Re: Steepest train/tram line

["Jeff B. Kurland" <kurlandj@erols.com>]

I wrote:

>I'm a little confused.  Does the xx of  1 in xx represent the
horizontal
>distance or the distance traveled (length of rail used).  In other
>words, if we imagined a certain steep hill as a 3:4:5 right triangle, 4
>being the horizontal distance, 3 being the vertical distance, and 5
>being the distance traveled, would it be called 1 in 1.66  (3 vertical
>in (5 distance/3 vertical)) or 1 in 1.33 (3 vertical in (4 horizontal/3
>vertical)) ?



...then James Robinson answered:
>It's based on horizontal distance.  In your example, it would be 1 in
>1.33, or 75% for those prone to using that other system.  It's done
this
>way as it is consistent with how the routes were surveyed.  Surveys are
>mostly done using a horizontal plane as reference.  In most railroad
>applications the difference is trivial.

...but Geoff Lambert answered:
>The former, strictly speaking.  But the two distances are so close for
>all reasonable grades, that it doesn't really matter.  See my earlier
>post regarding the equivalence of sin(theta), tan(theta) and theta.

..so now I still don't know!  Is the grade of an office elevator (lift)
1 in 1 or 1 in 0?