Friday, 12 September 2014

Wi-Fi in Schools

A friend of mine asks :

OLPC Class - Mongolia Ulaanbaatar
Question : What's the effect on the human body, of 20 children in a classroom, each downloading a 3 minute youtube video over Wi-Fi?

An excellent question!

As with all good science, let's start with an experiment.  I happen to have a 3 minute HD video on my network, so I can time how long it takes to copy across to my laptop:

missingbytes:$ time copy /NetworkDrive/HDVideo.mp4 .
real   0m6.550s
user   0m0.001s
sys    0m0.116s

So a single 3 minute video (3:19 to be precise) will use about 6.5 seconds of Wi-Fi time to copy.

With 20 students, and rounding up a little to account for congestion..

... lets call it 200 seconds of Wi-Fi activity total.

Transmit power

The transmission power for Wi-Fi signals is heavily regulated in the EU, the US and also in New Zealand where I'm performing the test.

The maximum 2.4-GHz transmission power is regulated by law, so lets assume it's 20dBm = 100mW = 0.1W ( source )

As we all learnt when we were in school, a watt is a joule per second, so 200 seconds at 0.1W is 20J.

Now we know that a class room of children downloading a youtube video results in 20 joules of microwave energy being emitted from the Wi-Fi router's antenna.

A brief diversion : Ionizing and Non-Ionizing radiation

Electromagnetic radiation forms a spectrum, from low frequency and radio waves, up through the microwaves, visible light, X-rays and on to gamma rays which have very high frequencies indeed.

Those high frequencies are characterized as ionizing, they're very dangerous to humans and their ability to cause DNA damage and ultimately cancer is well known. This is the reason why we need to be so careful around medical/dental imaging devices, and need to take precautions such as wearing sunscreen and polarized sunglasses when we're outdoors on a sunny day.

It's not necessarily the amount of energy, it's more the frequency that's the problem.  This high frequency ionizing radiation quite literally has the ability to rip electrons off their atoms.  It's these "ions" which go on to cause damage to biological systems.

By contrast, the lower frequency non-ionizing radiation (such as used in Wi-Fi, or FM radio) doesn't have the same ability to affect us in this way.

By itself, non-ionizing radiation can only cause heating in biological systems. Indirectly, it's this heating which slows down or speeds up chemical reactions and/or signalling within the cell, and it's these secondary effects which has the potential to cause problems.

Intuitively, this is why the 1000 watt microwave oven in your kitchen makes food super hot in a few minutes using microwave energy, but it doesn't actually make your food radioactive.  (You'd need an X-Ray oven for that!)

Anyway, lets continue, we've got 20 joules remember?


Now we need to make a pretty unrealistic assumption. Suppose that the entirety of those 20 joules of energy was somehow absorbed by one child.  Of course, this can't happen in the real world for two fairly obvious reasons:

  • A router transmits energy in all directions.  For all the energy to be absorbed by the child, the router would somehow need to be inside the child.
  • Microwave energy interacts only weakly with the human body.  That's one of the great benefits of Wi-Fi, it can pass right through walls and ceilings and straight through you and me.

But just for fun, lets continue on anyway and figure out what would happen if all of those 20 joules were absorbed by one child.

An average 6 year old child weighs about 22 kilograms.  (Of course, my 4 year old son also weighs 22 kilograms, but that's a blogpost for another day!)
The human body is about 65% water, so lets consider 14 kilograms of water.

The specific heat capacity of water is 4.18 J / gK

So we have 20 J / (14,000 g) / (4.18 J / gK) = 0.00034 K = 0.0004 °C
(That's 0.4 millikelvin for all you geeks out there.)


So there we have it, even with a wildly exaggerated assumption:

Answer : A classroom of children, all downloading a 3 minute youtube clip over Wi-Fi yields a maximum biological heating due to 2.4GHz microwave radiation of 0.0004 °C.

(0.4 millikelvin is about twice as small as it's possible to measure using a precision thermometer.)


We shouldn't really be too surprised.  Wi-Fi signals are incredibly weak. Consider this, those 20 joules of microwave radiation is the same amount of chemical energy contained in one thousandth of a teaspoon of sugar.

There's no way to prove scientifically that microwave radiation from Wi-Fi is safe in the human body. Science doesn't work that way. You can't prove a negative.

But we can try and make smart choices about tiny risks.

For example, the exposure from a banana is about 0.1 ╬╝Sv of harmful ionizing radiation because of their high quantities of naturally occurring radioactive potassium.

Yet who thinks twice about giving bananas to kids in schools?

Thoughts, questions or especially corrections?  Please feel free to leave a comment down below!