What is the optimum speed for a railway?

The response to the publication of the high speed rail proposals has been surprisingly cool. On one side, there is opposition from the NIMBYs, and on the other there seems to be a feeling that we need to do better with the railways we've got, and long before the projected completion date of the first stage of the new line.

Could it be that there is a growing understanding that the geography of Britain, and its pattern of settlement, are wrong for high speed rail?

France, Germany and Spain, which have the best-developed high-speed systems, are large countries with cities far apart, separated by sparsely-populated countryside. Britain has a completely different pattern of settlement, with 80% of the population living in less than one-third of the land area, but relatively spread-out within that area, in low-density suburbs that are difficult to serve economically by any form of public transport.

For these reason, most people's preferred mode of travel is the private car. Public transport is used primarily for travel within the denser areas of the larger cities and conurbations. Most rail journeys in Britain are made within London and the South East.

Diminishing returns
Rail remains important for inter-city travel but a typical inter-city journey in Britain is around 200km, perhaps even less. This is why high speed rail may not be a worthwhile investment. It comes up against accelerating costs and diminishing returns. At a start-to-stop speed of 100kph, a 200 km journey will take 2 hours from end to end. Increase the speed to 150 kph and the journey time goes down to 80 minutes, a saving of 40 minutes. A further increase in speed to 200 kph takes the journey down to 1 hour, a saving of another 20 minutes. The next 50 kph increase in speed reduces the journey time to 48 minutes, a saving of just 12 minutes. (see diagram) Each successive speed increment yields a smaller time saving.

At the same time, each successive speed increment costs more. Energy consumed is proportional to the square of the speed; a train running at 200 kph uses twice the energy of one at 140 kph. But things are much worse than that. There are critical speeds where the technology immediately becomes more expensive. At speeds of up to 40 kph, a railway can be run as a tramway or under what is known as a "Light Railway Order". Vehicles are lightweight and signalling is simple. Most of the preserved museum railways operate under this rule. Dispensations from the rules that apply to ordinary railways can also be given to railways operating at up to about 90 kph.

The next break-point is 160 kph, when the railway is classified as a high speed line and must comply with EU rules for such lines, which add an entire additional layer of costs.

In addition to these critical speeds where the lines become subject to different regulations, there are other break-points due to technical requirements. 120 kph is about the maximum speed at which the ventilation of trains by means of opening windows is acceptable. At speeds of above about 160 kph, more efficient braking systems are needed, the suspension system has to be very much more complex and the track must be constructed to different standards, using heavier rails and other components. The situation changes again above 160 kph, when some form of continuous in-cab signalling such as the European Rail Traffic Management System (ERTMS) becomes essential. It is also the case that at higher speeds, wear and tear on both trains and track become much heavier due to the higher forces involved, proportional to the square of the speeds.

What the diagram seems to indicate is that for the sort of inter-city journeys that are typically made in Britain, it is worth constructing new railways and increasing train speeds up to about 160 kph, just below the point at which the lines become subject to EU regulations, but no more than that.