Yep, it's pretty much straight down for a while - I can't say how far. But the whole mountain is mostly granite, so if you do happen to fall, after the first fifty feet or so it's just a mathmatics exercise - for the coroner.
I jad always wondered how H**ker's troops managed to climb up those rocks. The slope of the mountain is steep, but manageable, until about halfway up when you are faced with a wall of granite.
Then I finally understood that the Union soldiers didn't climb the granite bolders, they just sort of circumnavigated it from the West until they hit the plateau where the Cravens House stood about halfway up the mountain. Once that plateau was seized (after a rather fiece little fight), the Confederates considered their position on Lookout Mountain to be flanked. with H**ker's forces in a position to cut off the Confederate batteries and infantry on top of the mountain from the rest of Bragg's army at Lookout Creek and Missionary Ridge, they withdrew so as to save the artillary.
As a Boy Scout, my first hike was on the Blue Bever Trail which traced the path of H**ker's forces up to the Craven House. Then we took the Incline Railway back down the mountain.