The Breadth and Width of a Megabit

av Jörgen Städje den 29 Apr 2016

How many megabits can actually fit between Stockholm and Uppsala? How long is a data packet as it travels in the optical fibre?

Light doesn’t fly through the fibre infinitely fast. Instead it travels slightly slower than in space. As the speed is well known, one could theoretically measure a data packet inside an optical fibre with a ruler to estimate its length. After a packet has been sent out from Stockholm it takes some time for it to arrive in e.g. Uppsala. As the data packets have a well known length it should also be possible to calculate how many bytes are in transit in the fibre between Stockholm and Uppsala. This would be helpful to get some sort of approximation, some sort of humanely comprehensible view of what is travelling through the fibres. We will try to find out how long the packets are, and how many of them can be stuffed in a length of fibre.

The bits and pieces of an IP packet

All data sent over optical fibres is packaged according to the IP protocol. The IP protocol is a digital envelope around your text or images (your payload), and this is how the payload gets receiver and sender addresses attached, plus some error checking. The reason for doing this is that all the data ending up in your computer will always be correct, regardless of whether it has only gone five metres or half way around the Earth.

Oversimplified, an IP packet expressed in blocks looks like this. It begins with a header containing the receiver and sender addresses, data about the packet length, a sequence number and so on, enabling networking equipment to know where the packet is going, how long it should be, and which one it is in a sequence of packets, etc. The header is always the same size, i.e. 160 bits or 20 bytes.

The next block is the payload, that is, your text or parts of your image. The payload can differ in length but usually the longest possible is chosen: 12000 bits or 1500 bytes.

Finally there’s a checksum, containing proof that the data arrived undamaged. It is always 24 bits or three bytes in length.

So, a typical packet is 1523 bytes in length as it is sent out on the optical fibre.

The length of an email

The packet is typically sent on the fibre as a series of blinks of light, where one blink represents a ”one” bit and no blink represents a zero. On a 100 Gbps link this translates to one hundred billion possible blinks per second. You could view it like this.

An oversized light sabre? The picture shows the undersigned wielding a hand torch, sending a data packet. Suppose I have a really fast thumb so I am able to blink IP packets at 100 gigablinks per second. A data packet of the biggest size, with a 160 bits header and 12000 bits of payload might look like this. 24 metres in length. It would take about 0.12 microseconds to send.

Below is the size of the 160 bit header, some 33 centimetres. It wouldn’t be visible in the previous image.

An eight bit byte is a mere 1.6 centimetres long and would easily fit on a thumbnail.

(The above is only partly true. The transmission can be optimised by sending several bits at the same time on different wavelengths and different polarisations in the same fibre, and by sending several streams of data on several parallel fibres. Et cetera. But let’s forget about that.)

The speed of light in the medium

You’ll have to pretend that the medium in front of my torch is glass and not air. Light travels slower in glass than it does in air, and slower in air than in vacuum. This has to do with the index of refraction in the medium, which also is the parameter determining how sharply the light will bend when it passes out of one material and into another.

This is the reason we can see a prism breaking up sunlight into different colours. The refractive index of glass is different for different wavelengths, which is why they refract differently and spread out so nicely. The rainbow is exactly the same phenomenon. The higher the refractive index, the slower the light will travel.

The vacuum of space has the lowest index of refraction, namely one. The speed of light in vacuum is 299,792,458 m/s, very close to 300,000 km/s.

The index of refraction in air is somewhat greater, 1.0003, giving light a speed of some ~298.896.000 m/s in air.

Of greater importance to the average SUNET user is the index of refraction in glass, about 1.5, giving light a speed of ~199.000.000 m/s in an optical fibre.

Measuring Sweden in megabytes

This is how we are able measure the length of the data paths in megabytes. Take a look at the map below.

We can roughly cram in 62.5 kilobytes per kilometre of fibre. Thus, Sweden is 97.9 MB (1567) from Ystad in the south to Treriksröset in the far north.

But wait! There’s more!

In the near future, several nations will have established research colonies on the Moon, perhaps even within the lifespan of SUNET C, around the year 2030. How will they communicate with Earth? It is obvious that “Houston, we read you, over.” Beep. Crackle. “Tranquillity base…” will not be sufficient for the modern Internet man. Internet will have to be extended to the Lunar base. Laser-based communication with the International Space Station has already been tested and shown to work. For fast data transfers to the Lunar base, a laser will have to be set up on the Moon’s near side, pointed at Earth. As the Moon is not spinning with respect to the Earth, only one laser will be necessary. A suitable place for a Lunar base would be the Moon’s north pole, since it is always in sunlight, which spells out positive for the use of photovoltaic cells. There also seems to be water available in the craters in constant shadow in the same region.

But the Earth rotates with respect to the Moon, so the Earth needs several receiver stations. A few would be required on each continent, as a laser beam cannot penetrate clouds.

The distance between the Earth and Moon is about 350,000 kilometres. There will be room for about 1.46 gigabytes on a 10 Gbps link (remember that the speed of light in vacuum is 300,000 km/s). You shouldn’t hope for 100 Gbps, due to turbulence in the atmosphere.

The return delay of 1.16 seconds to and from the Moon will make telephone and video conferencing somewhat awkward, although you might eventually get used to it. The main effort will probably be put into services like Facebook and email, where the delay is not so irritating. Other services, like Netflix will also have a field day. There will not be any shortage of bandwidth.

As the first university is established on the Moon, it will undoubtedly have a connection to SUNET. SUNET will rent part of the NASA Earth-Moon link and name it “the Black Network”.