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 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
Sides
Central Angle
100
3.6
104
3.4615
108
3.3333
112
116
120
3.0
124
128
2.8125
132
136
140
144
2.5
148
152
Leg
Length
Angle Between the Legs 8
8.5 9
9.5 10
10.5 11
11.5 12

13. Best Matchings of the Central Angles to the Isosceles Triangle
Polygon Sides
Central Angle
Isosceles Triangle
Leg Length
Angle Measure Between Legs
100
3.6 8
108
3.3333
8.5
112 9
120 3
9.5
124 10
132
10.5
140 11
152 12
Values were chosen with a less than +/ degree error margin

14. Close Matchings of the Central Angles to the Isosceles Triangle
Polygon Sides
Central Angle
Isosceles Triangle
Leg Length
Angle Measure Between Legs
128
2.8125 10
136 11
148
11.5
Values were chosen with a greater than +/ degree error margin

15. General Matching of the Central Angle to the Isosceles Triangle
Polygon Sides
Central Angle
Isosceles Triangle
Leg Length
Angle Measure Between Legs
100
3.6 8
108
3.3333
8.5
112 9
120 3
9.5
124 10
128
2.8125
132
10.5
136 11
140
148
11.5
152 12
Those with a “ ” are best matching

16. HOW BIG ARE THESE THINGS???
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
Polygon Sides
Straight Tracks per Quadrant
Approximate Radius Length in Studs
Approximate Radius Length in cm./ in.
100 25
255
204 / 80
108 27
275
220 / 96
112 28
285
228 / 90
120 30
306
245 / 96
128 32
326
261 / 103
132 33
336
269 / 106
136 34
346
277 / 109
140 35
357
286 / 112
148 37
377
302 / 119
152 38
387
310 / 122

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 not produce 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)
Polygon Sides
Tracks per 60̊
Central Angle
Radius in Studs
Isosceles Triangle
to Use
102 17
259 8
108 18
275
8.5
114 19
290 9
120 20
306
9.5
126 21
321 10
132 22
336
10.5
138 23
351 11

25. Thank You
&
Leg Godt