Variety in bat weightsA little League player is trying to find a brand-new bat. Having determined on a particular length the player discovers that in enhancement to the selections of products (wood, aluminum, or composite), and the miscellaneous technologies (Vibration palliation System, Nitrogen bladders, piezoelectric shock absorbers, double walled barrels, composite materials) there is additionally a wide choice of bat weights. Consider the following list of 30inch tiny League bats which I currently have in the Acoustics activities at Kettering University. Several of these bat models are older, and may it is in no much longer be available, however the circulation of materials and weights space of interest.
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|Louisville Slugger 225YB||Ash (wood)||26oz|
|Sam Bat CD1 Rideau Crusher||Maple (wood)||26oz|
|Hoosier Bat HB6000 Dream®||Ash-Hickory-Maple||26oz|
|Louisville Slugger YB8||Aluminum||23oz|
|Louisville Slugger 225YB||Ash (wood)||23oz|
|Louisville Slugger 225YB||Ash (wood)||20oz|
|Easton LX10E black color Magic||Aluminum (V.R.S.)||20oz|
Some that the little League bats I have actually tested in Kettering University"s acoustics Laboratory.Bats in photo perform not exactly match list in table.
Do skilled Players use heavy or irradiate Bats?
|The answer to that concern is "both," though past players tend to have actually used heavier bats than perform today"s players. Baseball"s "king of swat" Babe Ruth reportedly started his hitting career using a 54 ounce (1.5 kg) hickory bat, and also is recognized to have used a 40oz bat in 1927 when he fight his 60 house runs.<1> Ty Cobb and also Joe Di Maggio both played with 42oz bats and Rogers Hornsby provided a 50oz piece of lumber. George Sisler, play for the St. Louis Browns in the 1920"s, make his bat heavier by hammering Victrola needles right into the barrel that his bat.<2> In the 1950"s Cincinnati Reds" Ted Kluszeski hammered tenpenny nails right into his bat to make it heavier. Other an excellent hitters including Ted Williams, stick Carew and Stan Musial used lot lighter bats: 31-33oz.<1> i get it Maris provided a 33oz bat to hit his 61 house runs in 1961. Numerous players have tried to do their bats lighter by drilling a hole in the barrel and also filling it through cork. Detroit Tigers" norm Cash admitted to utilizing a corked bat in 1961 as soon as he winner the batting title v a .361 median (though he slumped come .243 the following year through the same corked bat).<2>Kirkpatrick<3> reports that i get it Maris participated in a 1962 experiment in which the batted for distance with 5 different new bats who weights differed from 33 to 47oz. The hit 5 long fly balls with each bat and also the distances were measured and correlated to bat weight. The more heavier bats, ~ above average, resulted in more distance. However, Maris" wanted bat (which he supplied to rest Babe Ruth"s residence run record) was the lightest that the set, even though it developed the shortest street fly balls. Note McGwire provided a 35oz bat to hit his 70 house runs in 1998, and Barry Bonds used a 32oz bat come hit his 73 residence runs in 2001. Many of today"s major league players typically use 31-35oz bats.Physicists have actually shown,<3,4> indigenous a straightforward collision analysis, the the optimum bat load is in between 15 and 18oz. However, no skilled batter uses a bat this irradiate (in fact, you cannot make a lumber bat this light). NCAA regulations|
Ty Cobb and also his 42oz bat
Collisions and the preservation of Momentum
The influence between bat and ball is a collision between two objects, and in that is simplest analysis the collision may be taken to happen in one-dimension. In reality many collisions between bat and also ball (especially the ones i am able to make) room glancing collisions which require a two-dimensional analysis. It transforms out, in fact, that a glancing blow is vital to impart spin come the ball which allows it to take trip farther.<5> maybe I"ll write around this much more interesting, however more an overwhelming problem later, yet for right currently I"ll save things straightforward and look in ~ the collision in one-dimension only. The ball, m1, and also bat, m2, both have actually initial velocities prior to the collision (subscript "b"), v the ball"s velocity gift negative. After the collision (subscript "a") both bat and ball have positive velocities. The before and also after velocities and the masses of bat and also ball might be concerned each other through the physical relationship known as the preservation of linear momentum. Direct momentum is the product that the mass and also velocity of an object, p=mv. If the net pressure acting ~ above a mechanism of objects is zero then the total momentum of the mechanism is constant. While the bat and ball space in contact the player is exerting a pressure on the bat; the force needed come swing the bat. So, in a completely correct analysis, inert is not continuous because that this pressure exerted through the player swinging the bat. However, the force on the bat by the player is an extremely much smaller than the forces in between bat and also ball during the collision, and also the contact time between ball and also bat is an extremely short (less 보다 1 millisecond). This allows us to overlook the force on the bat by the player during the collision between ball and bat without significantly affecting ours results. If we overlook the pressure by the player ~ above the bat, we can express the conservation of linear momentum by setting the complete momentum prior to the collision same to the complete momentum after the collision.m1v1b + m2v2b = m1v1a + m2v2aUsually when a college student encounters the conservation of inert in a physics course the masses that both objects room given, along with the early velocities before the collision. A common homework or quiz question would be to identify the final velocities the the 2 objects after ~ the collision. As soon as one is in search of two unknown amounts one must have actually two equations. So, we need much more than simply the preservation of momentum. Because that our college student in a physics course this second equation is normally the conservation of energy. The preservation of energy relates the adjust in kinetic power (associated through motion), the readjust in potential energy (associated through springs and position), and any work-related done through nonconservative pressures (like friction) which action on the system. The readjust in kinetic energy has information around the velocities the the ball and bat before and also after the collision. During the collision the sphere undergoes a far-ranging amount the compression, and damping forces transform much the the ball"s initial kinetic power into heat. The adjust in potential energy and also work excellent by friction define how lot of the initial power is lost during compression that the bat and also ball. The way in which this energies room related throughout the bat-ball collision is rather complicated. However, the efficient relationship between the elastic nature of the ball and also the loved one velocities the bat and ball may be summarized in terms of the coefficient the restitution, (e)
The coefficient of restitution of a baseball or softball decreases with increasing incoming ball rate (v1b). Contemporary baseballs are made to have a coefficient of restitution of 0.55 for a 90mph key speed, if softballs are produced to have e=0.44 because that pitch speed of 60 mph. Presume a continuous pitch speed, we can incorporate two equations over and carry out a little algebra to fix for the velocity the the baseball ~ the collision:
This equation tells us exactly how the batted sphere velocity (v1a)depends ~ above the massive of the ball (m1) and bat (m2), the elasticity of the ball (e), the pitched ball speed (v1b) and also the bat swing speed (v2b). The properties of the ball may be treated as constants since they don"t adjust during a rotate at bat. The hitter has actually no regulate over the pitched round speed, and while it may vary considerably from key to key we"ll assume that it is a constant. The only two staying variables which identify the last velocity of the ball are the fixed of the bat, m2 and the initial speed of the bat, v2b. If we recognize these 2 parameters, we have the right to predict the batted ball speed. Together we will see, however, the problem is complicated somewhat by the reality that the rate with i beg your pardon a player have the right to swing a bat depends on the weight of the bat.
Bat Weight and Batted sphere Velocity
|To check out the impacts of bat weight and also bat speed, below is a an introduction of an experiment that I uncovered summarized in a 1980 high-school textbook, Physics the Sports arisen by Florida State University.<6> for this experiment, the sphere mass, key speed, and bat swing rate were all retained constant. Only the bat mass was changed. The data mirrors that a more heavier bat produces a faster batted sphere speed. This makes intuitive sense due to the fact that a heavier bat brings much more momentum into the collision. Doubling the fixed of the bat outcomes in boost of nearly 12mph. So, utilizing a heavier bat should an outcome in quicker hit balls, which way the hit round will travel farther. If a player deserve to maintain the exact same bat swing rate with a more heavier bat, the heavier bat will produce higher batted ball velocity and boost in distance. But, any type of player who has experimented swinging bats v widely different weights knows that it is easier to swing a irradiate bat than a heavier bat. Put another way, that takes much more effort to swing a heavy bat v the same speed together it walk a lighter bat, and most players can not swing a heavy bat as quickly as they have the right to a bat i m sorry is fifty percent the weight. So, we have to see how the batted round speed depends on bat totter speed.||Bat WeightBatted round Velocity|
|30oz (0.85kg)||76.2mph (34.0m/s)|
|35oz (0.99kg)||78.6mph (35.1m/s)|
Bat waver Speed and Batted sphere Velocity
|A similar experiment (from the exact same 1980 high-school textbook Physics of Sports occurred by Florida State University<6>) readjusted the bat swing speed while the the ball mass, key speed, and bat mass (30oz) were all maintained constant. The data shows that a quicker bat swing produce a much faster batted round speed. Doubling the swing rate of the bat outcomes in boost of virtually 22mph. So, it would certainly seem that swinging the very same bat much faster is more beneficial 보다 swinging a more heavier bat in ~ a the very same speed. Ideally, the best result would it is in to waver a more heavier bat faster. But, as I already stated, that is harder come swing a more heavier bat with the very same speed, let alone totter a more heavier bat faster. So, it looks favor we have two various effects (increasing bat weight and also increasing bat totter speed) i beg your pardon both result in much faster batted round speeds. However, the does no seem feasible to gain both effects at the exact same time. In fact, raising bat weight could decrease bat totter speed. So, we need to see how these two parameters are related before we can answer the concern "what is the final batted sphere speed?"||Bat swing SpeedBatted round Velocity|
|34.3mph (15.3m/s)||76.2mph (34.0m/s)|
|47.9mph (21.4m/s)||91.4mph (40.8m/s)|
Bat Weight, swing Speed, and Batted round VelocityAnyone who has swung a bat knows the it is less complicated to waver a lighter bat than it is come swing a heavier bat. More importantly, it is feasible to totter a lighter bat much faster than a more heavier bat. Exactly how the bat swing speed is related to bat load for a provided player is a little harder to determine. Terrycloth Bahill<2,7,8> and also his partner have broadly studied the relationship in between bat swing speeds and also bat weights because that a wide selection of players. Bahill emerged the Bat ChooserTM machine to measure bat waver speed, and also uses the results to determine the ideal Bat WeightTM for an individual player. This an equipment has been properly used by countless players that have greatly increased your batting averages after correctly choosing an ideal weight bat, as well as by several college groups who have gone on to success championships after finding their correct bat weights. His data reflects definitively the players cannot swing heavy bats as quickly as they have the right to lighter bats, and also the details vary rather from player to player and vary much more considerably depending upon the technological playing capacity of the individual. Because that example, using results from his released work<7,8> measurements of the bat speed a role of bat weight for a major League strength hitter as may be fit by the directly line equation v2b= - 0.42 m2 + 75 (power hitter)where speed is in mph and also weight is in ounces. In contrast, dimensions for a 10 year old little League player were better fit by a hyperbola(m2 + 28)(v2b+12.8) = 2728. (little leaguer)Let"s assume the the massive of the baseball is a constant m1=5.125oz, the coefficient the restitution is e=0.55, and that the early stage velocity of the baseball is representative the a common pitch speed, (v1b=-90mph because that the major League player and v1b=-40mph because that the small League player). Then we can substitute one of two people of the equations because that bat speed into the equation because that batted round speed and make some plots favor those presented by Bahill in his papers<2,7> and also book<8>. The blue dots v error bars represent measurements of bat swing rate for various bat weights. The blue curve in every plot shows how the bat swing speed decreases with increasing bat load according come the equations above. The red curve in every plot shows exactly how the result batted ball velocity depends on both the bat weight and the bat swing speed. Notification that the curves are very different because that the significant League power hitter and the small League. The skilled has much much more control end his bat swing speed, and also can develop much greater last ball speed.
Rules of thumb for encourage Bat Weights
But Wait - Bat weight is not as necessary as "Swing Weight" (moment-of-inertia)!There is a huge problem with the discusison that bat weight the I have summarized in this article. Every one of the physics used to derive the optimum mass and the batted ball speed assume that the sphere hits the bat at its center-of-mass. This really rarely wake up - access time at the sweet clues are numerous inches native the center-of-mass. Over there is another very important parameter that the bat which affects how conveniently you deserve to swing a bat, and also what the last ball speed is. This parameter entails the distribution the mass follow me the length of the bat and how that mass circulation affects the activity of a rotating object. In physics we describe this parameter as the moment the inertia. It transforms out that the moment-of-inertia (or "swing weight") matters an ext than mass..
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References<1> S. Ashley, "Getting great Wood (or Aluminum) top top the Ball," mechanically Engineering, 112(10), 40-47 (1990)<2> terrycloth Bahill and William Karnavas, "The best baseball bat," new Scientist, 130, 26-31 (April 6, 1991)<3> P. Kirkpatrick, "Batting the ball," American journal of Physics, 31(8), 606-613 (1963)<4> P. Brancazio, sports Science: physics Laws and Optimum Performance, (Simon and Schuster, 1984)<5> Robert G. Watts and Steven Baroni, "Baseball-bat collisions and also the resulting trajectories of rotate balls," American newspaper of Physics, 57(1), 40-45 (1989)<6> Physics that Sport, (Ginn and Company, 1980), component of the Individualized scientific research Instructional device for grades 9-12, emerged by Florida State University.<7> A. Terry Bahill and Miguel Morna Freitas, "Two techniques for Recommending Bat Weights," Annals the Biomedical Engineering, 23(4), 436-444 (1995)<8> Robert G. Watts and A. Terrycloth Bahill, store Your Eye top top the Ball: Curve Balls, Knuckleballs, and Fallacies that Baseball, amendment ed. (W. H. Freeman and Co., 2000) back to Physics and Acoustics of Baseball & soft ball Bats