Bill Brillinger’s post illustrating his list-driven car card system reminded me that one of my key objectives for the model railroad we’re building in my math classroom is to provide a visceral understanding of the circumstances that generate traffic on a transportation system.

One example is a problem that I pose for calculating car orders for empty gondolas to carry away scrap metal as a function of how many cars of sheet metal coils are delivered to a tin can fabricating facility.  

I’ve been stuck for a few weeks trying to decide how to break a log jam. The benchwork sections have been resting idle, loosely bolted together and leaning against the wall but not fastened to it. I have a new crop of students who have been happily learning the basics of car movement, coupling, inertia, switch operations, etc. on the Inglenook, but a few of them have begun to paw the ground, eager to get going on the big layout.

Since my regular math classes have their hands (and minds) pretty full right now with homework and new classroom routines, I got the model railroad project back under way last week during a once-a-week elective called Applied Math. We only had an hour, and most of the students in the elective were not among those who worked on the project last year, but they were very eager to contribute nonetheless.

Since Labor Day the month of September has been jammed with activity as the new school year gets underway. Until last Wednesday, none of that activity involved the model railroad.

A few years ago I saved the slats from an old, cheap bed that my daughter wasn’t going to use any more. I knew I’d find a use for them eventually and sure enough, we needed quite a few risers. In fact the slats were very good quality fir, much nicer than the 1x2 furring strips we’d used for the rest of the benchwork.

Maybe it’s just the mild climate here, but I’ve never had any problem with sagging roadbed when I’ve used a glued-together sandwich of Homosote and plywood over 16” spacing between risers. Even when I’ve used ½” plywood it always felt plenty stable, even overkill.

So for light weight and ease of handling, I decided to risk being scolded by wiser and more experienced modelers and used ¼” plywood on this layout. I admit that I’m nervous about having to eat crow, but so far I’m not seeing a problem.

Jackfull gets a bonus point for resourcefulness.                

Did everyone else finish their homework? Any questions? Some of you got stuck? Does this help?

Some of you probably remember the Pythagorean Theorem: the sum of the squares of the legs on a right triangle equals the square of the hypotenuse. Which means:

The actual math behind the cubic spirals of railroad curves is not normally a part of the middle school curriculum and I have no intention of drilling kids into proficiency with them. On the contrary. But I do try to illuminate the mathematical aspects of their everyday experiences and help them see how those connect to fields like engineering, economics, music, or whatever.

Imagine you’re riding your bicycle along a straight stretch of road. Up ahead you see that the road curves sharply to the right. You’re really flying along so you lean into the curve and keep pedaling until you emerge onto another straightaway.

It took a few more weeks but eventually we had all four sections complete and installed. Because the layout had to be lightweight and removable my benchwork design relies on the interaction of many components for rigidity. For example, the backboard is made from a 12” wide strip of 1/8” masonite which contributes a considerable amount to the stiffness when screwed to the panel frames. To protect the blackboard against which the backboard rests I had the kids install self-stick foam weather stripping.