These days, video games are becoming closer and closer to looking like real life. Battlefield 4 is one such example, with vehicles and weapons modeled down to the very last detail. In many ways, Battlefield 4 attempts to create a realistic and immersive environment. And then there’s this.
Yes, that is a tank being launched into the air with C4 and shooting a jet out of the sky. For all of its realistic graphics and audio, Battlefield 4 has to compromise on gameplay, and one of those compromises is friendly fire. In real life, the tank would just have been blown to smithereens, but in Battlefield, it takes no damage because the C4 was detonated by a teammate. Instead, all of the force of the C4 is transferred to the tank, propelling it into the air.
But would this really be possible? What if all of the force of a C4 explosion could be used to launch a tank? How much C4 would it take to do this? In order to calculate this, we need a very basic understanding of kinetic and potential energy. Then, we can C 4 ourselves. (ba dum tss)
First, I need to make a very rough estimate of the vertical distance that the tank traveled. In the third person view of the video (just over a minute in), you can see the distance marker on the tank which tells us how far it is from the viewpoint. It appears that the tank begins at 63 m away from the viewpoint and reaches its maximum height about 90 m away from the viewpoint. I’m going to assume that the tank is horizontal with the viewpoint at the beginning and that it travels completely vertically (both of these assumptions aren’t true if you look at the video, but bear with me here). Then, we can draw a simple right triangle:
The ’93’ should be a ’90’.
The Pythagorean theorem can tell us h, the vertical distance traveled by the tank. It’s about 64 m. When the tank is 64 m in the air, it has a certain amount of gravitational potential energy, and no kinetic energy. As it falls to the ground, this potential energy is converted to kinetic energy. Just before it hits the ground and explodes, all of the potential energy has been converted to kinetic energy. The amount of kinetic energy right before it hits the ground is the same as the amount of potential energy at its maximum height in the air.
In order to launch the tank into the air, we need to do the opposite: create kinetic energy which is then converted to potential energy as the tank rises. Therefore, to calculate the kinetic energy to launch the tank all we need to do is calculate the potential energy of the tank in the air.
Potential energy is equal to mass * gravitational acceleration * height. The mass of a Type 99 main battle tank, according to Wikipedia, is 55 metric tons, which is equivalent to 55,000 kg. The gravitational acceleration of Earth is 9.8 m/s^2. So we can plug in the numbers and find that the potential energy is 34.5 megajoules. Therefore, this is the same amount of energy required to launch the tank 64 m into the air.
According to WolframAlpha, 1 kg of TNT can produce an explosive yield of 4.2 megajoules. This table on Wikipedia tells us that C4 is 1.34 times as effective as TNT, so 1 kg of C4 produces 5.6 MJ. It would require 6.2 kg of C4 to launch a tank 64 m into the air. Of course, this is assuming that all of the energy of a C4 explosion is converted to kinetic energy, and none of it is converted to heat or sound energy, and that energy is somehow perfectly transferred into pushing the tank instead of dissipating into the air or ground.
In Battlefield 4, C4 is used in small packs, which look like this:
http://bf4central.com/wp-content/uploads/2013/08/battlefield-4-c4-explosives.jpg
In order calculate how many packs of C4 are required to generate 34.5 MJ, I need to know the mass of 1 pack of C4. I wasn’t able to find this online, but I was able to find the texture sheet used by the C4 model. Credit to elementofprogress for extracting this texture from the game.
According to this, 1 pack of C4 weighs 1.14 lb, which is about half a kilogram. Therefore, it would take just over 12 packs of C4 to launch a Type 99 tank 64 m into the air. Unfortunately, I’m not sure how many packs of C4 they used in the video, so I can’t tell you how accurate the game is. But sometimes, it’s just way more fun to be unrealistic!
go4-cracks
On C4 and flying tanks | May The Mass Times Acceleration Be With You
This is such a great post, both funny and informative. With my military knowledge, I know for a fact this cannot happen. The current US Battle Tank, the M1A4 Abrams, has never been destroyed by the enemy, and its been used since before Desert Storm. There would be A LOT of C4 to cause even slight damage, and it would require large, large piles of the C4, to the point where I would hope the driver could see the danger and drive away. But, then again, it is a video game….
I like how you included footage from “Myth Busters.” I used to watch it all the time. It seems you have the same interests as them. I like how it is clear to see the effort you are putting into your blog by adding multiple forms of media which urge your reader to continue so they can understand the content of the added videos and pictures. Awesome!