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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
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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:
> RAMP 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 for the lower ramp
Average: 32.8035 studs
So I think I'm happy with a guess of 32.8 studs of length for each ramp half.
For the record, the number of teeth in the ramps also provide some different
stats:
Curve: 223 on the inner rail side and 228 on the outer rail side
Ramps: 167 (both)
Long straight: 163
Start/Stop: 82
Short straight: 41
(Yes, my mind is now numb from counting)
So, if you assumed that the spacing of the teeth was constant for a piece of
straight track versus a ramp (it's obviously not always constant), you would
get:
Using the long track for a ratio: 32.7853 studs
Using the short track for a ratio: 32.5854 studs
Given that LEGO changes the tooth spacing for different monorail elements, I'm
not quite inclined to use that as a useful measurement, but interesting to
compare nonetheless.
DaveE
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In lugnet.general, David Eaton wrote:
> In lugnet.general, David Eaton wrote:
> > RAMP 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 for the lower ramp
> Average: 32.8035 studs
>
> So I think I'm happy with a guess of 32.8 studs of length for each ramp half.
>
> For the record, the number of teeth in the ramps also provide some different
> stats:
>
> Curve: 223 on the inner rail side and 228 on the outer rail side
> Ramps: 167 (both)
> Long straight: 163
> Start/Stop: 82
> Short straight: 41
> (Yes, my mind is now numb from counting)
>
> So, if you assumed that the spacing of the teeth was constant for a piece of
> straight track versus a ramp (it's obviously not always constant), you would
> get:
>
> Using the long track for a ratio: 32.7853 studs
> Using the short track for a ratio: 32.5854 studs
>
> Given that LEGO changes the tooth spacing for different monorail elements, I'm
> not quite inclined to use that as a useful measurement, but interesting to
> compare nonetheless.
>
> DaveE
OK wait, the number of teeth on the inside and outside of a curve are different?
I never took a monorail power unit apart but I always figured the gearing was
locked together from one side to the other. Does it have a friction clutch?
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In lugnet.general, Larry Pieniazek wrote:
> OK wait, the number of teeth on the inside and outside of a curve are
> different?
Yep! Easiest way to verify is just to look at the ends and compare them with the
midpoint. The teeth are directly opposite each other on the ends, but are off by
half-a-tooth in the middle, thanks to there being an odd number on the inside
and an even number on the outside. And counting indeed yields different numbers.
> I never took a monorail power unit apart but I always figured the gearing was
> locked together from one side to the other. Does it have a friction clutch?
Nah, it's simpler than that-- there's only one gear, not two! Hence, the
monorail will go about 2% faster if the gear is on the inner side of the rail
than if the gear is on the outer side.
And it'll also go faster on long straights than it will on short straights,
since short straights and start/stops have a slightly different tooth spacing.
I'm not quite interested enough at the moment to count the teeth on half curves
or switches, but those would be interesting to check as well...
DaveE
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In lugnet.general, Larry Pieniazek wrote:
> OK wait, the number of teeth on the inside and outside of a curve are different?
> I never took a monorail power unit apart but I always figured the gearing was
> locked together from one side to the other. Does it have a friction clutch?
That was a dumb question, there's only a gear on one side of the power unit, not
both. I was misremembering
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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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In lugnet.general, David Eaton wrote:
> For the record, the number of teeth in the ramps also provide some different
> stats:
>
> Curve: 223 on the inner rail side and 228 on the outer rail side
> Ramps: 167 (both)
> Long straight: 163
> Start/Stop: 82
> Short straight: 41
And just as a follow-up, because I know you were all on the edges of your seats
waiting for this:
Half Curve Right (part #2891) - 110 (inner), 115 (outer)
Half Curve Left (part #2892) - 113 (inner), 113 (outer)
Switch Right (part #2889):
when straight - 10 + 60 + 93 = 163
when curved - 10 + 59 + 43 = 112 (inner), 10 + 59 + 43 = 112 (outer)
Switch Left (part #2890):
when straight - 10 + 60 + 93 = 163
when curved - 10 + 59 + 40 = 109 (inner), 10 + 59 + 45 = 114 (outer)
DaveE
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In lugnet.general, David Eaton wrote:
> In lugnet.general, David Eaton wrote:
> > For the record, the number of teeth in the ramps also provide some different
> > stats:
> >
> > Curve: 223 on the inner rail side and 228 on the outer rail side
> > Ramps: 167 (both)
> > Long straight: 163
> > Start/Stop: 82
> > Short straight: 41
>
> And just as a follow-up, because I know you were all on the edges of your seats
> waiting for this:
>
> Half Curve Right (part #2891) - 110 (inner), 115 (outer)
> Half Curve Left (part #2892) - 113 (inner), 113 (outer)
> Switch Right (part #2889):
> when straight - 10 + 60 + 93 = 163
> when curved - 10 + 59 + 43 = 112 (inner), 10 + 59 + 43 = 112 (outer)
> Switch Left (part #2890):
> when straight - 10 + 60 + 93 = 163
> when curved - 10 + 59 + 40 = 109 (inner), 10 + 59 + 45 = 114 (outer)
>
> DaveE
Wow!
Thanks!
I was going to dig out mine and count, but... y'know... my old eyes and such...
not as good as they used to be....
Anyway, I do appreciate that you did this
Dave K
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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?
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 significant digits) in order to accurately (within, say,
1/10 inch) state the track length of a layout on the order of 2,000 feet. Is
that level of accuracy possible?
--Todd
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In lugnet.general, Todd Lehman wrote:
> Did you ever convert the final stud length measurements into inches or
> centimeters?
I've just assumed that LEGO's accuracy with stud-to-metric measurements is neigh
on perfect (or, too close for me to accurately measure discrepancies). So, I've
just assumed an interstud spacing of 8mm per stud.
> I'm curious what accuracy is needed (in terms of significant digits) in order
> to accurately (within, say, 1/10 inch) state the track length of a layout on
> the order of 2,000 feet. Is that level of accuracy possible?
I guess it depends on what the composition of the layout was. I'm pretty
confident in the "lengths" established for long straights, short straights,
start/stops, curves, half-curves, and switches (when straight). Ramps and
switches (when curved) are another matter.
So, in our recent record, the switches (when curved) are probably pretty
irrelevant, because we used so few of them (we tried to use them all pointed
straight, to maximize distance).
The ramps are (of course) another matter. There were something like 200+ ramps
used in our layout, which means for 1/10 inch accuracy, I'd have to be accurate
to within (roughly) +/-0.0008 studs for my ramp measurement, and I'd doubt I'm
that accurate.
I wonder if the patent office has any more accurate descriptions of the elements
that we could use...
DaveE
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In lugnet.general, David Eaton wrote:
> In lugnet.general, Todd Lehman wrote:
> > Did you ever convert the final stud length measurements into inches or
> > centimeters?
>
> I've just assumed that LEGO's accuracy with stud-to-metric measurements is neigh
> on perfect (or, too close for me to accurately measure discrepancies). So, I've
> just assumed an interstud spacing of 8mm per stud.
>
> > I'm curious what accuracy is needed (in terms of significant digits) in order
> > to accurately (within, say, 1/10 inch) state the track length of a layout on
> > the order of 2,000 feet. Is that level of accuracy possible?
>
> I guess it depends on what the composition of the layout was. I'm pretty
> confident in the "lengths" established for long straights, short straights,
> start/stops, curves, half-curves, and switches (when straight). Ramps and
> switches (when curved) are another matter.
>
> So, in our recent record, the switches (when curved) are probably pretty
> irrelevant, because we used so few of them (we tried to use them all pointed
> straight, to maximize distance).
>
> The ramps are (of course) another matter. There were something like 200+ ramps
> used in our layout, which means for 1/10 inch accuracy, I'd have to be accurate
> to within (roughly) +/-0.0008 studs for my ramp measurement, and I'd doubt I'm
> that accurate.
>
> I wonder if the patent office has any more accurate descriptions of the elements
> that we could use...
>
> DaveE
I know I'm speaking to two of the most 'detail oriented' people I've ever had
the fun of working with...
But you're thinking about this too much.
If we all agree on-
a straight equaling 10 inches
a quarter straight equaling 2.5 inches
a curve equaling 15 inches
ramps equaling 10 inches
a reverse switch equaling 5 inches
a switch--17.5 inches (I actually added the straight and the half curve)
a half curve equaling 7.5 inches
If we all agree on these parameters, then we can ascertain 'who has the biggest'
;)
I tried physically measuring the ramps, and seriously, the length that the
monorail train actually traverses isn't much more than 10 inches or a straight
piece--it's negligible. And if we're all agreed on the numbers above (or
whatever numbers you want to change them to--I'm good with that as well), then
that should be good 'nuff
As it is, DaveE's (et al) record is pretty much not going to be touched by me.
Though I may be convinced to try.
Going with this, I should actually inventory my collection again. As it was
inventoried 3 years ago, I have 276 feet of monorail track in my personal
collection. Dunno if that number's changed.
The latest OBB space layout has 146 feet of monorail track.
I can e-mail you guys the excel spreadsheet that I use to figure all this stuff
out :)
Dave K
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In lugnet.general, David Koudys wrote:
>
> Dave K
Talking about monorail for shows and such (since we were, indeed talking about
that ;) )....
Ever since the big 12.5 x 12.5 layout we did back in 2009 (I think), I've tried
to avoid putting switches into my show layouts. First, as we all know here,
switches get old, and with that age, become 'less functional'.
But, more importantly for shows, invariably someone will throw a switch or two
during the show. Since we usually have 5-6 monorail trains moving around, this
has led to some spectacular derailments (as much of our monorail is well above
the baseplate level)
This isn't saying that we don't experience monorails falling off tracks now--we
still do, but it isn't 'purposely caused'.
I do find that TD'ing a layout without switches is easier, and the separate
loops are more fun. Having completely separate loops offers lots more
flexibility and takes up less space. As well, all length of track will have a
monorail train traversing them at some point (which sometimes doesn't happen
when you add a bunch of switches, unless those switches are only for
turn-arounds). I've watched many families try to figure out where a monorail
train will go in the layout, and the kids have fun following the many trains
around.
In the future, I may add a switch or two back into the layout, but for now, I'm
good that they're not there. I'll save em for something important *cough* beat
DaveE *cough*
:)
Dave
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In lugnet.general, David Koudys wrote:
> But you're thinking about this too much.
... I'm not sure I understand this concept.
> If we all agree on-
>
> a straight equaling 10 inches
> ...
Inaccuracy! It burnsss usssssss!
> I tried physically measuring the ramps, and seriously, the length that the
> monorail train actually traverses isn't much more than 10 inches or a
> straight piece--it's negligible.
Yeah, it's not a huge amount-- 0.8 studs is only 2.5% of the distance of a
straight, so it'd take about 40 ramps (or 20 "complete" ramps) to make up the
distance of a single straight. But with that said, I figure when we get into the
ballpark of 400 individual ramps (200 bottoms, 200 tops), it's more than 8 feet
of track!
> And if we're all agreed on the numbers above (or whatever numbers you want
> to change them to--I'm good with that as well),
Oooo! I have some numbers to switch them to! (... Some of them may not be fully
rational, in more than one sense of the word!)
I was actually thinking I might make a quickie web calculator that did the messy
calculation for me-- the "easy-to-remember" numbers are all in stud lengths,
which are really bizarre in inches/feet/etc, and too long in metric for me to
remember. So I always do calculations by converting track sections to studs to
metric to feet (guh).
> As it is, DaveE's (et al) record is pretty much not going to be touched by
> me.
>
> Though I may be convinced to try.
Yeah, this latest one's pretty big. It could definitely get beaten with the
right participants, but it won't be easy. We certainly aren't looking to try
again in the near future. I'm still working on the final numbers (going through
photos to see what we ACTUALLY did versus what we PLANNED on doing). Should be
in the 1900 foot ballpark, if our 'rough' counts were correct.
DaveE
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In lugnet.general, David Koudys wrote:
> But, more importantly for shows, invariably someone will throw a switch or
> two during the show. Since we usually have 5-6 monorail trains moving
> around, this has led to some spectacular derailments (as much of our
> monorail is well above the baseplate level)
Yeah, we've had that happen for both monorail and 9v rail-- never a pretty
sight!
> Having completely separate loops offers lots more flexibility and takes up
> less space.
Yeah, we debated whether or not the "world's longest monorail" should mean that
it's a single loop, or merely CONNECTED track that ought to count. So if we had
(say) 3 loops connected by some switches, should we count the switches and
separate loops as one big number? Or just count the distance that a single train
would travel? We ended up playing it safe and counting only the loop that the
train traveled.
BUT, I have to say the temptation to make it take up less space is huge. The
amount of square footage necessary to make a layout that's on par with
world-record sizes is daunting, unless you do things like lots of little loops
and have vertical climbs!
> I've watched many families try to figure out where a monorail train will go
> in the layout, and the kids have fun following the many trains around.
Hmmm... I hadn't thought much about that, but it sounds like a great challenge
for kids, actually. I wonder if you could set up a REALLY long loop, and then
put different color "stations" on it, and have the kids determine the order of
the stations visited. Could be rather difficult depending on how complex you
made the loop!
> In the future, I may add a switch or two back into the layout, but for now,
> I'm good that they're not there.
Yeah, it definitely makes sense. The switches are fun to fiddle with, but they
do cause a lot of issues as you point out.
Oh, and from the "Learn Something New Every Day" department, I learned from
Abner at the recent BrickFair that apparently LEGO once took out a patent on a
monorail *CROSS* track. Dunno what the details are, but now I'll have to make it
a mission to find out more about it...
DaveE
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In lugnet.general, David Eaton wrote:
snip
>
> Oh, and from the "Learn Something New Every Day" department, I learned from
> Abner at the recent BrickFair that apparently LEGO once took out a patent on a
> monorail *CROSS* track. Dunno what the details are, but now I'll have to make it
> a mission to find out more about it...
>
> DaveE
I heard that as well! I've sketched out a design as to what I think could
potentially work, using the 'guts' of an existing switch track, but, alas, since
I don't own a 3d printer, I won't be prototyping anytime soon...
There was those .jpgs of the patents of the monorail track and train I 'copied'
from old web pages, but there was no monorail cross track.
Dave K
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