Subject:
|
How long is a length of monorail track?
|
Newsgroups:
|
lugnet.general
|
Date:
|
Fri, 8 Oct 2010 19:30:16 GMT
|
Highlighted:
|
(details)
|
Viewed:
|
17457 times
|
| |
|
|
How long is a length of monorail straight track? Easy-- 32 studs. But how long
is a length of CURVED monorail track? And (the kicker), how long is a length of
monorail RAMP?
<GEEK LEVEL="HIGH" CATEGORY="MATH">
CURVED TRACK:
For the curved track, it appears that 4 curves together are not a perfect
28-stud radius circle. If it were, the midpoint of each curve piece would be at
some wacky irrational number of studs-- but instead, LEGO wanted it to line up
EXACTLY on a stud so that they could make half-curves work. As a result, the
designers moved the midpoint of the curve out SLIGHTLY to make it center
perfectly on stud edges. But what did they actually do?
My guess with the curved track is that they still made the curve element a
quarter-circle-- but they adjusted the radius from the "expected" 28 studs to
some smaller number, and then extended the ends in straight lines by some small
number of millimeters.
Anyway, assuming that's the case, I calculated the radius (R), straight-length
distance out from each end (D), and the resulting curve length (L) all in studs:
R = 8/(1-1/sqrt(2))
D = 28 - R
L = (R*pi)/2 + 2*D
Which comes out to:
L = 4 * ((pi - 4)/(1 - sqrt(1/2)) + 14) =~ 44.277 studs
Does the above sound valid? Has anyone tried measuring the track that can
provide a better estimate?
RAMP TRACK:
Ok, here I'm stumped. Mathematically, I'm not sure if there's anything that's
more "reasonable" than anything else. Given that the shortest distance it can
traverse would be a straight line, I know it's at LEAST 260mm (about 32.56
studs), but the actual track is curved, not a perfectly straight ramp.
Measuring it myself yields numbers somewhere between 32.5 and 33 studs for each
ramp half, but I'm not sure exactly how much. Has anyone else endeavored to
discover this mysterious minutia?
</GEEK>
DaveE
|
|
Message has 3 Replies:
 | | Re: How long is a length of monorail track?
|
| (...) This is what I did for my calculations for our layouts-- Short Track--2.5 inches reversing Switch track--5 inches Straight track--10 inches Curve track--15 inches (as measured with a measuring tape--can't remember if it was inside, center, or (...) (14 years ago, 8-Oct-10, to lugnet.general)
| | | Re: How long is a length of monorail track?
|
| (...) Alright, I just tried to measure using my scanner. I figured there would be very little optical distortion on the bed of the scanner, so it'll make a reasonably good straight-on image. Results: 32.7903 studs for the upper ramp 32.8166 studs (...) (14 years ago, 9-Oct-10, to lugnet.general)
| | | Re: How long is a length of monorail track?
|
| (...) This reminds me of "How Long Is the Coastline of Britain?" ;-) Dave... Saw your followups... Awesome work! Did you ever convert the final stud length measurements into inches or centimeters? I'm curious what accuracy is needed (in terms of (...) (11 years ago, 13-May-13, to lugnet.general)
|
17 Messages in This Thread:
  
 
- Entire Thread on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
|
|
|
|
