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But…It gave a very basic overview of how to do itOnly showed one way & one size
Courtesy : RailBricks
How About Going Even BiggerThe 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
Triangle Geometry ReviewThe only triangle we need to be most familiar with is
the isosceles triangleA triangle with two equal sides (or legs) & two equal
angles is an isosceles triangleMatthes’ created a ½-8-8 (in studs) triangle and
“wedged” it between the tracksIncrease the length of two legs while keeping the
third side (or base) unchanged decreases the angle between the legs (example: ½-9½ -9½ triangle)
Triangle Geometry Review
A ½ - 8 - 8 triangle has an angle measure of3.58 degrees
A ½ - 9½ - 9½triangle has an angle measure of 3.02degrees
Polygon Geometry ReviewA “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)
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
What to ConsiderThe 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)
The Number Crunching is Done!Regular Polygons and
their Central AngleIsosceles triangles with
a base length of ½ studSides Central Angle
100 3.6
104 3.4615
108 3.3333
112 3.214286
116 3.103448
120 3.0
124 2.903226
128 2.8125
132 2.727273
136 2.647059
140 2.571429
144 2.5
148 2.432432
152 2.368421
LegLength
Angle Between the Legs
8 3.580403
8.5 3.369854
9 3.18269
9.5 3.015219
10 2.864491
10.5 2.728113
11 2.601429
11.5 2.490925
12 2.387151
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 3.580403
108 3.3333 8.5 3.369854
112 3.214286 9 3.18269
120 3 9.5 3.015219
124 2.903226 10 2.864491
132 2.727273 10.5 2.728113
140 2.571429 11 2.601429
152 2.368421 12 2.387151
Values were chosen with a less than +/- 0.04 degree error margin
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 2.864491
136 2.647059 11 2.601429
148 2.432432 11.5 2.490925
Values were chosen with a greater than +/- 0.04 degree error margin
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 3.580403
108 3.3333 8.5 3.369854
112 3.214286 9 3.18269
120 3 9.5 3.015219
124 2.903226 10 2.864491
128 2.8125 10 2.864491
132 2.727273 10.5 2.728113
136 2.647059 11 2.601429
140 2.571429 11 2.601429
148 2.432432 11.5 2.490925
152 2.368421 12 2.387151Those with a “ ” are best matching
So Far…We’ve got the triangles coveredWe’ve got the polygons coveredWe’ve got the combinations of triangle to polygon
covered
But…
HOW BIG ARE THESE THINGS???
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
Important Notes About the RadiusThe radius values given are from the inner most
edge of the curve to the center of the circleWhen 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 studsIn layouts using ballast, allow space for the wedge to
rest on and betweenup to 4 plates for depth width and length varies according to positioning and
size of wedge in use
Important Notes About the RadiusRunning two distinct (different radius values) curves beside
each other will not produce an 8 stud gap between track
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.
Additional NotesReminder: 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).”
Looking Into the FutureThe creation of gentile uphill/downhill paths that
curveThe creation of an “S” curve as shown below in this
aerial view of an LRV overpass
Courtesy : Google Maps
Looking Into the FutureA table for creating the 60˚ curve
(currently in the works)
Polygon Sides
Tracks per 607
Central Angle
Radius in Studs
Isosceles Triangle to Use
102 17 3.52941 259 8
108 18 3.33333 275 8.5
114 19 3.15789 290 9
120 20 3.00000 306 9.5
126 21 2.85714 321 10
132 22 2.72727 336 10.5
138 23 2.60869 351 11