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cushioncrawler
02-11-2007, 06:09 PM
I thort it best to start a new thread re comments on gearing arising from the thread "Bank shot using throw spin transfer" (and some other recent threads allso). "Gearing" is a term that describes the happening that sometimes arizes during a qball-objectball impact wherein zero balltoball slippage (gearing) is achieved at some time during impact. Of course, u karnt tell whether or when gearing occurs, and i doubt that gearing would ever help a shot -- duzzenmadder, this here stuff is for skoolkidz only.

I reckon that there are 2 main types of gearing.....

1A... Occurs where the qball and objectball have equal and opposite spin-rates and zero balltoball slippage.

1B... 1A Gearing in the horizontal plane, but slippage in a vertical plane. 1B wont be mentioned again.

2A... Occurs where there is zero balltoball slippage, but the spin rates are not "equal".

2B... 2A Gearing in the horizontal plane, but slippage in a vertical plane. 2B wont be mentioned again.

Earlier, i mentioned that i had a computer program that calculated spin-transfer for fullball impacts, and, after some teething troubles, this "verifyd" Dr Dave's figure of a ceiling of 35.71% spin-transfer for fullball impacts (for stun, all of this-here gearing stuff is for stun only). Anyhow, a number of questions aroze, particularly relating to non-fullball impacts. I have now upgraded my program to include non-fullball impacts, and i have runoff some figures etc, for any "skoolkidz" out there that might be interested, for comment.

At present, the program caters for only one impact-speed (1.26m/s) -- here i assume that the impact-speed is the speed of the objectball after impact. The qball's pre-impact speed is therefore taken to be 1.26m/s for a fullball impact ("e" assumed to be 1.00 here), and tending towards infinity for fine cut-shots here.

At present, the program duznt take into account any varyation of balltoball friction (during impact) due to varyation in impact-speed or due to varyation in balltoball slippage etc (during impact). But it duz allow me to nominate any (fixed) friction values that i wish, eg 0.040 or 0.080 etc.

Rezult A. Type 1A gearing is impossible for fullball impacts. But Type 2A might be possible if the qball spin is not too high. (We allready knew this from the old program and Dr Dave's stuff and Jim's stuff).

Rezult B. Type 1A gearing is possible for non-fullball impacts, if u uze a bit of inside-english, if the qball spin is not too high. (Dont forget, all of this stuff is for pure stun).

For a fixed friction of 0.060, and OB vel 1.26m/s, the impact angle (degrees) for 1A gearing is allways 18.05 times the qball's spin (m/s). (Here, fullball is zero degrees, and a halfball impact is 30deg).

Rezult C. If the qball's initial spin (m/s) is larger than 6.32 times the friction (eg 0.379m/s for 0.060, or 0.505 for 0.080 etc), then 1A gearing is impossible. (I think that "e" might affect this figure).

Rezult D. For 1A gearing, the slippage friction energy (heat) loss is allways equivalent to 70% of the qball's initial spin energy. (For 2A gearing, the heat loss was allways 35.71%). (Friction factors, varyble or not, wont affect this 70%, but "e" and V would).

Rezult E. With 1A gearing, the max objectball throw angle (deg) is allways achieved when slippage ends at the same instant as impact ends, and is allways 113.9 times the friction, eg for 0.060 it is 6.843deg. (I think that Jim said that the 1A throw angle was fixed).

When slippage ends early, ie when the qball initial spin is "too low", the throw (deg) is allways 3.434 times the "ratio" of "qball initial spin" / "spin for max throw".

Nuff for now. Submitted for peer review (and for skoolkidz). madMac.

Jal
02-12-2007, 12:49 AM
Hi Mac,

I'm exhausted trying to translate your results into the ones I'm familiar with, so I'll be terse with my responses. No offense I hope.

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult A. Type 1A gearing is impossible for fullball impacts. But Type 2A might be possible if the qball spin is not too high. (We allready knew this from the old program and Dr Dave's stuff and Jim's stuff).<hr /></blockquote>Agreed. Just to add that 2A can occur at any cut angle if the spin is within a certain window surrounding the exact gearing value (no slippage during any part of impact).

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult B. Type 1A gearing is possible for non-fullball impacts, if u uze a bit of inside-english, if the qball spin is not too high. (Dont forget, all of this stuff is for pure stun).<hr /></blockquote>Agreed.

<blockquote><font class="small">Quote cushioncrawler:</font><hr>For a fixed friction of 0.060, and OB vel 1.26m/s, the impact angle (degrees) for 1A gearing is allways 18.05 times the qball's spin (m/s). (Here, fullball is zero degrees, and a halfball impact is 30deg).<hr /></blockquote>I get 18.19, but whose counting, and using the tangent of the impact angle as approximately equal to the angle itself (in radians).

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult C. If the qball's initial spin (m/s) is larger than 6.32 times the friction (eg 0.379m/s for 0.060, or 0.505 for 0.080 etc), then 1A gearing is impossible. (I think that "e" might affect this figure).<hr /></blockquote>I get:

RW &lt;= (7u)Vcos(theta) - Vsin(theta)

which comes from the condition for gearing to take place (1A or 2A):

uVcos(theta) &gt;= (1/7)(Vsin(theta) + RW)

We know Vcos(theta) = 1.26 m/s, but we don't know Vsin(theta) (it can be anything), so I don't see how your condition can be sufficient?

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult D. For 1A gearing, the slippage friction energy (heat) loss is allways equivalent to 70% of the qball's initial spin energy. (For 2A gearing, the heat loss was allways 35.71%). (Friction factors, varyble or not, wont affect this 70%, but "e" and V would).<hr /></blockquote>1A gearing is just a special case of 2A gearing, so the energy loss in terms of the cueball's initial spin energy should also be 35.71%.

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult E. With 1A gearing, the max objectball throw angle (deg) is allways achieved when slippage ends at the same instant as impact ends, and is allways 113.9 times the friction, eg for 0.060 it is 6.843deg. (I think that Jim said that the 1A throw angle was fixed).<hr /></blockquote>I get 57.3 times u (=mu). Whenever the cueball slides for the entire impact, the tangent of the throw angle is equal to u. Taking the tangent as nearly equal to the throw angle in radians, the 57.3 is the conversion factor to units of degrees. The 1A impact angle isn't fixed, in general, but for a given cueball speed it will have a specific value for maximum throw. (I think this is what you mean, but in case there's a misunderstanding...)

<blockquote><font class="small">Quote cushioncrawler:</font><hr>When slippage ends early, ie when the qball initial spin is "too low", the throw (deg) is allways 3.434 times the "ratio" of "qball initial spin" / "spin for max throw".<hr /></blockquote>I get something pretty close to your answer, but with one important difference.

For some cut angle and cueball speed, let q be the ratio of the initial surface speed which produces less than max throw, to that which produces max throw. These surface speeds include Vsin(theta) as well as the surface speed from spin. Let the combined surface speed for less than max throw be S, and for max throw be Smx:

S = Vsin(theta) +/- RW

Smx = Vsin(theta) +/- RWmx

where Wmx is the spin producing max throw. In the general case RW may add or subtract from Vsin(theta). Then:

q = S/Smx

and the tangent of the throw angle is the coefficient of friction times q.

tan(gamma) = uq

Again, taking the tangent as essentially the throw angle, and converting from radians to degrees, the throw angle is 57.296uq = 57.296(.06)q = 3.44q.

So we agree (if u = .06), except that I think you need to use the ratio of surface speeds rather than spins.

Jim

Isshi
02-12-2007, 07:54 AM
Jal wrote to the one who started this thread:

'Hi Mac,

I'm exhausted trying to translate your results into the ones I'm
familiar with, so I'll be terse with my responses.'

Well, I'm exhausted trying to translate too, and I can't get past
a dozen words of Mac's writing, so I'll be even terser with my responses:

Look, Mac, the value placed on something is often indicated by the
effort you put into it. If you can't be bothered to make the slightest effort
to write in a recognizable manner, indeed if you intentionally disregard
or violate basic spelling, doesn't that reveal your laziness and/or disregard

If you treat others that way, you can't expect a serious or respectful response,
although you might get it. You won't from me.

Perhaps this offends you. If so, you can be comforted that it's mutual.

Sincerely, Isshi.

Jal
02-12-2007, 12:34 PM
<blockquote><font class="small">Quote Isshi:</font><hr> ...Look, Mac, the value placed on something is often indicated by the
effort you put into it. If you can't be bothered to make the slightest effort
to write in a recognizable manner, indeed if you intentionally disregard
or violate basic spelling, doesn't that reveal your laziness and/or disregard

If you treat others that way, you can't expect a serious or respectful response,
although you might get it. You won't from me.

Perhaps this offends you. If so, you can be comforted that it's mutual.

Sincerely, Isshi. <hr /></blockquote>Isshi,

You of course have every right to feel about his style of writing as you do. Some others feel the same, but I'd like to register a dissenting vote.

Over the last year or two he's sent me excerpts from his book "The Cushion Crawlerz Bible" and it didn't take long to get used to it. In fact, I find it strangely refreshing, apart from the insights he has about various effects that take place, most of which I wouldn't of had a clue until he described them.

He's also done a lot of tests and if you knew the extreme care he takes in performing and analyzing them, "laziness" would have to be the last word that comes to mind. He also happens to be a very strong player who places high in Australia's open billiards events (I found this out on my own).

As for me, I'm just grateful that he's willing to share, in whatever manner he C's fit.

Jim

cushioncrawler
02-12-2007, 02:48 PM
Hi Isshi -- I appreciate your comments. I know that i have copped a lot of criticism for my english, lots of it facetoface from local players etc. Funny, mostly from "new-australians", ie born in non-english countries (if any now exist) -- i guess that people who struggle slightly with "straight" english find it especially difficult to read "bent" english.

The second "front" is from technical people, ie highly educated, ie used to writing and reading "papers" in perfect english only. This mob feels most offence (i think), but rarely says anything -- very uppity -- inkloodz some of my team-mates actually.

I must admit that i thort that english-teachers would like the idea of some sort of simplyfyd spelling, ie that they would be familiar with the changes and improovments in english over the centuryz, and be aware of the lack of change in the past 150 years. It appears that the last person to (try to) do much for improoving english was Teddy, back in about 1906. I reckoned that nowadayz the biggest threat to advancement is the Chinese and Japanese, koz, they are swelling the numbers in the first group that i mentioned earlyr. But now i have to add english teachers. Not that i am very serious about any of this "Society for Simplified Spelling" sort of stuff, i just like to play with words a bit. madMac.

cushioncrawler
02-12-2007, 04:52 PM
<blockquote><font class="small">Quote Jal:</font><hr><blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult D. For 1A gearing, the slippage friction energy (heat) loss is allways equivalent to 70% of the qball's initial spin energy. (For 2A gearing, the heat loss was allways 35.71%). (Friction factors, varyble or not, wont affect this 70%, but "e" and V would).<hr /></blockquote>1A gearing is just a special case of 2A gearing, so the energy loss in terms of the cueball's initial spin energy should also be 35.71%.

<blockquote><font class="small">Quote cushioncrawler:</font><hr>Rezult E. With 1A gearing, the max objectball throw angle (deg) is allways achieved when slippage ends at the same instant as impact ends, and is allways 113.9 times the friction, eg for 0.060 it is 6.843deg. (I think that Jim said that the 1A throw angle was fixed).<hr /></blockquote>I get 57.3 times u (=mu). Whenever the cueball slides for the entire impact, the tangent of the throw angle is equal to u. Taking the tangent as nearly equal to the throw angle in radians, the 57.3 is the conversion factor to units of degrees. The 1A impact angle isn't fixed, in general, but for a given cueball speed it will have a specific value for maximum throw. (I think this is what you mean, but in case there's a misunderstanding...) <hr /></blockquote> Jim -- Thanks for the comments. It looks like i must have one 2 too many somewhere in my program -- or, my error might be a bad "1/2". I will try to digest this and the other stuff u mentioned.

I admire yor (mathematical) equations -- they implicitly, or iz it "explicitly" (where iz Isshi when u need him), show where and why things happen -- unlike my iterations which dont explain much, unless i throw the rezults into a graph(s), which iz what i allwayz do. If my (arithmetical) iterations give very similar rezults to your (mathematical) calulations then this remoovz some of my fear and distrust of equations here and in general. I might be forced to go one step further and remoov my ignorance of equations.

Az u know, i use excel, and the program that i cooked up steps throo an impact in about 7000 slices. I could improov the accuracy of my rezults by perhaps one decimal if i stretched the program to say 14000 steps, but it is allready about 21 Megabytes. Anyhow, i shood send a PM when i eventually "see the light", it will take some time. madMac.