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1 Jamie: You're forgetting one thing, Adam. We can't access the Internet through 300 metres of water. The signal won't get through.
2 Jamie: Two things! We're inside a submarine. A metal box. It's a perfect Faraday cage.
3 Adam: We could open a window and stick our phone outside. And then close it real quick.
4 Jamie: You can't solve everything by opening and closing windows!
4 Adam: It works for Microsoft tech support.
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A Faraday cage is an enclosure of electrically conducting material. Thanks to the good old laws of electromagnetics, the conduction of electric charge on the surface of the enclosure is such that electromagnetic radiation with a wavelength longer than any holes in the surface can't penetrate from outside into the interior or from the interior to the exterior.
Faraday cages are commonly used to shield materials from disruptive, dangerous, or undesirable electromagnetic radiation, usually radio waves and microwaves, as these have fairly long wavelengths and so can be shielded quite easily with a metal mesh screen. Your microwave oven has a Faraday cage around the cooking cavity, to prevent the dangerous microwaves from leaking and cooking your flesh. You can see the grid of metal mesh inside the glass of the microwave oven door.
While most people might be familiar with Faraday cages that are actual cages, with bars that you can see between, a solid metal wall works just as well, if not better. Basically, if you're inside a submarine, your mobile phone ain't gonna be picking up any signal. Even if you weren't underwater, which is also a really good blocker of radio waves.
 Incidentally, this is why you should never peel the metal mesh off a microwave oven door to try and get a better view of the cooking food.
While I absolutely agree with the Faraday cage effect/concept of a submarine hull it does not completely work in reality. I have made and/or received mobile phone calls from inside at least 3 different types of submarines (boats), but you do need to be in the right place inside the boat for it to work. They were all alongside wharfs or laid up so hatches were open and there may or may not have been holes in the hull. The main problem is there are hull penetrations with cables, pipes, hydraulics, etc, going through them that are often not shielded and/or earthed at one end, so we have re-radiation possibilities, sometimes things are just the right length for a frequency (as you seem to be aware of). Having said that at 300 metres Jamie and Adam are going to need to go to the communications centre and transmit an emergency signal on the LF transmitter or they could release one of their distress buoys. Oh, hang on a moment, this is a homemade boat, I bet they didn't think of those things during the design phase!
Surface ships (ships), once closed down (upperdeck hatches and ventilation trunks closed) can become positive air pressure citadels, meaning they too should be effective Faraday cages but again they are not. Here though, there are way more through bulkhead and deck penetrations that can reradiate and mobile phone calls are possible throughout the internal areas of most ships.
Hatches on both ships and boats are not necessarily a full metal to metal contact, there is (understandably) a non-metallic material with a bit of flexibility that forms the seal when the hatch is closed. Often the hinges are made of brass or other nonferrous materials with neoprene washers etc, so a hatch cover is not reliably earthed making it effectively a hole for the right RF frequency. On ships, earth bonding wires are often applied to the large hatches and flaps but not so on boats. Firstly they are typically much smaller, secondly it would cause underwater noise and thirdly because their hatches do have a reasonable metal to metal contact due to the "teeth" on each side that drive the hatch closed "harder" than on surface ships. Ultimately ship upper deck hatches aren't necessarily water tight, however the requirements for boat hatches are a fair bit more strict!
As you are well aware of though when you are inside a metal structure sitting in water you can't expect a signal strength of 5 and perfect reception. My experience is similar to what you see in the movies when someone needs to make a mobile call from a remote area. Signal strength is suspect, you have to "chase" it and calls are subject to dropping out and/or terminating completely. However SMS is fairly reliable.
The other thing I have done while off the coast of Australia is patch my (old non smart, without and internal antenna) mobile into the ship/boat antenna distribution fields and made/received calls way further off the coast than mobile phone coverage is guaranteed. Boosting your mobile with high gain active antenna arrays is a marvel to behold, image the surprise of a mobile cell tower receiving a 5W signal from a Nokia!
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