Help me figure out a math/measurement problem

[N. W. Perry]

I found a measurement discrepancy in set 21004 between the LDraw version and the real thing. I know that sometimes things don't work out precisely between the two, but in this case there's a mismatch of exactly 4 LDU, and I'm trying to pinpoint why.

This involves the rotunda section with its stacked 6x6 dishes and 4x4 round plates, and the 6L axle that supports it. Here are the precepts:

• The 6L axle has a length of 120 LDU, nominally equal to 48mm in real life.
  
• As we know, plate height is 8 LDU (12 with the studs), so two stacked plates are 16 LDU high (20 with studs).
  
• The center of the 6x6 dish has the ordinary plate height of 8 LDU, and the cavity adds another 8 LDU, making it equal to two stacked plates in height.
  
• As a result, the 4x4 round plate sits entirely flush within the 6x6 dish.
  
• Per the instructions, and confirmed in the physical set that I own, the 4x4 round plate at the top of the assembly sits fully within the uppermost 6x6 dish, and the bottoms of both that dish and the 4x4 dish should be at equal height.
  
• The axle hole in the 4x4 dish is 12 LDU deep.
  

So, here's an image showing the problem; the axle assembly and the stacked dishes are shown offset for clarity, but at their correct vertical position:
   

As you can see, the 4x4 dish and plate at the top are 4 LDU too high, because the rest of the assembly is only 104 LDU high rather than the necessary 108. Where is that extra 4 LDU coming from?

I thought perhaps the axle hole in the 4x4 dish should be 16 deep instead of 12, but a rough measurement of the real part suggests that 12 is correct. All of the dishes seem to be modeled at their correct height, too, so the only thing I can think of is the axle. Indeed, measuring the real axle shows that it's just a bit over 47mm long, not 48. It may even be 47.2mm, leaving it 2 LDU short of its theoretical length, but that still leaves another 2 LDU to account for. Could the height of the embossed stud logo account for that (see the 2x2 round plates at the bottom), or just the natural physical play between parts?

[Philippe Hurbain]

Most of the "problem" can be explained by idea/physical differences. Axles are a bit shorter physically than ideal (between 1.2 and 2 ldu depending on 6L axle measured), stud height with logo is 4.5ldu instead of 4 (generally it doesn't matter, but here two of them are head to head), and stacking introduces some more play...
I had the opportunity yesterday to participate in the dismantling of a huge (275000 pcs) MOC, and I learnt that between the core made of stacked bricks and the "skin" made mainly with plates there was a height discrepency of a half plate...

[N. W. Perry]

Most of the "problem" can be explained by idea/physical differences. Axles are a bit shorter physically than ideal (between 1.2 and 2 ldu depending on 6L axle measured), stud height with logo is 4.5ldu instead of 4 (generally it doesn't matter, but here two of them are head to head), and stacking introduces some more play...
I had the opportunity yesterday to participate in the dismantling of a huge (275000 pcs) MOC, and I learnt that between the core made of stacked bricks and the "skin" made mainly with plates there was a height discrepency of a half plate...

Hmm, so if the axle really is 2 LDU short, and the stud logo adds another 1 LDU (is it really that much? I had thought 0.25, at most), that leaves 1 LDU for "play"—and that's about how close the upper structure comes to being flush with the uppermost 6x6 dish in reality.

I have a feeling you're right, and there's nothing more to it than that, but it seems oddly anti-climactic. Since it was a nice even 4 LDU difference, I secretly hoped there was some hidden yet elegant mathematical consideration at play, or even that I'd made some simple error myself.

This makes me mildly curious, has there ever been discussion of modeling parts to their true dimensions, at least for certain applications like this?

[Michael Horvath]

This makes me mildly curious, has there ever been discussion of modeling parts to their true dimensions, at least for certain applications like this?

There is also the issue of technic axle hole height (and likely other things I am unaware of). In reality technic axle holes are several fractions of an LDU higher than in they are in LDraw parts. Meaning you may not be able to build your LDraw technic models IRL.

Not sure what everyone's plans are in this regard. This issue has been known for decades.

[N. W. Perry]

There is also the issue of technic axle hole height (and likely other things I am unaware of). In reality technic axle holes are several fractions of an LDU higher than in they are in LDraw parts. Meaning you may not be able to build your LDraw technic models IRL.

Not sure what everyone's plans are in this regard. This issue has been known for decades.

Oh yes, I read Cailliau's treatise on that with (subdued) fascination. For my question, what I envisioned was perhaps a bit of metadata that's included whenever a part is authored that encodes the part's real-life dimensions, alongside its theoretical LDraw measurements. Then, an LDraw editing program could include a selectable option for using a part's real measurements; otherwise, the usual dimensions we're familiar with would be the fallback.

(Could something like that work for the axle hole height? Could an editor program be designed to re-calculate the positions of these primitives on the fly?)

[Roland Melkert]

(Could something like that work for the axle hole height? Could an editor program be designed to re-calculate the positions of these primitives on the fly?)

You could edit connhole.dat in LDCad's shadow library.

But this will only work when the primitive is used non rotated/mirrored.

Also there are plenty of techic connection holes which are modeled without the use of a primitive.

So you would need to edit all those parts' shadow files too.