Hey there, and welcome to Play Noggin.
I'm Julian, your brain's Player Two.
Few characters embody the 90s like Sonic the Hedgehog.
At the time of the first Sonic game's release, he oozed more attitude than any game character
before him.
I mean, come on.
Did you want to play as a chubby plumber in overalls?
Or a way-past-cool hedgehog with rad red sneakers?
Probably, the choice wasn't up to you -- you got the mascot of whichever console your parents
bought for you.
But for Sega kids in the 90s, Sonic was THE BEST.
Sonic's whole thing is his speed.
The opening song of the good Sonic the Hedgehog cartoon makes the claim that he's "the
fastest thing alive."
Yeah, I called it the good one.
Come at me.
Now, in reality, hedgehogs aren't known for their speed.
In fact, they top out at around 10 kilometer per hour (~6 mph), and even then they only
achieve that speed in short bursts.
They do roll up into balls to protect themselves, but spin dashing is right out -- their quills
would catch the ground and keep them from going anywhere.
And in the wild, foxes prey on hedgehogs.
Sure, Tails might LOOK adorable, but he's making plans.
Dinner plans.
Eesh, get away from me, you little monster.
Anyway, let's assume he is the fastest thing alive except for when Eggman is making his
escape.
Then he must be faster than the real world record holder, the peregrine falcon, which
tops out at over 320 kilometers per hour.
Maybe that's not a fair comparison, since the falcon hits ludicrous speeds thanks to
gravity and amazing aerodynamics while Sonic's got to do it by pounding pavement.
The fastest thing running is of course the cheetah, which can clock in at 120 kph in
short bursts.
If we want to be even more generous, we can say Sonic is the fastest thing on two feet,
beating out the ostrich's top speed of over 97 kph.
Of course he's named Sonic because he's supposed to be able to run at the speed of
sound, which is 1,225 kph at sea level.
It gets slower with altitude though because sound travels through air and when it gets
thinner, the speed of sound slows.
You may have noticed I'm meandering a bit and that's sort of the point.
Sonic's speed has been done to death, and you'll get a hundred different answers depending
on who you ask or what game you play.
Players who have measured his height and compared it to the time it takes to complete a level
report he only runs 36 kph, but he's been different heights in the same game.
The game claims he can run at the speed of light provided he's wearing the right shoes,
which is impossible IRL, regardless of how fabulous your footwear.
So rather than muddle through all that we wanted to narrow the focus a bit and look
at how Sonic's speed relates to how he handles loop-de-loops.
Admit it, when you were a kid playing Sonic 1 for the first time, the moment Sonic flew
down a hill and up and around a loop, you lost your prepubescent mind.
It's nothing to be ashamed of.
The human body was not built to handle the Sega Genesis's BLAST PROCESSING.
We take it for granted that Sonic, moving as fast as he does, could easily clear a loop
like that.
But what sorts of physical laws are at play to make that possible?
Whether it's Sonic or a toy car or a real car, it's amazing to watch something do
the loop de loop because our experience tells us that at the top of the loop it should just
fall down.
That's the point where gravity is pulling on Sonic and the track has flipped from supporting
him to working against him.
So just what's keeping him up there?
You may have heard the term centrifugal force used to explain what keeps objects from falling
down, but it turns out it doesn't actually exist.
Sure if you've ever ridden a roller coaster through a loop it feels like something is
pulling you outward, but it's an illusion.
If the roller coaster car were to suddenly derail it would shoot off tangentially to
the loop before horribly killing you because objects have a property called inertia, and
when they're in motion they tend to travel in a straight line unless acted on by an outside
force.
That "outside force" pulling you in towards the middle of the loop is called centripetal
force, and in the case of the roller coaster or Sonic's loop it's provided by the track.
Combine inertia and momentum, and to the object in the loop it feels like something is pulling
it outward.
That's the apparent force known as centrifugal force.
Still, you can use this apparent force to calculate just how fast sonic would need to
travel to avoid being a spiky splat on the ground below.
Up there gravity is pulling him downward, and assuming he's on Earth it's doing
it at about 9.8 m/s2.
So Sonic has to be traveling fast enough at that point that at the very least, the force
of gravity would make him travel in a curve that's the same radius as the loop.
The formula for that equation is Velocity = the square root of gravitational acceleration
times the length of the radius.
Since gravity is always going to be the same, that means that's sonic speed for successful
loopage is dependant on the radius of the loop, and the bigger the loop, the faster
he goes.
Though it doesn't scale linearly.
If he was in a loop with a 5 meter radius, he would have to be going 7 meters per second
at the height of the loop.
If he ran into a circle with twice the radius, 10 meters, he wouldn't have to run twice
as fast, but just under 10 meters per second when he hit the apex.
It's important to note that at that speed he would start losing traction because he'd
be going just barely fast enough to stay on the track, so to be safe he'd have to run
a little faster to keep his feet planted.
And he'd need a higher entry speed because he'd lose some when he started going uphill
and had to fight the force of gravity on his way up.
Keep that in mind if you're going to try this at home.
Also don't try this at home, just play Sonic instead.
Or ride a roller coaster or something.
Of course a roller coaster isn't a perfect comparison.
They're clamped onto the track, so even if it doesn't have enough speed to make it
around the loop, worst case scenario you get stuck upside down while you wait for rescue
and the lunch you just ate to show up.
Not comfortable, but better than plummeting to your death.
While you're up there you might notice that the loop is not a perfect circle like the
loops in Green Hill Zone.
They're slightly more tear-shaped, as though they were pinched at the top.
These are known as clothoid loops.
And they have some advantages over perfectly circular loops.
Because the initial curve has a longer radius, riders don't feel as many gs on the gentler
curve.
But because the radius at the top of the loop is much smaller, the car doesn't have to
travel as fast to clear it.
It also means that the car can have a lower entry speed, and you want that as a rider
because a coaster car, unlike Sonic, doesn't have a way to propel itself.
Still if you need to feel like a hyperfast bolt of blue, a roller coaster is the closest
to being Sonic the hedgehog most of us are ever going to get.
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