Subject:
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Exact Lego brick dimensions
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Newsgroups:
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lugnet.general
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Date:
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Sun, 3 Sep 2000 16:10:40 GMT
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Viewed:
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1010 times
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I have been toying a little bit with some Lego(tm) bricks, a ruler and a
pocket calculator and this is the result. I'm prepared to be shot down on
this, so feel free to notify me of any errors or suggest improvements.
Axel
P.S.: I found last years thread regarding brick dimensions at
http://news.lugnet.com/faq/?n=376 only after I had written this, so
parts of it may be redundant, but I thought I'd post it anyway
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Axel Poqué o,=g 50° 46' 17" N / 06° 05' 18" E
_c--/_ home: http://home.t-online.de/~axel.pq
(_)\+(_) Lego page: http://home.t-online.de/~axel.pq/lego
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The Exact Lego(tm) Brick Dimensions Fact Sheet
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Disclaimer:
Although I tried to make the included information as accurate as
possible, I cannot take responsibility for any damage (to Lego bricks or
anythings else) or loss of money, sanity, hair, or significant other
occuring due to the use or misuse of this text.
This fact sheet does not try to convey any production or trade secret.
All information included here can be obtained using a ruler and a few lego
bricks.
Lego is a trademark of The Lego Company, Danmark.
Measurements: ------------------------------------------------------------
(1) a wall of 36(*) studs is 287.8 mm long
(2) a tower of 30(*) bricks is 287.8 mm high
(3) a wall of 61 studs approximately equals 62 1 x 1 bricks in length
(*) the number of studs was chosen such that:
a) I could measure it with my puny 30 cm ruler (a longer wall would
yield more accurate values, but only if measured with a rigid ruler,
not with tape measures or folding rules, which are inherently
inaccurate).
b) to reflect Lego(tm) aspect ratio (10)
Assumptions: -------------------------------------------------------------
All original Lego(tm) dimensions were designed in inches, since the
Lego(tm) brick is based on the british Kiddicraft brick from the
1940s. [1]
Everything was designed using integer multiples of fractional inches
(1/2, 1/4, 1/8, 1/16, 1/32, etc.).
Shrink factor: -----------------------------------------------------------
Factor by which a single 1 x 1 brick is smaller
than stud pitch
using (3)
62 1 x 1 bricks = 61 studs =
(4) 61 / 62 = 0.983870967045
Stud pitch: --------------------------------------------------------------
(5) approx. 5/16" [1] = 7.9375 mm
thus a wall of 36 studs would be 285.75 mm,
but according to (1) it is about 287.8 mm, so
_
measured stud pitch = 287.8 / 36 = 7.994 mm
converted to fractional inches this yields
exact 5/16" + 5/2048" =
(6) 645/2048" = 7.9951171875 mm
Brick width (1 x 1): -----------------------------------------------------
using (6) and (4)
stud pitch * shrink factor =
645/2048" * 61/62 =
634.5967743196/2048"
rounded to
635/2048" = 7.87548828125 mm
(7) => exact gap size = 10/2048" = 0.1240234375 mm
=> exact shrink factor:
63.5 studs = 64.5 1 x 1 bricks =
63.5 / 64.5 = 0.984496124031
compare with (4)
=> exact brick width/length:
using (6) and (7)
studs * stud pitch - gap size =
n * 645/2048" - 10/2048" =
(8) (n * 645 - 10) / 2048"
Stud diameter: -----------------------------------------------------------
according to [1]:
approx. 3/16" = 4.7625 mm
assuming fractional dimensions analog to (6):
exact 3/16" + 3/2048" =
(9) 387/2048" = = 4.79970703125 mm
the 3/2048" difference between exact & approx.
stud diameter provides the "clutch" power (?)
Wall thickness: ----------------------------------------------------------
(stud pitch - stud diameter) / 2
approx.
exact (5/16" - 3/16") / 2 =
2/16" / 2 =
1/16" = 1.5875 mm
Aspect ratio: ------------------------------------------------------------
(10) 6:5
Brick height: ------------------------------------------------------------
using (10)
approx. 5/16" * 6/5 = 6/16" = 3/8" [1] = 9.525 mm
but according to (2)
_
287.8 / 30 = 9.593 mm
again converted to fractional inches
exact (5/16" + 5/2048") * 6/5 =
6/16" + 6/2048" =
3/8" + 3/1024" = 387/1024" = 9.5994140625 mm
Sources: -----------------------------------------------------------------
[1] Jim Hughes Technica: Technic Geometry
http://w3.one.net/~hughesj/technica/registry/geometry/geom_1.html
[2] The Lego-DIM FAQ
http://www2.ctrl-c.liu.se/ftp/IMAGES/INCOMING/LEGO/LEGO-DIM.FAQ
[3] The rec.toys.lego FAQ - Material, Technology and Measurements
http://www.multicon.de/fun/legofaq.html#a13
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