need math lesson

[TBat55]

I have flex track curve and want to cut in a turnout. I don't know the radius.

How do you determine the radius of a circle if you don't know (or cannot get to) the center? I am sure there's a math formula using the chord or similar.

[SpaceMouse]

This is not mathematical, but if you were to draw a line from several of the ties, they should converge. then measure from the convergence point.

[Seamonster]

To figure out the radius, you'll need to know either the diameter (which is 2X the radius) or the circumference (distance around) the complete circle. Since math was my worst subject in high school, I depend on calculators. Check out this site: http://www.onlineconversion.com/circlesolve.htm. If you can figure out the circumference of your curve, it will calculate the diameter for you and the radius is half of that. I've got that site's home page bookmarked as it's got every conceivable conversion there is. Hope this helps.

[selector]

It will take a few minutes, but you can mark the centres of the two end ties of your curve. Be quite accurate, to within 1/32". Then, draw a line parallel to the axis of those last ties so that they intersect at the centre of that curve. Start at end-tie midpoint A and draw a line of at least 20" (if practical to do). Do the same for the other tie midpoint. Those lines should intersect at the centre of the curve. From there, simply measure the radius.

[mcouvillion]

Terry,

I remember from long, long ago how to find the center of a circle using geometry. Your questions indicates that you might not be able to physically get to the center of the curve. Can you trace the curve so that you can move the measurement away from the layout? Roughly cut a piece of poster board to slightly larger than the size of the curve, then lay it on the track and press down, leaving an imprint in the poster board. Mark two points on the curve and their corresponding locations on the poster board. Now, move the poster board to a table or the floor.

Using another piece of poster board, attach it to the curved piece on the inside of the curve. You will need a large compass (the drawing type, not the magnetic type), a pencil, and a straightedge. From each of the points on the curve that you previously marked (hopefully towards the ends of the curve), draw an arc about two-thirds the distance to the other end of the curve both above and below the curve. Do the same from the other end point. The arcs should overlap. Where the arcs overlap, connect these points and draw a straight line toward the center of the curve, past where you think the center of the curve will be. This will be your reference line. From each end point, draw a straight line toward the reference line that is 90 degrees (right angle) to the curve at that point. The two lines from the end points should intersect the reference line at the same point. This is the center of the curve. Measure from that location to the arc of the curve and you have your radius.

Boy, this brought me back to my sophomore year of high school and geometry class. I knew I would use this stuff one day.

Mark C.

[cuyama]

QUOTE: Originally posted by TBat55

I have flex track curve and want to cut in a turnout. I don't know the radius.

You can certainly use the chord (and one other measurement) to determine the radius. A simple google search for "chord to radius" turned up several useful links, including this calculator:
http://www.1728.com/circsect.htm

It would probably be easiest in your situation to use the chord length and segment height to determine the radius.

But that alone probably won't tell you how to fit in a turnout. Normal "straight" turnouts (#4, #6, etc.) aren't actually curved uniformly through their length, as you probably know. Even "snap" turnouts that are measured in radius have a section of straight track in front of the points.

So a curved turnout seems like it might be the answer, but even these are not usually a perfectly consistent radius throughout. So even if you were lucky enough to find a turnout labeled as the same radius as the curve that is already there, it probably won't fit perfectly.

There is also the issue that unless you were very, very precise in laying the flex track curve originally, it probably varies in radius slightly from the tangent points to the middle of the curve -- just the physics of flex track. The middle of the curve tends to be slightly sharper in radius than the sections of the curve near the tangent points -- even if you did not intend to create easements.

In my opinion, the bottom line is that you will probably need to pull up a larger section of the track to work the turnout into place. If the radius is reasonably large to start with, it should not be too hard to rework the area to incorporate the turnout. But it seems unlikely that it could be a cut-out-and-drop-in operation without introducing some troublesome kinks.

Given this situation, you might be able to lay a couple of turnouts or full size copies along the curve to eyeball what will work well and how much track will need to be taken out and re-laid. The chord-to-radius calculation above would certainly give you a place to start in terms of exploring turnout options.

Regards,

Byron
http://www.modelrail.us

[rrinker]

Turnouts (other than the snap-track and specific curved ones) do not have a fixed radius, there is always a straight segment. Snap track ones have an 18" radius to match the track sections and with the 1/2 length curve they drop right in to an 18" radius curve. Specific curved turnouts are avaialble in various radii from different manufacturers, Walthers has probbaly the largest selection in code 83. Atlas Custom-Line #6 and #4 jave various 'substitution radii' which are listed in John Armstrong'sTrack Planning for Realistic Operation. Atlas Custom-Line #4's actually have a #4.5 frog angle, so they are not quite as tight as other brands of #4.

--Randy

[TBat55]

Thanks cuyama. I calculated the radius using the chord (end-to-end) and segment height (middle of chord to middle of curve). This is approximate since turnout radii are complex and the flextrack changes angle.

Thanks to others who contributed.