Physics background and mathematical formulas supporting many of the principles in The Illustrated Principles of Pool and Billiards.
NOTE: This information will be of interest only to people with strong physics and mathematics backgrounds.
Proceed at your own risk.
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Chapter 2 – Fundamentals
Chapter 3 – Executing Basic Shots
- TP 3.1 – 90° rule
- TP 3.2 – Ball speeds and distances after stun-shot impact
- TP 3.3 – 30° rule
- TP 3.4 – Margin of error based on distance and cut angle
- TP 3.5 – Effective target sizes for slow shots into a side pocket at different angles
- TP 3.6 – Effective target sizes for slow shots into a corner pocket at different angles
- TP 3.7 – Effective target sizes for fast shots into a side pocket at different angles
- TP 3.8 – Effective target sizes for fast shots into a corner pocket at different angles
- TP 3.9 – Pocket target center offsets based on angle to the pocket (see TP 3.5 through TP 3.8)
- TP 3.10 – Pocket margin of error regions for a slow shot (see TP 3.5 and TP 3.6)
- TP 3.11 – Pocket margin of error regions for a fast shot (see TP 3.7 and TP 3.8)
- TP 3.12 – Object ball angle error based on cut angle (see TP 3.4)
Chapter 4 – Spin and English
- TP 4.1 – Distance required for stun and normal roll to develop
- TP 4.2 – Center of percussion of the cue ball
- TP 4.3 – Spin-induced throw effects
- TP 4.4 – Relationship between the amount of throw and cut angle
Chapter 6 – Bank and Kick Shots
- TP 6.1 – Parallel midpoint-line banking method geometry
- TP 6.2 – Mirror-image kick-shot method geometry
- TP 6.3 – Increase in bank rebound angle due to the rail coefficient of restitution
Chapter 7 – Advanced Techniques (Shot Making)
- TP 7.1 – Two-rail parallel-line kick-shot geometry
- TP 7.2 – Corner-5 three-rail diamond system formulas
- TP 7.3 – Ball-rail interaction and the effects on vertical-plane spin
Additional proofs not referenced in the book:
- TP A.1 – Half-ball hit, foot-spot carom shot
- TP A.2 – Carom shot vs. cut shot example
- TP A.3 – Minimum cue elevation required for a head-spot-to-foot-spot center-ball-hit shot
- TP A.4 – Post-impact cue ball trajectory for any cut angle, speed, and spin
- TP A.5 – The effects of ball inelasticity and friction on the 90° rule
- TP A.6 – The effects of ball inelasticity and friction on the 30° rule
- TP A.7 – The effects of sidespin on the 90° rule
- TP A.8 – The effects of sidespin on the 30° rule
- TP A.9 – Cue accelerometer measurements
- TP A.10 – The effect of bridge length on contact point accuracy
- TP A.11 – Analysis of a common fractional-ball aiming system
- TP A.12 – The relationship between cue ball spin and cue tip offset
- TP A.13 – Number of lines of aim required for different types of shots
- TP A.14 – The effects of cut angle, speed, and spin on object ball throw
- TP A.15 – Controlling the cue ball direction in a frozen cue-ball shot
- TP A.16 – Final ball speeds, distances, and directions for natural roll shots
- TP A.17 – The effect of the amount of friction on throw
- TP A.18 – Distance required for stun and natural roll to develop for different tip offsets
- TP A.19 – Massé shot aiming method, and curved cue ball paths
- TP A.20 – The effect of spin, speed, and cut angle on draw shots
- TP A.21 – Comparison of bisector-point and double-angle-bisect draw systems
- TP A.22 – “Tips” of english
- TP A.23 – Ball-hit fraction vs. cut angle
- TP A.24 – The effects of follow and draw on throw, and OB swerve
- TP A.25 – The relationship between spin-rate-factor and percent-english
- TP A.26 – The amount of sidespin required for “gearing” outside english
- TP A.27 – Spin transfer
- TP A.28 – Throw plots for all types of shots
- TP A.29 – Using throw to limit cue ball motion
- TP A.30 – The effects of cue tip offset, cue weight, and cue speed on cue ball speed and spin
- TP A.31 – The physics of squirt
- TP B.1 – Squirt angle, pivot length, and tip size
- TP B.2 – Rolling resistance, spin resistance, and “ball turn”
- TP B.3 – Throw calibration and contour plots for various cut angles, speeds, English, and roll
- TP B.4 – Stroke speed and acceleration vs. distance
- TP B.5 – Rolling CB, direct-hit hop and ball travel distances
- TP B.6 – Cue ball table lengths of travel for different speeds, accounting for rail rebound and drag losses
- TP B.7 – Effect of squirt on the amount of spin
- TP B.8 – Draw shot physics
- TP B.9 – Draw shot spin vs. spin ratio
- TP B.10 – Draw shot cue elevation effects
- TP B.11 – Shallow-angle contact-point mirror kick system
- TP B.12 – Optimal tip height for speed/distance control
- TP B.13 – Rolling cue ball carom angle approximations
- TP B.14 – Draw shot cue ball angle approximations
- TP B.15 – Pocket geometry calculations
- TP B.16 – CB-OB distance for follow cling
- TP B.17 – Maximum Drag-Enhanced Sidespin Tip Contact Point
- TP B.18 – Pendulum Stroke Cue Tip Trajectory
- TP B.19 – Comparison of cue ball deflection (squirt) “endmass” and stiffness effects
- TP B.20 – Peak forces and tip contact distance during a break shot
- TP B.21 – Small-gap-combination throw effects
- TP B.22 – How peak tip contact force and contact patch size vary with shot speed, and drop tests
- TP B.23 – Cue Pivot Point Required for Known CB Carom Angle
- TP B.24 – Estimating Rolling CB Carom Angle with 1/4 Cue Point
- TP B.25 – Percentage Sidespin Required for Maximum SIT at Any Cut Angle
- TP B.26 – BHE/FHE Pivot Percentage Relation to Cue Natural Pivot Length
- TP B.27 – Sliding Bank System Comparison
- TP B.28 – Sliding-Bank-Shot Table Comparisons From Careful Measurements
- TP B.29 – Simulation of a CB striking two frozen OBs along their line of centers
- TP B.30 – Outside vs. Inside Spin Margins for Error
See also:
- High-speed pool and billiards video clips
- Normal-speed pool and billiards video clips
- Instructional articles
Dr. Dave keeps this site commercial free, with no ads. If you appreciate the free resources, please consider making a one-time or monthly donation to show your support: