Large Curves Using Straight Track

1. Large Curves Using Straight Track

2. Origins The Holger Matthes article in RAILBRICKS issue #1 2007 Courtesy : RailBricks

3. But… • It gave a very basic overview of how to do it • Only showed one way & one size Courtesy : RailBricks

4. How About Going Even Bigger • The RAILBRICKS article mentions using only 23 tracks but it can be more than that! • By understanding the geometry behind the large curves that will allow us even larger and more gentile curves using 9V straight tracks

5. Quick Geometry Review • Review of Triangles • Review of Polygons

6. Triangle Geometry Review • The only triangle we need to be most familiar with is the isosceles triangle • A triangle with two equal sides (or legs) & two equal angles is an isosceles triangle • Matthes’ created a ½-8-8 (in studs) triangle and “wedged” it between the tracks • Increase the length of two legs while keeping the third side (or base) unchanged decreases the angle between the legs (example: ½-9½ -9½ triangle)

7. Triangle Geometry Review A ½ - 8 - 8 triangle has an angle measure of 3.58 degrees A ½ - 9½ - 9½ triangle has an angle measure of 3.02 degrees

8. Polygon Geometry Review • A “regular” polygon has “n” number of sides, each of equal length and vertices of equal angle measure. • The central angle is the angle made at the center of the polygon by any two adjacent radii of the polygon. • By making a full “circle” using only straight tracks we are in fact making some regular polygon (example: 100-gon or hectogon)

9. Polygon Geometry Review An example of a regular polygon and location of the central angle

10. Visualizing the Central Angle of a Polygon Made of Straight Tracks Red triangle shows the central angle of the polygon for the inside curve Blue triangle shows the central angle of the polygon for the outside curve The inside curve is made from a 100-gon & the outside curve is from a 108-gon

11. What to Consider • The large triangle created using the radii & central angle of the polygon is proportional to the small isosceles triangle being wedged between the tracks • The angle measure of the isosceles triangle between the tracks should equal or approximate the central angle of the particular polygon in use • When making 90˚ curves, the regular polygons selected should have values divisible by 4, thus allowing for easy creation of quadrants (example: 128-gon ÷ 4 = 32 tracks per quadrant)

12. The Number Crunching is Done! • Regular Polygons and their Central Angle • Isosceles triangles with a base length of ½ stud

13. Best Matchings of the Central Angles to the Isosceles Triangle Values were chosen with a less than +/- 0.04 degree error margin

14. Close Matchings of the Central Angles to the Isosceles Triangle Values were chosen with a greater than +/- 0.04 degree error margin

15. General Matching of the Central Angle to the Isosceles Triangle Those with a “ ” are best matching

16. So Far… • We’ve got the triangles covered • We’ve got the polygons covered • We’ve got the combinations of triangle to polygon covered But… HOW BIG ARE THESE THINGS???

17. Radius Values of Matched Pairs

18. Important Notes About the Radius • The radius values given are from the inner most edge of the curve to the center of the circle • When planning for layouts, be sure to add 8 studs for track width and up to 4 studs more depending on the triangle wedge in use • example: 128-gon has 326 studs radius + 10 studs (8 for track & 2 extending from wedge) = 336 studs • In layouts using ballast, allow space for the wedge to rest on and between • up to 4 plates for depth • width and length varies according to positioning and size of wedge in use

19. Important Notes About the Radius

20. Important Notes About the Radius • Running two distinct (different radius values)curves beside each other will notproduce an 8 stud gap between track

21. Important Notes About the Radius • To avoid the “It’s not 8 studs!” issue, go back to what you did with regular curved tracks. • For your outside curve, use a polygon with the same radius of the inside curve • Adding some straight tracks at the 0˚ & 90˚ marks of the outer curve will help align the two curves and give the 8 stud gap between the tracks.

22. Additional Notes • Reminder: inserting such curves into a layout requires a lot of space and leaves a big footprint! • Matthes noted in his article that there can be changes in electrical resistance “While electrical continuity is preserved, resistance might increase with this design, i.e., heavy trains far from the pickup might slow or stop. A simple solution, if such a problem arises, is to use two or more electrical pickups from the same controller, distributed around the track (just be sure to connect them with the same orientation).”

23. Looking Into the Future • The creation of gentile uphill/downhill paths that curve • The creation of an “S” curve as shown below in this aerial view of an LRV overpass Courtesy : Google Maps

24. Looking Into the Future • A table for creating the 60˚ curve (currently in the works)

25. Thank You & Leg Godt