Baseball–bat collisions and the resulting trajectories of spinning balls

Watts, Robert G.; Baroni, Steven

doi:10.1119/1.15864

Cited by 28 publications

(15 citation statements)

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“…These data are roughly consistent with C L = S, independent of Re, which is the parametrization used by Watts and Baroni. 4,6 The data of Alaways 8,9 were obtained using a high-speed motion analysis technique to measure the spin vector and track the trajectory of a pitched baseball. From these data C L was extracted for S in the range S = 0.1-0.5 and for speeds up to approximately 75 mph.…”

Section: Previous Determinations Of the Magnus Forcementioning

confidence: 99%

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The effect of spin on the flight of a baseball

Nathan

2008

American Journal of Physics

119

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Measurements are presented of the Magnus force on a spinning baseball. The experiment utilizes a pitching machine to project the baseball horizontally, a high-speed motion analysis system to determine the initial velocity and angular velocity and to track the trajectory over 5 m of flight, and a ruler to measure the total distance traversed. Speeds in the range v = 50-110 mph and spin rates ͑topspin or backspin͒ in the range 1500-4500 rpm were utilized, corresponding to Reynolds numbers of Re= ͑1.1-2.4͒ ϫ 10 5 and spin factors S ϵ R / v in the range 0.090-0.595. Least-squares fits were used to extract the initial parameters of the trajectory and to determine the lift coefficients. Comparison is made with previous measurements and parametrizations, and implications for the effect of spin on the flight of a baseball are discussed. The lift coefficient C L is found not to depend strongly on v at fixed values of S.

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Section: Previous Determinations Of the Magnus Forcementioning

confidence: 99%

“…Computational studies of the effect of spin on the flight of hit baseballs have been reported by Rex, 3 Watts and Baroni, 4 and Sawicki et al 5 These studies utilized models of the Magnus force based on the available experimental information, which will be reviewed in Sec. II.…”

Section: Introductionmentioning

confidence: 99%

The effect of spin on the flight of a baseball

Nathan

2008

American Journal of Physics

119

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“…7 Typically, complications only arise when the ball impacts either at an oblique angle or if the object impacts while spinning. Many experimental and theoretical studies [7][8][9][10][11][12][13] have been performed over the years to investigate the interactions between an impacting object and the surface of a material. The authors have been developing a material where common knowledge does not apply because non-spinning objects …”

Section: Embedding Simple Machines To Add Novel Dynamic Functions To mentioning

confidence: 99%

Embedding simple machines to add novel dynamic functions to composites

Tang

O’Brien

Hawkins

2005

JOM

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One unique property of a machineaugmented composite (MAC) is its ability to convert a compressive force into a shear force, and vice versa, simply by the geometry of its angled sidewalls. The authors have discovered that a non-spinning ball dropped at a normal angle onto the MAC's surface rebounds from that surface at an oblique angle and develops a signifi cant rotational velocity. Through fi nite-element analyses, analytical study, and experiments, the magnitude and direction of the spin can be precisely controlled by tailoring the stiffness of the MAC through the properties and dimensions of its constituent materials.

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“…16 for spindown with little or no translational velocity was used in Ref. 17 as justification for neglecting spin-down entirely. These results 16 predict a baseball spin-down characteristic time of about 250 s. It is difficult to determine if the spin-down rate will increase or decrease when a large translational velocity is added.…”

Section: Spin-downmentioning

confidence: 99%

Comment on Norsen’s defense of Einstein’s “box argument”

Shimony

2005

American Journal of Physics

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In 1927 Einstein 1 presented a precursor of the much better known argument of Einstein-Podolsky-Rosen ͑EPR͒ 2 that the quantum mechanical description of physical reality is either incomplete or violates locality by tacitly assuming superluminal causality in the measurement process. He proposed a thought experiment in which the support of the wave function of a ball is contained within two boxes, B 1 and B 2 , that are carried arbitrarily far from each other. When a measurement is performed to detect whether the ball is in B 1 , not only is a positive or negative answer found regarding that box, but simultaneously a negative or positive answer is obtained regarding box B 2 . He concluded that either the wave function is an incomplete description of the ball, requiring supplementation by additional information concerning its location, or else an experimental intervention in B 1 immediately causes a determination of its presence or absence in B 2 , which would constitute non-local causation.Norsen 3 has deplored the neglect of Einstein's ''box'' argument, claiming not only that it is valid, but is superior to EPR because of its simplicity: it involves only a single system, considers only the position of that system rather than a pair of non-commuting properties, and above all avoids the need to invoke counterfactual reasoning. ͑EPR not only infers the position of particle I from the position of particle II, or vice versa if position is measured on one of the particles, but they infer the momentum of one particle from the momentum of the other if momentum is measured on either.͒ However, there is a serious flaw in Norsen's defense of the box argument in my opinion. If Q 1 is the projection operator representing the physical proposition that the ball is in B 1 and Q 2 is the projection operator corresponding to the ball's location in B 2 , then the logical structure of the lattice of projections in the quantum mechanics of localizable systems ensures that Q 1 and Q 2 are orthogonal, that is,independently of the quantum state of the ball. Hence any state that is an eigenstate of Q 1 with eigenvalue 1 or 0 will also be an eigenstate of Q 2 with respective eigenvalue 0 or 1. ͑The relation of Q 1 and Q 2 to B 1 and B 2 , which is accepted intuitively by physicists, is generalized and presented with mathematical rigor in Mackey's discussion 4 of projectionvalued measures on Borel spaces.͒ Because Eq. ͑1͒ is independent of the quantum state of the ball, the inference from a measurement yielding the location or non-location of the ball in B 1 to the respective non-location or location in B 2 does not rely on any contingencies, and therefore it is fair to say that it is a matter of logic rather than of causality. Hence if one rejects Einstein's contention that quantum mechanics gives an incomplete description of the ball, in the sense that its location is definitely in B 1 or B 2 even when the wave function does not vanish identically in either box, one is not forced to accept non-local causality as the only alternative. The ...

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Baseball–bat collisions and the resulting trajectories of spinning balls

Cited by 28 publications

References 0 publications

The effect of spin on the flight of a baseball

The effect of spin on the flight of a baseball

Embedding simple machines to add novel dynamic functions to composites

Comment on Norsen’s defense of Einstein’s “box argument”

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