As several of his walking companions described it, he had a distinctive "swinging" gait. And, like many a serious runner of today, he "made a practice of increasing his speed when ascending a hill
I also found a second, earlier post in the Boston College magazine to the same effect:
Walking was essential, to bring his books into being, and to calm the effects of his intense engagement with his characters. Repeatedly his letters mention extended periods of walking as he worked toward a new project. The activity of walking allowed him to think his way into new fictional worlds, while allaying the increased restlessness that came upon him when he was still in a state of uncertainty.own experiences touring the streets of London.
The article reminded me of another mind who liked to wander, Lise Meitner (the co-discoverer of fission). According to Rhode's The Making of the Atomic Bomb during the 1930s she averaged walks of 10 miles per day. She was a petite woman, and would have made an excellent marathoner in another world. But she was not unusual; I've read many physicists of the time were quite taken to sports. Neils Bohr was an avid ping pong player and hiker. Hawking, before the onset of ALS, rowed for Oxford. A certain chemistry prof in my department used to run the 100 dash. Physical activity is pretty damn good for the mind, so it seems. Out-of-shape intellects are, thankfully, the rarer breed.