Physics Behind Hitting A Homerun
A Physics Guide to Hitting a Homerun:
As technology advanced over the years, the baseball world has become introduced to new statistics and data points. Two of these have become incredibly important in explaining hitters' results: Exit Velocity and Launch Angle. So, if your goal is to become a power hitter in the MLB and maximize your homeruns in a season, what is the maximum launch angle you should use?
To first do this, we should establish the physics behind the actual homerun.
The Pitch
Ideally to hit a homerun, hitters want to hunt fastballs. Not only from the baseball side in which they move the least amount and are overall easiest to hit, but physics wise, they are the easiest to hit fast. This comes from the energy of the pitch. Fastballs have the highest velocity out of every pitch at about 93 miles per hour. Curveballs average velocity is about 77 miles per hour. A baseball is 5 oz. To convert all of these into SI units and to multiply the mass and velocity values to each other, the fastball has a momentum of about 5.82 kg*ms vs the Curveball that has an average momentum of about 4.82 kg*ms. The most important part of the pitch however is the energy that each pitch has. The more energy that a pitch already has, the less energy that will need to be exerted by the hitter in order to hit a homerun. This makes it easier for the hitter and explains why they look for the higher velocity pitch. Fastballs are thrown with a kinetic energy of 120.96 Joules.
As technology advanced over the years, the baseball world has become introduced to new statistics and data points. Two of these have become incredibly important in explaining hitters' results: Exit Velocity and Launch Angle. So, if your goal is to become a power hitter in the MLB and maximize your homeruns in a season, what is the maximum launch angle you should use?
To first do this, we should establish the physics behind the actual homerun.
The Pitch
Ideally to hit a homerun, hitters want to hunt fastballs. Not only from the baseball side in which they move the least amount and are overall easiest to hit, but physics wise, they are the easiest to hit fast. This comes from the energy of the pitch. Fastballs have the highest velocity out of every pitch at about 93 miles per hour. Curveballs average velocity is about 77 miles per hour. A baseball is 5 oz. To convert all of these into SI units and to multiply the mass and velocity values to each other, the fastball has a momentum of about 5.82 kg*ms vs the Curveball that has an average momentum of about 4.82 kg*ms. The most important part of the pitch however is the energy that each pitch has. The more energy that a pitch already has, the less energy that will need to be exerted by the hitter in order to hit a homerun. This makes it easier for the hitter and explains why they look for the higher velocity pitch. Fastballs are thrown with a kinetic energy of 120.96 Joules.
The Swing
The swing of the batter is in order to maximize the velocity of the ball leaving the barrel of the bat. The key to swinging the baseball bat is momentum. The ball is thrown with a certain momentum and in order to propel the ball forward, the bat must be swung with a force that will create an impulse that will propel the ball forward. Different rotational forces are used to create the most amount of force and momentum heading in the opposite direction of the baseball to achieve this.
Flight Path of the Ball
Now what is the optimal flight path of the ball? This concept deals most heavily with projectile motion and other forms of kinematics. First, in order to base our questo for finding the optimal launch angle behind the Homeruns, we need to establish the fence size we are going to use. In MLB ballparks, the average distance of the fence, after averaging the distances to the corners, gaps, and center and averaging all of those, is 109.73 meters. We will assume that any ball hit this far is going to be considered a homerun. Next we are going to use the average exit velocity of the baseball hit by Major league baseball. The average exit velocity of an MLB batted ball is 39.79 m/s and the statistic for the Barreled Ball is 43.81 m/s. These are the two velocities we will use to determine the optimal launch angle for hitting home runs.
We need to create an equation for the Ball to determine the most optimal flight path for the ball. To do so, you must deal with the projectile motion by accounting for the x and y components of motion. Time is the variable that relates these two components together so we will solve each equation separately for t. To do this we used the equation x= vi*t + ½*gt. When setting them equal to each other, we simplified and found that Vy= -½*g*t which turned into t=(2Vy)/g and plugged it into the x equation. This allowed us to find our ultimate equation to determine the perfect launch angle to hit a homerun. This equation was x=(2v^2*cos(θ))/g *(sin (θ)). I then plugged this equation into a graphing calculator to determine how different values of theta impact the distance the ball would travel.
For both the average exit velocity and the threshold for the batted ball rate, the most optimal launch angle was found to be π/4, which in degrees would be a 45 degree launch angle. Because this would increase the most time in the air while still establishing significant horizontal exit velocity. For the average batted ball velocity being 39.79 m/s, our findings suggest that if a ball is being hit at from 0.375 radians (21.5 degrees) to 1.195 radians (68.5 degrees) the ball will be a home run. For a hard hit batted ball, anywhere between 0.298 radians (17.1 degrees) and 1.273 (72.9 degrees) would be a homerun on the average fence of 106.7 meters.
The swing of the batter is in order to maximize the velocity of the ball leaving the barrel of the bat. The key to swinging the baseball bat is momentum. The ball is thrown with a certain momentum and in order to propel the ball forward, the bat must be swung with a force that will create an impulse that will propel the ball forward. Different rotational forces are used to create the most amount of force and momentum heading in the opposite direction of the baseball to achieve this.
Flight Path of the Ball
Now what is the optimal flight path of the ball? This concept deals most heavily with projectile motion and other forms of kinematics. First, in order to base our questo for finding the optimal launch angle behind the Homeruns, we need to establish the fence size we are going to use. In MLB ballparks, the average distance of the fence, after averaging the distances to the corners, gaps, and center and averaging all of those, is 109.73 meters. We will assume that any ball hit this far is going to be considered a homerun. Next we are going to use the average exit velocity of the baseball hit by Major league baseball. The average exit velocity of an MLB batted ball is 39.79 m/s and the statistic for the Barreled Ball is 43.81 m/s. These are the two velocities we will use to determine the optimal launch angle for hitting home runs.
We need to create an equation for the Ball to determine the most optimal flight path for the ball. To do so, you must deal with the projectile motion by accounting for the x and y components of motion. Time is the variable that relates these two components together so we will solve each equation separately for t. To do this we used the equation x= vi*t + ½*gt. When setting them equal to each other, we simplified and found that Vy= -½*g*t which turned into t=(2Vy)/g and plugged it into the x equation. This allowed us to find our ultimate equation to determine the perfect launch angle to hit a homerun. This equation was x=(2v^2*cos(θ))/g *(sin (θ)). I then plugged this equation into a graphing calculator to determine how different values of theta impact the distance the ball would travel.
For both the average exit velocity and the threshold for the batted ball rate, the most optimal launch angle was found to be π/4, which in degrees would be a 45 degree launch angle. Because this would increase the most time in the air while still establishing significant horizontal exit velocity. For the average batted ball velocity being 39.79 m/s, our findings suggest that if a ball is being hit at from 0.375 radians (21.5 degrees) to 1.195 radians (68.5 degrees) the ball will be a home run. For a hard hit batted ball, anywhere between 0.298 radians (17.1 degrees) and 1.273 (72.9 degrees) would be a homerun on the average fence of 106.7 meters.
Conclusions
The main conclusion of this lab is that for the average hit ball the most optimal launch angle for homeruns is about 45 degrees. But we also determined all of the possible launch angles that a homerun would be able to be hit for the average exit velocity and the Barreled ball Statistic.
The main conclusion of this lab is that for the average hit ball the most optimal launch angle for homeruns is about 45 degrees. But we also determined all of the possible launch angles that a homerun would be able to be hit for the average exit velocity and the Barreled ball Statistic.