## [LandXML] Re: LandXml question spiral types 'cubic' and 'cubic Parabola' and 'rev'

• From: "John Keays" <john@xxxxxxxxxxxx>
• To: Alfonso.Ruiz@xxxxxxxxxxxxxxxxxxxx
• Date: Tue, 22 Jul 2008 09:32:03 +1000 (EST)

```To Alfonso,

As a developer of software I have to include spiral details into my
software.  My attitude to spirals is that for road design you can live
without them.  Maybe for railways a spiral is needed for low speed track
work.  If you put a spiral in the system you will need a surveyor on site
for checking.  It generally adds to the cost of construction specially if
the project includes bridges.  If you look at formula One racing the
tracks are flat and the race line is probably a spiral but the track is
done with circular curves.  Arton Senna died when there was a bump on the
track that lifted the car off the ground.  Construction toleerances are
important.  Generally the race cars pull several G's around a curve.
Spirals are usually introduced so that there is approximately zero G
forces around the curve.

I went to Tasmania last week and travelled on a rail track designed and
built around 1880-1900.  It was done with old railway curves and boning
rods.  I don't think any curve was properly calculated for spirals.  They
just used a deflection per rail length with a length of transition from
curve to straight.  Checking curve deflections per length is pretty close
to the Euler spiral.  it might be bumpy now but it is okay and they built
the rail line in two years from start to finish in terrible terrain.

Each country will have an academic that prefers a method.  The original
cubic parabola is a formula that could be calculated on a hand held
calculator or done long hand as the additional terms of the Euler curve
are only required for the longer spirals. With computer software it
doesn't matter how many terms are used.  I found that 4 or 5 is enough for
normal curves.  I found millimeter differences between the cubic parabola
(2 terms) and the MOSS Euler (5 terms) at a 40 or 50 metre length.  The
ride ability is the same.  I used three different curves for 20 years.  I
added Nathan's curves in after I got hold of his paper.

To set out the curve in hte filed we just create an XYZ table of points at
an agreed interval and set out either as an EDM with a surveyor or as a
chainage and offset if there is only a foremen present.

In writing the software I use the Newton Rapson technique to solve for a
line spiral intersection and it works the same for the different curve
formulas.  I only need say 6 or 7 functions for the different spirals that
give a length, delta x and delta y off the tangent and the angle of the
tangent relative to the TP point along the X Axis.  Only an additional
twenty or so lines of code for each spiral type. That way I don't have to
suggested which formula is appropriate.  Let the user decide. I worked
through each of the funny formulas that Nathan Crews found from his
travels.  The Bloss the cosine seem to come from the German train
technology as it gives a better pull on the train around the curve at low
velocity.  My guess is that technology was passed to the Japanese around
World War 2 just like Siemans and Fujitsu with communications technology.
The Japanese like to write their own software so its fitting they have
their own spirals.

I really enjoyed looking at Nathans paper on the curves.  We all have our
own way of doing things.

Cheers

John Keays

John said > Alfonso.Ruiz@xxxxxxxxxxxxxxxxxxxx
>>> Dear colleagues,
>>> having a look to the different Spiral types there are several spiral
types
>>> available:
>>> - what is the difference between  'cubic' and a 'cubicParabola' ? -
when should I use the 'rev...' types (e.g 'revBloss' or 'revCosine'
instead of 'Bloss' or 'Cosine' ?
>>> best regards

--
John Keays,Keays Software PO Box 80, Toowong, Q 4066
9/621 Coronation Drive, Toowong, Qld 4066, Australia
Phone +61-7-3870-1711 fax +61-7-3870-1784