Do elephants run, trot or just walk rapidly?

This sounds like an obvious question, but what do we actually mean by running? One definition is that all of an animal's legs leave the ground at once, which is obvious when humans are running, but the same happens when a dog or horse runs. In this case an elephant definitely doesn't run as it always has a leg on the ground, but when the elephant is moving fast it does look more dynamic than a walk so what is going on?

A slightly more sophisticated definition is that when you are walking your total amount of kinetic and gravitational potential energy is about constant, so if your centre of mass moves up you slow down and vice versa, but if you are running energy is stored in springy tendons in your legs and your total kinetic and potential energy goes up and down.

Norman Heglund from belgium has tried to investigate this in elepants, by going to an elephant sanctuary in Thailand and then building a large elephant proof track which measures the forces the elephant is applying to the ground - which involves some quite serious engineering.

They have found that elephants sort of run. Their front legs bounce in a running manner, but their back legs walk in a smooth manner. It is like elephants are almost running but are too heavy to do it properly. Not that this would make a lot of difference if you are facing a charging 4 tonne elephant of course.