I really appreciate Dr.Dave's advice when I was making this video and all invaluable advice from AZB forum. Reference: Dr.Dave's technical papers on deflected CB angle billiards.colostate.edu/technical_proofs/TP_3-3.pdf billiards.colostate.edu/technical_proofs/new/TP_A-4.pdf 1988 Wallace and Schroeder paper on deflected CB angle: aapt.scitation.org/doi/10.1119/1.15455
I have been really looking for this data! Thanks for putting it in a graph. SO much easier to understand. So really say 15 to 50 degrees of approach, you get the 33 degree peace sign. Roughly.
I like to generalise this as you can get over 30 degree from 1/4 to 3/4 of the ball, but in the middle (1/2 of the ball) it is slightly bigger (up to 40 approx).
Left A Like. I would like to mention that angle of approach is less and less meaning full the further the cueball is from the object ball. I think it would be a great follow up to do a video with thickness of hit being the standard of judging interaction between cueball and object ball. A rail level view of the thickness of hit, keeping the above view of hit and the resulting deflection. I really like the overhead view with the angle laid out on the table. A distance of around 3 feet and a slow rolling hit would be ideal (imo). Also using the center of ball as the reference to indicate the angle of reflection of the object ball would be more accurate than using the light reflection as the reference. Nice video.
@@puboh I think this is because the ball gains the rolling momentum that eventually makes a substantial impact on the resulting angle. Think about this as like the ball "wants" to roll in the potted direction no matter what, and even after the impact it corrects the new direction because of the residual spin momentum and the friction with the table. During this action the trajectory is slowly slopes towards initial direction, which often described as parabola, until the friction and initial spin momentum settle one another.
@@BradEnquistThanks! it's open source, you can find it on openCV documentation page. Just look for opticalflow openCV. Although you might need different strategies for different types of tracking. Sometimes just using HSV color tracking is better choice.
I'd love to see your method used analyzing the difference in Q-ball path due to speed. For example: using top on a ball at slow speed creating a sharp parabola and and top at fast speed stunning further creating a wider parabola. I struggle teaching people this concept.
This is very well done. I tend to use the angle created by the deflection plus the path of the object ball, which should be close to 90 degrees - did you find that?
Yes, when the cue ball has stun at impact ( no tip/bottoms spin), the two balls separate at 90 degrees. But for rolling cue ball this is a better approximation
@@mrkymrk99 He is. You can read his phd thesis online. It reads like a user manual. Somehow UT austin thought tinkering with some robotic pipe holder is worth a phd in mechanical engineering. I know of at least 3 other hacks who got their phd from ut austin.
I wonder if the theoretical angles are invalid because of the tangent line slide. You can even see this effect when the two balls make contact and you go to the side before it curves forward. I like that your chart goes farther than the ones I have seen from dr. Dave. It's crazy at 85° angle there is still a 10 degree change. Clearly making contact in the center half of the object ball is around 30 degrees but it doesn't seem to drop rapidly as you become thinner, actually I feel like it's more of a smooth slow reduction in the degree change
The graph I showed is the same as Dr.Dave. If anything, I only plotted finitely many points, so it was not as accurate as Dr.Dave's. You are right that two balls colliding will separate at 90 degres *initially*. But if your cue ball is rolling, then the final direction (after it's done curving) of the cue ball follows this 30 degree rule. There are no conflicts here.
@@puboh man I'm not attacking you I like your video. I also like the compass on the table. I was just pointing out that real-world does not match perfect world. It's been a long time since I looked but I feel like doctor Dave's top end was about 34°. I have tried to look at his actual papers before but I have to admit the math there is above me. I'm not sure if his calculations include the tangent line before the angle or not. But after noticing the light tangent line curve on your path lines I started to wonder if that affects the angle slightly. A reason for the discrepancy between real life and math life.
@@shanesoldner9117 I'm just discussing with you😂, don't worry man. The theoretical values don't match the real world data because the values I'm using didn't take into account the friction. You are right that the real world is much more complicated than the ideal situation, so slight deviation from the prediction is always expected. But the calculation did take into account the 90 degree separation immediately after impact.
Hi, Great work on explanation of the 30 deg rule. I notice the 'spot' of light is not on the EXCACT center of the balls, like at 2:27. This could be from the light position relative to the balls. Would it be better to use the background, like a green screen to isolate the balls, draw a 2.25" circle, and then find the center of the circle? Also a Telecentric lens would remove 'perspective' of an image.
You are right, the spot is not exactly at the center, because it is the reflection caused by the strong light I used to shoot highspeed footage. Even if I position my light directly above the ball, the spot will move as soon as the ball moves. But as long as the ball doesn't move too much, the relative location of the spot isn't changed significantly, so it's still an accurate representation of the ball's movement. I also tried your method, but I didn't manage to make it work. I'll try to make it better, thanks for the advice!
Very handy knowledge to know. I'm basically looking at 3 zones. 15 to 50 degree angle of approach is around the 30 degree, peace sign deflection rule. Most shots. Thin shots of say 10 degree and down still have say 20 degrees? Small but not zero. Handy to know for those longer 8 ball shots where the corner pocket looks huge for the cue ball. If anything, overcut the ball. Fat shots not much data but probably like thin shots might have around 20 degree offset. If anything, add to your curve. Do another 10 data points on each side of the "bell curve". You can be the next Dr. Dave if you create a couple more rules of thumb for thin and fat shots.
Haha, thanks! Dr.Dave and others had pretty much deduced everything about the deflected angle, which is expressed analytically using trig functions, and there are various approximations you can do about the deflection angle for a rolling cue ball. I can do another video on this, but a lot of useful information is summarized here /billiards.colostate.edu/bd_articles/2021/sept21.pdf
His theory is with the cue ball having a natural roll, no sliding. Hitting the object ball with the cue ball at that close of a distance is extremely difficult to be consistent. You should put the cue ball further away so that you know the cue ball won't be sliding anywhere, and will be rolling naturally.
I had the pleasure of being one of the editors of Phil Capelle's "Play Your Best 8 Ball." Because in visual terms, "up" means "away," one of the suggestions I made was that the shooter should shoot up the page. Why was this important? As I explained to Phil, when I'm in a crowded New York subway car, I don't want have to turn the book around to see the shot picture from the point of view of the shooter!
If you are interested, here is Dr.Dave analysis on rolling cue ball path with inelasticity and friction taken into account. billiards.colostate.edu/technical_proofs/new/TP_A-6.pdf
Thanks for the useful video. Does 30 degree rule apply for billard libre also? Since i have heard about 45 degree rule in libre,is it be ause of smaller diameter of pool balls?
