Billiards Blueprint | Physics Lab

Diamond-size reference 7 ft · 80 × 40 in · 4½ in pockets

Ready

Pocketed: none

TIME

INITIAL VELOCITY

Travel so far · Cue: Object:

Coaching & physics details

Plays until both balls stop. The actual 80 × 40-inch playing area stays fixed. White trail = cue ball; colored trails = numbered balls. Dark teal dashed = cue prediction; purple dashed = same speed/height without sidespin.

Spin & friction readings

Contact slip is the speed mismatch where the ball meets the cloth. It is not cue-ball launch speed.

INITIAL SPIN

SLIP AGAINST CLOTH ⓘ

Calculated 2D motion · 80 × 40-inch playing area · 2¼-inch balls · 18 diamonds. Realistic Teaching mode calculates inelastic ball contact, cut/spin throw and transferred object-ball side spin. Pocket geometry and Diamond cushion coefficients remain provisional. The dotted rotation is conceptual. Aim is ball launch direction; cue squirt, swerve and cue elevation are excluded.

BLUEPRINT COACH · INSTRUCTION LAYER

Existing character artwork unavailable. Text fallback with character asset hook.

Physics model

REALISTIC TEACHING

Use realistic mode for predicted outcomes. Switch to ideal geometry to isolate the textbook 90° tangent without ball friction or collision loss.

Balls on the table · 1–15

Tap a number to add or remove it. Drag any ball to place it.

Teaching target

Stun follows the first ball in the aim path. Aim at object ball uses the selected target.

Choose Stun, aim at an object ball, then change the stroke speed. The cue-ball marker moves to show the suggested low hit for stun at contact. This is a simulation estimate; practice and table conditions matter.

Dimensioned schematic · generic pocket cuts & uncalibrated rails

Diamond 7-foot · Simonis 860 · Diamond rails · Provisional

Speed & spin

Drag a ball or hold the cyan aim spot. Paths update before you lift your finger.

Tip height Left / right English Idealized contact beyond 0.50R

LEFT ← · rear view · → RIGHT
Top = follow · bottom = draw

Stroke strength

Cue-ball launch speed

Ball-to-ball gap Cut offset

Shape target · solve speed

For Stun mode, enter travel to rest along the first tangent leg. Targets past a rail are not solved.

Desired tangent travel (in)

Shot direction

Exact ball positions (inches)

Measured from the top-left cushion nose to each ball’s center.

Cue X Cue Y Object X Object Y

Drag either ball. Hold and drag the cyan aim handle or felt to preview both ball paths live.

Pockets open · uncheck for rail practice

Equipment & calibration

Reference equipment
Diamond Pro-Am 7-foot table · 80 × 40-inch playing surface · 94 × 54-inch cabinet · 4.5-inch pocket mouths · Simonis 860 cloth · Diamond rails.

Cloth product specification: 90% wool / 10% nylon, approximately 410 g/m². This does not determine friction. The particular Diamond cushion generation is not specified.

Provisional coefficients — not manufacturer measurements.

Simonis 860 reference: sliding 0.20 and rolling 0.010 are provisional, not calibrated.

Sliding friction μs Effective rolling resistance Rail energy restitution (uncalibrated) Cushion friction (uncalibrated) Spin decay (rad/s², provisional)

Spin decay is a constant angular deceleration, independent of rolling resistance. Default 10 rad/s² is uncalibrated.

Nose height / ball diameter

Nose fraction 0.635 is a WPA reference, not a measured Diamond setting. Cushion friction 0.14 is a literature starting point, not a Diamond measurement. Energetic restitution controls recovered compression work, not a fixed outgoing speed ratio. This is a generic reference, not measured Diamond cushion behavior.

Ball restitution e Ball friction model

The speed-dependent option uses μ = 0.01 + 0.10e^−0.98v, with relative contact speed v in mph. Restitution 0.94 is a literature reference, not a measurement of this ball set.

Sliding 0.20, rolling 0.010 and cushion rebound 0.75 are illustrative starting values, not verified Simonis or Diamond coefficients. Cloth calibration does not calibrate cushions. Bank-angle accuracy still requires rail measurements.

Estimate rolling resistance

Measure a naturally rolling ball’s starting speed and distance to rest on level cloth. No cushions. Use independent footage or a speed measurement; a guessed stroke label is insufficient.

Measured speed (mph) Distance to rest (feet)

This estimates rolling resistance only; sliding friction and collision restitution remain assumptions.

SIMULATED CONTACT

OBJECT-BALL THROW— TRANSFERRED SIDE SPIN— PATH SEPARATION—

Setup guidance & limits

Example launch speeds, not universal stroke definitions. Adjust to match a measured shot.

Initial edge-to-edge gap. Balls are 2¼ inches in diameter. A cut makes travel to contact slightly different from the gap.

Zero offset gives a straight-in hit. A real offset creates a cut angle and changes both paths.

Pocket gates are closed for banking practice. Open pockets uses a simplified capture model.

Drag anywhere on the rear cue-ball face to combine high/low and left/right. The dashed circle is a typical practical contact limit. Aim is the launch direction after the tip: ball-contact throw is calculated in Realistic Teaching mode; cue squirt and swerve are not.

0.50R default contact limit · optional 0.80R radial exploration · dashed circle marks 0.50R, a typical miscue boundary. Outside that band: idealized extrapolation, not reliable cue-ball control. 10 mph launch-speed ceiling · ball speed after tip separation, not cue-stick speed.

Predicted distances, model limits & integration

Predicted travel to rest

SIMULATION ESTIMATES · NOT REAL-TABLE MEASUREMENTS

CUE BALL · TOTAL PATH

Includes forward travel and any reversal.

CUE BALL · AFTER CONTACT

OBJECT BALL · TOTAL PATH

From its starting point to rest.

BOTH BALLS STOP BY

Simulation time; cue preparation excluded.

Table-path prediction includes cushion losses and repeated ball collisions. Travel totals include every bank. Cushion response is a provisional coupled cushion/cloth impulse model; pocket capture is approximate.

Calculated physics

Vector translation and spin, sliding-to-roll transition, repeated equal-ball collisions and cushion rebounds. Realistic Teaching mode adds normal restitution, speed-dependent tangential ball friction, cut/spin throw and transferred vertical-axis spin. Ideal Geometry mode preserves elastic, frictionless contact for comparison.

Model limits

Table playing dimensions, ball diameter and diamond spacing use physical units. Pocket cut details, cushion impulse and pocket drop behavior are approximations. No cue squirt, elevation, masse, jump, swerve, miscue or deformable-rubber model. Cushion nose height and friction are provisional; exact rail outcomes require measurement. Real-table banking accuracy has not been validated.

Validation & integration

Existing BBPA geometry, scores, Blueprint Play, Player Cards and coaching systems remain untouched.

Download validation report & integration plan ↗

Physics bridge integration test ↗

Billiards Blueprint Physics Lab

Diamond-size reference 7 ft · 80 × 40 in · 4½ in pockets

Predicted travel to rest

Calculated physics

Model limits

Validation & integration