# Underneath the Arches: Exploring One Stud Radius Curves.

One of the great things about LEGO bricks is the system: the way elements fit together and interact with each other, sometimes in unexpected ways.  Studs and tubes are easy to understand. As are minifigure hands and the way they plug into the end of a tube or anti stud, or clip over a 3.18mm bar. Every so often you come across a new set of interactions, and wonder just how far these relationships between elements extend.

This happened to me this week: While my sorting continues, I was browsing through my holding bin of bricks with bows and arches.  Look, over there, a distraction. And before I knew it, I found myself considering the 1x4x2 arch and what I can place snugly under this arch.  Fortunately, during The Sort, most of the the relevant parts end up in the ‘bricks with a curved surface’ bin.

The arch fits nicely over the top of a window frame 1x2x2 2/3 (Design ID 30044).

The curve of this arch perfectly describes a semicircle, with a radius of one stud (that is, a length of a 1×1 square plate).  This is the same circle described by a 2×2 round plate, brick, tile or droid body.  Also the base profile of a 2×2 ‘dome brick’ officially known as final brick 2×2 Design ID: 30367. But more on that element later.

I have several other bricks that look like they should fit underneath this arch, with a studs up orientation. Those parts are a few of the bricks with arches and/or bows, including:1x1x1 1/3 with arch; (Design ID:6091); and 2×3 with arch (Design ID: 6215); brick 2×2 with bow and knobs (Design ID:30165) and 1x4x1 1/3 (Design ID: 10314).  Let’s see how they all line up after the break…

#### Lining up the likely suspects

Let’s see if the curve that each of these elements features is the same.  I lined these elements up on a plate, and adjusted them so that the top of each element coincides.

Lined up, side by side and adjusted for height, it appears obvious that most of these elements all follow the same curve:

These elements can line up under either the arch, or underneath design ID 92903 (1x2x3brick with ins and outs. Bow – now in the running for most confusingly named element.) The technique for placing the 1x1x1 1/3 arch under this brick was demonstrated in Mexels set 41574 “Compax”

As you can see, the brick with bow and knobs fits in nicely, with the studs fitting into the underside of the arch.  The 1x4x 1/3 brick also fits in under these arches nicely, especially when effaced back to back with identical elements.  The bricks with half arch do not follow the full curve, and cannot fit under the 1x2x4 arch. But that’s ok: they aren’t really the same shape. They do, as mentioned earlier, fit in under the 1x2x3 curved brick.

You can take the 2×2  round plates, round bricks and round tiles, and they will also fit the curve under the arches nice and snugly. And importantly, the arch can wrap over the top and bind firmly onto the baseplate.

#### The System Stumbles

However, there is one brick that this excercise doesn’t work with nicely.  The dome with stud on the top. Design ID 30367, referred to offically as ‘Final Brick 2×2.’  At its base, this is a round brick, fitting onto a column cleanly. The base is described as a circle with a radius of one stud: it matches up perfectly with the 2×2 circular bricks and plates.

Now, there are a couple of variations occurring in elements sharing this design ID:  bricklink.com lists several variations on the element: with a closed stud, and no bottom axle holder (553a); with a closed stud and bottom axle holder(553b) and with open stop and bottom axle holder (553c).

Following up the sets that these specific elements are included in reveals several things (by looking up the element IDs in the instruction manuals): internally, these elements are regarded as equivalent by the LEGO Group; and some of us have a little too much time on our hands to actually look into it.

BUT does ‘the Final Brick’ fit under the arch?

As you can see, both of these variations (553a and 553c) illustrated above are the same height as the 2×2 brick with bows and knobs and the curve in the vertical plane appears very similar to its side profile.

The stud fits, somewhat firmly under the arch. However, when adjusted for height, and using 2 offset plates to centre the arch over the dome, the legs of the arch piece do not sit as flush with the underlying plate as they did straddling the other curves looked at today. This would suggest that the Final Brick does not form part of as sphere, but is rather slightly compressed.

What would account for it? The Final Brick 2×2 30367 is 3 plates high, the same as any other brick. The dome does not describe a perfect hemisphere: If the circle is one stud in diameter, this is equivalent to 2½ plates thick.  I would have expected half a plate would typically be more than enough height for the studs to bind into an uncurved aspect at the bottom of the dome.  However, placing it next to a brick that shows the full curve, it seems that the 30367 has higher shoulders, running vertically from the bottom than this other curved element. I would suggest then, that the shape of the dome is does not follow a circular dome, but is rather a slightly squashed, with the shoulder a tiny bit higher than would allow it to fit under the arch neatly.

Just why, however, I have no idea!

#### And Finally:

The ‘one stud radius curves’ provide a useful set of tools to round off sharp edges in LEGO creations, and can fit neatly inside other curved elements to allow interesting color banding or building techniques.  This utility does not however extend to the 2×2 ‘final brick.’ This part is also used as the basic shape for an astromech droid head in the Star Wars sets.  This domed element has a slightly raised shoulder, which means that the curve of the dome does not form a circular arc, such that be placed closely under a 1x4x2 arch.

I do not expect this observation to change your life.  It probably won’t change mine. However, I am curious to know if this element has this shape because it was a better approximation of an R2 unit’s head dome than if it were to be a perfect dome, or if there were more important structural elements being taken into consideration when it was initially designed.

I had been pondering a moonbase in the future involving a series of domes being braced by arches over the top.  As such, I may need to rethink the scale of these for now:

What do you think? Are these curves useful for you in your modelling? Does this level of obsession worry you? Why to leave your comments below, and follow the blog where you will find that I don’t always dig this deeply into minute detail.

Until next time

Play Well.

## 2 thoughts on “Underneath the Arches: Exploring One Stud Radius Curves.”

1. This gives me a couple of very valuable techniques for putting a domed window covering over a window!! Thanks, I’m always looking for new architectural details for my city!

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