstant angular acceleration caused by the moment of the friction force about the ball center: FRI mgR 25mR2 5 g 2 RAngular speed when sliding stops: '+ td+ 5 g 2 RtdAt time , the ball is in stun ( , no spin), so.

2 Ts ts 2R(( )) 5 gThis equation applies only if <0 to begin with, giving > time , the ball is rolling without slipping, so:td v' ' R v gtd+ R 5 g2td td g + 521 v R td 2 7 g(( v R ))for a stun shot ( =0): td 2v 7 gDistance and time are related with the following constant acceleration relation: x+ vt 12at2 vt 12 gt2So the Distance for stun to develop (with <0) is: ds v 2R 5 g 12 g 2R(( )) 5 g 2 2R(( )) 5 g v (( ))R5 Non-Commercial Use OnlyAnd the total Distance for sliding to stop and rolling to begin is: d 2v 7 g(( v R )) 12 g 2 7 g(( v R )) 2 d 2 7 g v2 R v 2 49 g + v2 2R v R2 2 d 2 49 g 6v2 5vR (( R ))2 for a non-overspin shot ( < v/R), d 2 49 g 6v2 5vR (( R ))2 for a stun -drag shot ( =0): d 12v2 49 gThe final ball speed, after sliding stops and rolling begins, is given by: v' v gtd v g 2 7 g(( v R )) + 57v 27R Note that the final ball speed is independent of the ball and table , 5/7 ( ) of the final speed comes from the initial translational speed (v), and 2/7 ( ) comes from the spin component (R ).

3 For a stun shot ( =0): v' 57vTherefore, the final ball speed, for an initially sliding ball, is always 5/7 of the initial speed!D ilidih lidldhdi( )diNon-Commercial Use OnlyDuring sliding, the linear and angular speeds change over Distance (x) according to: v((x))2v2 2ax v((x)) v2 2 gx x vt 12 gt2 + 12 gt2 vt x0 t v v2 2 gx g(only the "-" solution of the quadratic equation is meaningful" because theequations only apply during slidingwhile the friction force is acting) ((x))+ t+ 5 g 2Rt+ 5 2R v v2 2 gx Changes in speed and spin over Distance with drag shots: ball/cloth sliding COF D R D2ball diameter and radius vslow 3 vmedium 7 vfast 12 dskid((,v )) 2 49 6v2 5vR (( R ))2 vskid((,,vxd)) ||||||||||||ifelse<xd v2 2 x v2 2 d skid((,,,v xd)) ||||||||||||||||ifelse<xd + 5 2R v v2 2 x + 5 2R v v2 2 d ddhNon-Commercial Use Onlydraw-drag shots: slow vslowR medium vmediumR fast vfastR vvmedium draw medium=dskid ,vslow slow ddraw=dskid ,vmedium medium ,vfast fast shots: stun0 =dskid ,vslow stun dstundskid ,vmedium stun =dskid ,vfast stun speed vs.

4 Distance : x,.. 0 ,,vxdstun (())vskid ,,vxddraw (())x(())Non-Commercial Use Onlyball spin vs. skid ,,,v stunxdstun (( 60)) skid ,,,v drawxddraw (( 60))x(())Non-Commercial Use Only