Modular Road Ramps

[boformer]

I don't have much room, so I'm planning to build a compact LEGO city. To make the layout more interesting, I want to raise the buildings in the back row. Therefore I need sloped roads!

To avoid having hard edges or gaps, I came up with the idea to use Pythagorean triangles, right triangles where all side lengths are positive integers. Some of the recent modular buildings such as the boutique hotel also use these to achieve their interesting shapes.

There are two triples that are particularly interesting:

1. 9/40/41 (3 bricks / 16 bricks / 16 bricks + 1 plate)
2. 11/60/61 (3 bricks + 2 plates / 24 bricks / 24 bricks + 1 plate)

Both have relatively shallow angles (12.7° and 10.39°), and on the bottom side they are multiples of 8 bricks, so they fit nicely onto baseplates (or MILS modules).

For now I went with the first option and doubled it (6 bricks height difference on a 32x32 baseplate).

The hard part is to figure out where and with what parts the sloped road can be connected to the baseplate, because it only lines up in a few places.

To figure out these points, I drew the ramp in Inkscape and overlayed 2 LDU (0.25 plate) grids for the straight and diagonal sides:

I was first planning to use the classic 3937 hinge, but the geometry didn't work out. Instead I went with the more modern tow ball + socket pieces. I also used the new 1x2 cheese slopes on the upper edge:

Here is the prototype. It turned out very sturdy with only 4 tow ball connections:

As you can see, the height difference is exactly 6 bricks, with no gaps.

I guess I need to order more of those cheese slopes in dark gray 

It would also be possible to use normal plates and tiles on the slope, and place the cheese slopes on the connecting module instead, like in the first image of this post.

It's also possible to add sidewalks with a curb, using the same technique, by simply raising the base by one or two plates.

Here is my plan for the city. You can see the 3 ramps with sidewalks. The one hidden on the right uses the even shallower 11-60-61 triangle, so I guess I need to figure out how to build that one too…

 

Edited 16 hours ago by boformer