Table 1 - uploaded by A. Terry Bahill
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The equations of physics for bat-ball collisions were coupled to the physiology of the muscle force-velocity relationship to compute the ideal bat weight for individual baseball players. The results of this coupling suggest that some batters use bats that are too heavy for them, and some batters use bats that are too light, but most experienced bat...
Contexts in source publication
Context 1
... data were collected with a different set of bats than that described in Table 2 energy (1/2 mv2) put into a swing was zero when the bat weight was zero, and also when the bat was so heavy that the speed was reduced to zero. The bat weight that allows the batter to put the most energy into the swing, the maximum-kinetic-energy bat weight, These data were collected with a different set of bats than that described in Table 1 occurred somewhere in between. This led to the suggestion that the batter might choose a bat that would allow maximum kinetic energy to be put into the swing. ...
Context 2
... player of the bottom graph was a slugger. These data were collected with a different set of bats than that described in Table 1 We tried to correlate the slope of the straight line fit with height, weight, body density, arm circumference, present bat weight, running speed, etc., but had no success. However, we noted that the subjects who had large slopes were described by their coaches as being "quick." ...
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Citations
... Pitch speed was 92 mph yielding a ball speed of 83 mph at the bat-ball collision point: pitch backspin was 2000 rpm. Contact occurred at the bat's point of maximum horizontal sweetness 12/29/2020 and the speed of the bat's collision point was 62 mph (Bahill and Karnavas, 1989). The coefficient of friction, μ, was measured to be 0.5. ...
This chapter is independent of the rest of this book. It derives equations for the three forces that affect the flight of the ball: the force of gravity, the drag force and the lift force due to the Magnus effect (the force due to a spinning object moving in an airflow). The lift and drag forces depend on air density. Altitude and weather affect air density, which in turn affects how far a batted baseball or softball travels. This chapter shows that air density is inversely related to altitude, temperature and humidity, and is directly related to barometric pressure. Regression analysis is used to show the relative importance of each of the four factors (altitude, temperature, humidity and barometric pressure) and to look for interactions between them. As shown by this model, on a typical July afternoon in a major league baseball stadium, altitude is easily the most important factor, explaining 80% of the variability. This is followed by temperature (13%), barometric pressure (4%) and relative humidity (3%). A simple linear algebraic equation presented in this chapter predicts air density well. A different model shows how the batted-ball’s range depends on both the drag force and the Magnus force and considers the relative importance of the drag and Magnus forces. As asides, this chapter shows that a home run ball might go 26 feet farther than in San Francisco in Denver and it answers the question, “Can a tennis ball be thrown farther than a baseball?”
... Bahill and Karnavas [5] examined the relationship between bat weight and swing speed from the viewpoint of the kinetic energy of the bat, and found that swing speed relative to changes in bat weight differed among players. Oikawa et al. [6] and Maeda [7] reported that baseball batting swings differ among players, and thus changes in the characteristics of the bat have a different effect on the swings of different individuals. ...
The important characteristics to consider when analyzing a baseball bat swing include the centre of gravity, moment of inertia, and the length and mass of the bat. The present study investigated the effects of the mass and centre of gravity of a swung baseball bat. The knob of an experimental bat was equipped with accelerometers to measure the three linear and three angular components of acceleration applied to the bat when swung by trained baseball players. These six components of acceleration were measured using the experimental bat for 25 combinations of mass and centre of gravity. The mass and centre of gravity of the bat were found to affect both linear and angular acceleration during the swing. Thus, bat features relative to individual players must also be considered when analyzing the swing of a baseball bat.
... [20,[30][31][32][39][40][41][42] as well as Worth Sports Co. (personal communication) and Easton Aluminum Inc. (personal communication). In our ideal bat weight experiments [4,43] and our variable moment of inertia experiments [2] for adult bats, the center of the sweet spot was defined to be 5 in. (13 cm) from the barrel end of the bat. ...
... The pitch speed is 85 mph (38 m=s). The speed of the sweet spot of the bat is 60 mph (27 m=s): this is the average value for the San Francisco Giants measured by Bahill and Karnavas [43]. These speeds would produce a CoR of 0.54. ...
... Pitch backspin is À1800 rpm and pitch speed is 85 mph (38 m=s). Contact occurs at the bat's area of maximum horizontal sweetness and the speed of the bat's contact point is 60 mph (27 m=s) the average value for the San Francisco Giants [43]. These speeds produce a CoR of 0.54. ...
445 This chapter discusses the pitch, the bat–ball collision, and the swing of the bat. Section 16.1, based on Bahill and Baldwin [1], describes the pitch in terms of the forces on the ball and the ball's movement. Section 16.2, based on Bahill [2] and Bahill and Baldwin [3], discusses bat–ball collisions in terms of the sweet spot of the bat and the coefficient of restitution (CoR). Section 16.3 based on Bahill and Baldwin [3], presents a model for bat–ball collisions, a new performance criterion, and the resulting vertical sweet spot of the bat. Section 16.4, based on Bahill [2] and Bahill and Karnavas [4], presents experimental data describing the swing of a bat and suggests ways of choosing the best bat for individual batters. This chapter is about the mechanics of baseball. To understand the whole baseball enterprise, read Bahill et al. [5]. They populate a Zachman frame-work with nearly 100 models of nearly all aspects of baseball.
... There is an ideal bat weight and a best weight distribution for each batter Karnavas, 1989 and1991;Bahill & Morna Freitas, 1995;Bahill, 2004). The team helps the individual select and acquire the right bat; column 1 (what), row 4 (technology model). ...
Frameworks help people organize integrated models of their enterprises. This organization helps ensure interoperability of systems and helps control the cost of developing systems. The Zachman framework for enterprise architecture is a six by six classification schema, where the six rows represent different perspectives of the enterprise and the six columns illustrate different aspects. To ensure a complete and holistic understanding of the enterprise architecture, it is necessary to develop models that address the perspectives and aspects that constitute the rows and columns, respectively, of the framework. In this paper, a Zachman framework is populated with models for Baseball. These models should be easy to understand without a steep learning curve. Most of the cells in this example are filled with quantitative simulatable models that have been published in peer-reviewed journal papers. The other cells are filled with simple thought models. Jacques Barzun (1954) wrote, "Whoever wants to know the heart and mind of America had better learn baseball, the rules and realities of the game." From the perspective of the Zachman framework, the way to learn Baseball is to define the models within the framework, as presented in this paper.
... Clearly, the speed at which a player can swing a bat is central to baseball and softball. Recent experimental studies of bat swing speed include Bahill & Karnavas (1989), Welch et al. (1995), Crisco et al. (1999) and Fleisig et al. (2002). The test subjects in these previous studies were skilled adult baseball and fast-pitch softball players. ...
... Reported average speeds are generally in the range of 25 to 29 m s -1 for bats with masses close to typical playing mass. Bahill & Karnavas (1989) also include data for very lightweight bats for which average swing speeds greater than 31 m s -1 were observed. ...
... Adair (1990) and Welch et al. (1995) present descriptions of the motions involved in swinging a bat and representative values for key physical features of a swing. Based on the measurements of Bahill and Karnavas (1989), Bahill and Freitas (1995) provide an empirical correlation between optimum bat mass and player size. Analysis of the momentum and energy transfer during a bat/ball collision and prediction of the subsequent final ball speed requires knowledge of the rotational and linear motions of the bat prior to the collision. ...
The speed at which a player can swing a bat is central to the games of baseball and softball, determining, to a large extent,
the hit speed of the ball. Experimental and analytical studies of bat swing speed were conducted with particular emphasis
on the influence of bat moment of inertia on swing speed. Two distinct sets of experiments measured the swing speed of colege
baseball and fast-pitch softball players using weighted rods and modified bats. The swing targets included flexible targets,
balls on a tee and machine pitched balls. Internal mass alterations provided a range of inertial properties. The average measured
speeds, from 22 to 31 m s−1, are consistent with previous studies. Bat speed approximately correlates with the moment of inertia of the bat about a vertical
axis of rotation through the batter's body, the speed generally decreasing as this moment of inertia increases. The analytical
model assumes pure rotation of the batter/bat system about a vertical axis through the batter's body. Aerodynamic drag of
the batter's arms and the bat is included in the model. The independent variable is bat moment of inertia about the rotation
axis. There is reasonable agreement between the model and the measured speeds. Detailed differences between the two suggest
the importance of additional degrees of freedom in determining swing speed.
... This act is easier if the right bat is used, but it is difficult to determine the right bat for each individual. Therefore, we developed the Bat Chooser 1 to measure the swings of an individual, make a model for that person, and compute his or her Ideal Bat Weight 1 [4], [5]. The Bat Chooser uses individual swing speeds, coefficient of restitution data, and the laws of conservation of momentum, and then it computes the ideal bat weight for each individual, trading off maximum batted-ball speed with accuracy. ...
In selecting a baseball or a softball bat, both weight and weight distribution should be considered. However, these considerations must be individualized, because there is large variability in how different batters swing a bat and in how each batter swings different bats. Previous research has defined the ideal bat weight as that weight that maximizes the batted-ball speed based on measurements of individual swings, the concept of the coefficient of restitution, and the laws of conservation of momentum. In this paper, a method is given that extends this approach to recent bat designs where the moment of inertia can be specified. The data presented in this paper show that all of the players in our study would probably profit from using end-loaded bats.
... The bats with highest MOIs (W and M1) had the lowest batted ball speeds. Bahill and Karnavas (3,4) and Bahill and Freitas (2) have reported that there is an optimal bat weight for each player, but we studied too few players and bat models to examine this issue. Applying the principle of conservation of momentum to the ball-bat impact, one would conclude that batted ball speeds would be faster with a heavier bat swung at the same speed as a similarly constructed lighter bat. ...
Although metal baseball bats are widely believed to outperform wood bats, there are few scientific studies which support this. In a batting cage study, Greenwald et al. found that baseballs hit with a metal bat traveled faster than those hit with a wood bat, but the factors responsible for this difference in bat performance remain unidentified. The purpose of this study was to determine the effects of swing speed, impact location, and elastic properties of the bat on batted ball speeds.
The pitched ball, batted ball, and swings of two wood and five metal baseball bats by 19 different players were tracked in three dimensions at 500 Hz using a passive infrared motion analysis system.
Increases in the batted ball speeds of metal bats over those of wood bats resulted from faster swing speeds and higher elastic performance with an apparent increase in the ball-bat coefficient of restitution. The contribution of these variables to batted ball speed differed with metal bat model. The "sweet spot" associated with maximum batted ball speeds was located approximately the same distance from the tip of wood bats as it was from metal bats.
The variables that correlated with differences between metal and wood bat performance, and most notably differences in the percentage of faster batted balls, were identified using a novel kinematic analysis of the ball and bat. These variables and their correlation with bat performance should be applicable to other players and bats, although more skilled players and higher performing bats would likely result in even faster batted ball speeds.
... Clearly, the speed at which a player can swing a bat is central to baseball and softball. Recent experimental studies of bat swing speed include Bahill & Karnavas (1989), Welch et al. (1995), Crisco et al. (1999) and Fleisig et al. (2002). The test subjects in these previous studies were skilled adult baseball and fast-pitch softball players. ...
... Reported average speeds are generally in the range of 25 to 29 m s -1 for bats with masses close to typical playing mass. Bahill & Karnavas (1989) also include data for very lightweight bats for which average swing speeds greater than 31 m s -1 were observed. ...
... Adair (1990) and Welch et al. (1995) present descriptions of the motions involved in swinging a bat and representative values for key physical features of a swing. Based on the measurements of Bahill and Karnavas (1989), Bahill and Freitas (1995) provide an empirical correlation between optimum bat mass and player size. Analysis of the momentum and energy transfer during a bat/ball collision and prediction of the subsequent final ball speed requires knowledge of the rotational and linear motions of the bat prior to the collision. ...
The properties of the bat and biomechanical aspects of the batter determine the successful hitting of a baseball. In this study, a data acquisition system was developed to quantify swing speeds. The effectiveness of this system was demonstrated by the inertial properties test.
... Such experiments waste time and probably degrade performance. So, to ameliorate the bat weight conundrum, we applied principles of physics and physiology to find the best bat weight (4,5,14). First, we used the principle of conservation of momentum that states that the momentum of the bat plus the ball must be the same before and after the collision. ...
... This plot was chosen because it shows the type of player that would profit most from switching to a lightweight bat. Players like this are often described by their coaches as being quick (4). His eye-hand reaction time was a relatively quick 192 ms. ...
Baseball players swung very light and very heavy bats through our instrument and the speed of the bat was recorded. These data were used to make mathematical models for each person. Then these models were coupled with equations of physics for bat-ball collisions to compute the Ideal Bat Weight for each individual. However, these calculations required the use of a sophisticated instrument that is not conveniently available to most people. So, we tried to find items in our database that correlated with Ideal Bat Weight. However, because many cells in the database were empty, we could not use traditional statistical techniques or even neural networks. Therefore, three new methods were used to estimate the missing data: (i) a neural network was trained using subjects that had no empty cells, then that neural network was used to predict the missing data, (ii) the data patching facility of a commercial software package was used, and (iii) the empty cells were filled with random numbers. Then, using these fully populated databases, several simple models were derived for recommending bat weights.
... There are two principle parts to the model used in (Bahill & Karnavas, 1989). ...
... After having a subject swing bats with a wide range of weights, an equation can be fit to the data. In their paper, Bahill and Karnavas (1989) fit straight lines, hyperbolas, and exponentials to the bat swing data. I will only discuss the straight line fit here. ...
