Could spider-man really stop a train
Spider-man is a pretty useful guy to just have hanging around as the ever vigilant protector of his city
He fights crime with synthesized silken super-strength
He can stop supervillains and their henchmen sure, but can he stop a train?
Today's thought experiment comes to us from the much loved and many memes
spider-man 2 in it Peter Parker stops a train full of people with nothing more than
multiple strands of spider silk and one heck of a grip spider silk is
Spectacularly strong in real life and you've been asking me to look into this scene for years. So get out your Spidey calculators
It's finally time for some spider mass hit first if we are taking a purely theoretical approach here
We need to define what stopping a train really means
Right on time. Ooh, that's the into the spider versus Oscar. Oh
If you're gonna be stopping a train we're gonna be doing physical work on that train
Which can also be considered a change in kinetic energy
and so we're gonna have to find some kind of way to transfer the energy of the trains motion into something else our
Web because the Train is gonna be coming to a complete stop at the end of our analysis
This term is going to go away and fall to zero
and so what we are left with is this
Can the spider silk or more organically?
Enhanced a mutated spider silk do enough work on the Train absorb enough energy such that the work
Equals the full kinetic energy of a runaway train only using as many web lines as we see in the movie
All right
so how much kinetic energy does the train in spider-man two have
Well if Spidey is swinging around New York City then each of those train cars is gonna weigh a hefty thirty eight
Thousand kilograms and in the movie I counted six of them
Also Doc Ock before he jumps off makes the Train go 80 miles an hour or 35 meters per second. Whoa
Jeez, what a gallery of rogues. Am I right?
Okay
Now we don't know exactly how many people Octavius is forcing Peter Parker to save in this scene
but I'm gonna assume that all the cars are in near capacity and everyone inside has an average human mass of
62 kilograms this adds a full 62 metric tons of people meet for spider-man to save wait. Wait Wow
Putting all these values together we can calculate just how much energy Peter's spider silk has to Tobey acquire
Do the math and you get a kinetic energy value for our runaway train of a hundred and eighty seven million
Joules now, this is obviously quite a lot
It's within an order of magnitude of the kinetic energy a space shuttle landing at
380 km/h
Has oh no a viscous ecto symbiotic neural active out of lagoon mutual and stop
Now that we know how much energy we have to absorb we need to look very closely at spider-man's webbing
I'm taking pictures for the beauty
the amount of energy a material can absorb while deforming like stretching is called that materials toughness a
Common way to visualize the toughness of different materials in material sciences with a so called stress versus strain curve
Stress is how much force per unit area some material is subjected to and strain is how much the material is deforming?
compressing or stretching based on its original length
This is a common stress-strain curve for steel
As you can see in the beginning steel can be subjected to an awful lot of force without changing shape very much
But at this point called yield strength the steel starts to deform a lot
Without much change in the force. This is like a steel beam
resisting motion and then completely folded and at this point the material ruptures the
area underneath this curve is how much energy you had to put in the material to take it and
Deform it until rupture
This is the materials toughness and the units work out to be how many joules of energy some sample of material can absorb
Per volume of stuff that you have before it fails
failing
Just a sec
Sorry, I am needed some me time
Toughness is where spider silk is truly spectacular
I'm fine as
spiders evolved to fill the catch fast-moving objects with strong stretchy fibers in each their silk developed an impressive balance between strength and
stretchiness as you can see here on the stress-strain curve while steel is
Stretching and totally failing spider silk is stretching but taking on more and more
Stress as it goes on showing more and more toughness. I guess. You know what they say with great power comes great
extensibility
While the steel in our example may have a toughness of 6 million joules per cubic meter the dragline
spider silk of the golden orb weaver spider for example has a toughness of
150 making it 25 times
Tougher and this is very important because the toughness of spider silk
Real or otherwise will determine whether or not we can truly stop a train
speaking of which
Ok, so let's get to calculating because we're moving at like 80 miles morales per hour over here if we divide the kinetic energy of
This train by the toughness of the spider silk
We are using and divide all of that by the volume of web that Peter Parker uses in the movie
Then we can find out whether or not enough webbing is used to transfer all the kinetic energy of the Train
Into the toughness of the spider silk. So now we need the volume of the web
Alright, so looking at the movie the lines actually look like some kind of woven web rope in that each one of the web lines
has eight contact points on the surrounding apartments and
Spider-man shoots out eight of these rubbish lines from each hand. This gives a combined
128 web lines each one of these web lines looks like it has maybe the radii of a pencil maybe three point five
millimeters and each one of these lines based on the width of New York City streets
Which I checked based on the movie could maybe be around 15 meters long each
This gives us the volume of our web
and now remember if this equation gives us 1 or less than 1 it means
that we have just enough webbing or more webbing than we need to stop the kinetic energy of the Train and I calculate
1/3 13 times 2 little spider silk save me
Let's try this again because if we change a few variables around we might just pull this off
Ok, so instead of orb-weaver silk. Let's try the toughest biological material ever tested silk from Darwin's bark spider
Hang on buddy
This silk of the bark spider here is 10 times tougher than Kevlar and remember when we plug this into our equation
we want a value of 1 or less and that means we have enough web to stop our train and I get a value of
4
All right fine
Maybe the movie was taking some statues of Liberty here using our same numbers
How many strands of webbing would it take that look to be the correct size to stop our train doing all the same math?
We did before and using the toughest spider silk available. I get 70, that's
35 web lines per hand
Theoretically now we have enough toughness to stop the train in spider-man 2 because our equation that we set up earlier gives us
1 and everybody gets one
This show and many others are built on nerdy analyses like these but I don't want to just give you some
Numbers like there now Cannon and some voiceover and call it a day. No, I want to actually learn this stuff with you
So now I'm gonna show you just how much our assumptions can change our conclusions
For example, if we want spider-man to catch a train
But we don't want to have him shoot an absurd number of lines like 70 out of his hands
All we have to do is simply initially assume that the webbing is not pencil with it is twice as wide and then our equation
Pops out a 1 and you can get the observed number of lines shot from his hand with the requisite toughness
However, if this is the case
Then the amount of webbing he has to be holding on to is
Absurdly large like holding on to scaffolding or we could just simply state that
spider-man's
Mutated organic silk has a toughness
higher than anything ever
Tested by humans pop this into the equation and we get a 1 and the observed number of web lines in spider-man 2 works
However, this is higher than anything we know of and then doesn't really fit with material science
You see when you do this kind of thing. You have to balance
fiction and reality
assumptions and variables and come to an acceptable conclusion and when you do that and only when you do that
Can you become something of a pop-culture scientist yourself?
all day
so could spider-man and his silk really stop a train like in spider-man 2
well
theoretically
Yes using the toughest spider silk that we know of he could use enough web lines such that they would have enough toughness to absorb
all the kinetic energy of that runaway train however to do exactly what we see him do in spider-man 2
We'd really have to give old webhead
the benefit of the doubt his web lines would have to be either much thicker than they look or much tougher than
Anything that we know of if he did that then it would push this move into the spider verse of plausibility
Otherwise it would be close but no cigar
Because science and I still want those pics as a spider-man
I
Know we got a little bit meta with how these kinds of videos are made with assumptions and variables and etc
So, let me just add a few more for you super nerds
We are
assuming in this episode a very very simple model that the Train is no longer accelerating when Peter Parker tries to stop it is just
Coasting which isn't really accurate and we did not consider the extensibility of spider silk. It cannot stretch what looks like
Miles in the movie even if spider silk stretched that far it would still put some deceleration on the passengers
But I did check even if the spider silk stretches just a little bit within known values
then the passengers would only pull, you know, 20 to 30 G's while hitting a
steel
box of death
Thank you so much for watching Christopher
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