30-degree
and 90-degree Rules Dr.
Dave's answers to frequently-asked questions (FAQs),
mostly from the BD
CCB and AZB
discussion forums
maintained for the book: The
Illustrated Principles of Pool and Billiards
and the monthly Billiards
Digest "Illustrated Principles"
instructional articles
for more information, see Sections 3.03, 3.04, 5.05, and 7.02 in The Illustrated Principles of Pool and Billiards
How do you aim a carom shot that isn't in the 30-degree rule direction?
If the object ball is not in the 30-degree path, one option is the try to line up the shot for a 90 degree cue ball carom. Normal videos NV 7.2-7.4 and my March and June, 2004 instructional articles explain how to use the 90 and 30 degree rules to aim carom shots.
If you need to plan a carom shot that cannot be conveniently set up in the 90 or 30 degree directions, the 90 and 30 degree rules still give you good points of reference. The amount of cue ball vertical spin (follow, stun, draw) will determine where it goes relative to the 90 and 30 degree directions. With full stun, the cue ball will head exactly in the tangent line direction. With complete roll, the ball will deflect in the 30 degree direction. For other shots, it is difficult to reliably know exactly where the cue ball will go, so it is best to not attempt caroms in these cases unless you have no other options. Like many things in pool, all you can do is practice a bunch and develop intuition for how much the cue ball deflects with various amounts of vertical spin. Also, as described in my March, 2005 instructional article, shot speed also affects the exact cue ball trajectory. However, the 90 and 30 degree directions are still good to know to have some definite points of reference.
How do ball conditions affect the 90-degree and 30-degree rules?
Diagram 1 in my April '05 instructional article illustrates the effects of inelasticity (i.e., the coefficient of restitution) and ball friction (i.e., throw) on the 90 degree rule. TP A.5 shows the detailed analysis along with example numbers.
Diagram 1 in my May '05 instructional article shows the effects of English. The details for that are in TP A.7.
I illustrate the effects on both the cue ball and object ball for all cases. If you have a specific question that you think is still unresolved, let me know.
Only inelasticity affects the cue ball direction. Friction,
from collision-induced throw and/or English, theoretically (and I think practically)
has no affect on the cue ball direction for a stun shot (for which the 90 degree
rule applies).
Dr. Dave's peace-sign technique
How does the peace-sign technique work?
See NV 3.8 for a demonstration. For more information and demonstrations, see:
FYI, my June '05 article wraps up a series of 12 (a year's worth!) of articles dealing with the 90 and 30 degree rules. In Diagram 2 of this article (see below), I show how you should move your hand to adjust for speed. It is fairly self-explanatory, but you can see the article for more details. I hope some people can find this useful in their games. I use my 30-degree-rule-peace-sign quite often when I want to know where the cue ball will be heading. As I show in my articles, the 30 degree rule applies for a wide range of shots.
How can you tell if your peace-sign is the correct angle?
See NV B.44. Also, I have a set of angle templates in the instructor and student resources section of my website to help with learning how to use the 30-degree rule to predict cue ball motion for various roll shots. The templates can be used to help you train and calibrate your hand peace-sign (see my April '04 and June '05 articles). Here's a direct link to the templates.
from Billy_Bob:
Make peace sign,
use other finger at tips of piece sign fingers to measure how wide the fingers
are spread, then see where 30 degree finger is pointing. What I did was use a
protractor to see how wide my fingers need to be to make 30 degrees, then place
other finger at tips [of peace sign fingers] to see how that lines up. (So the
finger over the tips of the two piece sign fingers forms a triangle.)
That's a great idea! Thanks for coming up with that. My V-sign is pretty well calibrated ... and with a slight stretch, I can fairly accurately change my hand from 30 degrees (average deflection angle) to 34 degrees (maximum deflection angle at a 1/2-ball hit). However, for players new to the 30 degree rule, your finger trick can take all of the guessing out of it. See NV B.44.
Now, if people don't have a protractor or a 30-60-90 drafting triangle handy, they can cut out a piece of paper to use as a template to calibrate their finger measurement. A right triangle 12" on one side and 6 15/16" on the other will create a 30 degree angle (see my April '04 article for more information).
Do people really use the 30-degree-rule peace-sign at the table?
If I have a critical shot close to a scratch, requiring precise caroms, needing ball break-up or avoidance, or with tight "traffic" of balls to negotiate, I most definitely pull out my well-calibrated fingers. When I do, I know with confidence almost exactly where the cue ball will go. I adjust my peace sign slightly for the cut angle, because I have practiced and calibrated my hand for various important angles using the 30-degree rule angle template. I even adjust for speed, as shown in my June '05 article. My well-calibrated fingers are still much more accurate than my intuition-based visualization.
Here are some videos Mike Page put together on the half-ball hit:
As always, excellent videos! I think these are the most important principles in pool and billiards. It has always surprised me how little (if any) coverage is dedicated to these subjects in pool and billiards books on the market. These effects have been understood at least as early as 1835 (see Coriolis' book). Maybe if you, Bob, others, and I keep writing articles and posting videos on these topics, maybe they will become more "mainstream."
Your Gem #4 is the basis of the 30-degree rule, which states that for a rolling CB, the deflected angle is very close to 30 degrees for all cut angles between 1/4-ball and 3/4-ball hits (not just a 1/2-ball hit). I think this gem is the single most important and useful principle in pool, especially when used in conjunction with the peace-sign technique. FYI to you and others, here are some additional resources with lots of illustrations, examples, and video links related to this principle:
I really like your Gem #4 proposition demonstration with the carom shot from the foot rail. NV A.1 shows a similar "sure-thing" proposition. My June '04 article also illustrates and discusses the shot in detail, and TP A.1 and TP A.2 present an error analysis and look at the effects of table size.
Your Gem #2 is explained and illustrated in detail in my January '06 article. The concept is also extended into the "trisect draw-shot aiming system" in my March '06 article. This is also a very useful "gem."
Math and physics backing up Gems 2, 3, and 4 can be found in TP 3.3, TP A.4, and TP A.16.
As with all of your past videos, I've added links to these in the NV section of my website (see NV B.1 - B.6) so people can easily find and refer to them in the future.
Does the cue ball deflect the most for a half-ball hit?
FYI, I just added some stuff to TP 3.3. It probably won't be of interest to most of you out there, but I thought I'd share it anyway (for the physics geeks in the crowd).
The most interesting addition concerns the maximum cue ball deflected angle (see the bottom of TP 3.3). It turns out that the maximum deflected angle does not occur exactly at a half-ball hit. I think many people (including myself in the past) often assume this. The maximum angle (33.75 degrees) actually occurs at a cut angle of about 28 degrees, which corresponds to a 0.53 ball-hit fraction. For most people, these numbers are close enough to 30 degrees and a 1/2-ball hit, but I thought others might be interested in knowing the exact numbers.
Are there easy ways to remember the 30 and 90 degree rules?
Here's some poetry:
30-degree rule:
If you let one finger stay,
The other finger points the way.
Peace.From Billy_Bob:
When a rolling ball is on the way,
and you let one finger stay,
The other finger points the way.
90-degree rule:
When the ball has stun,
this is something you should not shun:
Point your finger, and the cue ball will follow the thumb.
If you do this, nobody will think you are dumb.
What resources are available to help me learn how to use the 90-degree and 30-degree rules accurately?
My March '05 instructional article illustrates and describes how to use the peace-sign technique for the 30-degree rule. Also, my June '05 article shows how to account for speed effects. These and other issues and effects and principles are summarized in my 30-degree-rule and peace-sign technique document. Also, I have 12 articles that address all of the intricacies of and uses for both the 90-degree and 30-degree rules.
FYI, I have convenient access to all these and other teaching and learning resources in the Instructor and Student Resources section of my website.
when the 30-degree rule applies
For what kinds of shots can the 30-degree rule be used?
The 30-degree rule is very useful for:
- scratch avoidance
- carom shot aiming
-
cluster busting
- obstacle avoidance
- position play
- etc!
Here are some important things to keep in mind:
- the 30-degree rule applies only for natural roll shots.
- the 30-degree rule applies for the entire range of cut angles between 1/4-ball and 3/4-ball hits. This range includes the 1/2-ball hit (which is at the center of the range).
- the cue ball always leaves initially along the tangent line, which is 90 degrees away from (i.e., perpendicular to) the impact line (AKA object ball direction, line-of-centers, target line, etc.). However, for slow to medium speed natural roll shots, the cue ball deflects to the 30 degree direction almost immediately (i.e., the curve in the trajectory is almost imperceptible). Only at higher speeds does the travel down the tangent line become significant (e.g., see NV 3.8 vs. NV 4.20).