# Talk:Fall line (topography)

Latest comment: 14 years ago by 79.138.193.102 in topic Mathematical/physical errors

## Mathematical/physical errors

"That is, the direction a ball would roll if it was free to move on the slope under gravity" First of all, you'd need to harden the slope, or use a light large ball, or it would sink in the snow. Now, disregarding that, the ball would be affected by its inertia, and would sometimes go uphill (imagine dropping the ball from the lip at the upper end of a half pipe). At first, I was going to edit it so that the ball had no mass, but then it wouldn't roll anyways...

"Mathematically the fall line is the negative of the gradient (which points uphill) and perpendicular to the contour lines." Not true either. I can't think of any reasonable way to describe the mountain we're skiing on as a function of three dimensions, so it would have to be a scalar function of two dimensions (altitude as a function of latitude and longitude). And if that's the case, the gradient exists in the lat-long plane, and thus does CAN NOT point uphill or downhill. There is quite simply no up or down in the horizontal plane, just like a temperature of 39 degrees doesn't point to the right. The gradient points in the direction IN THE PLANE that would take us uphill quickest.

I guess it makes for an easy explanation, but it's just not true. As should be apparent from the above, though, I just don't have enough word-skills to write up a better explanation, so I'm leaving the "wrong-but-understandable" stuff in the article for now. 79.138.193.102 (talk) 18:22, 29 September 2009 (UTC)