Re: Steepest train/tram line

[James Robinson <NOSPAM@ERIE.NET>]

Krel wrote:
> 
> On 6 Dec 1998 17:44:38 GMT, markbau1@aol.comQQQQyuk (MarkBau1) wrote:
> 
> >Apart from Australia and that little island off France are there any other
> >countries that still use the 1 in XX instead if the % system?
> >
> On a similar subject - Is there anywhere apart from North America that
> measures curves by degrees instead of distance for sharpness. I don't
> understand how a right angle curve could be described as a 2 degree
> curve :-).
> 
> Surely radius, in yards, metres, chains, feet, anything makes more
> sense.

Radius actually isn't much use in describing curves, other than as a
number written on a map.  Degree of curvature as a measure has a more
practical use.

Measuring curves by the degree of curvature was called the American
system, and was only used by railroads that adopted American practice. 
This measure should not be confused with the total included angle of a
curve, but is a measure of how sharp or tight the curve is.  On the
other hand, to confuse things, there is also a metric measure for degree
of curvature, which is different from that used in the US and Canada,
and which is used in Mexico, as an example.  

The definition of degree of curvature, using the English system is: the
number of degrees of central angle of a curve, subtended by a chord of
100 feet.  Thus, a one degree curve will have a radius of about 5730
feet. (1746.4 metres)  A two degree curve will have a radius of about
2865 feet (873.2 metres) As the value of the degree of curvature rises,
the curve gets progressively sharper.

The practical use for degree of curvature comes when a surveyor wants to
lay out a curve on the ground.  One does not lay out the curve by
measuring from the centre with a string or giant compass, rather the
curve is laid out by staking the curve from one end to the other.  If
you work from the above definition, and some fancy geometry, you will
find by the rule of congruent triangles that a surveyor can lay out a
curve by swinging the transit by the degree of curvature every length of
survey chain. (100 foot chains) 

To describe the process: The surveyor will sight on the previous stake,
dump the transit (flip it 180 degrees to look in the opposite direction)
then turn the desired number of degrees in the proper direction.  This
will point at the location for the next survey stake, which will be
placed the length of one chain away. (100 feet)  These steps are
repeated at each new stake until the curve is fully laid out.

In the metric measure, the chord length is 20 metres instead of 100
feet, which conforms with the metric survey chain length.  This
unfortunately results in a different curvature value for the same curve,
but the practicality and ease of laying curves out using the 20 metre
survey chain remains.  This chain length was probably selected to
closely match the Gunter survey chain length of 66 feet, which at one
time was fairly common.

Lesson for the day is over.  Any questions?