Methodology
In order to find out if the train could be stopped, we must calculate the energy required to stop the train and the kinetic energy of the train. Then, these need to be compared and if the energy capable of being absorbed by all the webs (known as the toughness) is greater than the kinetic energy of the moving train, then the webs could bring the train to a complete stop and vice versa. In this process, we make the assumptions that the train, spiderman, and the buildings the webs are joint to are indestructible.
Since our main source of data is a video clip from the movie, in order to make measurements we must devise a suitable method. By finding a real-life equivalent object in a frame and comparing its dimensions in pixels and metres, we can yield a metre: pixel ratio, allowing for the measurement of the dimensions of all other objects in the frame (as long as they are roughly the same distance and angle from the camera).
Step 1- calculate the energy required to stop the train
In order to calculate the energy required to stop the train, we must calculate the kinetic energy of the train using the following equation:
Finding the mass of the train at full capacity (since it is sensible to have conservative assumptions) is fairly simple as the producers revealed that they used a train of the 2200 series (CTA), whose specifications are known. Each train car as a mass of each train car is 47,400 lbs, which is 21,500.28 kg. Since there are 5 train cars in the movie, the total mass of the train is 107501.4 kg.
Secondly, we need to find the velocity of the train. This can be done using 2 frames at different times with a similar camera angle. Figure 1a shows the position of the train at the timestamp 27.07 seconds. Figure 1b shows the position of the train at the timestamp 27.77 seconds. These frames have a similar camera angle and so can be compared using pixel measurements.
In this case, the real-life equivalent object we can use is the train itself. The train’s dimensions are publicly available (check previous source) and so the train’s width (2.64 m) can be used. From this, we found out that 19.26 m is the distance the train moves in 0.7 seconds, giving it the speed of 27.51 m/s.
Now that we have both the velocity and the mass of the train, we can find its kinetic energy-
Therefore, the webs need to absorb 40691210.54 J of energy to stop the train.
Figure 1a.
Figure 1b
Step 2- Calculate the energy that the webs can absorb
Toughness is the measure of the ability of an object to absorb energy without fracturing. For naturally occurring spider silk (as this version of spiderman produces webbing naturally rather than using artificial web shooters), this is about 200 MJ m-3 or 200,000,000 J m-3
Firstly, we can measure the radius using Figure 2a as it has a suitable view of the diameter of the webs, which is shown by the red line (apologies for how small it is) on the rightmost side of the train. However, we encounter a problem when trying to find a real life equivalent measurement to find the metre : pixel ratio. Although the width of the train could be used, it is very likely to be a computer-generated image and so may not be representative of the real-life train. Therefore, the most reliable object would be Spiderman himself, as he is definitely not computer generated and can be compared with the real-life Tobey Maguire. Toby Maguire’s height is about 1.72 m. However, we can’t use this measurement directly for this image as Maguire’s full body isn’t shown. Thus, we must resort to a more unusual method- using a different picture of Tobey Maguire which shows his full body and measure the distance between the centre points of his eyes which is perhaps the only factor that would remain the same over the period of time in between the filming of the movie and the taking of the photo. The calculations are as follows:
Figure 2b is a picture of Maguire standing several years later. The long red line represents his height, which is about 1388 pixels. Thus, the metre : pixel ratio for this image is
The distance between the centre points of his eyes is 62 pixels (shown by the shorter red line), thus the distance between his eyes is
which is reasonable as the average distance between an adult’s eyes ranges from 5.4-7.4 cm
Using his eyes as a scale, the radius of the web is 0.0135 m.
Figure 2c shows the best frame we have to measure the full length of the webs. Here, the width of the train can be used as the frame is likely to be not completely CGI due to the fact that footage from the real Chicago-loop was taken during the making of the film. From this we get 14.02 metres to be the length of each web.
Now, the volume of the web can be measured using the formula for the volume of a cylinder:
There are 16 webs in the image, 8 on the right and 8 on the left.
Assuming that the volume of each of the webs is the same, the combined volume is, 0.128 m^3.
Finally, we can calculate the combined toughness of the web is as follows:
Figure 2a
Figure 2b
Figure 2c
Step 3- Compare the energies calculated
Before comparing the energies, we must address the assumptions made during the comparison:
1. There is no air resistance, which can be calculated but is negligible for large objects such as the train
2. The train is moving on a frictionless surface. The friction created by the tracks and the train can’t be calculated since there is a lack of information and using average values would discredit the experiment from my point of view.
Since 25687119.23 is lower than 40691210.54, the train wouldn’t be able to be stopped by the webs as they would fracture quickly.
Final Thoughts
Although the conclusion here was disappointing, this was still a very fun and exciting challenge to pursue.
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