Something that always troubled me was that fuel lines are flowing and pressurized. Fuel tanks are also insulated. How could they freeze? The Day After Tomorrow simply demanded too much from me - I could not sufficiently suspend my disbelief to enjoy the film.
I shall seek to answer this question. Whether it is possible to freeze a flying helicopter's fuel system?
The current standardized NATO kerosene-based aviation fuel, the JP-8, has a freezing point of -47°C (-52.6°F).
I have a limited and rudimentary understanding of physics. So be gentle if there are glaring errors in my methods. Now, we know hat cooling is the transfer of thermal energy. I've never taken college physics, but my father once taught me the three methods of thermal energy transfer - convection, radiation, and conduction.
Because the fuel tank inside the helicopter and insulated from convention (it is internal) and radiation (rubber encased in aluminum), I will assume that conduction is primarily the method of which mother nature managed to freeze the JP-8 in the helicopter.
Due to my limited mathematical skills and the unavailability of schematics for the SH-3 Sea King helicopter, I will assume that the fuel tank is sphere, was not fixed internally, but was rather exposed to the outside world.
Applying Fourier's Law...
k = material's conductivity
A = surface area
Δt = time
ΔQ = quantity of heat
ΔT = change in temperature
x = thickness of conducting surface separating temperature gradient
We want to find out the ΔQ (quantity of heat).
Since the helicopters froze instantly, I will say ΔT will be 1 seconds.
So...
I will further assume that the JP-8 fuel was previously stored in an underground tank. The contents of the tank, being buried under ground, will reflect ambient temperature, which is typically at 10°C (50°F). Since the film claims the pocket of cold air was at -101.1°C (-150°F), we have a change in temperature (ΔT) of 111.1 Kelvins.
The tank, being made out of rubber compounds, should have a thermal conductivity similar to rubber (k = 0.16 W/(m·K)). I also found that the aviation industry thickness for a self-sealing fuel bladder is approximately 0.00216 meters.
Assuming that the tank was round, we can calculate the radius of the sphere, which will allow us to calculate the surface area of the sphere. The UK variant of the SH-3 Sea King holds 3700 liters or 3.7m^3 of fuel.
Now we just have to plug in the numbers!
ΔQ = 95,299.11 Joules.
So we now know that in the cinematic world of The Day After Tomorrow + my crude assumptions, around 95,299 Joules of heat could be transferred from the fuel tank to the cold air in one second!
If someone can instruct me on how to calculate the thermal mass of 3700 liters of JP-8 fuel at 10°C (50°F), we would be able to determine whether or not it was indeed possible to freeze the helicopter's fuel. But in the mean time, this will have to do.
5 comments:
Too much time on your hands.
Saw the movie just last night on TV. The whole tank does not have to freeze, just the fuel lines with their much smaller cross-sectional area. The movie is fun to watch if you don't get wrapped up in the science.
I actually considered this possibility - but sadly, high-pressured flowing fuel lines will not freeze before the contents of a fuel tank.
That bothered me also as well as several other issues: like falling air warms due to compression. I live on the eastern side of the Rockies and we get this phenomena all the time. In fact, the Native Americans have a word for this: chinook. So that air falling from the upper atmosphere would actually warm. And the faster it fell, the warmer it would get....
Yea, the movie was a great depiction of a "what if" scenario, but the scenario was completely implausible in many many ways.
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