While I'm waiting for Bayonetta 2's release here in the states, I've been listening to the sound track, particularly the remix of "Fly Me to the Moon" waaaaay too much. It did get me thinking, though. Iron Man uses his repulsors for combatand propulsion. What if Bayonetta wanted to use her guns to fly? What if she wanted to fly to the Moon? Granted, I realize this is a bit of a stretch. I mean, she's a witch, so there's probably an easier way to do this, but let's just roll with it.
To figure this out we need a few things — first is the amount of energy it actually takes to get to the Moon. That's dependent on both the mass of our payload (in this case Bayonetta) and what speed we'd need her to achieve to make it the 230,000 miles. To figure how much Bayonetta herself weighs, we need an idea of how much space she takes up as well as her density. Lastly, we'll need to get a sense for how powerful her guns are and how much thrust they can provide. So let's get started.
Going off Brian Ashcraft's old article about Bayonetta being something around 250 centimeters tall is a little strange, but it's actually among the more accurate figures out there. Most others are straight estimations based on the average height of normal people, but even in her universe, it's clear Bayonetta isn't normally proportioned. So if we use the estimation of 250 centimeters, we can get a rough sense of scale for her legs and torso.
To get a sense for how much space Bayonetta takes up, I treated her legs as a set of cylinders and cones. For her torso, I estimated total surface area and used some standardized measures of torso thickness. Her arms were a bit tougher. Most pictures don't give you a clear sense of their size, but after I consulted some medical texts about what mass the arms have in relation to the rest of the body, I got a figure I was comfortable with. Putting all this together, we can roughly (and I do stress roughly) figure her volume as being the neighborhood 134,361 cubic centimeters. The average person is about 1.063 grams per cubic centimeter. Given that Bayonetta is skinny and extremely athletic, I found a higher figure for the average body density of women athletes in a medical journal (1.14 grams per cubic centimeter).
Combining those two figures tells us that Bayonetta weighs 153.171 kilograms, or 337.68 lbs. That may sound like it's way off, but it's actually pretty reasonable given her insane height. Most people aren't 8 feet tall, and those that are tend to weigh over 400lbs. Robert Wadlow, the world's tallest man was almost 9 feet tall and he was 492 lbs. Now that we know how much mass Bayonetta has, we need to get a sense for how fast we'll need her to be going.
For this figure I actually called NASA (something I didn't know you could just do until today). They explained that we'd need to know the total "Delta V budget" or change in velocity we need to achieve. This figure isn't affected by mass, though. It's just the number we need to achieve our goal of putting Bayonetta on the moon. Thankfully, the folks at NASA have this stuff pretty well figured out. The number I got was around 15.73 kilometers per second. That accounts for atmospheric drag and everything else. It also technically refers to two distinct numbers, one to achieve low earth orbit, and one to achieve a lunar insertion trajectory (fancy talk for putting someone on the moon).
With that figure we can calculate the total energy we need to put out, and not at all surprising to anyone, it's a huge number. Almost nineteen billion joules. To give that a human scale, that's the same food energy you can find in 15,791 Snickers bars. Now all we need is how much energy her guns produce with each shot.
Using her shoes and her height as a point of reference, we can see that her pistols are absolutely massive. The barrels have a diameter that's just over an inch. The closest non-military weapon of that size is .950 JDJ, which is, as you'd expect, .95 inches in diameter. Because a bullet needs to fit snugly in a gun barrel to be effective, bullets increase in size dramatically along with the barrel. That means they need more and more gunpowder to… well go as fast as bullets are supposed to. But in the case of the .950 JDJ, the bullets are so large that when they leave the gun, they have the same energy as a two-ton car going 20 miles per hour. That's one bullet. The guns used to fire these things are often over 100lbs and can only be fired from a bench or sturdy bipod. Each bullet has a whopping 52,450 joules of energy when it leaves the muzzle, and Bayonetta has four guns each kicking out these massive shells. I get that these games aren't realistic, but just firing one shot would shatter her arm.
Now, because Bayonetta is a witch, we have to assume that she reloads these guns with magic. That's lucky for us because it means we don't have to add in the weight of the fuel or anything else into our equation. All we need to do is divide the energy we need by the energy each shot provides. Our result is 361,292.1, or just 361,293 since she can't fire one tenth of one shot. Using gameplay footage we can also see that she fires up to 10 rounds per second. So if she were to use all of her guns at once and just shoot until she hit the moon, it'd take her 9,032 seconds to get up to speed. That's a lot longer than the Apollo missions which averaged a few short rockets burns lasting only a couple of minutes each. So strapping guns to your heels isn't exactly an efficient way to get around – even if you're a witch.
You're reading Numbers, a blog on Kotaku that examines games and culture through the lens of math and statistics. To contact the author of this post, write to firstname.lastname@example.org or find him on Twitter @dcstarkey.
Top Image:Robert Wadlow
Bottom Image: Optimus Break