A portion of today's episode is brought to you by the Google Pixel 3. (shut up and take my money!)
Miles "Tails" Prower is supposed to be an unmatched engineering genius. The guy has an IQ of 300,
he's a skilled mechanic, and apparently has...
"I built a TV out of paperclips."
"And reprogrammed a super computer using dishwashing detergent and a tooth pick." Basically, he can do
anything. Well, anything except fly.
That was embarrassing. At least he's got his tails! Or does he? (subtitles made by the following: Tyler Williams, Dalva phillips, and Olivia may.)
Hello Internet, welcome to Game Theory! Where today, we're rolling around at the speed of a relatively slow
tractor trailer.
Three months ago, I said I wouldn't be doing another Sonic physics video until 20 million subscribers,
but man! With everyone talking about that new real-life Sonic movie - and how could they not be?
I mean, look at those legs! Like really, look at them.
Ughhh...
Anyway, I figured now was THE perfect time to explore other ways that reality is gonna ruin this franchise,
meaning that I'm turning my theorist magnifying glass on to Tails. "But what did poor Tails ever do to you MatPat?",
said someone who has a lot of emotional attachment to a video game character. And to that I say...
He's actually had this coming for a long time! Ever since I learned how to do helicopter physics calculations back during the Chun-Li episode,
I've had Tails in my theoretical cross hairs to see if his tails actually have the lift power the game says they do,
or if he would crash and burn under the power of real-world physics.
Tails is unquestionably everyone's favorite
anthropomorphic fox who uses his tails to form a single-rotor system spinning fast enough to hover off the ground, propel himself forward at
some pretty incredible speeds, and even go fast enough to keep up with
Sonic - which, according to my old math, isn't that hard because he's slow but if you're following his canon top speed that's over Mach 1,
so pretty darn fast. Now, because we like Tails so much
we need to grant him a little bit of leniency here right off the bat. Having two tails
but presumably no actual rotor mechanism - you know, in that tushie region of his - Tails's
tails would actually just become tangled if he tried to spin 'em all the time. But to write off his powers...
That way is just no fun.
So we're gonna assume that he has some magic butt pivot going on in his foxy hindquarters to make it happen.
I'm also gonna assume that the planet Mobius isn't dealing with any intense wind speeds and that, basically, he's functioning in our own atmosphere,
otherwise, we would just have nothing to base our calculations on. So, with those ground rules set,
we'll be busting out our calculators and comparing what we know about Tails to real helicopter aerodynamics
to see if he truly has what it takes
to take off. To find out if anything will lift off the ground,
we need to know how much it weighs so we know how much gravity we're gonna be fighting against. According
to Sega, Tails has a canon weight - yeah, you could learn a thing or two Nintendo - of 20 kilograms, which is one enormous fox,
by the way. Foxes usually top out at about 14 kilograms or about 30 pounds, whereas Tails here is 20 kilograms or over
44 pounds, the weight of an average six-year-old.
SO...
Already, Tails's chunky frame ain't gonna be helping out his lift off because Tails would have to generate 196.2
Newtons of force to enter a stable hover.
The next important factor is the length and width of each tail, and when you detach and measure the size of his fully extended
tail against his body, we can see that each tail is equivalent to his canon height of 0.8 meters.
We can also measure that the width is
0.26 meters but these measurements aren't the same for all Sonic games, 'cause of course they're not. The math is never that easy.
So here again,
we have a measurement for classic Tails and another one for modern Tails, where
original Tails's tails extend to the ends of his body and modern Tails's tails extend past his body, giving him a larger propeller
length and thereby making it easier to generate lift. Eh, not looking so bad for the little guy. And by little guy,
I actually mean enormous guy. Remember, he is larger than even the largest of foxes.
So, with that now doubling all the calculations that we need to do, all you Sonic apologists in the comments -
don't say I never did anything for you. Now on to the fun part, turning Tails into a helicopter.
Helicopter physics is really complicated
so we reached out to some engineers from Duke University to help us out with the math and the equations for this episode.
So, if you remember our work with the Chun-Li Skull Crushing kick,
we started talking about helicopter physics there and we'll be able to use those same principles as a jumping-off point for this theory.
Helicopter physics is based on the idea of lift, which is essentially the force needed to overcome gravity and get something off the ground.
Thanks to Newton's Third Law, planes can lift off the ground when the force upward underneath the wings becomes greater than gravity, but
helicopters work a little bit differently. because they don't glide through the air, they rotate.
So, we can start off with the equation for lift
which you can see here. Lift equals: one-half times
Rho times V squared times the coefficient of lift times the area of the wing
BUT we actually need to change a couple things here.
You know how when you do anything with a circle, all of a sudden you have to calculate everything in terms of pi and the radius? Well
it's the same deal here because helicopter blades move in a circle to generate lift.
So, when we're working with this equation
we're gonna end up solving for V - the velocity of the blade spinning - but V is actually gonna be something called angular velocity.
I'm gonna make a judgement call here and save you the headache of walking through some of the behind-the-scenes math here because I'm assuming that
people who clicked on a video about learning if Tails could fly are probably not super invested in deriving an equation for radians.
But, if you ARE one of those people and you ARE interested in the details, well,
I have a link to this type of math down in the description that you are more than welcome to check out.
Look at me! Citing my sources!
Truly, I am a changed man. Actually, that's not true my sources
technically, were Duke University mathematicians that I could talk about this in real time,
BUT, here is a source that you can use that vaguely
approximates some of the conversations that I had with them. So we can now use our equation for lift and plug in all the stuff
we know, which is, surprisingly, a lot. The lift equals Tails's weight.
Remember, that is the force that we need to overcome
which is just his mass times gravity or 20 kilograms times gravity at 9.81 m/s². The area of the wing in meters
we just replace with the area of his tails in meters, and this is specifically referring to the actual area of his tail not the
circles that they create when they're spinning in air, which in our case is 0.208 meters squared in classic Sonic and 0.416 meters squared in
modern Sonic, and Rho is the density of air at sea level which is a constant 1.225. It's actually surprisingly simple.
You only see these things in equations and you're like, "Oh, that's a really intimidating Greek letter,
how am I ever gonna solve for that one?" but 9 times out of 10
it's just like look it up online and just plug it in.
The only thing we don't officially know is the coefficient of lift which is
extraordinarily difficult to calculate when you're dealing with things that shouldn't technically be used to fly.
So I'm just gonna give it a similar estimate to what we did with our Chun-Li calculations: 0.2. Just for reference,
that's a very low coefficient because, to be fair, a live fox similar to a pair of female legs would not make for an efficient or
aerodynamic helicopter. From this point we could just plug and chug our way through this equation and we get ourselves an answer in the form
of radians, which, again...
circles.
Luckily radians can be easily
converted to miles per hour which tells us how fast the tails need to spin to get Tails to hover off the ground, which is
337 miles per hour for classic Tails and
240.5 miles per hour for modern Tails.
Oh boy! That is one fast fox. Or, at least, his butt is fast. Anyway, it's
surprisingly typical for a fox-sized
helicopter. Our rotating tail speeds equate to 1343.4 revolutions per minute -
1,000 revolutions per minute for modern Tails and
3630 revolutions per minute for classic Tails
- which actually matches with drones that fly using very similar rotor mechanisms like mini helicopters.
Big helicopters with massive blades might have a typical rpm of 400 revolutions per minute,
but the smaller the blades, the faster you have to spin those blades to fly,
which is why heavy lift drones similar to the weight of Tails actually have a rpm of a thousand or more,
just like our foxy little friend here. This one, for instance, goes up to 6300
rotations per minute.
So, yeah.
Biologically speaking, a fox with two tails that are
permanently attached to his butt with no rotor system trying to make 1343
revolutions per minute of those tails? It ain't gonna happen. It is physically impossible.
BUT if you assume that Tails does function like a helicopter, and you compare him to other similarly sized helicopters
the math makes perfect sense. His calculations aren't totally ludicrous.
Hey, I can't believe it! First, Sonic doesn't have arthritis from running so hard so fast, and now, Tails can actually fly...?
It's like some sort of Sega curse on my theories. Must be retribution for calling Sonic slow or something.
No, there's got to be something here. There's got to be something that
~gasp~
not so fast!
Take a look at this picture of Tails, and now take a look at this picture of an actual helicopter. You notice something off?
Yeah,
outside of the fact that one is a precision piece of flying
technology and the other is an anthropomorphic fox who does not really exist. The thing to notice here is that helicopters have two
rotors. They've got that big one on the top like Tails, sure, but most of them also have these other ones in the tail, and it
turns out that's not just like a glamour rotor that's just there for decoration.
The reason for that small rotor tail - or other secondary rotors that you see on helicopters - goes back to the most fundamental
physics out there.
Newton's Third Law tells us that for every action there is an equal and opposite reaction.
Helicopters are no exception.
If you have helicopter blades spinning in one direction,
that means the helicopter underneath is spinning circles in the opposite direction.
So, when he actually got up in the air, Tails's tails would be spinning in one direction
exactly as fast as his body would have to be spinning in the other.
Single rotor helicopters avoid this problem in the real world with tail rotors - the small blades on the tail that spin in the opposing
direction to the top blade - specifically to counteract the forces that are making the helicopter want to spin itself into oblivion.
Without those tail rotors, the helicopter is completely unflyable.
It just becomes the world's most intense eggbeater ride ever.
In fact,
all functioning helicopters have to have two rotors somewhere on them specifically because of this problem.
Even drones have an even number of rotors on them that are spinning in opposite directions
for greater control and stability. Without
any sort of counter rotor system to keep him steady,
Tails isn't just not gonna be able to keep up with Sonic. He is spinning completely out of control.
So, in the most ironic twist of this whole theory,
it looks like the thing Tails is missing is - you got it - yet another set of tails.
Oh, sure.
All the math proves that he could absolutely fly, or at least make it off the ground in a basic hover-y sort of way.
But once he was up in the air,
he'd have no control over his directionality because the thing that gives
helicopters their ability to actually go anywhere isn't the blades on top,
It's the blades in the tail. If Tails could design himself a tail rotor assembly to wear while he flew - like, say, on his foot
or something - he could technically have a chance, but as he's currently biologically structured now, Tails, just like every other fox, is grounded.
Done in by physics yet again.
BUT HEY, that's JUST A THEORY! A GAME THEORY!
Thanks for watching. Sure the math may not have added up for our two-tailed friend,
but you know what it does add up for? Our sponsor for this part of today's episode
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I need to go figure out what next week's Game Theory is on 'cause I'm not 100 percent sure...
Red Dead Redemption, maybe? I have a lot of theories on Red Dead. Hmm...
Subtitles By: Bryson Fisher. Edited by Tyler Williams and others.