Are personal electronics (of present or recent past; e.g. cell phones, mp3 players, iPads) a risk to commercial air travel? Is the typical request to "turn off all personal electronic devices" based on any reasonable data?
From ABC News (2007):
An aviation safety database maintained by NASA shows a handful of incidents each year reported by pilots who suspected cell phones and other electronic devices had caused a problem during flight. Despite these reports, not a single air crash has been proven to be caused by the use of a cell phone onboard a plane.
John Nance, an ABC News consultant and veteran airline pilot, says there's little reason to worry about cell phones interfering with an airplane's navigational equipment. He says an airplane's electronic systems are "all heavily shielded. That means that stray signals cannot get into those systems."
The airlines can't allow cell phones to be used in flight until the technology has been proven safe. However, according to Nance, the Federal Communications Commission and the Federal Aviation Administration "have not done their job over about a 25-year period. And the airlines have quite properly said … if you're not going to tell us, then we're just going to default to the most conservative position and say we're not going to use them in the air."
Here is a study done in 2003 that concludes "Cellphones and other electronics are more of a risk than you think"
regulations already permit a wide variety of other portable electronic devices--from game machines to laptops with Wi-Fi cards--to be used in the air today. Yet our research has found that these items can interrupt the normal operation of key cockpit instruments, especially Global Positioning System (GPS) receivers, which are increasingly vital to safe landings.
There is no smoking gun to this story: there is no definitive instance of an air accident known to have been caused by a passenger's use of an electronic device. Nonetheless, although it is impossible to say that such use has contributed to air accidents in the past, the data also make it impossible to rule it out completely.
Consumer devices that meet FCC emission limits can exceed safe interference limits set by the FAA for avionics, because the FCC and the FAA do not harmonize their regulations.
At present, we believe that passenger use of electronics on board commercial aircraft should continue to be limited and that passengers should not be allowed to operate intentionally radiating devices such as cellphones and wireless computer equipment during critical stages of flight.
Let's presume there is a 0.01% chance that cell phones can cause a crash. Worldwide there will surely be more than 10.000 flights per day. So even with such a low percentage it would mean at least one crash per day. Looking at it this way I can understand the ban.
Cell phones present a separate category, as they actively and intentionally transmit (i.e. generate E-M field), while the other appliances produce only a E-M noise, which is a lot weaker, see Small Aircraft RF Interference Path Loss:
For various reasons, many devices such as laptop computers are allowed during flights, while intentional transmitters such as wireless devices and phones are prohibited.
One particular issue with cell phones is that when they get far from the ground station (or lose connection to the ground station), they transmit a lot stronger signal to maintain the connection or to discover a station (the transmitted signal power varies in range 20 mW - 3 W, see also Mobile phone radiation). While one cell phone doing this would still most likely still be quite weak, having 400 cell phones transmitting at full intensity is something which could create an interference. This also explains why phones are not "confiscated" (like a knife would be) - a few of them left active does not matter, but having many of them could.
Besides of aircraft safety there are other concerns: active cells phones in the plane are bad for the phone operators, as the ground infrastructure is not designed for a situation like this. While the phone is quite far, it has a direct visual connection to many ground stations. See Mobile Phones and Aircraft
As the number of lines available in a particular cell is limited, the cells are sized according to the predicted number of simultaneous users. Inner-city cells are smaller than rural ones, based on the likelihood that there will be a greater demand for lines. Consequently, there are more cells per unit area in cities than elsewhere. It is also worth noting that the line-of-sight link from a mobile phone to a particular base station in a city is likely to be obstructed by buildings.
An aircraft could be carrying 500 cellphones. While passing directly over a city and thus unhindered by buildings, these phones could be in the line-of-sight of hundreds of base stations and could try to register with all of them. This would impose a temporary but extreme load on the network. The speed of the plane passing over the small inner-city cells would also result in an unusually rapid handover from cell to cell, possibly far in excess of the network's design limits.
It would be possible to provide an infrastructure on the plane to avoid the issues above, by having a dedicated station on the plane, which phones on board would connect to (this can be done with a weak signal, and with no need of any handover during the flight), and this station would then connect by one link to the ground network by some special means, e.g. using a satellite link. One paper attempting to design a scheme like this is ETSI White Paper No. 4, GSM operation onboard aircraft.
Clearly they do not interfere every time, and not every interference would result in a crash, and proof after the fact would be difficult. So the fact that no crashes have been blamed on this is not, by itself, proof that they pose no risk.
As to why all devices might be banned, airlines tend to err on the side of less lawsuits and less violations. The regulatory policy is clear that Airlines (in the US) are responsible for the effects of electronic devices operated on their planes, so they are going to be very hesitant to allow usage -- especially since research by the RTCA shows that some devices do interfere.
It appears it is based on reasonable data. I have no knowledge about any FAA research, but (not so recently) the Mythbusters tackled the myth that it is forbidden to use cellphones to force you to use the on-board phones.
They had to build their own mock-up cockpit and throw a whole lot of interference-causing stuff at it, which sort of worked. However it supposedly only worked because the wires in their mock-up weren't properly shielded. This would be supported by their failure to cause any sort of interference in a corporate jet (a Hawker 800XP).
As to no reported incidents, there is at least one. It was due to a passenger's refusal to turn off a boom box which interfered with the aircraft's navigational equipment. See, US v. Hicks, 980 F. 2d 963 (5th Cir.1992) retrieved from: https://scholar.google.co.th/scholar_case?case=6625292697406630772&q=boombox+interference+with+flight+crew&hl=en&as_sdt=2003