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, 8 Aug 1999 00:51:07 GMT
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Viewed:
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5142 times
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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
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