dr_dave

07-16-2005, 02:53 PM

FYI, I just completed and posted a detailed analysis of ball friction and throw effects. It can be found in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf) on my website (http://www.engr.colostate.edu/~dga/pool/). Let me warn you ahead of time: It is full of lots of complicated math and physics, so you might not want to look at the whole thing. However, I encourage everybody to look at and comment on the plots and concluding remarks in the last 4 pages of the document, or at least look at some of the conclusions summarized below. The plots compare to experimental, theoretical, and qualitative results presented by Marlow, Sheppard, Koehler, and Jewett. The analysis and results cover both collision-induced throw (CIT) and spin-induced throw (SIT). The effects of cut angle, speed, and spin are also considered.

The model of friction I use is more complete and accurate than any other I have seen presented before. First, I include the effect of speed on friction, based on experimental data from Marlow. And more importantly, I correct an error that appears in many analyses of collisions with friction (e.g., in Shepard's work). The error involves not taking into account the potential loss of relative sliding motion between the CB and OB during impact. I have accounted for this effect, and it significantly affects the results. I hope some of the physics nerds out there will look at this closely and think about it to make sure they agree.

Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):<ul type="square"> Both CIT and SIT are larger at slower speeds.

CIT increases with cut angle, but levels off at higher cut angles.

CIT is larger for stun shots.

SIT is larger, and most sensitive to sidespin, with stun shots. But SIT is not nearly as sensitive to small amounts of sidespin as some people think. The more accurate model of friction affected these results significantly.

Inside English increases CIT, especially at small cut angles.

Outside English can create SIT that overcomes CIT.

Outside English creates maximum SIT at small cut angles.

"Gearing" outside English results in absolutely no throw.[/list]

Again, there are no big surprises here, but it is reassuring to see a theoretical model shed some light on and improve understanding of all of these effects. Also, an accurate model lets one ask and answer other questions in the future quite readily.

Regards,

Dr. Dave

The model of friction I use is more complete and accurate than any other I have seen presented before. First, I include the effect of speed on friction, based on experimental data from Marlow. And more importantly, I correct an error that appears in many analyses of collisions with friction (e.g., in Shepard's work). The error involves not taking into account the potential loss of relative sliding motion between the CB and OB during impact. I have accounted for this effect, and it significantly affects the results. I hope some of the physics nerds out there will look at this closely and think about it to make sure they agree.

Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):<ul type="square"> Both CIT and SIT are larger at slower speeds.

CIT increases with cut angle, but levels off at higher cut angles.

CIT is larger for stun shots.

SIT is larger, and most sensitive to sidespin, with stun shots. But SIT is not nearly as sensitive to small amounts of sidespin as some people think. The more accurate model of friction affected these results significantly.

Inside English increases CIT, especially at small cut angles.

Outside English can create SIT that overcomes CIT.

Outside English creates maximum SIT at small cut angles.

"Gearing" outside English results in absolutely no throw.[/list]

Again, there are no big surprises here, but it is reassuring to see a theoretical model shed some light on and improve understanding of all of these effects. Also, an accurate model lets one ask and answer other questions in the future quite readily.

Regards,

Dr. Dave