Grade School

After 45 years of driving mountain roads, I discovered something that came as quite a surprise.  Now, I'm wondering: did virtually everybody know this except me?  I bet not.  

This type of sign is often seen on mountain roads, especially on high mountain passes.  The grade percentage varies widely, of course; the vast majority are single-digit in the 5-8 range but I've seen them as high as 21%.

 What is that sign above really telling us?  8% of what?  I'd never really thought about it.  If asked, I would have said it meant an 8 degree angle.  I would have been wrong.  The sign is telling us that for every 100' of horizontal distance, the road loses 8' in vertical distance.  

So, a 100% grade would mean that for every 100' of horizontal distance, there's a loss of 100' of vertical distance.  If you sketched this on graph paper, you'd find that a 100% grade yields a 45 degree angle.

Any questions?  No?  Okay, it's time for recess.  You may go outside and play now.