At halftime of Saturday’s game against Montreal, when Austin FC was down to 10 men and the prospects of leaving Canada with a point seemed bleak, a question was posed in Los Verdes Slack:
As soon as I read this, I started thinking about it a lot as well. In fact, I haven’t been able to think about anything else for the past 72 hours. So I decided to dust off my physics textbooks to see if there’s an answer to this query.
Unfortunately, the short answer is that there is no answer: to apply an amount of force necessary to keep a soccer ball aloft for at least 45 minutes would cause the ball to instantly disintegrate. If by some miracle the ball survived the initial impact, it would explode within its first few seconds of flight as the difference in air pressure between the inside of the ball and the outside atmosphere became too great. But those answers are boring and counter to the spirit of the original question (and counter to the spirit of The False 9 itself), so I’m going to ignore them. It’s time to get theoretical, y’all.
The Science
Let’s assume that we have a regulation soccer ball that is indestructible and experiences no drag effects whatsoever. Let’s then say that a player receives the ball at the opening kickoff and kicks it straight into the air at an angle perpendicular to the ground. We know how long we want the ball to stay aloft (45 minutes, or 2700 seconds), and we know the force that will be acting upon it for the duration of its flight (the acceleration due to gravity of roughly 9.81 m/s2). Thanks to the laws of kinematics, we can figure out the initial velocity of the ball that is needed to make this happen:
t = 2v0 / g, where t equals time, v0 equals initial velocity, and g equals gravitational acceleration
2700 = 2v0 / 9.81
v0 = 13,243.5 meters per second
So upon immediate impact, our ball will be hurtling straight up in the air at approximately 38 times the speed of sound. That’s pretty fast! I imagine that the resulting sonic boom would be indistinguishable from the sound of heavy artillery fire and the match officials would call for the game’s immediate postponement out of concern for public safety. Let’s ignore that too.
A regulation soccer ball has an average mass of 0.43 kilograms. With knowledge of the mass and the initial velocity, we can then calculate the kinetic energy exerted upon the ball:
Kinetic Energy (as measured in joules j) = (½)*mass*velocity2
(½)*0.43*(13243.5)2 = 37,708,912 J
37.7 million Joules is equivalent to 10.4 kilowatt hours, or roughly enough energy to power a single-family home in Austin for an afternoon in July. That’s not so bad, right? I mean, it’s still the force of 18 pounds of TNT being exerted directly and instantaneously onto a soccer ball, but it wouldn’t take a Hiroshima-level event to keep the ball in the air for 45 full minutes. It’s not an incomprehensible exertion of energy.
But the problem is that, once airborne, the ball would never come down.
Defying Gravity
To understand why, let’s talk about escape velocity. Escape velocity is the velocity any object needs to counteract the effects of gravity between itself and a celestial body such as a planet. Simply put, if a body moves at a fast enough speed away from a planet, then the body can “outrun” the gravitational pull back down. The body in motion would never reach the apex of its trajectory. Instead, it would merely slow down (but never stop) on its journey away from the planet. Escape velocity can be calculated for any planet using the following formula:
Vₑ = √(2GM/R), where G is the gravitational constant (6.674×10−11 m3⋅kg−1⋅s−2), M is the mass of the planet, and R is the radius of the planet.
On Earth, with a planetary mass of 5.9723 * 1024 kg and a radius of 6,371 km, the escape velocity is roughly 11,186 m/s. Thus, the initial velocity of our soccer ball (13,243.5 m/s) would be greater than the escape velocity of planet Earth. Once kicked, the ball would just drift off into the cosmos until it stumbled upon the gravitational field of some other celestial body. It wouldn’t even help if you kicked the ball at some incredibly shallow angle in the hopes of keeping it in suborbital space – any object moving that fast will always eventually escape the influence of gravity.
So even in our imaginary universe of indestructible, perfectly aerodynamic soccer balls, there isn’t any way to launch the ball hard enough to keep it off the ground for 45 minutes. Thus, when a team finds itself trying to kill off an entire half of play, the “the kick it really, really high” strategy is bound to fall short. Perhaps the simpler solution would be to smuggle a few high-powered leaf blowers onto the pitch and hope that the referee doesn’t notice.
H.E. Pennypacker
H.E. Pennypacker spends far too much time thinking about Austin FC, much to the consternation of his friends, family, and employers. He could really go for a sandwich right about now.