Subject:
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Re: [Building FAQ] What are the dimensions and aspect ratios of LEGO(r) bricks?
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Newsgroups:
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lugnet.faq
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Date:
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Sun, 22 Aug 1999 23:56:12 GMT
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Viewed:
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5089 times
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Supplement to conversion I added in:
Adam Howard <abhoward10@hotmail.com> wrote in message news:FG4FGJ.9Fn@lugnet.com...
> I have added a general conversion for mm to LD units.
>
> Robert Munafo <munafo@gcctechNO.SPAMcom> wrote in message
> news:FFwwJG.K90@lugnet.com...
> > I have added the notes on dimension relationships originally from Jef • Poskan:
> >
> > Subject: What are the dimensions and aspect ratios of LEGO® bricks?
> > Topic-Level: 1
> > Content-Language: en
> > Originator: Fred M. Sloniker, 1998-11-28
> > Revision: Robert M. Dye, 1999-11-20
> > Revision: Steve Bliss, 1999-11-30
> > Comment: The above two dates (1999-11-20 and 1999-11-30) are known to be • wrong
> > Revision: Robert Munafo, 1999-07-22
> > Reference: http://www.lugnet.com/news/display.cgi?lugnet.general:853
> > Reference: http://www.lugnet.com/news/display.cgi?lugnet.general:933
> > Location: /build/
> >
> > <P><I>From Robert M. Dye:</I></P>
> >
> > <P>
> > A 2x2 brick is 5 plates wide, so the aspect ratio is 1 (stud-to-stud)
> > to 2.5 (thickness of plates). Or, 1 (brick thickness) to 1.2
> > (stud-to-stud). Or, 1 (plate thickness) to 0.4 (stud-to-stud).
> > </P>
> >
> >
> > <P><I>From Steve Bliss:</I></P>
> >
> > <P>
> > The basic ratio is 2:5, for stud-spacing to plate-height -- which is
> > why you see Technic models with beam-plate-plate-beam stacked up: this
> > allows beams to be placed vertically, and connected to the other
> > beams.
> > </P>
> >
> > <P>
> > In LDU (LDraw units), the measurements are:
> > </P>
> >
> > <P><PRE>
> > Brick height = 24
> > Plate height = 8
> > Stud pitch = 20
> > </PRE></P>
> >
> > <P>
> > I believe the LU (LEGO Unit) measurements are:
> > </P>
> >
> > <P><PRE>
> > Brick height = 6
> > Plate height = 2
> > Stud pitch = 5
> > </PRE></P>
> >
> >
> > <P><I>From Jef Poskanzer (jef@netcom.com)</I></P>
> >
> > <P>
> > Approximate dimensions in millimeters:
> > </P>
> >
> > <PRE>
> > Spacing of stud centers: 8
> > Diameter of studs: 5
> > Height of block: 9.6
> > Height of studs: 1.7
> > Thickness of brick walls: 1.5
> > Outer diameter of cylinders
> > (found on underside of bricks): 6.31
> > Thickness of cylinder walls: 0.657
> > </PRE>
> >
> > <P>
> > Formulas:
> > </P>
> >
> > <P>
> > (height of brick) =
> > (spacing of stud centers) * 6 / 5
> > </P>
> >
> > <P>
> > (thickness of brick walls) =
> > ((spacing of stud centers) - (diameter of studs)) / 2
> > </P>
> >
> > <P>
> > (height of studs) =
> > (height of brick) / 3 - (thickness of brick walls)
> > </P>
> >
> > <P>
> > (outer diameter of cylinders) =
> > sqrt(2) * (spacing of stud centers) - (diameter of studs)
> > </P>
> >
> > <P>
> > (thickness of cylinder walls) =
> > ((outer diameter of cylinders) - (diameter of studs)) / 2
> > </P>
> >
> >
> > <P><I>From Robert Munafo:</I></P>
> >
> > <P>
> > The actual dimension (rather than the ratios) can be determined by • carefully
> > measuring a properly constructed "wall" of bricks. Vertical dimensions are
> > prone to error caused by sloppy stacking, but long horizontal walls • constructed
> > from two or more layers of overlapping bricks are not prone to such error. • A
> > wall of this type built from Technic beams made in the late 1990's shows • that
> > the stud pitch distance is 7.986 millimeters, plus or minus 2 microns, • when the
> > parts are at 25 degrees centigrade (77 degrees Farenheit).
> > </P>
> >
> > <P>
> > It is also worthwhile to note that LEGO bricks are always made a little • smaller
> > than this dimension would suggest. For example, the length of a 2x4 brick • is a
> > little less than 4 times 7.986 millimeters. The length is diminished • slightly
> > so that there will be a small gap when bricks are stacked next to each • other.
> > This gap allows for dust, marred surfaces and other imperfections. If the • gap
> > were not there the bricks would tend to push each other apart and the • overall
> > construction would be less strong.
> > </P>
> >
> > <P>
> > Using the ratios above and converting to imperial measurements yields the
> > following figures for all three dimensions:
> > </P>
> >
> > <P><PRE>
> > Brick height 9.582 mm 0.37724 in
> > Plate height 3.194 mm 0.12575 in
> > Stud pitch 7.985 mm 0.31437 in
> > </PRE></P>
> >
> > <P>
> > The following popular approximations are often used. Note that the • Imperial
> > approximations are each about 1 percent smaller than the corresponding • S.I.
> > (Metric) approximation:
> > </P>
> >
> > <P><PRE>
> > S.I. Imperial
> > Brick height 9.6 mm = 48/5 mm 0.375 in = 3/8 in
> > Plate height 3.2 mm = 16/5 mm 0.125 in = 1/8 in
> > Stud pitch 8.0 mm 0.3125 in = 5/16 in
> > </PRE></P>
> >
> > <P>
> > There seems to be no authoritative answer as to why the 5-to-6 ratio • mentioned
> > above was chosen, rather than a more obvious 1-to-1. However, the answer
> > probably has to do with the size and shape of real-world bricks used to • make
> > buildings. This makes sense since most early LEGO building sets were • oriented
> > around the general idea of making buildings out of bricks.
> > </P>
>
> A general conversion is 1mm = 2.66666666667LD units (The large number of 6's
> reduces error). This conversion can be found from a brick wall thickness:
> 4LD = 1.5mm. Another source shows the lego brick wall thickness as 1.6mm
> (making the conversion 1mm = 2.5LD units). For myself, to determine which
> was more accurate, I used a caliper accurate to .001inches and measured the
> thickness of ten walls from various parts. The measurements ranged between
> 0.062 and 0.058 inches or 1.5748mm to 1.4732mm. I decided the 1.5
> approximation worked best (using the
> 1mm = 2.5LD units conversion looks nicer, but is less accurate for longer
> measurements).
> Note: This conversion should be used carefully and you must make sure the
> part you are building conforms to existing brick dimensions. But for areas
> that are not uniform or have odd curvatures and do not fit with any other
> bricks, you can use the conversion above to estimate the correct dimensions.
> Adam
After taking some more samples I have decided I need to take a lot more. So far I've measured about 20 parts varying in size from a
2x2x1 to a 1x6x1 as well as odd parts like a horse's hooves. What I have found is contrary to my original conversion and seems to
support the 1mm=2.5LD units more, but not quite. Here is what I've found lately:
1in = 64LD
1mm = 2.51968503937LD
I used two calipers to take the measurements. One only measures in inches and is accurate to 1/1000". The other measures both mm
and inches and is accurate to 1/20mm and 1/1000". Essentially I took a number of measurements to find a number of conversion
factors. Then choose a number of random LD brick dimension and converted them to mm and inches using each of the conversions. Then
I measured the brick dimensions with both of my calipers and looked to see which conversion matched best at each of the random
dimensions chosen. This showed me that the 1mm = 2.667LD was off slightly for very large LD (>120), and that the 1mm = 2.5LD was
also off. However, using 1mm = 2.51968503937 or 1in = 64LD seemed to provide consistent results. But, I still don't believe this
is accurate enough. I think we ought to start a statistical repository of brick dimensions. Then once we have- ohh say 1000 or so
we can start running them through the statistical mill to determine a good conversion factor.
This message does contain new info for the FAQ, but any further discussion should probably be moved to lugnet.cad or lugnet.cad.dev.
I don't have that nifty Follow-Up to field so please make sure you edit the newsgroup field when replying.
Thanks,
Adam
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