Re: Katoomba Scenic Railway not steepest?

[David Johnson <trainman@ozemail.com.au>]

Michael Roebuck wrote:

> >3 of these sites give a gradient of 72.7%, which is pretty tame compared to
> >Katoomba (100% = 45 degrees)
>
> sections of the Pilatus mountain railway here in Switzerland (a rack
> incline) are at a gradient of 49%. I've always believed this to be the
> world's steepest passenger railway.

Sigh.  We went through a long discussion about gradients, but no-one seems to
remember any of it.

For these formulae,
Gradient in % = "GP"
Gradient in degrees = "GD"
Gradient in rise:horizontal distance = 1 in "GH"

GP = (tan (GD)) * 100
GP = (1 / GH) * 100

GD = inv tan (GP / 100)
GD = inv tan (1 / GH)

GH = 1 / (GP / 100)
GH = 1 / (tan (GD))

OK, does anyone dispute that?

For the examples at the top, the Pilatus mountain is claimed to have a gradient of
49%.  This would be 1 in 2, or 26.1 degrees. This is not very sensational.

The Tennessee railway is claimed to have a 72.7 degree AND a 72.7% gradient.
If it was 72.7 degrees, it would be 321% or 1 in 0.31.  I find this very hard to
believe.  These figures are getting very close to elevators which are 90 degrees.
The more likely figure is 72.7%, which equates to 36 degrees or 1 in 1.37.

The Scenic Railway at Katoomba is 52 degrees, which is 1 in 0.78 or 128%.

Does anyone dispute any of my working?

--
David Johnson
CityRail Guard
trainman@ozemail.com.au
http://www.ozemail.com.au/~trainman/