## What are all of the factors that affect how much throw a shot will have?

TP A.14 contains a thorough analysis, and TP A.28 contains graphs for all types of shots. Let me warn you ahead of time: TP A.14 is full of lots of complicated math and physics, so you might not want to look at the whole thing, but the results in TP A.28 might still be of interest. If not, or at least look at some of the conclusions summarized below. Plots in TP A.14 compare well to experimental, theoretical, and qualitative results presented by Marlow, Sheppard, Koehler, and Jewett. The analysis and results cover both cut-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.

Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):

• 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.
• CIT is larger for stun shots close to a 1/2-ball hit (30° cut angle), per the plot on page 6.
• SIT is maximum for stun and a medium amount of sidespin, per the plot on page 7. “Medium” corresponds to 50% english. Additional sidespin does not result in more throw; in fact, the model predicts a loss in throw with excess sidespin, because friction is less for higher relative speeds between the balls.
• 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 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.
• The theoretical plot of throw vs. cut angle for stun shots matches up with Bob Jewett’s experimental data very well (see “Throw – Part II: results” – BD, September, 2006).
• For a stun shot, the amount of CIT is independent of speed at small cut angles.
• For a stun shot, CIT is largest in the half-ball hit range (30° cut angle range).
• For a stun shot, at larger cut angles, CIT is larger for slower speeds.
• For a half-ball hit, throw is greatest for a stun shot with no sidespin or with 10% outside english. For 50% outside english with a half-ball hit, there is no throw.

A complete list of all squirt, swerve, and throw effects, along with supporting resources, is available on the squirt/swerve/throw effects summary page.

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