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 Google’s Pixel 3 phone, which, in addition to being an incredible smartphone is also, without question, the single best camera that I own. And because of what we do for a living, we own a lot of cameras. Way too many cameras, in fact, so saying that a phone is our best camera is pretty high praise. Let me explain. Say hypothetically you’re a blue hedgehog who was born in the 90s and who runs around at the speed of sound, but you still want to show the world that you’re hip and cool. Well, first order of business, don’t make a live-action movie about your exploits. You’re just gonna get a lot of hate for that sort of thing. But what you can do is get that online photo profile up to snuff. Enter the Pixel 3’s camera. Most cameras that try to capture you mid-run will literally turn you into the blue blur. But not the Pixel 3! The phone’s motion autofocus tracks a subject while they’re moving, ensuring that you’re getting the best selfie on the go – even when you’re REALLY on the go. And that’s not all. Let’s talk top shot. Every time you press the shutter button, the phone’s camera is smart enough to capture 15 separate frames and the AI in the phone actually recognizes which one is the best, literally offering you THE top shot. Closed eyes? No smile? No more! Your eyes are open and your smile is wide every single time, unless of course you’re my grandmother who doesn’t really like to smile, so in this case your eyes are open and your smile is there under the surface. Long story short? You’re taking fewer photos to find the perfect post. Not that it matters anyway because with the Pixel 3 you get unlimited storage of all photos that you ever take with Google Photos, which uploads them to the cloud automatically when you’re on a Wi-Fi connection so you never have to waste another minute or another megabyte syncing photos manually or risk running out of space. Efficiency, thy name is the Pixel 3. And speaking of speed, since we all gotta go fast there’s the super fast fingerprint sensor on the back that unlocks your phone before you even see the screen. No more swiping in patterns or facial recognition locks. You simply unlock your phone with a simple swipe of your finger as you hold it. It’s a feature that single-handedly, or, should I say, single-fingered-ly converted Chris – a guy on our team – to become a Pixel user, and he’s never turned back since. Add to that wireless charging and what you have is more than a phone. It is a life optimizer. So to find out more about the Pixel 3, click the link in the description. #TeamPixel! Now, if you’ll excuse me, 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.

## 100 Comments

have you ever taken a rope or string and spun the end of it like fan or rotor blades? tail's tails could "spin" using the same principal without needing a pivoting joint.

3:29

I like em big, I like em-

1:59

Tails is everyones favorite anthropomorphic fox

Fox mc'cloud: hold my beer

Nick Wilde: hold my pawpsicle

Robin hood: hold my bow

Mr. Fox: hold my animation

Tod: hold my hound

All the eevelutions: hold my evolutions

MAJIRA STRAWBERRY:

laughs in gayBUT IM REALI was playing sonic while watching this video 😂

MatPat…. naturally Tails would weigh more than a normal fox…. he's an 8-year-old Anthropormorphic yellow fox.

Also, stop applying logic to the Sonic series. I learned that long ago.

best sponsor ever

PIXEL BEST PHONE

How the heck did I miss this?

What if the two tails are spinning in opposite directions?

I like soinc

What about spy kids pigtail helicopter

Did anyone hear fgteev walk like Shawn

Tails and Amy Rose are my fav

Wait a second… Just wanted to double check something. You took Tails' weight of 20 kilograms and multiplied by the force of gravity.

Did you need his 'Weight' or his 'Mass'?

I've always understood (correct me if I'm wrong) that your weight was your mass multiplied by the effect of gravity. It's why your weight on Jupiter would be different than on Earth, but your mass would be the same.

If you needed his mass but used the 20kg, that calculation of 20 multiplied by 9.8 would essentially be his mass multiplied by 9.8 twice.

What if tails has tail move one way and one is moving the over way

Hai

L: lifting. I: irregular. F: flying. T:Tails

L.I.F.T

I love tail

its a game geeze

MAYBE HE USES ONE TAIL AS THE TOP BLADE AND THE OTHER AS A THE BACK BLADE

ray the squarle is a plane and tails is a helicopter k

How dare you mess with tales

#MATH

9:09 sonic.exe wants revenge

9:23 this is the only thing I notice

Wow your trying hard to prove tails can't fly,are you sure you did'nt miss anything?

Well tailes isn't real so physics don't really have to affect him so he could fly without the tale blade if the creator saids he can so this was a waste of time but entertaining

what if one tail spines clockwise and the other anti clockwise?

I have a question now we know you said sonic isnt as fast as they say he is but lets say he is and the boosting in the modern games makes him faster exactly how fast would that be and would it be deadly to him?

10:17 I see that Slovakia symbol or erb i didnt know we have money forsomething like that

Huh

1

my god this dude is cringy, it's been years since I last saw a video of his and he's still using that picture of him holding his chin as a meme (except he's using it so much in this video it's almost reached the point of self obsession), guess there was a reason why I haven't watched this anymore

If Tails has some magic butt pivot, wouldn’t that magic allow him to fly?

When he said "miles per hour" I thought he said "miles prower"

You forgot to mention, Tails has another friend called Cream the Rabbit. She can fly with her ears, but I’m pretty sure she can’t go as high as Tails.

Which fox is better Foxy from Five Nights at Freddy's or Tails from Sonic boo

What if he uses one tail for flying and the other is used for control 🤔

Wouldn't this mean that every time Tails flies he is ripping his own body apart? If his tails spinning one way means his body spins the other, and you know, screws tell us that if two attached devices go the opposite direction, they detach.

can you explain how rose(black pink) turning her hand not trying to be rude, your theory is true but tails could have that

WHAT IF ONE OF HIS TALES SPINS THE OPPOSITE WAY????????? WHOULD HE FLY???????

see there's one thing you didn't catch matpat, is that what if tail's left tail is going left and tail's right tail is going right? I've finally beat you matpat >:D

what if one of tails tails is spining twice as fast,and the other is the counter acting proppeler so he can fly

i'm wondering how does tails survive the plane crashes?

It looks like you trying to expose them😒😒😒😒😒😒😒

you can see that effect of out of control in GTA V when you shot the helicopter in the back roter (is that right?)

Wat!!!!!!!

Matpat: "Could tails really fly?"

Tails:

"Hold my bear"What if one tail spins in opposite direction

tails has 2 tails so why would he not be able to use one as a counter roter

I love how it’s totally normal for MatPat to have a 20 second intro.

This video is kinda wired

Every action has an equal opposite reaction,

thanks to hamilton our parties are breakin' down like fractions.

I know how it can work

MAGIC!!!

Take that into consideration MatPat!!!

Revolutions per minute is how the the French measure most things

So I get that you're saying about Trails needing a second rotor to counteract the habit of autorotation in helicopters (the counter-spin if the body relative to the rotor). My idea centers around the concept of coaxial-rotor helicopters that have two counter-rotating sets of rotors on a single mast. No need for a tail rotor because the spin of the second rotor in the opposite direction to the first counteracts the force of the other. It's less stable than a traditional rotor arrangement, but it offers far superior maneuverability and speed. So… if Tails does function as a helicopter and can spin his tails that fast, would it not be possible for his twin tails to counter-rotate as a coaxial rotor helicopter would? After all, we don't ever see the direction of the individual tails, just a blur that indicates they're spinning…

He goes to much into his videos

He milks it XD

I feel like you are focusing on the wrong flying character here I always felt there was some explanation for tails but meanwhile cream never made sense her ears can make her fly and it’s just weird because how do those small things hold her up

Lol tails the 🦊

If you didn't now his tails spin in opposite directions.

Anybody else hear walk like shawn in the background..?

I know a lot of people that take your theories seriously and I'm just like "do you even HEAR what he says at the end of EVERY VIDEO?!?!?!?"

He's a kitsune. He doesn't have to abide by the laws of reality.

There is a helicopter that has no tail rotor called a K-MAX. It is a very funky looking helicopter and thin as well. It has 2 blades spinning at an angle. Still with tails only spinning both tails the same way as in the game he could not fly. Maybe if it was more like how the K-MAX then it would be a maybe.

Amy's Hammer.

what if his tails spun in different directions?

I think Tails should quit his flying planes job

He just builds planes to crash them over and over

Dude I’m not going to lie watching that part where tails was spinning around while flying, made me laugh harder than it should 😂

You always ruin everything

You are the worst

11:46 do it

Average weight of a 6 year old? Isn't tails cannon age 6 years? Sega does more research on real life things than nintendo. Then again modern sonic games are meant to be more realistic

Y u do dat

What if one of his tales spins in one direction and the other spins in another? Would this make sense?

He built the tails into himself so he can fly because of science.

Miles prower=miles per hour

Favorite character (tails)

I'll never get tired of this intro music

Did any of you here the music in the background it sounds like walk like Shawn

Everyone already knows that

What if he spun 1 tail in each direction would that not fix the spinning?

Hey MatPat you didn't not mention that Miles Prower practice his tails for years, that makes him a little bit of weight. Have you even noticed Miles Prower can still fly even though he is still a child since he was created, also have you noticed that Miles Prower practice his tail for 18 years?

Tails is a kitsune but he don't have powers like a kitsune should have

Okay wait tails. Body lens the way he wants to go

7:39

Thats Tails’ name.

😱

Why do u think maro is faster than sanic?

Actually mobius atmosphere is 2x our own.MAT PAT!!!

I have a theory tails can't die so when sonic dies he respawns so does time reset to when you hit the last check point A-does the checkpoint control time B-when sonic dies does time reset C-can tails die

if tails can make a paperclip TV he can fly like a helicopter matpat it dosent take even science to know that

MatPat, if you see this comment:

I did the research, and on the low end, helicopter blades are 40 ft long. Multiply this by pi for the circumference, and then by 60 for feet per minute. Then for Miles per Hour, divide this by 5280, and you get that a small helicopter blade spins at approximately 14.3 miles per hour. Tales has, on the low end, 1343 MPH…

Now divide this by 2 for the average for 1 tail, which will be 671.5 MPH. For one tail. And he has 2. He has more than enough Miles per Hour per tail to have one act as a front propeller and one as a back, especially since in both cases his tails AT LEAST are as long as his body…

Please reply if you have a reason why this is wrong, I am no university head scientist, so please correct me so I can see what I did wrong. Also, I only did the calculations for Classic Tails, the faster of the two, then later found out it even works for Modern Tails. So, MatPat, if you see this, and it turns out to be right…

Game Theory: Could Tails Really Fly? (Sonic the Hedgehog) (PART 2)

How has tails a IQ of 300 if he is official 8 years old.

8:37 I heard of the story of Tails' (Miles Prower), it was in real an birth mutation, that caused his two tails and propelling ( and fly ) ability.

9:07 I'm kinda starting to be an Sonic.EXE fan.

C'mon man ıt's just a game

Where’s the Knuckles theory? He can glide, climb walls, and punch open walls with a single punch. You have a lot to look into

But tales does fly and if he can’t then how does he

oh yeah and how does reqaza fly?

This is funny for some reason

Me : oh math time!

Matpat:u know what I'm going to skip the math!

Me:noooooo

Matpat:go check the link

Me : left the vid

1:35 me