Introduction
Last month, I went to watch the new ‘Godzilla Minus One’ and a scene in the movie piqued my interest. Unfortunately, I can’t find the scene online so here is a short description (spoilers, of course): In order to defeat Godzilla, a plan is made to lure him into Sagami Bay (1500 metres deep, then release freon gas into the water to reduce its buoyancy, causing Godzilla to sink and then die due to the overwhelming pressure at the bottom of the bay. If that plan didn’t work, they planned to rapidly lift him upwards to kill him through explosive decompression. For this investigation, I want to find out how much freon gas (by volume) it would take to make Godzilla sink, with a secondary goal being to estimate whether Godzilla would be killed due to the pressure at the bottom of the ocean. I do not plan to discuss explosive decompression as to model that one would need to know Godzilla’s anatomy, which as he is of a fictional species, and it would take too many assumptions to make a somewhat accurate conclusion on this.
Methodology
Buoyancy is the tendency of an object to float in a liquid. An object floats when its density is less than that of the fluid. The buoyant force, which acts opposite to weight, is defined by the following equation:
My first objective is to find the volume of freon gas required to reduce the buoyance force enough for Godzilla to sink. For that, we firstly need Godzilla’s mass, which varies but in this movie is 20,000 metric tonnes. Along with that we need to know the volume that Godzilla occupies- in order to calculate this, I have assumed that Godzilla is a cylinder (because that is the standard shape closest to Godzilla’s proportions, from my judgement) with a height of 50 metres (his cannon height) and an average width (diameter) of 10 metres, the latter of which is assumed as I don’t have movie clips to make a better judgement. Furthermore, we require the densities of seawater and freon gas, which are as follows-
Freon gas- 4 kg m^3
Seawater- 1030 kg m^3
Another piece of information required is the depth at which the force exerted by water pressure exceeds weight, at which point the water wouldn’t need to have freon gas to cause Godzilla to sink. For this, we will need to use the equation for pressure in a fluid, which is:
As fluid pressure acts in all directions equally, we will need to isolate the force exerted downwards as that is the one we are interested in. This can be done by calculating the force exerted on the parts of Godzilla which can be seen from top down, with our assumption, the top of the cylinder which is a circle.
By calculating the depth at which the pressure is enough for Godzilla to sink, we can find the volume of water whose density needs to be reduced and thus the volume of freon gas required.
Another issue to discuss is whether the pressure at the bottom of the ocean would kill Godzilla, for which I have taken value for the yield strength, which is the pressure that can be applied to a material to the point that it faces some plastic deformation, for a femur, the strongest bone in the animal kingdom. This is assuming that Godzilla is made of the strongest biological material there is. In addition, I have assumed viscous drag to be negligible as I don’t have enough data on Godzilla’s shape to model drag and modelling drag for a cylinder would be wildly inaccurate in this case.
We can divide this process into a few steps:
1. Calculate the buoyant force of Godzilla while he is partially above water, then subtracting that from his weight to calculate the extra thrust that he is providing to stay up (as his density is greater than that of water).
2. Using the thrust and the maximum buoyant force as the forces acting upwards, find the depth at which pressure + weight exceeds the combination of these forces.
3. Use the depth to find the volume of water whose density needs to be reduced, then use this information to find the volume of freon gas required.
4. Calculate the pressure exerted on Godzilla at the bottom of the ocean.
Finding the volume of freon gas
In the first instance, when Godzilla is partially out of the water and no freon gas has been deployed, the buoyant force acting upwards would be about half of the total buoyant force (as about half of his body is out of water), which is
Godzilla’s weight is
This means that sensibly, Godzilla is providing a lot of additional thrust, i.e.
It is safe to assume that this thrust remains constant as we don't have sufficient information to model how this would change.
At some point, the force exerted on the top by pressure would be greater than the sum of the thrust and the maximum buoyant force, which is
When the force downwards applied by the seawater exceeds this, the seawater no longer needs to be aerated- this will help us calculate the volume of seawater that needs to be aerated. The downwards force provided by the pressure can be expressed as follows-
I modelled this on an excel spreadsheet (link given) and found the depth at which this force overcomes the upwards forces to be 262.203 m. With this, I can calculate the volume of water which needs to be altered- as we are taking Godzilla to be a cylinder moving downwards, this volume can be calculated by taking the radius of the cylinder and the depth to be its height, which is
To model the change density in excel, I modified the equation for density,
to get
where x is the volume of freon gas added. The numerator the expression shows the total mass of the system- as freon gas is added, water volume is replaced by gas volume. For every addition x to the volume of freon gas, there is a subtraction x from the volume of water. 4 and 1030 are the densities of freon and water respectively. Using excel, I got 12307.984 m^3 to be the volume of freon gas required for this operation. To put this into perspective, this is the equivalent of 162 large freight containers or 108 industrial sized gas tanks, which would have a combined mass of 49231 kg. The ships used to deploy the freon tanks are 2 destroyers (in the film). On average, a destroyer can carry between 2000-10000 metric tonnes, which is more than enough for our masses of freon tanks. Provided that one has enough freon, this should be somewhat possible to do in real life.
Could Godzilla survive the pressure at the bottom of the bay
The pressure at the bottom of the bay is
The ultimate tensile strength of a femur bone (strongest in the animal kingdom) is 135 MPa. Therefore, Godzilla would survive assuming that his structure is the strongest that is possible biologically. This is a huge speculation of course as Godzilla’s biology is fictional and there is little canonical information about it.
Conclusion
This investigation was something I was prompted to do while watching the movie for the first time- the scene particularly struck me as something with some scientific basis. I really enjoyed the specific references to sensible physics in the movie—which is uncommon in science fiction--which made me almost convinced that this could be done in real life. About the investigation itself, it was a shame that I couldn’t find movie clips to analyse factors like acceleration and rate of gas deployment further. If I find the movie clips sometime in the future, I may return to this to delve deeper into the scene.
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