- I definitely don't need it.
Who lives in a treedome under the sea?
Sandy Cheeks does.
But remember that the sea
is very heav-y,
so if a dome was under that kind of load,
would Sandy's treedome quickly implode?
Are you ready?
(upbeat techno music)
(deep laughing) Yar.
In Spongebob Squarepants, the character Sandy Cheeks
is a squirrel from Texas that lives under the sea
with the assistance of a giant transparent dome,
complete with oak tree, picnic table, and running wheel.
It looks like a decent reverse aquarium,
but could it really stand up
to the crushing ocean pressures?
That depends first and foremost on the weight of water
directly above Sandy's dome.
If you divide that by the area we're concerned with,
you get a pressure, and you can calculate
this hydrostatic pressure by taking the density
of the water above the dome, multiplying that by gravity, g,
and multiplying that by h,
or the height of water above the surface
that we are concerned with.
Now, if that gives us a pressure that is too much,
Sandy's gonna have a bad time.
(glass breaking)
So what would that h be?
The popular theory is that Bikini Bottom
is actually at the seafloor of Bikini Atoll,
an atoll in the Marshall Islands
that was famously home to 23 different nuclear tests
in the 1940's and the 1950's.
The seafloor of Bikini Atoll doesn't get much deeper
than 53 meters, or around 175 feet.
So that's going to be the height of our water column.
Nuclear test?
Does that mean, does that mean they're all mutants?
And to find the force of this water,
we need the weight of all this water,
which means we need first the volume of all this water.
According to SpongePedia or whatever you want to call it,
Sandy's treedome is about 10 meters tall,
so that's going to be the radius of our hemisphere.
If we use that, and a little bit of math,
we can get the volume of this water column,
and multiply it by the density of water
times the surface gravity on Earth,
and get the weight, or the force.
If we do all that, we can get the volume that we want,
and therefore the weight that we want.
And when you do you get 1.62
times 10 to the eighth Newtons.
162 million Newtons,
or 36 million pounds of force in sea water.
That does sound like a lot of force for a dome to withstand,
but what we still need to find is pressure.
(whispering) Pressure.
Pressure is force divide by area.
We just found the force, so now we need to find the area,
which is the surface of Sandy's treedome,
which is a hemisphere.
We already know it has a radius of 10 meters,
and from geometry, we know that the outside
surface area of a hemisphere is equal to two pi r squared.
Doing a bit more math, the pressure comes out to
33 pounds per square inch,
or just over two atmospheres worth of pressure.
But that number doesn't really mean anything
if we don't know how much pressure the dome can withstand,
which is dependent on the material,
which Sandy says isn't glass, but polyurethane,
and polyurethane has a compressive strength
of 20,000 pounds per square inch.
This stuff can certainly make a very strong dome
(thudding) depending on the thickness.
I thought you were supposed to be strong.
(groaning) Oh, oh.
(cracking)
My leg!
The internal stress in a thin-walled spherical
object like Sandy's treedome is equal to
the pressure pushing down outside,
times the radius of the treedome,
divided by two times the thickness.
So if we assume a decent thickness for Sandy's treedome,
maybe like a meter,
and then plug in our values that we've already found,
we get a total internal stress of 176 psi.
Far below our limit.
So that means if you threw
all of Bikini Bottom's water down on top of the treedome.
(water running)
- [Narrator] Three days later.
- It would continue to be fine.
In fact, given these decent estimations,
Sandy's treedome could exist at much deeper depths
before experiencing any kind of failure.
10 meters of water pushes down on a surface
with about one atmosphere of pressure,
or 14 pounds per square inch.
So, if Sandy had a 10 meter tall,
one meter thick polyurethane treedome,
it could survive many tens of meters below the surface.
You're good.
You're, you're good.
Keep going, you're good.
You're good.
Stop!
With the dimensions we assume,
Sandy's treedome could withstand the kinds of pressures
found at over 2.5 kilometers underneath the sea.
This is deeper than where giant squid prowl.
(nasally grunting)
Rather than messing with dome depth,
we could also mess with dome thickness
since that isn't established.
At the bottom of Bikini Bottom
using our internal stress equation,
Sandy's treedome could have walls
that are just one centimeter thick.
That thick and it would be fine.
(thumping)
Right? Still pretty impressive.
(thwacking) Nice try!
San-day.
Of course, none of this matters
if Sandy can't actually live in a treedome under the sea.
So let's do a quick check.
Being about 50 meters under the surface of the sea,
Sandy's treedome is firmly in the Euphotic zone,
meaning that light from the sun can still penetrate
meaning that photosynthesis may, in fact, still be possible
within the dome itself and a giant oak tree 10 meters tall
definitely puts out enough oxygen for one little squirrel.
So, all Sandy would have to do is provide it
with enough carbon dioxide and nutrients to sustain itself.
It all kinda checks out.
We know that because we've kind of done this.
That's an underwater garden.
So would Sandy's treedome implode
at the depth it's at at the bottom of Bikini Bottom?
No, according to our math it could go kilometers deeper
before it experienced any kind of structural failure.
Though, Sandy wouldn't want to test that limit
or else then she'd be so deep that no light
would penetrate and then there'd be no oxygen
and then no Sandy.
But, who could live in a treedome under the sea?
Sandy, maybe.
Because science.
(upbeat techno music)
Wait, if we're under water how could there be, oh.
Well I guess it could be like a chemical fire
like Magnesium!
(rock music) Yes, yes!
(laughs) Yes.
Science!
Yes!
Thank you so much for watching, Martin.
No, not you, your friend Martin.
If you want even more silliness,
check out my show with colleague Dan Casey
(singing) Muskwatch
where we get very silly about a very serious man
and if you want something a bit more premium,
check out my show The Space Program
by subscribing to Alpha at ProjectAlpha.com
and if you do that you can also get this show
two days earlier than anyone else.
(stuttering) Like dumb normies do.
Thanks, bye (laughs).
(upbeat techno music)
(pencil writing)
(rolodex flipping)