What is this?

Looks like Lionel Double O track.

southern Railfan posted:

Looks like Lionel Double O track.

I know the Brand-it’s MTH

Its the divergence of the plane of the arc off the straight line as it relates to a common center that I want to determine. 

Thanks 

It clearly states the brand🤪

An  easy basic step is to assemble a 90 degree arc. 

Place the two ends at the edges of a sheet of plywood. 

Measure from the center rail to the corner.  Make sure both center rails are the same distance to the corner. 

Double that number, that is the O-number..  The diameter of your circle.

If you reading is 36", it is 0-72.

If your reading is 27" it is 0-54.

doing a little trig.... take a straight edge or a ruler greater than 14" and lay it down as a chord between the end points of the center rail on a single piece of track.  at the center of that chord, measure the distance from the straight edge to the center rail.  if it is O72 (16 pieces to a circle) that measurement will be 0.70".  if the track segment is 1/12 of an O54 circle, that measurement will be closer to 0.90"

unfortunately just measuring the chord on an O72 (16 piece circle) or an O54 (12 piece circle), they turn out to be pretty darn close to equal.  a 22.5° chord on a 36" radius circle is 14.04" and a 30° chord on a 27" radius circle is 13.96".  too close to differentiate in measurement with toy train accuracy.

math is fun!
cheers...gary

[edit... corrected some math]

Knowing the different lengths of those cords would be key.

for O54 track... (27 - 27cos 15°) = 0.92"

for O72 track... (36 - 36cos 11.25°) = 0.69"

the chord length need not be part of the equation.  the key is really what track MTH based the radius on... by now i'm hoping manufacturers have decided that the center rail be the ruling track radius.  you have to assume the accuracy of the arc length in being close enough to create a smooth 360° circle.

If you know the cord length of an 072 piece all you need to do is measure the piece you have.  No math needed.

The open forum question then is simply what is the cord length of an 072 piece.  Done

Tom Tee posted:

Isn’t eternity the same “long time” for being right?

Sorry for the confusion sir, that last line is just my signature, not a reference to our conversation .

As to our conversation, your approach and calculations are absolutely right.  My style is usually try to make forum speak as straightforward and simple as possible.  Both approaches can yield the same result in determining the diameter of the piece in question.  Your approach is free standing, mine needs to have a comparative sample.  All's good.

Or possibly O-82.  But for some reason I thought the size was marked on the track.

Just checked my stash of track.  The O-82 is in-fact marked.  But the O-72 is NOT marked, so these pieces are most probably O-72.

Ron