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For more than 10 years from 1843, a train without a locomotive plied the two-mile route between Kingstown (now Dún Laoghaire) and Dalkey. Trains running every 30 minutes were propelled up the 1-in-110 gradient to Dalkey by atmospheric pressure.. Returning trains coasted down to Kingstown under gravity. A 15-inch cast-iron pipe was laid between the railway tracks, and a piston in the pipe was linked through a slot to the front of the train. The slot was sealed by a greased leather flap to ensure it was air-tight. The air in the section of pipe ahead of the train was exhausted by a steam-driven air pump in an engine house at the Dalkey terminus. With a partial vacuum ahead, the atmospheric pressure behind the piston drove the train forward. Available technical data are scant, but adequate for some back-of-the-envelope calculations to estimate average speeds and travel times. Pressure is force per unit area. The atmosphere presses on the piston from both ends; the nett force is the pressure difference multiplied by the area. The area of the piston face follows from its diameter, and, with a working vacuum of about 15 inches of mercury, or half an atmosphere, the pressure difference is 500 hPa. Then the force on the piston comes to about 5,700 newtons (more details on thatsmaths.com).

Don’t forget about friction Using Newton’s Law, we can divide the force by the mass of the train to get the acceleration. Assuming a train of mass 10 tonnes, the acceleration comes to about 0.6 metric units. This may be compared to the 10 metric units of the acceleration due to gravity but, with the small gradient, only about 1 per cent of the gravitational acceleration acts along the pipe, so the nett acceleration is about 0.5 metric units. Now a standard equation of elementary mechanics comes to the fore: the square of the terminal speed is twice the acceleration times the distance. Knowing the acceleration and the length of the line (2,800m) we can estimate the maximum speed and journey time. The formula gives a maximum speed of 190km per hour and an average speed of half this value. However, we have neglected friction, which reduces this considerably. Typical running speeds of 40km per hour would give a journey time for the up-train of about four minutes. This is consistent with reported times. We can also estimate the maximum speed on the downhill journey by invoking energy conservation. At Dalkey, the train has gained potential energy (mass times gravitational acceleration times height). The terminus at the Dalkey end was 25m above sea level. Supposing the potential energy to be converted completely to kinetic energy (half mass times speed squared), maximum speed would be about 80km per hour. A mean speed of 40km per hour is an over-estimate, as frictional losses have again been ignored. According to contemporary reports, the return journey under gravity was “lady-like”, the average speed being about 30km per hour and the journey taking between five and six minutes. Although reasonably successful, the atmospheric system had several operational inconveniences and was abandoned. But a system using similar pneumatic principles is running today in Jakarta, and another, called Aeromovel, is proposed for construction in Brazil. So air power, which seemed like a white elephant 160 years ago, may again provide fast, clean and frequent urban transport for Dublin.

Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com