In the fictional New York City of the Marvel Universe, citizens may see the Friendly Neighborhood Spider-Man swinging from building to building with ease. At one point or another, we have all wanted to be Spider-Man and experience the pure freedom and bliss of being able to swing through the concrete jungle. Many have dismissed this as a fantasy, but could this actually be possible? Let’s take a look at a few factors.
Pendulum/Tarzan Swing
Spider-Man has many different ways to zip around the city, but a common form of his swinging is through the use of pendulum motion. This may also be labeled as the “Tarzan” swing as it is quite similar to the way Tarzan swings through the jungle from vine to vine. Pendulums typically have a period of motion which is the time it takes for one oscillation; an oscillation is the motion of the pendulum moving forward and back. The period of motion is dependent on the length of the pendulum. Spider-Man only needs half an oscillation for a swing, and an equation can be used to determine the swing time necessary based on the angle and length of the web. Once the swing time is deduced, the average horizontal swinging speed or velocity can be calculated using the horizontal distance of the swing divided by the swing time. The data for the average horizontal velocity based on web length and angle is modeled by the graph:
As is represented in the graph, a longer web with a larger starting angle typically yields a higher average horizontal swing velocity. A longer web increases velocity as a long swing sweep covers a greater distance. A starting angle of 80 degrees gives the best average speed for a swing because any starting angle above 80 degrees results in a loss of time; Spider-Man wastes time by having to move vertically at the start and end of each swing for any starting angle above this angle. As our example, let us examine the maximum velocity of a 20-meter web, which at an angle of 80 degrees is approximately 7.8 m/s or around 17.44 mph. However, Spider-Man can likely swing faster than this because he is no regular human like Tarzan. Let’s explore another swinging method.
Projectile Swinging
Aside from pendulum swinging, Spider-Man has another method that is far more efficient. Spider-Man is a superhuman with special powers that allow him to swing in ways that Tarzan cannot. In Tarzan’s pendulum swing, he must go through one swing until it stops. For Spider-Man, however, he is able to let go before a swing stops, allowing him to act as a projectile to almost fly through the air. We can determine his average velocity by plotting and modeling his trajectory. If we use an initial speed of 8 m/s on a 20-meter web at a starting angle of 45 degrees, Spider-Man’s average horizontal velocity would be about 15.9 m/s which is far faster than the pendulum swing. Essentially, Spider-Man would be swinging from a 45-degree angle, letting go at around 90, then deploying another web at another 45-degree angle. However, this high speed is due to the high starting velocity; if we take his speed while on the web, it averages out to 14.3 m/s which is still significantly faster. For simplicity’s sake, let’s round these two values to 15.0 m/s or around 33.554 mph, which is about the speed of a car in the city.
Spider Silk
Now that we’ve determined how fast Spider-Man can swing, would his webs actually be able to hold him? To determine this, we would have to find the force applied to the string. Assuming that he swings in a parabolic arc, the forces of gravity on Spider-Man would be at their highest at the bottom of the arc. To calculate this, the net force would be equal to the tension (T) of the string minus the force of gravity on Spider-Man (mg) as this is just a simple vector. Since we know that Net Force= Mass Acceleration, we can determine the equation, T-mg=ma . To determine the acceleration, we use the change in velocity at the bottom of the arc as well as the radius of the arc (r) to create similar triangles and get the formula v2r= vt, the equation for circular motion. Thus, the tension would need to produce sufficient centripetal acceleration to sustain Spider-Man’s tangential velocity. Since the change in velocity divided by the change in time (vt) equals acceleration, by the transitive property we can say v2r=a . Now we can plug this into the equation to get the force to equal mv2r. Marvel claims Spider-Man weighs 167 pounds which equals 75.8 kg. Using our 15 m/s average velocity and 20-meter web from before, we determine the tension of the string to be around 850 Newtons. However, since he can likely swing far faster than 15 m/s, if we double his velocity we find that the tension on the string would be 3411 Newtons. Now, that is quite a lot of force that is being placed on this string, but would spider silk be able to withstand this? The tensile strength of spider silk is 1.75 giga-pascals (GPa). This means that a 1-meter wide strand of spider silk would be able to withstand 1.75 billion Newtons of force. Assuming that the width of Spider-Man’s web is quite tiny, it would still be able to withstand around 100,000 Newtons of force which is more than necessary to hold our webhead as he swings around the city.
Conclusion
Well, would you actually be able to swing like Spider-Man? Theoretically yes, as spider silk would be able to withstand your body weight and allow you to swing around New York City like the webhead himself. However, you would still need superhuman powers, a place to store a tremendous amount of silk on your person, and the engineering knowledge to craft advanced technology to shoot lengthy spiderwebs. While in theory, the laws of physics could potentially allow you to zip around a metropolis, to truly swing around like the Amazing Spider-Man would, unfortunately, be a thing of fiction.
