Re: Steepest train/tram line

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

James Robinson <NOSPAM@ERIE.NET> wrote:

>Ron BEST wrote:
>>
>>  <on measuring gradients> 
>> 
>> Wot's it got to do with going Metric? 

>To conform with most of the railways in the rest of the metric world.

>> "1 in 100" is 1 metre up in 100 metres
>> of track, or 1 Outer Mongolian Cathump up in 100 Outer Mongolian Cathumps of
>> track. Much more obvious what it means than a percentage! 

>Not necessarily more obvious. It is a counterintuitive measure in that
>steeper gradients earn a smaller number.  Calculations are also simpler
>with the percentage measure in that resistances are directly
>proportional rather than inversely proportional. 

Strictly speaking, resistance is not proportional to grade expressed
as a fraction/percentage.  Resistance is proportional to the sine of
the angle of inclination.  However, for small angles such as are
represented by railway grades, sine(theta), tan(theta) and theta are
all approximately equal.  Tan(theta) is the grade expressed as a
ratio.