TP B.9 Draw shot spin vs. spin ratio

Transcription

1 technical proof TP B.9 Draw shot spin vs. spin ratio supporting: The Illustrated Principles of Pool and Billiards y David G. Alciatore, PhD, PE ("Dr. Dave") technical proof originally posted: 3//9 last revision: 3//9 v v v s m m s d drag With a straight draw shot (with no cut angle), the amount of draw is determined solely y the amount of CB spin at contact with the OB (-ω'). This is the topic of TP B.8. Here we want to also look at the spin-to-speed ratio (-ω'/v'). For some cases, it is more important to maximum spin-to-speed ratio instead of spin. Examples include shots where you don't want to hit the OB too hard (e.g., to leave the OB y a pocket if you can't or don't want to pocket it, or to increase the effective size of the pocket) while still maximizing draw (e.g., to achieve position for the next shot or to play a safety), and trying to keep the draw angle as narrow as possile when there is a cut angle (e.g., to avoid a all or a pocket, or to get straight up or down the tale etter). All of the data and equations and parameters elow are from TP B.8. Typical shot distances: d drag_short 1ft d drag_medium 4ft d drag_long 8ft Miscue limit and tip offset range: max 1.1in max.63in in max

2 elevant physical parameters: μ s. μ r.1 typical all-cloth coefficient of sliding friction typical all-cloth coefficient of rolling resistance 6 m r typical all-mass-to-cue-mass ratio (m /m s ): 19 η.87 rpmmin sec typical cue tip efficiency revs per second v slow 8mph v medium 1mph v fast 14mph v power 19mph v s_slow v s v slow v s ( v).63mph 9.11 mph 1 m r v v s_medium v s v medium v s_fast v s v fast v s_power v s v power 6.79mph 1.mph v μ s v drag vx μ s gx ω ω drag vω xμ s v v μ s gx sign v d skid vω μ s ω d stun vω μ s ( ω) v μ s g 6v vω ( ω) 49μ s g ( ω) v skid ( vω) 7 v 7 ω sign v d roll vμ r v ( ) μ r g v μ r v roll vxμ r gx v s vv s 1 η 1 η 1 m r 1 m r ωv s vv s

3 Now let's see how CB spin and spin ratio, at OB contact, varies with cue speed, tip offset, shot distance, and tale conditions. SN: Spin and spin atio v vv s ω ωv s d stun if SN v s d drag μ s μ r d stun vω μ s d stun d drag "CB hits OB with topspin" d pre_roll d skid vω μ s if d pre_roll d drag "CB rolls efore OB contact" v pre_roll v skid ( vω) d_roll_stop d roll v pre_roll μ r if "CB doesn't reach OB" v' d_roll_stop d drag d pre_roll otherwise "CB rolls into OB" v' v roll v pre_roll d drag d pre_roll μ r v' ω' otherwise otherwise ω' "CB slides into OB with partial roll" ω' ω drag vω d drag μ s v' v drag vd drag μ s "CB hits OB with ackspin" v' v drag vd drag μ s ω' ω drag vω d drag μ s v' T SNv s d drag μ s μ r d drag μ s μ r SN v s d drag μ s μ r ratiov s d drag μ s μ r SNv s d drag μ s μ r 1

4 Spin and spin ratio vs. tip offset for various cue speeds: max d drag d drag_short min. max min min max A _slow d drag μ s μ r _medium d drag μ s μ r _fast d drag μ s μ r _power d drag μ s μ r max B _slow d drag μ s μ r _medium d drag μ s μ r _fast d drag μ s μ r _power d drag μ s μ r max

5 max d drag d drag_medium min. max min min max 3 C _fast d drag μ s μ r _power d drag μ s μ r max 1 D _fast d drag μ s μ r _power d drag μ s μ r max

6 Spin and spin ratio vs. tip offset for various shot (drag) distances: v s v s_medium 1 1 E d drag_short μ s μ r max 1 1 F d drag_short μ s μ r max

7 v s v s_fast G d drag_short μ s μ r d drag_medium μ s μ r max 1 H d drag_short μ s μ r d drag_medium μ s μ r max

8 v s v s_power 3 I d drag_short μ s μ r d drag_medium μ s μ r d drag_long μ s μ r max 1 J d drag_short μ s μ r d drag_medium μ s μ r d drag_long μ s μ r max

9 Useful conclusions from the graphs aove, which are consistent with generally accepted "est practices" and good-player intuition: 1.. Generally, to get more spin at contact with the OB, you must hit the CB harder and lower. However, as you approach the miscue limit, you get a smaller gain in spin. And for longer drag distance shots, the amount of spin actually decreases as you approach the miscue limit (see Graphs A and I). See TP B.8 for more info and results. More tip offset results in a greater spin-to-speed ratio at OB contact (except for long drag shots, especially if conditions are "sticky") (see Graphs B and J). So to get a etter spin-to-speed ratio, hit as low as you can on the CB without eing at too high a risk of miscuing.