Here's how Spider-man's iconic webbing actually works. (From 2014)
Based on these calculations, it looks like carbon nanotube rope is the only thing that would work. Well, the steel cable could work but it would have to be much thicker with a radius of 2.5 mm.In the recent versions of Spider-Man, it seems that all the webbing “ammo” is contained in a small watch-sized wrist thing.
In order to estimate the amount of webs, Spidey can shoot, I need to first settle on the webs. I am going to go with carbon nanotube rope. According to Wikipedia, this could have a density of around 0.55 g/cmHow much webbing would Spider-Man need for just one shot? It seems like he primarily uses the webs for swinging. If I were Spider-Man , I would aim for a height of about 5 to 10 stories high. Let’s say this requires a web length of about 20 meters. Using my initial estimate of a 1 mm radius web, this would be a super skinny and long cylinder. The volume of this cylinder would be:. That might be a little difficult to visualize in terms of the size. How about a comparison to the volume of a standard pencil with a radius of 0.25 cm. If all of this webbing was put into a pencil, the pencil would be 3.2 m long. That’s a long pencil and remember, that’s for just one of his typical web shots. Well, then how big of a container would he need to have a reasonable number of shots? Let’s say he wants 50 uses of the web for each hand. If I were Spider-Man, that’s what I would want. In that case, we can find the web volume estimation by a factor of 50. That gives a total volume of 0.00314 mWhat would this look like if it fit around a wrist? If I use my own wrist for a basis, then I find that it has a circumference of 16.5 cm. In my web container design, I will let the cartridge go back 10 cm along my arm. Now I can calculate the thickness of this container. Maybe a picture will help. Here is a look at my device looking down the arm. Using the values from my estimates, I get a container radius of 9.6 cm or a height above the wrist of 7 cm. Here is what that would look like.Yes. That looks a little awkward. But just imagine how large this thing would be the webs were something like nylon or steel cable instead of nanotube rope.I already said that it seems like these webs should be able to reach at least a 10 story building . What kind of launch speed would a web need to get this high? Let’s just start with the assumption that that the front of the web is just a particle and that air resistance is negligible. Yes, that is obviously not realistic but I will proceed anyway. As a bonus, isn’t it great that I can say “not realistic” when talking about Spider-Man? This is what makes the Internet so great. If a web is launched straight up, there will be only one force on it - the gravitational force. This constant force will make the vertical velocity decrease as it rises. At the highest point, the web velocity will be zero m/s . This will give an average vertical velocity of: Since the web is slowing down with an acceleration of -g, I can find the total time to get to the top of the building using the definition of the acceleration. Now I can use the average velocity and this time interval to get an expression for the change in vertical position. And there is your expression for the launch speed of the web. Sure, you could have just used one of the kinematic equations but what fun would that be? Using a the value for the change in height of 30 meters, the web launch speed would be 24.2 m/s . That doesn’t seem too bad, does it? But wait. What about air resistance. I’ll admit that calculating the air resistance in this case can be quite tricky. I could use the typical model for air resistance that say the force from air is proportional to the square of the speed:and A is the cross sectional area of the web. The problem is with the value of C which is a coefficient that depends on the shape of the object. If a web is like a cylinder, a longer cylinder has a different drag coefficient than a shorter web. This means that I will just have to guess at a value for C. Here is the next problem. As the web rises, it goes slower. With a slower web there is also less air resistance. This means that there is a non-constant acceleration on this rising web. In cases like this, the only practical method for solving for the motion is to use a computer to create a numerical model. It’s not too difficult, but if you want the detailsFor this simulation, I am going to assume carbon nanotube webs with a radius of 1 mm and a length of 2 meters in a cylindrical shape. The mass of this section of web can be found from the density of 0.55 g/cm
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