Angels in the Outfield Analysis

Today, I’m here to analyze this scene, from the 1994 film Angels in the Outfield. In the scene, one of the Angels’ batters hits an outstanding home run, with a little bit of help from an actual angel. This kickstarts the success of the team after a season-long losing streak. While the movie’s got a great story, I’m here to analyze some of the physics in the film, specifically from this scene. Of course, I’ll ignore the fact that they’ve got angels there to help him, since the end of the movie shows that they were able to win without the help of the angels, and presumably that the angels only existed in the mind of the main character. I’ll also try to collect as much factual evidence that can be correctly assumed from the film, since the film itself doesn’t give us many hard numbers.

This scene deals with two relatively common concepts in physics: Projectile Motion and Impulse. For the Projectile Motion problem, we’re going to find out the velocity of the baseball after it was hit by the batter, since that a hard number to calculate due to the movie, along with it being needed for the next problem. The formula for this is R = vi2 sin (2θ) / g. First, we need to find range of the baseball. The baseball appears to have been hit down center field, and hitting the back of the board before it landed. Unfortunately, there seems to be a lot of variability between baseball parks, but an average number for the distance from home plate to the center field fence is 410 feet. The height of the fence is 8 feet, and the ball hits about 20 feet above that at the back wall. The ball was already at a pretty steep angle by the time it hit the wall however, so we can assume that the ball would have only travelled about another 40 feet or so before hitting the ground. That brings our range to about 450 feet.

Next up is the launch angle of the baseball. The best angle to hit a baseball, for the most optimal home runs, is about 30 degrees experimentally. The force of gravity on the ball is simple, since the film takes place on Earth, meaning 9.81 meters per second squared. Next up, we need to double the angle to 60 degrees, then find the sine of that, which is the square root of 3 divided by 2. Convert the 450 foot range into 137 meters, and finish doing the rest of the math. The answer should give us an initial velocity of 39.4 meters per second, which sounds about right for when the ball was hit.

For part two, we need to find the force exerted by the batter on the ball. We’ll use the formula F ∆t = m ∆v. The mass, m, of a baseball is estimated to be about 0.145 kilograms. The ∆v would be the change from the ball being thrown to the ball being hit by the bat. An average MLB fastball clocks in at 90 miles per hour, or about 40 meters per second. The second velocity was calculated in the last problem, 39.4 meters per second. Now, since the ball completely changes direction, the difference between the velocities is actually 79.4 meters per second. These numbers also tell us that the baseball did not lose much velocity from hitting the ball, which is ideal for a batter. The ∆t is actually a bit of an issue, and part of the reason why I thought the scene was unrealistic. ∆t represents the amount of time the ball was in contact with the bat. With a normal bat swing, this time is about 0.7 milliseconds, which is tiny. However, the swing in this scene is different in that the bat shatters as it hits the ball, which actually means a much longer contact time. It’s incredibly hard to calculate, but you can be sure it would cut the batter’s transferred energy by at least a quarter, so we’ll use a ∆t of 2.8 milliseconds to simulate that. Calculate all that together, and you get a grand total of 4,112 Newtons of force being applied to the ball.

Here’s where we start running into problems. About 4,000 Newtons is nowhere near enough to send a ball out of the park, since an estimated force of 18,000 Newtons is required to hit a ball travelling at 90 miles per hour back into the outfield at 110 miles per hour. On top of that, the increased contact time between the ball and the bat due to the splintering would make even more force required in order to hit a homerun. In conclusion, while the idea of an amazing redeeming hit with a shattering bat sounds cool, it’s highly impossible. Though, I suppose that’s the idea of the movie, since they have the help of the “angels”. But, in reality, the movie also infers that the angels never even existed. So, I guess the batter just had some sort of sudden roid burst at that moment.