## A train without a locomotive used to run between Dún Laoghaire and Dalkey – let’s figure out how long it took

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).

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.