How to find curve radius/diameter

Take 8 or 12 of the same size and make a circle. Obviously measure across the circle for the diameter.

So far as postwar tubular track is concerned, measure from the ground to the top of the railhead. O-27 track is 7/16" high and makes a 13.5" radius (or 27" diameter, hence the name) curve.

"O" gauge (again, in postwar vernacular) is 11/16" high and makes a 15" radius (about 31" diamater, depending on whether you measure to the center or outer rails.

There were 0-72 curves that made a 36" radius or 72" diameter curve, but they were only made with the taller 11/16" rails.

---PCJ

Thanks for the reply. I'm geometrically challenged, so finding the same size pieces is hard for me. Especially in just one short section of track. I was hoping there might be some measurement I could do on one piece that would tell me the diameter (short there being the diameter printed (hidden) somewhere on the track itself)...

There is also 042 diameter in 027 profile height track. Confusing...I don’t remember if it had a different name to reflect the diameter being 042.

You could always scribe different arcs on a piece of cardboard or something and see which piece matches with which arc.

@Owen37a posted:

Thanks for the reply. I'm geometrically challenged...

@lionelsoni posted:

If you have a piece of any size, you can accurately calculate the radius of any rail by measuring the chord (the straight line distance between the ends of the rail) and using the following formula:

r = c/(2*sin(a/2))

where a is the angle of the curved section (e.g., 45 degrees for O27 and O31) and c is the chord measurement.

For various section angles a, the values of 2*sin(a/2) are

45:    .765
30:    .518
22.5:   .39

1.  Lionel only made two curves in O Gauge track in the Post War Era: O-31 with three ties, and O-72 with more ties.  They’re both heavy gauge steel.

2.  Lionel only made one curve in O-27 in the Post War Era.  It’s lighter gauge and flimsier steel.

Beyond that, the easy way to figure out MODERN ERA track quickly is by laying the curves on top of on another.  You’ll quickly see that the wider curves stick out farther.

Jon

@rattler21 posted:

Are the ties black or brown? John

Rusted or paint peeled off... But they _look_ like they were/are black...?

Thank you everyone for your answers! It is challenging to begin any hobby...

Black ties whose base is curled in the cross track direction are 0-31 profile.  Brown ties with four vertical sides are O-27 profile.  John

Stack the sections into piles of similar sizes.

Set a curve on a flat surface. Take a yard stick and place it across the end of the rails (remove the pins.)  Draw a line along the yardstick. Do it again at the other end of the section. Where the lines intersect, make a mark. Take a protractor and find the angle between the lines. Divide the answer into 360. That is the number of sections required for a circle. Place that number of similar sections in a circle. Measure the diameter of the circle. There are the answers to how many and what diameter.

Post a few pictures and just about everyone here on the forum will tell you what you have just by looking

I always used Ogauge with black ties.

3 ties per piece was 031

4ties was 042

5 ties was 054

6 ties was 072

Thanks for all the replies. I found this on Youtube:

(Not applicable to Owen37a problem)

When working with a CAD program and reality, I found out that what it says and what it really is are two different things. I tried measuring the distance from center-rail to center-rail for one piece of curved track and convert from straight line to arc, and, it didn't go too well, the track can get bent, hard to get right on center. Best way I found was assemble a circle of track and measure across at several different angles and use the average. Again, I used center rail to center rail, makes it easier in CAD (the outer rails are basically window dressing).

I am presently using NanoCAD, a Russian-made AutoCAD 2D knock off.

(Some edits for clarity).