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In lugnet.general, David Eaton wrote:
> 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
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 outside radius)
Ramp--10 inches -- didn't account for the actual ramp--it was too close to the
straight length so didn't bother with the difference
right/left point--17.5 inches--10 inches for the straight and half a curve
small curve--7.5 inches -half a curve (see above)
that's how we derived the 259.38 linear feet of monorail track in our big layout
I have a spreadsheet set up so you just type in the # of pieces used in a layout
and it lets you know the linear feet
Our big layout--
379.50 32 x 32 baseplates
259.38 linear feet of monorail
95.25 linear feet of 9v track
87.50 linear feet of road baseplates
175.929 square feet coverage...
That's if all my calculations wer done correctly :)
Dave K
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In lugnet.general, David Koudys wrote:
> Short Track--2.5 inches
Wait, you mean you wacky Canucks use inches now? Aren't you guys supposed to be
on the metric system?
> Curve track--15 inches (as measured with a measuring tape--can't remember if
> it was inside, center, or outside radius)
Looks like the outside-- by my calculations, the outside ought to measure about
14.93 inches. In my previous post, I should clarify I was using the center of
the track.
> Ramp--10 inches -- didn't account for the actual ramp--it was too close to
> the straight length so didn't bother with the difference
Yeah, it's a minuscule amount-- although I *am* interested from a geek
perspective to figure out what that might be...
> I have a spreadsheet set up so you just type in the # of pieces used in a
> layout and it lets you know the linear feet
:)
I have something similar-- my own track weighs in at 79.41 feet in my system,
but it looks like I go up to 81.67 if I use your approximations! An extra 2+
feet of track, woot!
DaveE
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In lugnet.general, David Eaton wrote:
<snip>
> :)
> I have something similar-- my own track weighs in at 79.41 feet in my system,
> but it looks like I go up to 81.67 if I use your approximations! An extra 2+
> feet of track, woot!
>
> DaveE
It's that Canadian conversion, eh!
:)
Dave K
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