Finding the Centre of Gravity of a Train

Finding the Centre of Gravity (COG) of an irregular shape by cutting the shape out of cardboard, hanging it from various points and using plumblines to locate the COG is a nice school practical. How is it done in practice for large real objects? I'm sure these days CAD does it all for you very accurately at the click of a mouse button. But how about 'back in the day'?

In 1936, a new high speed railway line was being planned and the engineers needed to be certain that the lines were canted (angled) enough on corners to make sure the trains didn’t derail, even at high speed. To know how much to cant the rails, they needed to know exactly where the trains' COGs were, since that would determine their stability.

The Drawing Office - who held all the designs for locomotives, tenders and coaches - were given the job of estimating the height of a locomotive's and tender’s COGs above the rails, based on the weight and location of every component part. Quite a fiddly job, and liable to error.

So, at Doncaster Works, their result was checked practically. How? By freely dangling a 50-tonne steam locomotive and using plumblines, just like we do in schools but on a rather bigger scale:

If you look closely, you might notice that the locomotive seems to have two COGs. This is because it was measured twice: once with the locomotive's boiler full of water and once empty - I'm sure you can work out which is which.

They then did the same thing with the tender (the 'coal truck' which sits behind a large locomotive):

Here, the difference between the 'full' and 'empty' COGs is much bigger since, without coal or water in, a tender is really just an empty steel box on wheels.