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In lugnet.faq, Jeremy Sproat writes:
> Adam, do you have an inch <-> LDU conversion constant as well?
Conversion constants are much more relevant to the stud pitch than the brick
height or width, because brick heights and widths are subject to the error
caused by the fact that LEGO always designs elements so there will be tiny gaps
when assembled, to make them fit better even when marred or dirty.
The stud pitch in LDU is given by Steve Bliss's section of the FAQ answer,
which says that the stud pitch is 20 LDU (LDraw units). That's an exact figure,
because of the LDU's role as a way to make it easier to position pieces at
integral stud-positions when you're building a model in LDraw.
The stud pitch in the physical world is (from my section of the FAQ answer)
7.986 millimeters plus or minus 2 microns. Expressed as a percentage the error
is 0.025 of a percent (or 1 in 4000).
The inch to millimeter conversion is (by international standard) exactly 25.4
millimeters to an inch. That is also an exact figure (by international
agreement).
When you do the math, you get the following conversion factors, each with its
corresponding error term:
1 LDU = 0.3993 +-0.0001 millimeters
1 millimeter = 2.5043 +- 0.0006 LDU
1 LDU = 0.015720 +- 0.000004 inches
1 inch = 63.611 +- 0.016 LDU
- Robert Munafo http://www.mrob.com/
LEGO: TC+++(8480) SW++ #+ S-- LS++ Hsp M+ A@ LM++ YB64m IC13
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Robert Munafo wrote:
> The inch to millimeter conversion is (by international standard) exactly 25.4
> millimeters to an inch. That is also an exact figure (by international
> agreement).
This surprises me. *Exactly* 25.4 mm / inch? I thought that the conversion
rate was kind of one of those irrational numbers (1) that had digits
trailing off into infinity or, failing that, Imelda Marcos' shoe closet.
:-,
> When you do the math, you get the following conversion factors, each with its
> corresponding error term:
> 1 LDU = 0.3993 +-0.0001 millimeters
> 1 millimeter = 2.5043 +- 0.0006 LDU
> 1 LDU = 0.015720 +- 0.000004 inches
> 1 inch = 63.611 +- 0.016 LDU
*This* is cool. Thanks for the table!
Cheers,
- jsproat
1. Arguably since we're converting between metric and an irrational
measurement system, but I digress. :-P
--
Jeremy H. Sproat <jsproat@io.com>
http://www.io.com/~jsproat
Darth Maul Lives
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In lugnet.faq, Jeremy Sproat writes:
> Robert Munafo wrote:
> > The inch to millimeter conversion is (by international standard) exactly • 25.4
> > millimeters to an inch. That is also an exact figure (by international
> > agreement).
>
> This surprises me. *Exactly* 25.4 mm / inch? I thought that the conversion
> rate was kind of one of those irrational numbers (1) that had digits
> trailing off into infinity or, failing that, Imelda Marcos' shoe closet.
Yes. Here is a table provided by Lycos:
http://infoplease.lycos.com/ipa/A0001729.html
scroll down and notice that the value for inch->millimeter is given as
"25.4000"
The story I heard is that, at some point around 100 years ago it was decided to
redefine the English weights and measures in terms of the SI (international
system or "metric") and when they looked at the units of length they discovered
that the inch was so close to being 25.4 millimeters that the error term in the
measurement of the inch (which had hitherto been defined by the length of a
rod) was greater than the difference they would impose by choosing a value of
exactly 2.54. So, the value of exactly 2.54 was chosen, much to the convenience
of scientists and schoolchildren everywhere.
Since then the meter has been redefined (twice, I believe) and the inch got
redefined right along with it.
- Robert Munafo http://www.mrob.com/
LEGO: TC+++(8480) SW++ #+ S-- LS++ Hsp M+ A@ LM++ YB64m IC13
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Sproaticus wrote:
>
> Robert Munafo wrote:
> > The inch to millimeter conversion is (by international standard) exactly 25.4
> > millimeters to an inch. That is also an exact figure (by international
> > agreement).
>
> This surprises me. *Exactly* 25.4 mm / inch? I thought that the conversion
> rate was kind of one of those irrational numbers (1) that had digits
> trailing off into infinity or, failing that, Imelda Marcos' shoe closet.
The inch was redefined some time ago to make it equal 2.54 centimeters
exactly.
It used to be slightly larger, but it was close enough that it didn't
really make
any difference when they changed it.
--
Tim Buchheim
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On Wed, 25 Aug 1999 00:19:30 GMT, Timothy Carl Buchheim
<tcb@cs.hmcSPAM.edu> wrote:
> Sproaticus wrote:
> >
> > Robert Munafo wrote:
> > > The inch to millimeter conversion is (by international standard) exactly 25.4
> > > millimeters to an inch. That is also an exact figure (by international
> > > agreement).
> >
> > This surprises me. *Exactly* 25.4 mm / inch? I thought that the conversion
> > rate was kind of one of those irrational numbers (1) that had digits
> > trailing off into infinity or, failing that, Imelda Marcos' shoe closet.
>
>
> The inch was redefined some time ago to make it equal 2.54 centimeters
> exactly.
> It used to be slightly larger, but it was close enough that it didn't
> really make
> any difference when they changed it.
I *thought* I felt taller all of a sudden ...
Steve
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