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| Electron micrograph of a spider spinneret producing spider dragline silk. (photo credit MicroAngela) |
First up on my list is the 2002 version of Spiderman. It struck me that Peter Parker must have an enormously high protein diet
to generate all that spider silk (which is made from protein) he goes through. So being the geek that I am I
set about working out what his protein consumption must be and
putting it in terms of eggs eaten/100m of spider silk.
Here goes (and feel free to pick me up on any mistakes).
I started with the assumption that Spidey produces spider's silk that has the same characteristics as dragline silk produced by the European garden spider Araneus diadematus i.e. it has a tensile strength ,about equal to piano wire, of 1.1 Giga pascals (Gpa) and a density of 1.3 g/cm3.1
1.1 Gpa = 1.1x109 Newtons per meter squared (N/m2)
Spiderman weighs 75kg (according to Marvel)2 so the force he exerts is 75 x the acceleration due to gravity which is 9.8 m/s/s = 735 Newtons
Therefore cross sectional area of spider silk required to support Spiderman = 735N/1.1x109N/m2 = 6.68x10-7 m2 = 6.68x10-3 cm2. That works out to be a bit of silk with 0.046 cm radius. Pretty cool huh, you could hang from a piece of spider silk about 1mm thick!
Therefore cross sectional area of spider silk required to support Spiderman = 735N/1.1x109N/m2 = 6.68x10-7 m2 = 6.68x10-3 cm2. That works out to be a bit of silk with 0.046 cm radius. Pretty cool huh, you could hang from a piece of spider silk about 1mm thick!
A 1m long piece of silk has a volume of 0.668 cm3 which would weigh in (given a density of 1.3g/cm3) at just 0.87g. Therefore 100m weighs about 87g
There’s about 6g of protein in an egg. So it looks like Spidey only needs about 15 eggs for breakfast if he plans to use 100m of silk. That’s not too bad.
But, spider silk consists predominantly of a protein call fibroin which is about 42% glycine.3 Whilst egg consists of just 10.7% glycine and serine (I’m counting serine because it is easily metabolised to glycine). So lets say Spidey needs 60 eggs for his 100m of silk.
The thing is I’m not quite happy with that, I think he’d need a reasonable safety margin, I’m sure he doesn’t what to hang about on a thread just barely strong enough to hold his weight. Plus he’s busy swinging from tall buildings whilst carrying Mary-Jane Watson around. So lets go for a thread 5 times thicker than what’s barely adequate. So that gives us 300 eggs/100m of Spidey silk.
But that’s not really the end of it either. After all what happens if he leaps from a building to save a falling MJ and deploys his webslingers to save the day (like at 1hr 6 min into the movie). Hmm...I’m guessing he’s still using his drag silk (which stretches by 27%). He could got for the flag silk, its not as strong (tensile strength = 0.5 Gpa) buts its got amazing elastic properties; it can stretch to 2.7 times its original length! But that might be a bit too bouncy.
In the scene I’m talking about Spidey leaps from the balcony and falls for 7 seconds before his silk starts to arrest his fall. He’s caught MJ so lets say their combined weight is 125kg. How much silk is he going to need here?
Spidey accelerates at 9.8m/s2 for 7 seconds giving him a velocity of 68.6 m/s. Given that velocity =√2.g.h we can work out Spidey fell for 240m (wow, that’s one high balcony). So assuming the silk stretches to its maximum that gives us a stopping distance of 64.8m. The impact force on the silk rope as they slow down is F=1/2mv2/d = 4,538 N (where d is the stopping distance, m is mass and v is velocity)
That’s not too bad, just 6.17 times greater force than Spidey just hanging around by himself. But still he’ll need 1288g of silk (minimum) to catch his fall. So I reckon he must have had about 860 eggs from breakfast that morning. I think Aunt May might have noticed.
Anyone what to check my working?
p.s. As for the scene at the end of the movie where he catches a cable car full of kids, I draw the line there.
p.p.s I know, I know in the comic books he has some wrist mounted devices, but in the films he glads the silk out of his wrist, so that's what I'm working with here
1.Lin Römer and Thomas Scheiber, The elaborate structure of spider silk. Structure and function of a natural high performance fiber, 2008 Prion 2:4, 154-161
2. Marvel directory http://www.marveldirectory.com/individuals/s/spiderman.htm (accessed Jan 2012)
3. S.O. Anderson. Amino acid composition of spider silk. 1970. Comparative Biology and Physiology, 35, 705-711
4.http://en.wikipedia.org/wiki/Egg_(food) (accessed Jan 2012)
You ignore the fact that the spider that bit Peter Parker was genetically enhanced-there’s a reason that they had it there in the lab in the first place. Perhaps its dragline was significantly stronger than that of the wild-type. Also you should use yield strength instead of tensile strength. Tensile strength only tells you to what extent the material obeys Hooke’s Law. The yield strength, at which point the material fails, for a biopolymer is likely substantially higher. And Peter could supplement his diet with gelatine, at 30% glycine, rather than eggs. His glandular production of spider silk can be explained away. But what of his increased body mass from the time the thin Peter passes out at home after being bitten by the GM spider and the time he wakes up to find he has the body of a young Schwartzeneger? What happend to the law of the conservation of matter?
ReplyDeleteFair point on the spiders silk strength, but can you explain how a genetically engineered spider acquires the power to transfer its genes to another species?
ReplyDeleteAs for Peter's transformation maybe he gorged himself on protein supplements on the way home and that scene ended up on the cutting room floor?