PDA

View Full Version : 30/90 degree rules and carom shots?



Billy_Bob
01-26-2005, 09:38 AM
It just occured to me yesterday that the 30 and 90 degree rules would also apply to carom shots. Maybe the reason I can't make any carom shots is because I'm incorrectly thinking the ball will come off at 90 degrees? Does the 30 degree rule apply for carom shots?

dr_dave
01-26-2005, 10:27 AM
<blockquote><font class="small">Quote Billy_Bob:</font><hr> It just occured to me yesterday that the 30 and 90 degree rules would also apply to carom shots. Maybe the reason I can't make any carom shots is because I'm incorrectly thinking the ball will come off at 90 degrees? Does the 30 degree rule apply for carom shots?<hr /></blockquote>
Please see my Aiming carom shots using the 30 &amp; 90 degree rules (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=171111&amp;page =&amp;view=&amp;sb=&amp;o=) posting for information on how to do this.

bsmutz
01-26-2005, 11:24 AM
99 Critical Shots has a couple of pages on how to aim carom shots. I don't have it handy or I would show an example.

dr_dave
01-26-2005, 11:35 AM
<blockquote><font class="small">Quote bsmutz:</font><hr> 99 Critical Shots has a couple of pages on how to aim carom shots. I don't have it handy or I would show an example.<hr /></blockquote>
The pages are 89-91, and 93.

FYI, carom shot aiming is covered in "The Illustrated Principles of Pool and Billiards" on pp. 205-209.

Bob_Jewett
01-26-2005, 12:18 PM
<blockquote><font class="small">Quote Billy_Bob:</font><hr> It just occured to me yesterday that the 30 and 90 degree rules would also apply to carom shots. Maybe the reason I can't make any carom shots is because I'm incorrectly thinking the ball will come off at 90 degrees? Does the 30 degree rule apply for carom shots?
<hr /></blockquote>
It's not clear from your post, but perhaps you're not aware that having follow or draw on the cue ball (or an ojbect ball that hits another object ball) will change the final angle the caromming ball takes from the object ball. The same principles apply to a cue ball leaving an object ball and an object ball leaving another object ball. (I assume you meant the latter case, although it's not clear from your post. Which did you mean?)

The so-called "30 degree" rule is a little deceptive. First, the actual carom angle for a half-ball hit and a smoothly rolling cue ball is about 35 degrees. Moreover, since there is some slide to the side as the follow on the cue ball takes, the apparent angle from the object ball will be even larger than 35 degrees, and will increase with more speed. This is well illustrated in Byrne's "New Standard Book of Pool and Billiards." In the case of an object ball caromming off another ball, the amount of follow the ball will have depends on many factors, including the distance and speed of its travel before it hits the other ball. Most short shots will not achieve smooth rolling.

The 90-degree rule applies perfectly to a very, very small set of shots. In the object-ball-to-object ball-case, there will probably be some follow on the first object ball if it has travelled some distance.

Stretch
01-26-2005, 12:23 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote bsmutz:</font><hr> 99 Critical Shots has a couple of pages on how to aim carom shots. I don't have it handy or I would show an example.<hr /></blockquote>


I don't know if this was covered in those refrences but it's handy to know that there are usually 2 ways to make the same carom (from follow shots less than 30 degrees). Either make them with a thin cut, or by going "through" the carom ball. Playing them through the carom ball will take a lot of speed off the cueball so your "just" going to make the ob and pocket it in most cases, while a thin cut might be a better choice if you need to get movement off the cue ball after the ob hit.

Another Cool shot on a related note, is the Kiss back carom, where the carom ball is frozen to the rail. You hit it with low draw. If your looking at a full ball hit on it or very close one way or another you can control whitey off it very well. Like kicking a jarred ball in, or putting a lot of distance between it and the cue ball while leaving it on the rail. St.

Bob_Jewett
01-26-2005, 12:31 PM
<blockquote><font class="small">Quote Stretch:</font><hr>...

I don't know if this was covered in those refrences but it's handy to know that there are usually 2 ways to make the same carom (from follow shots less than 30 degrees). Either make them with a thin cut, or by going "through" the carom ball.... <hr /></blockquote>
Byrne covers this well. However, I think the OP was referring to one object ball caromming off another, and then you usually do not have a useful thick/thin carom option.

Billy_Bob
01-26-2005, 04:48 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> It's not clear from your post, but perhaps you're not aware that having follow or draw on the cue ball (or an ojbect ball that hits another object ball) will change the final angle the caromming ball takes from the object ball. The same principles apply to a cue ball leaving an object ball and an object ball leaving another object ball. (I assume you meant the latter case, although it's not clear from your post. Which did you mean?)
<hr /></blockquote>

I meant an object ball which hits another object ball to carom off into a pocket (You aim to shoot object ball A to hit object ball B so that object ball A caroms off of object ball B at an angle which will make object ball A go into a pocket).

And I was guessing that an object ball once hit would be rolling and then the 30 (35?) degree rule would apply?

Bob_Jewett
01-26-2005, 06:35 PM
<blockquote><font class="small">Quote Billy_Bob:</font><hr>...
And I was guessing that an object ball once hit would be rolling and then the 30 (35?) degree rule would apply?<hr /></blockquote>
It may or may not be rolling smoothly, and the half-ball carom angle rule may or may not apply.

dr_dave
01-27-2005, 10:04 AM
FYI, my March '05 instructional article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) shows the effects of speed and various amounts of draw and follow on the 90 and 30 degree rules.

Bob_Jewett
01-27-2005, 12:33 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> FYI, my March '05 instructional article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) shows the effects of speed and various amounts of draw and follow on the 90 and 30 degree rules. <hr /></blockquote>
Hi Dave,

There seems to be a major error in Diagram 2 of that article. Shouldn't all of the final paths be parallel? (This assumes smooth rolling.) The paths shown for A, B and C are clearly physically impossible. Also, the curved parts seem not to be parabolas (as they should be), but I suspect most people will not notice that part.

dr_dave
01-27-2005, 01:37 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> FYI, my March '05 instructional article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) shows the effects of speed and various amounts of draw and follow on the 90 and 30 degree rules.<hr /></blockquote>
Hi Dave,
There seems to be a major error in Diagram 2 of that article. Shouldn't all of the final paths be parallel?<hr /></blockquote>
They should be parallel only if the cue ball has same amount of topspin for each shot. I meant for the shots to have different amounts of speed and spin. For example, shot "d" is hit very firmly, with only a little bit of follow, so the cue ball path should not turn as much as with the other shots.
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>(This assumes smooth rolling.) The paths shown for A, B and C are clearly physically impossible.<hr /></blockquote>
You are absolutely correct, the way the spin diagrams are shown, paths "a," "b," and "c" would most certainly exhibit pure rolling at impact, in which case they should all have the same final direction (i.e., same final tangents). Furthermore, this direction should be in the 30 degree range, per Diagram 4.

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>Also, the curved parts seem not to be parabolas (as they should be), but I suspect most people will not notice that part.<hr /></blockquote>
Good eye, Bob. You are correct ... all of the paths should be parabolas (assuming the friction force is assumed to be constant during the entire trajectory). I regret that the shapes in the diagrams were drawn by hand and were not taken from my technical analysis (TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_A-4.pdf)). As you probably know, it is very easy to make mistakes with illustrations in the "virtual pool" world. Thank you for pointing out these errors. Valid shapes for both draw and follow shots are shown in TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_A-4.pdf). When I get some time, I will correct the diagrams in the articles.

Regards, Dave

dr_dave
01-31-2005, 10:40 AM
<blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> FYI, my March '05 instructional article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) shows the effects of speed and various amounts of draw and follow on the 90 and 30 degree rules.<hr /></blockquote>
Hi Dave,
There seems to be a major error in Diagram 2 of that article.<hr /></blockquote>
Good eye, Bob. You are correct
...
When I get some time, I will correct the diagrams in the articles.<hr /></blockquote>
The online article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) is now corrected. Also, I was able to get new diagrams to BD before the files went to the printer, so the magazine version should also be correct when it comes out. Bob, thank you so much for spotting this error. I owe you one.

FYI, I have also expanded and improved my technical analysis (TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-4.pdf)). The cue ball trajectories in the new diagrams came directly from this analysis file.

Thanks again,
Dave

Bob_Jewett
01-31-2005, 05:17 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> ...
...
When I get some time, I will correct the diagrams in the articles.<hr /></blockquote>
The online article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) is now corrected. ... <hr /></blockquote>
Unfortunately, that file is a PDF. The system retention time (caching) for PDFs is very, very long, somehow. The file I get when I click on that link is the old file. When updating/correcting PDFs, you MUST change the name of the file, such as march05_v2.pdf. So far as I know, there is no way for me to reset/clear the intervening web caches -- even when I fetch the file from a different computer, I still get the old file.

dr_dave
01-31-2005, 05:27 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> ...
...
When I get some time, I will correct the diagrams in the articles.<hr /></blockquote>
The online article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf) is now corrected. ... <hr /></blockquote>
Unfortunately, that file is a PDF. The system retention time (caching) for PDFs is very, very long, somehow. The file I get when I click on that link is the old file. When updating/correcting PDFs, you MUST change the name of the file, such as march05_v2.pdf. So far as I know, there is no way for me to reset/clear the intervening web caches -- even when I fetch the file from a different computer, I still get the old file.<hr /></blockquote>
I'm not sure exactly what you are talking about. Does your server somehow disallow you from refreshing or reloading current versions of PDF files or other websites? The PDF file comes up fine on every computer I have checked. Have you tried pressing your browser "Refresh" or "Reload" button with the Shift key held down while the PDF file is loaded. That usually forces an update of the current page (even a PDF file).

Is anybody else having trouble seeing the new article (with the corrected Diagrams)?

Bob_Jewett
01-31-2005, 09:07 PM
<blockquote><font class="small">Quote dr_dave:</font><hr>... I'm not sure exactly what you are talking about. <hr /></blockquote> PDFs are cached differently from .htm(l) files. It is sometimes impossible to get them refreshed. I have run into this twice before when I updated PDFs on sfbilliards.com and cssainc.org. Neither the person who wanted to see the new version nor I could see the new version no matter how many times we attempted to refresh/reload. The solution is the one I mentioned. Probably the cache would time out after a day or two, but the retention time was more than a few hours.
I have also seen the cache updated immediately when the file is changed.

I can now see the new version. Unfortunately, Diagram 2 is still wrong. If the quality of follow (ratio of spin to speed) is the same for the four shots (a-b-c-d) (and it looks like they should all be rolling smoothly), the curved, parabolic sections of their paths should be similar in the technical geometrical sense, with the final straight sections of the paths parallel. That is clearly not the case in the current diagram.

For a correct diagram, see http://www.sfbilliards.com/follow_curves.pdf Those curves are all the same shape, and the curved sections are parabolas. I think the details of the drawing are important, at least to those trying to understand the physics.

dr_dave
02-01-2005, 10:05 AM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>I can now see the new version. Unfortunately, Diagram 2 is still wrong. If the quality of follow (ratio of spin to speed) is the same for the four shots (a-b-c-d) (and it looks like they should all be rolling smoothly), the curved, parabolic sections of their paths should be similar in the technical geometrical sense, with the final straight sections of the paths parallel. That is clearly not the case in the current diagram.<hr /></blockquote>
Bob,

Everything you say is correct and I agree with you completely, except for the part about the Diagram being wrong. Diagram 2 only shows "portions" of the trajectories (due to size constraints). The shapes come directly from the technical analysis in TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-4.pdf). Trajectories "c" and "d" do eventually turn to the 30 degree direction, but it takes much longer due to the speeds of those shots. The plots in TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-4.pdf) show more complete trajectories and Diagram 4 in the article shows the 30-degree effect more clearly.

Bob_Jewett
02-01-2005, 01:03 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> ... Diagram 2 only shows "portions" of the trajectories (due to size constraints).... <hr /></blockquote>
I assume that Diagram 2 is drawn to scale. I think the ball speeds for the four cases are fairly high relative to the range of speeds used in play. I think it is important for the clarity of presentation to show the full curved portion of the path and part of the straight portion. The fact that the straight portions are parallel is a very, very important idea in position play, and the diagram should show it.

dr_dave
02-01-2005, 02:00 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> ... Diagram 2 only shows "portions" of the trajectories (due to size constraints).... <hr /></blockquote>
I assume that Diagram 2 is drawn to scale.<hr /></blockquote>In the instructional article, I didn't include speeds, so the scale is a relative thing. However, the shapes are correct. To see the scale and how it relates to exact speed values, please see the plots in TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-4.pdf). I didn't think many people would be interested in that level of detail so I left it out of the article, but it can be found in the technical analysis (the plot scales are in meters).

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>I think the ball speeds for the four cases are fairly high relative to the range of speeds used in play.<hr /></blockquote>I've added more details to the analysis showing the speeds in various units. I agree that the high speeds are larger than you would want in typical play. However, for carom shots, the cue ball may not be in the straight part of the trajectory when it collides with the second ball, so it is important for people to know that the trajectory takes longer to curve at faster speeds. I've added an additional plot at the end of TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-4.pdf) showing complete trajectories at slower speeds. Unfortunately, the analysis (like the article) is also posted as a PDF file. I hope your computer and browser don't hide it from you for too long. /ccboard/images/graemlins/wink.gif

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>I think it is important for the clarity of presentation to show the full curved portion of the path and part of the straight portion.<hr /></blockquote>Again, I show this in Diagram 4 in the article (http://www.engr.colostate.edu/~dga/pool/bd_articles/march05.pdf).

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>The fact that the straight portions are parallel is a very, very important idea in position play, and the diagram should show it.<hr /></blockquote>I agree completely. That's why I show this in Diagram 4. This is the basis of the 30-degree rule, of which I am quite fond.