Hey, Vsauce, Joey here. Sonic the Hedgehog- every gamer knowns him. But, I ask you to
consider the implications of a human-sized blue hedgehog that can run at supersonic speeds.
It's time to explore the science of Sonic.
But first, a question: How fast can Sonic run, officially? Well, some games show Sonic
running at up to 5 times the speed of sound, or more. Plus, there's that whole lightspeed
dash which explicitly states that he can move at the speed of light. But, according to Einstein's
Theory of Special Relativity, that would mean Sonic either has no mass or uses infinite energy.
Both options give me a headache, so, let's stick with the possibilities that don't break
physics.
At the very least, there's consistent proof over the years that Sonic moves at least at
the speed of sound, which is 768 MPH, or 343 m/s at sea level. This is otherwise known
as Mach 1, and each multiple of the speed of sound is Mach 2, Mach 3, and so on.
Some real life references might be helpful. Normal hedgehogs are known to sprint up to
6 MPH, less than 1% of Mach 1. The record for fastest human goes to Usain Bolt, who
can run up to 27 MPH. The fastest land animal in the real world is the Cheetah, which has
a top speed of 75 MPH, or about 1/10th of Sonic speed. And the fastest animal on the
planet is the Peregrine Falcon, which, in a full dive, can reach 200 MPH, about 1/4th
of Mach 1.
So, it turns out that there's nothing in nature that really comes close to Sonic the Hedgehog.
So, what effects might breaking the sound barrier have on an unprotected hedgehog? Well,
Sonic's about the weight and height of a small human, so, let's treat him as such.
On October 14th, 2012, Felix Baumgarnter became the only human to travel faster than the speed
of sound without the aid of a vehicle. You can try this at home by skydiving from a height
of 39 KM.
Felix reached the speed in an atmosphere that was thinner than what we experience at sea
level, meaning that the speed of sound was slower where he was. However, he still achieved
Mach 1.24, so, his experience is useful. For one, there was no undue stress on him caused
by breaking the sound barrier- Felix didn't even notice it.
People don't feel velocity, they feel acceleration, which is the change in velocity. If you're
traveling down the highway at a constant speed, you'll feel the same forces as you would sitting
on a park bench. But, come to a sudden stop, and you'll feel that change in acceleration.
Roller Coaster's can accelerate people at up to 2 or 3 times Earth's gravity, known
as a "G." Military pilots are conditioned to handle combat maneuvers at up to 7 G's,
which would make most people black out.
Attributing the same limitations to Sonic, we find that he can go from 0 to Mach 1 in
about 5 seconds without fear of losing consciousness. And that holds for slowing down, too.
But, if there's one thing that people know about supersonic travel, it's the "sonic boom."
An object creates a series of pressure waves when it moves through the air- much like a
boat in water. These waves travel at the speed of sound, and, as the object, itself, breaks
the sound barrier, they're compressed into a shockwave cone that travels behind the object.
Plane's often cause sonic booms, but would Sonic, himself, cause a sonic boom? If we
go back to good ol' Felix, he gives us some insight. He did create his own sonic boom,
but, it was a relatively quiet one. There exists a figure to characterize the intensity
of sonic booms, called the "Figure of Merit." Anything below a value of "1" is considered
an acceptable level of annoyance to observers. The concord, a supersonic passenger jet, had
a value of 1.4. An object the size of Sonic, or Felix, approaches a figure of merit of
"1" only in close proximity- within 5 meters or so. Outside of that, you probably wouldn't
notice them at all. A humanoid simply doesn't displace enough air to be a wide-ranging disturbance.
Another question involves Sonic talking at Mach 1: Would you even be able to hear him?
Sonic, himself, and any friends traveling at the same supersonic speed next to him,
would not be able to hear him at all, since Sonic would be moving faster than the sound
escaping his mouth. Everyone's ears are situated infront of the sound wave cone.
For stationary observers, anything Sonic says would be compressed into that shockwave, and
just add noise to the previously discussed sonic boom. And, besides, at Mach 1, he wouldn't
be able to say anything intelligeable anyhow. In the time it takes me to say this sentence,
Sonic would have already travelled one mile. It doesn't make for good communication.
Another thing to consider is that high speeds, heating due to air friction, or, more specifically,
drag, becomes a concern. If you stick your head out a car window going down the highway,
you've met drag-force.
Basically, air is dense enough to push back on any object that enters through it at a
high speed. And that work done can create heat. The question is, is this heat significant
enough to effect Sonic?
As speed increases, the drag-force that an object needs to overcome is squared. Take
an object the size of Sonic, assume he's a sphere, not hard to imagine, and this force
can reasonably be fully converted into thermal energy. Using that assumption, Sonic would
heat up at a rate of 37 degrees Celsius, per second.
Now, this is a rough number and doesn't account for factors that would make Sonic cooler or
warmer, like convective cooling through the atmosphere, or adiabatic heating, respectively.
One could convincingly argue that the heating Sonic experiences would only be a fraction
of this because of the cooling effect of the wind whipping by his face. But, it gives us
a good idea of the forces that Sonic needs to work against on a daily basis.
This actually makes more sense in the context of the short sprints Sonic utilizes. He can
only run for so long before he needs to cool off for a bit. The real life effects of such
heating can be seen with the SR71 Blackbird. It generated so much heat while flying at
Mach 3, that its titanium skin plates were designed with gaps in between them that actually
leaked fuel while sitting at rest. But, this design allowed the heated plates to expand
during flight and fill the gaps, ensuring supersonic travel didn't tear the skin apart.
So, with all that in mind, I have one more question: How much energy would Sonic expend
to run at the speed of sound? Everyone knows that jogging is great exercise, so, hey, Mach
1 probably really sheds the pounds.
Well, there are two really relevant forces at work here: The first is the energy Sonic
uses to move his legs- literally get up and go. Using a Harvard health study that shows
calories burned while running, we could extend that data out from 10 MPH to 760. Granted
it's very sketchy to extrapolate data, linearly, that far, but, it's the best approximation
we've got. That said, we could expect Sonic to burn about 2500 calories if he runs at
the speed of sound for 2 minutes. That's about the average of what it would take him to run
through a stage at full speed; however, that darn drag-force means that Sonic must expend
more energy to simply push back against the air.
The power needed to overcome this force is cubed as speed increases. And, since power
is the rate at which energy is used, we can find the energy needed in calories, as well.
So, to overcome air drag, Sonic needs to burn an extra 210,000 calories every 2 minutes.
To put that in perspective, Sonic would need to consume 686 chili dogs every time he runs
through a full stage at supersonic speed. That's almost 62,000 M&M's, or 386 Big Macs.
Hopefully Sonic has a pretty healthy appetite...
So, there are plenty of strange consequences of supersonic speed, whether you're in a plane,
a pressurized suit, or red sneakers. But, if you're traveling by sneaker, don't forget
to stash an extra bag of M&M's in your pocket. And, as always, thanks for watching.
Do you need even more video game related videos? Come to my own personal YouTube channel at
Clan of the Gray Wolf. I've got reviews, retrospectives, explanations of video game tech. Ahh come
on over, we'll have a ton of fun.