best to use AI....but here it is...Here's an explanation of the friction model based on Marlow's data: 1. Key Observation: • Marlow's data, presented in Table 10 of "The Physics of Pocket Billiards," demonstrated that the coefficient of friction between a billiard ball and the cloth decreases as the ball's speed increases. 2. Mathematical Model: • To capture this relationship, the following equation is used: μ(v) = a + b * e^(-c * v) • Here, μ(v) represents the coefficient of friction at a given ball speed v. • The coefficients a, b, and c are constants determined by fitting the model to Marlow's data. 3. Coefficients and Their Meanings: • a: This represents the minimum value of friction, which occurs at very high speeds. • b: This controls the initial value of friction at low speeds. • c: This determines how quickly friction decreases with increasing speed. 4. Incorporating Data: • The specific values of a, b, and c found for this model are 0.01, 0.108, and 1.088, respectively. • These values were derived through a process of fitting the model to Marlow's data, ensuring a close match between the model's predictions and the actual behavior of billiard balls. 5. Implications for Throw Angle: • This friction model is crucial for accurately predicting throw angle in billiards. • Friction significantly affects the ball's trajectory after impact, especially when spin is involved. • By incorporating the speed-dependent nature of friction, this model allows for more realistic and reliable throw angle calculations.
@ThomasMcDowell-i3q
3 ай бұрын
I was looking to make an app where you would choose the cue tip position and speed and it will tell you the throw...but I would need a fair amount of interest
@vyacheslavboyko6114
3 ай бұрын
Unfortunately, the equetion you specified in the comments is not ,at least, the full Set of equetions you Show in the video. Th closest mathematical explanation I found is the equetions from Dr. Dave.
@CueballcontrolSometimes
3 ай бұрын
Do you have a term that you use to articulate a cue ball that has forward roll as well as inside spin. The frictional force would come down in a chopping manner possibly at 45 degrees.
@Soniccues
3 ай бұрын
All our instructional efforts are to have everyone keep all aspects of spin, side and vertical, as separate entities. They both cause different reactions to the cue ball. Vertical tends to affect the tangent trajectory or the cue ball, the exit path of the cue ball from the object ball. Side spin tends to affect the path of the cue ball after hitting a rail. Your example also includes a great deal of downward angle which is a third factor. This can cause the cue ball to take a curved path. Keep all this separate in your mind. Yes the cue is hitting one spot on the cue ball but think individually about the spins, don't combine them. Vertical spin is path from object ball. Side spin is path after a rail. Angle of cue is swerve of lack of swerve depending on angle. The combined total gives an overall outcome.
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