NEW! Our resident physicist Mark Branham has taken his mathcad model which calculates how far a softball will fly and put it into an Excel sheet for ease of use. His model even accounts for air drag. You can adjust for your own batted ball speed in cell B6 and play around with launch angle in cell B7. The program calculates the ball’s height as it flies outward. He put a marker at 300ft on the graph so you can see if the ball clears the fence, or hits it, or short hops it.
Download the spreadsheet below and have fun!
Softball Trajectory
The Science
We all have wondered how we can hit the ball further, and why the ball flies as it does and how conditions change the results. Over time I have collected a few papers by physicists at Penn State University, the Univ. of Illinois, Arizona State Univ. and elsewhere that explain the phenomena pretty well. Because so many things change as a function of temperature, air pressure, humidity and especially the different impacts due to different swing speeds, many of the calculations are wildly non-linear and exact solutions change by the hour depending on the environment.
As time permits, I will be posting several of the papers I have collected and may also add some of the mathematical models I have built so that you can predict your individual performance and use the models to help in your training program to be a better softball player.
Before we get to the library of reference materials, a few quick tips and facts:
1) Softball compression is a much larger factor than COR in determining how far a softball will fly. All softballs are designed, calibrated and tested for their specifications at 72 F. Also, they will lose 5lbs of compression for every degree above 72F. So while a warm more compliant bat will flex farther in warm weather, the decrease in the stiffness of the softball more than makes up for the benefit in the bat. You also want to be careful of playing conditions below about 60F. The bat and ball become so stiff that the bat becomes much more susceptible to cracking.
2) Speaking of bat compliance, bat flex is a large factor in hitting performance. Old style aluminum bats from the 70′s era had an effective BPF of 1.0 unlike today’s 1.2 to 1.21 factors. While that does not mean that the ball kicks off at 20% more speed than the bat speed at contact, it does mean that the average composite bat adds about 4-7mph to the final batted ball speed above your bat swing speed depending on how much you compress the bat wall during your individual swing. That extra kick translates to about 5 feet extra distance per mph at the optimum launch angle therefore, the total distance due to bat performance can be from 20 to as much as 35 feet depending on how your bat conditions as it ages.
3) The BESR standard was originally based on an average player with a 70mph swing and a 10mph average pitch speed. ASA statistics however show the average D-player swings at 81mph while the average A player swings at 89mph. The true average pitch speed is 25mph not 10mph. Governing bodies changed the old 85mph standard to 98mph but the BESR standard still underestimates the performance of the new high tech composite bats. As such, the BESR standard has been replaced by most governing bodies by the BBCOR standard.
I will attach here a very solid article on the mechanics of swinging a bat published in the American Journal of Physics by Rod Cross at the University of Sydney Australia: Bat Swing Mechanics
For the more mathematically inclined here is a good description of the parameters that go into modeling the swing force and batted ball parameters that determine just how far the ball will go. The article, How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories by Gregory S. Sawicki and Mont Hubbard, Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, William J. Stronge Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom,
Page 3 gives a pretty good list of the parameters so you can see how which ones change with playing conditions. The value of calculations like this is that you can use them to see what parts of your game are most important to work on to improve your overall performance.
A link to a good explanation of the sweet spot for a bat is here:
http://www.acs.psu.edu/drussell/bats/sweetspot.html
The best trampoline effect for a composite bat is usually about 6″-8″ from the end of the barrel, a good article is here:
http://www.acs.psu.edu/drussell/bats/cop.html
This brings us to bat/ball interactions. As a general rule of thumb, the tensile strength of the bat is roughly 10 times that of the ball. For example, the typical aerospace grade carbon fiber used in a bat has a young’s modulus of about 4,200 psi, while the compression of the ball is defined as the force required to squeeze the ball by a total of 1/4″. In our case the ball takes 375 lbs of force to compress the ball by 1/8″ on both sides or a total of 1/4″ deformation. In a typical bat/ball collision,(and strongly dependent on your swing speed), the ball deforms along the bat wall to a spot anywhere from the size of quarter to as much as 2″ or more in diameter. Much of the energy that goes into the deformation of the ball is lost, (this is how COR gets defined), the left over energy goes into the ball in the form of the bat speed that is maintained through contact plus the velocity of the bat wall as it rebounds out and adds its kick to the ball. The batted ball velocity is then the swing speed through contact plus the bat wall rebound kick velocity.
This is a good example of why many hitting instructors emphasize hitting through the ball. If you allow the bat to slow down just before or during contact, then much less energy is put into the ball and the ball flight distance is greatly reduced.
Next Topic area: in addition to the pure technology and physics involved in the bat/ball collision and the final exit velocity of the ball, another very important factor in effective hitting involves the hand eye coordination required to hit the ball effectively. In this area, a key topic is that of the relationship of both handedness and eye dominance. To clarify, the muscles which control the eye’s ability to focus the lens are typically stronger on one side of a person than another. This is similar to the fact that in most people, one hand is stronger and more dexterous than another. In the general population, this divides into about 90% right handed people and 10% left handed. It has also been found that about 1/3rd of the population is left eye dominant. (Study in the UK by McManus et.al.)
This leads to a condition where a significant number of people have cases where the dominant eye is opposite to the dominant handedness. In these cases, there can be significant parallax error perception and a loss of depth perception. There have been many studies in baseball, cricket, archery and the shooting sports that validate the difficulties these differences cause. It is important to understand that the body is in effect “hard-wired” toward the tendency of having one eye dominant over the other just as it is for handedness. Some people claim to be able to “cure” this problem, but a more reasonable goal is to do exercises which balance the relative eye strength. While it has been shown that that drastic training can modify either eye or handedness dominance, it has also been shown in studies in the 50′s and 60′s that teachers who imposed right handed behavior in an effort to make all left handed students into right handers, those original left handed students were much more at risk for dyslexia and other similar disorders. So can eye or handedness be modified from one side to the other?, yes, but not without risky consequences.
There are several easy tests you can give yourself to assess your relative eye strength. The first, called the Miles Test, is a test where one takes the index fingers and the thumbs, place them to just touch each other to form a small diamond shape hole between where your fingers touch. Look at a far away object, then extend your arms and sight the object through the diamond shaped hole with both eyes open. Close one eye and note if the object jumps out of the diamond hole. close the other eye and make the same note. The eye that is open when the object stayes in the opening is your dominant eye. The Porta Test is similar but involves making a small circle with the index finger and thumb of one hand and sighting a far away object similarly at arm’s length.
If you find yourself consistently hitting the top or bottom of the ball, (in golf it would be either topping the ball or hitting it fat seemingly no matter what you do) you may have something like this going on. As noted above the parallax error your body interprets leads your hands to a slightly different than where the ball really is. A typical eye exercise you can do is to string three beads on a string about 6 to 10 feet long. Place a bead near each end and one in the middle. Tie one end to a stationary position near head level and stretch the other end of the string to touch your nose. Focus for a few seconds on each successive bead. When you move your focus from one bead to another, change your focus as quickly as possible, this exercises the cilia which bend your eye lens. Typically, you will get tired after only a few minutes of this exercise, work up in increments until you can do this for something like 10 minutes without feeling too much eye strain.
