So the other day we were trying to get some bounds on how far Gandalf and the Balrog fall. This is difficult since the geology of middle earth is not cannonical. However, we thought perhaps we could get a good bound by estimating how long it took Gandalf and the Balrog to run from the bottom all the way to the top (and then subtracting the height of the mountain). This can be done, but we can't answer the question because we don't know how fast Gandalf can run up stairs. Any suggestions?