Re: Steepest train/tram line

[G.Lambert@unsw.edu.au (Geoff Lambert)]

"Jeff B. Kurland" <kurlandj@erols.com> wrote:

>I wrote:



>...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?

The latter.  The closeness of the two ratios only applies for
realistic adhesion-worked railways, say with grades shallower than 1
in 20:

% 	1 in	degrees		theta radians	sin(theta)	tan(theta)
2	50	1.1457		0.0200000	0.01999600	0.01999733
100	1	45.000		0.7853982	0.70710678	1.00000000

For 1 in 50 they're all effectively  interchangeable, so it doesn't
matter whether you use the ratio of the opposite to the adjacent
(tangent) or the opposite to the hypotenuse (sine).

But it does matter for grades like 1 in 1.	

Geoff Lambert