3. What is the optimum launch angle for achieving greatest range?

To effectively swing the bat with optimum power, it is essential that a throw like pattern is utilised to ensure that the maximum velocity of each of the body segments is transferred through to the bat at the end of the kinetic chain process.
Projectile motion can be defined as "The motion of an object projected at an angle into the air." (Blazevich, 2010.) To ensure the greatest range the batter needs to hit the ball at an appropriate angle. If the object is projected at a 90 degree or 70 degree angle it will be too steep and the ball will not have enough horizontal velocity to overcome the effects of gravity and it will fall too short. On the other hand if the object is projected at a smaller angle at about 30 degrees it will not have enough vertical velocity to reach sufficient range (Blazevich, 2010). In baseball this guide for estimating the projectile of an object is greatly affected by a number of different factors such as speed of the ball, speed of the bat, amount of undercut on the ball, and whether there is a top spin or back spin produced on the ball. When batting in baseball the release height is relatively the same for all shots as the pitcher is required to throw the ball between the shoulders and knees. A study shown by Sawicki et al. (2003) a number of parameters were varied and the results showed that the optimum release angles from the optimally batted balls varied slightly from 26.3 to 24.3 degrees.

References

 

Adair, R. (2002). The physics of baseball. New York: Harper.

 

Blazevich, A. J. (2010). Sport Biomechanics The Basics: Optimising Human Performance. London: A&C Black Publishers.

 

DeRenne, C. (1993). High-tech hitting: science vs. tradition. St. Paul: West.

 

Fortenbaugh, D. (2011). Biomechanics of the Baseball Swing. International Journal of Sports Biomechanics, 9(3), 170-249.

 

Nathan, A. M., Smith, L.V. (2010) Effect of ball Properties on the Ball-Bat Coefficient of Restitution. 1-6.

 

Sawicki, G. S., Hubbard, M., Stronge, W. J. (2003). How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories. American Journal of Physics, 71 (11), 1152-1161.

2. What is the coefficient of restitution and how does it affect the energy of the ball?

 

Coefficient of Restitution affects the batted ball speed and can be described as “The proportion of total energy that remains with the colliding objects after the collision” (Blazevich, 2010).

Figure 3. Coefficient of restitution (Blazevich, 2010).

 

When the ball compacts on impact with the bat it undergoes restitution and loses some of its energy which is displaced into the bat and through sound vibrations. The less energy lost in the collision, the greater the coefficient of restitution (Blazevich, 2010). A slower ball that will collide with a bat will rebound at a slower rate and will not have as much speed as a faster ball, this is due to a lower restitution than the faster ball (Nathan, 2010).

Restitution is measured as an amount between 0 and 1, with 0 being all energy is lost in the collision and 1 being that all energy is saved (Blazevich, 2010). However, an increase in velocity may decrease the coefficient of restitution. By hitting a homerun in baseball off a faster pitched ball may just be the result of greater momentum, rather than the coefficient of restitution being of a greater value (Blazevich, 2010).

1. What is the best way to achieve the greatest range by using optimum spin?

For a typical fastball, the best way to increase optimum range is to undercut the ball at 2.65cm and swing upwards at an angle of 0.1594. For a curve ball the best way to strike the ball is at a straight angle, as it already has the top spin produced on it. Increasing the bat speed will optimise the range that the ball will carry. For every 1mph faster bat speed, the ball will carry four meters further.

 

 

When looking at the speed of the bat and ball it is more beneficial to have greater bat speed than ball speed when aiming for distance. Blazevich (2010) states that for each 1mph faster bat speed, the ball will travel five feet further. However, for each 1mph faster ball speed, the ball will only travel one foot further. This information indicates that a fast pitched ball along with a fast ball speed will produce the longest range that the ball will travel.

 

 

The spin of the ball plays an important role in the end result and it is most important when hitting for range. When a batter puts spin on the ball it will gradually follow a trajectory towards the spin direction that it has upon it (Blazevich, 2010). An example is if a batter undercuts a curve ball, during the ball flight it will swing slightly downwards, as it has a top spin effect on it. This movement of the ball changing its trajectory towards the direction of the spin is called the Magnus effect (Blazevich, 2010). The movement of the ball towards the spin direction is because of the pressure difference in the air around the ball. Objects will always want to travel from areas of high pressure to low pressure.  

 

 

Figure 2. This table displays the optimum control variables and maximum range for typical pitches (Sawicki et al. 2003)

The optimal range for three balls, knuckleball, fastball, and curve ball were tested for undercutting and bat angle. Given the result in the table above it shows that the ball speed of the batted fastball is higher than that of the curve ball. However, the backspin of a battered fastball is lower than that of the curve ball. This decrease in batted ball speed is due to the spin on the ball which has to be reversed on impact from a fast ball (Blazevich, 2010). The curve ball pitched already has a top spin produced on it, so then on impact with the bat this is increased, which in turn provides a better optimal range by a distance of over 120 meters.

Baseball Biomechanics

As most sports that involve a racquet/bat a baseball batter’s objective is to deliver the maximum amount of energy possible at impact. This energy is then transferred to the ball, accelerating it to a high velocity (Adair, 2002). A batted ball with high velocity can result in one of at least two successful outcomes, depending on the ball's trajectory. With a lower trajectory, the result is a hard ground ball or line drive, these types of hits can more easily pass by the infielders or at least significally decrease the chance of them being successfully fielded (Adair, 2002). If the trajectory of the ball is higher, the ball can land deep in the outfield for an extra base hit or possibly go over the fence for a home run (Adair, 2002). All of these results are quite favourable for the batter.

 

The best way to hit a homerun in baseball is to hit the ball the furthest possible. There are two considerations to look out for when doing this and this is the impact of the ball and the flight of the ball. The objective for coaches and batters is to maximise the range of variables and time for which the batter has control of (Sawicki et al., 2003). This will allow for a more accuracy result and will minimise any errors.

The Importance of the Kinetic Chain in Baseball

DeRenne (1993) states that, energy is created by the batter through his utilisation of the kinetic chain (DeRenne, 1993). Linear and angular momentum are transferred from the ground up through the lower limbs, trunk, and upper limbs body (Blazevich, 2010). Each proximal segment passes momentum to the connecting distal segment, such as the upper arm to forearm to hand (Blazevich, 2010). DeRenne (1993) further states that to increase the resultant momentum, the muscles of the proximal segment provide an additional unique momentum before passing it to the next segment (DeRenne, 1993). Blazevich (2010) illustrates that in batting, the bat is gripped firmly at the hands, and the bat, in essence, becomes the final link of the kinectic chain. While the ultimate goal remains to maximise the linear and angular bat velocity, the kinetic chain theory clearly shows that each segment must do its part to contribute to the resultant bat velocity (Blazevich, 2010).

 

An important factor of the kinetic chain is the coordination, or timing pattern, of each of the links of the chain (Fortenbaugh, 2011). Maximising the velocity of each of the body segments is critical, but the transfer of momentum and energy can only be optimised if it is passed along at the right time (Fortenbaugh, 2011). Fortenbaugh (2011) states that, by transferring the energy too early or too late, the proximal segment is not travelling at its maximum velocity, reducing the total energy available to impart on the ball at contact. Further complicating the task for hitters is that incoming pitches are thrown by the pitcher with varying arm angles and speeds, creating a multitude of different potential planes of movement (Fortenbaugh, 2011).

 

Adair (2002) states that the pelvis and upper trunk motions clearly show a significant role in batting biomechanics. Fortenbaugh (2011) proposes in a study that the pelvis rotated significantly faster and had a more open angle at bat collision on inside pitches than outside pitches. A larger open pelvis rotation angle at bat collision was also associated with increased bat end velocity, illustrating its importance.

 

The arms play an important role in the kinetic chain which focuses on the actions of the lead shoulder and the trail elbow. Since both of the arms are gripping the bat, the swing is a closed chain movement. This means that both arms have to work together to move the hands along an efficient path (Blazevich, 2010).

 

The final link in the kinetic chain of batting is, of course, the bat itself. The motion of swinging the bat can be described by an axis of rotation, its rotational speed and location in space (Smith, 2001). According to Estivalet and Brisson, range is an increasing function of bat velocity, the faster a bat is swung, the greater the batted ball velocity and the farther the ball will travel (Estivalet & Brisson, 2009).

 

Fortenbaugh (2011) describes optimum bat angle in a study that the bat elevation angle at bat collision was significantly greater on high pitches than low pitches (Fortenbaugh, 2011). It is important to make solid contact with the ball to maximise ball exit velocity (Adair, 2002). When the ball is coming to contact with the bat it is important for the batter to adjust the bat’s orientation to optimise contact. This can be done by rotating their head according to track the ball. This shows that batters are focused and keep their eye on the ball and they can turn less to hit high pitches and more to hit low pitches (Fortenbaugh, 2011).

Figure 1. This diagram indicates the swing process of the batter who makes four separate perceptual/cognitive judgements about the trajectory of the pitch (Gray,2009).