Bat Weight, Swing Speed and Ball Velocity
Thursday, April 10th, 2008A Little League player is looking for a new bat. Having decided on a certain length the player discovers that in addition to the choices of materials (wood, aluminum, or composite), and the various technologies (Vibration Reduction System, Nitrogen bladders, piezoelectric shock absorbers, double walled barrels, composite materials) there is also a wide selection of bat weights. Consider the following list of 30inch Little League bats which I currently have in the Acoustics Laboratory at Kettering University. Some of these bat models are older, and may be no longer be available, but the distribution of materials and weights are of interest.
| Model | Material | Weight |
|---|---|---|
| Bombat 9000Q | Aluminum | 27oz |
| 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 |
| YardstickTM | Ash (wood) | 23oz |
| Louisville Slugger 225YB | Ash (wood) | 23oz |
| Easton LK20 | Aluminum | 21oz |
| Louisville Slugger 225YB | Ash (wood) | 20oz |
| Easton LX10E Black Magic | Aluminum (V.R.S.) | 20oz |
| Combat CB-YB1 | Composite | 18oz |
It is interesting to note that the heaviest bat in this collection is an aluminum bat, not wood. Furthermore, there are different types of wood bats and aluminum bats at almost every weight. I’ll deal with the issues of different wood types, metal-vs-wood and composite-vs-aluminum elsewhere on this website. For now let’s assume that the material from which the bat is made does not matter, and focus solely on the issue of bat weight. Which would be better: a heavy bat which packs more punch or a lighter bat which a young player can swing easier? We might start by looking at whether professional players use heavy or light bats.
Do Professional Players use Heavy or Light Bats?
The answer to that question is “both,” though past players tend to have used heavier bats than do today’s players. Baseball’s “king of swat” Babe Ruth reportedly began his hitting career using a 54 ounce (1.5 kg) hickory bat, and is known to have used a 40oz bat in 1927 when he hit his 60 home runs.[1] Ty Cobb and Joe Di Maggio both played with 42oz bats and Rogers Hornsby used a 50oz piece of lumber. George Sisler, playing for the St. Louis Browns in the 1920’s, made his bat heavier by hammering Victrola needles into the barrel of his bat.[2] In the 1950’s Cincinnati Reds’ Ted Kluszeski hammered tenpenny nails into his bat to make it heavier.
Other great hitters including Ted Williams, Rod Carew and Stan Musial used much lighter bats: 31-33oz.[1] Roger Maris used a 33oz bat to hit his 61 home runs in 1961. Many players have tried to make their bats lighter by drilling a hole in the barrel and filling it with cork. Detroit Tigers’ Norm Cash admitted to using a corked bat in 1961 when he won the batting title with a .361 average (though he slumped to .243 the next year with the same corked bat).[2]
Kirkpatrick[3] reports that Roger Maris participated in a 1962 experiment in which he batted for distance with 5 different new bats whose weights varied from 33 to 47oz. He hit 5 long fly balls with each bat and the distances were measured and correlated to bat weight. The heavier bats, on average, resulted in further distance. However, Maris’ preferred bat (which he used to break Babe Ruth’s home run record) was the lightest of the set, even though it produced the shortest distance fly balls. Mark McGwire used a 35oz bat to hit his 70 home runs in 1998, and Barry Bonds used a 32oz bat to hit his 73 home runs in 2001. Most of today’s major league players typically use 31-35oz bats.
Physicists have shown,[3,4] from a simple collision analysis, that the optimum bat weight is between 15 and 18oz. However, no professional batter uses a bat this light (in fact, you cannot make a wood bat this light). NCAA regulations[x] recently imposed a -3 rule (length in inches minus weigh in ounces cannot exceed 3) so that 34 inch bats must weigh 31oz. So far no such rule exists for Little League play, and -12 composite bats were introduced for the 2003 season. This brings us back to our original questions: which is better: heavier or lighter bats? So, what is the optimum bat weight, and what criteria influence this choice? Let’s start by looking at the collision between ball and bat.
Collisions and the Conservation of Momentum
The impact between bat and ball is a collision between two objects, and in its simplest analysis the collision may be taken to occur in one-dimension. In reality most collisions between bat and ball (especially the ones I am able to make) are glancing collisions which require a two-dimensional analysis. It turns out, in fact, that a glancing blow is necessary to impart spin to the ball which allows it to travel farther.[5] Maybe I’ll write about this more interesting, but more difficult problem later, but for right now I’ll keep things simple and look at the collision in one-dimension only. The ball, m1, and bat, m2, both have initial velocities before the collision (subscript “b”), with the ball’s velocity being negative. After the collision (subscript “a”) both bat and ball have positive velocities. The before and after velocities and the masses of bat and ball may be related to each other through the physical relationship known as the conservation of linear momentum. Linear momentum is the product of the mass and velocity of an object, p=mv. If the net force acting on a system of objects is zero then the total momentum of the system is constant. While the bat and ball are in contact the player is exerting a force on the bat; the force needed to swing the bat. So, in a completely correct analysis, momentum is not constant because of this force exerted by the player swinging the bat. However, the force on the bat by the player is very much smaller than the forces between bat and ball during the collision, and the contact time between ball and bat is very short (less than 1 millisecond). This allows us to ignore the force on the bat by the player during the collision between ball and bat without significantly affecting our results. If we ignore the force by the player on the bat, we can express the conservation of linear momentum by setting the total momentum before the collision equal to the total momentum after the collision.
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