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

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


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.

100 thoughts on “Game Theory: Could Tails Really Fly? (Sonic the Hedgehog)”

  1. 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

  2. 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?

  3. 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

  4. 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.

  5. 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.

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

  7. 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

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

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

  10. Every action has an equal opposite reaction,
    thanks to hamilton our parties are breakin' down like fractions.

  11. 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…

  12. 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

  13. 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?!?!?!?"

  14. 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.

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

  16. 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

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

  18. 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?

  19. 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

  20. 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)

  21. 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.

  22. 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

  23. 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

  24. I have a theory, could tail's twin tail's might have a special piece of bone or organ in his butt that allows him to fiy???

  25. yet you wold be right but tails tails spin won way and then anuther… like he twist them up then he untwist them and then twist back up and so on.

  26. Look I'm not a Sonic fan, I'm really not. But I played one Sonic game in my childhood…
    It was Sonic Adventure. Here he gets an upgrade to his shoes. The jet anklet. So with jets attached to his shoes he should be able to counteract the spinning out of control. Meaning he can fly… In one game and one game only.

  27. This suggests that Mobius is unlike planet Earth, and that this universe in which Mobius is located does not obey the same scientific laws that our universe does.

  28. Now just saying it may not be possible for tails to fly but what about using his tails for horizontal thrust like he does when he is fallowing Sonic in some games.

  29. Actually you could fly with one rotor, but you have to keep going forward, and have aerodynamic design, the wind rushing pass the aircraft would keep it straight. This is a tactic used in the event of tail failure.

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