*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' ? >>> Thanks in advance for your efforts and explanations. >>> 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 Web home page: www.keays.com.au

**References**:**[LandXML] LandXml question spiral types 'cubic' and 'cubicParabola' and 'rev'***From:*Alfonso . Ruiz

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