S. Berliner, III's Labyrinth Continuation Page 2 keywords = labyrinth labyr labrys path circuit rosette petal lunation cusp foil turn quadrant classical medieval Chartres maze Redwood Shores Armenian Heritaghe Park deck

Updated:   30 Oct 2016,  12:15  ET
[Page created 03/04 Jun 2015;
    original AT&T Worldnet Website begun 30 May 1996.]

URL:  http://sbiii.com/labyr-02.html

S. Berliner, III
Consultant in Ultrasonic Processing
"changing materials with high-intensity sound"

[consultation is on a fee basis]

Technical and Historical Writer, Oral Historian
Popularizer of Science and Technology
Rail, Auto, Air, Ordnance, and Model Enthusiast
Light-weight Linguist, Lay Minister, and Putative Philosopher



note - The vast bulk of my massive Web presence (over 485 pages) had been hosted by AT&T's WorldNet service since 30 May 1996; they dropped WorldNet effective 31 Mar 2010 and I have been scrambling to transfer everything.  Everything's saved but all the links have to be changed, mostly by hand.  See my sbiii.com Transfer Page for any updates on this tedious process.


S. Berliner, III's

Labyrinth

Continuation Page 2


PAGE INDEX:

[Please note that I rearranged the main page and the first continuation page and added
    this second continuation page on 09 Jun 2015 to balance out the coverage better.
 Accordingly, I have removed all prior NEW and REV'D icons.]

On Main Labyrinth Page:
    Introduction to the Labyrinth.
    Labyrinth Terminology.
    The Chartres Labyrinth.
    Designing a Labyrinth.
    Miniature and Finger Labyrinths.
    Building a Garden Labyrinth.
    Building a Deck Labyrinth. (moved to Continuation Page 2 on 09 Jun 2015).
    Building a Tape Labyrinth (moved to Continuation Page 1 on 16 Nov 2013).
    Redwood Shores Labyrinth (moved to Continuation Page 1 on 09 Jun 2015).
    Glastonbury Tor Labyrinth?   new (30 Oct 2016)
    Labyrinth Links.

On Labyrinth Continuation Page 1 (moved from main page on 16 Nov 2013)):
    Building a Tape Labyrinth (moved from main page 16 Nov 2013).
    Chartres Labyrinth Proportions and Dimensions.
    Nominal Dimensions and Precision.
    Redwood Shores Labyrinth (moved from main page on 16 Nov 2013).
    Grace Cathedral (S.F.) Labyrinth.   added (24 Oct 2016)
    Armenian Heritage Labyrinth.   new (09 Jun 2015)
    Clark Estate Labyrinth {???}.   new (27 Jul 2015)

On this Labyrinth Continuation Page 2:
    Building a Deck Labyrinth. (moved from main page on 09 Jun 2015).




Building a Deck Labyrinth

[My gratitude to Jeff Saward of Labyrinthos for permission to reproduce drawings and a photograph from his site.
My gratitude also to Robert Ferré and LG Moriarty for helpful advice.]

Having moved in July 2010 from Long Island's North Shore to West Medford, Massachusetts, ostensibly on Boston's North Shore but more realistically some 4 miles west-northwest of Hahvid Squayeh in Cambridge, we ended up with no room for a labyrinth in the yard.  We DO have a concrete pad-cum-patio-cum-deck in the back, though.  The available rectangle measures 238" (19' 10" or 7.3m) by 174" (14' 6" or 5.3m).  One long side abuts the back wall, so I have to leave 15" (38cm) shoulder clearance there.  The other long side is alongside an in-ground pool, but there is a 3' (90cm) pool coaming so there's plenty of clearance there.  The short ends abut a sunken walkway and a concrete stoop, limiting the available width.  Nothing daunted, I designed a nominal 154" (12' 10" or 3.9m) by 252½" (21' ½" or 6.4m) rotated mini-Chartres but, unwilling to sacrifice the long pad, I extended it by the simple expedient of cutting it in half and inserting an 84" (7' or 2m+) rectangle, thusly:
  [moved from main page on 09 Jun 2015]

ExtLaby1
EXPANDED MINI-CHARTRES LABYRINTH
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

[The green lines represent joints² in the concrete.]

This has five courses and an 11" (28cm) path, not terribly generous but, happily, my wife has small feet.

How did we get to this point?  First, I rotated a Chartres design 90° counter(anti)-clockwise:and then did a rough sketch on a rotated 7-course mini-Chartres:

Chartres Chartres90
Chartres - Traditional and Rotated (Diagrams after J. Saward, by S. Berliner, III 2013)

Chartres90
Rotated and Expanded Mini-Chartres7

I'd already long-since played with 7- and 5-course diagrams (see Designing a Labyrinth on the Main Page).

You don't HAVE to have a computer with a CAD (Computer Assisted Design - it used to be Drafting) program but it sure helps!

First, I played around with the computer and came up with this early, rough version:

EarlyRough5
EXPANDED MINI-CHARTRES LABYRINTH
{Early Version}
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

That had no shoulder room at the back wall.  Refining it a bit gave this (plus a try at squeezing in 7 courses):

Refined5 Trial7
Refined 5 (L.) || Trial 7 (R.)
(CAD drawings by and © 2013 S. Berliner, III - all rights reserved)

The wasted spaces on either side of the rosette really bothered me.  A labyrinth is neither a racetrack nor an endurance course, but the longer the path, the more time can be spent in meditation. So, I gave it some thought and - EUREKA! - I came up with this arangement:

FirstIntExtLaby
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH I
{Discarded First Attempt}
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

Please don't even ask how I managed to have the left inner area droop so; so back to the drawing board:

SecondExtLaby
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH I
{Second Attempt}
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

Now, we're getting somewhere!

Cogitating further (too far, by far!), I then disgorged the "INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH II":

IntExtLabyII
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH II
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

That's almost disgusting!  Worse, the inner runs are too short and the inner turns come up too fast and would leave your head spinning!

So, it was back to square (squayeh? - well, rectangle) one!  Some fine detailing and some dimensional refinement of the rosette and we have our final design:

IntExtLabyIII
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH III
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)
  rev (03/05 Sep 2013)
{the fine detailing was revised 03 Sep 2013 to smooth the turn immediately above (in this view) the entry
and again on 05 Sep 2013 to revise the lunations (and fill them).}

Note that, by moving the rosette off center and adding the extra inner runs, although it sure doesn't look it, we gain some 65' more path length!

I thought I finally had this all down pat until I noticed, as I started to lay it out on the concrete on 12 Sep 2013, how awkward the turn and labryses just above the entry still were.  Accordingly, I revised it yet again to give a broad, sweeping 22" turn there (in violet):   added (13 Sep 2013)

IntExtLabyFinal
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH FINAL
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved;
revised 12 Sep 2013)

IntExtLabyIIIFinal
INTESTINALLY-EXPANDED MINI-CHARTRES LABYRINTH III FINAL
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved;
revised 12 Sep and 02 Oct 2013)

Note also that there are six (6) concentric extended circles ("ovals") in Labyrinth III, enclosing 5 paths, or circuits.  If you were to measure the labyrinth from edge to edge, directly (vertically, in this view) through the center, you would first encounter 5 circuits, then the center, and then 5 circuits again on the other side.  You have the center plus ten (10) circuits.  However, and in addition, Labyrinth III also includes 4 "sneak" (or 2 folded) circuits inside the innermost primary circuit, in the space behind the rosette, resulting in an apparent 14 circuits.  You can see that perhaps more easily in a path diagram:   rev (05 Sep 2013)

PathDiagram
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved;
revised 12 Sep 2013)

I revised this path drawing on 12 Sep 2013 to depict the sweeping 22' radius just above the entry, as noted above.

All this was supposed to have been etched into the fully-hardened old concrete but it turned out to be too difficult (and inherently dangerous) to do on my own so I was going to settle for an etching paint.  That's when I had the deck power washed and found out it had a bad coating of epoxy!  Punt!  I have now had to settle for a deck paint suitable for use on concrete.

I am doing my layout line work on the concrete in two kinds of felt-tip markers; temporary lines are drawn with washable markers (it really works well; everything I did disappeared in the first rain).  Permanent markings, those that will be painted over, are done with (surprise!) permanent markers of the paint color.  The felt wears down quickly but it doesn't matter at all if you work to the center-line of the marks.

Now, here's where I got really clever. I drilled ½" (12.7mm) holes in the concrete at the two curve centers, inserted ¼" (6.5mm) lead plugs, rough drilled and tapped them for ¼" screws, and inserted ¼" stainless steel flat-head machine screws:

PivotScrewAnchor
Pivot Screw Anchor
(Photograph by and © 2013 S. Berliner, III - all rights reserved)

I got the idea from the bronze pop-up pool cover anchors:

PoolAnchor
Pool Cover Anchor - Up (L.) and Down {Flush with Concrete} (R.)
[Pool Anch = Poulenc?]
(Photographs by and © 2013 S. Berliner, III - all rights reserved)

added (03 Sep 2013)

Then I cut an 8' piece of steel strapping, the kind with alternating ⅛" and ¼" holes every inch.  Starting at one end with an ¼" hole for a pivot point, I marked off every 10½", 11", and 11½" set, for 11", 22", 33", 44", 55", 66", and 77" radii:

OverallView
Overall View of Pivot and Strap

LeftViewPivot&Strap
Left View of Pivot and Strap

PivotEndDetail OuterEndDetail
Pivot End (L.) || Outer End (R.)
(Photographs by and © 2013 S. Berliner, III - all rights reserved)

If you use steel strapping, be sure to file or grind the corners; that stuff can be vicious (no, I did NOT cut myself but I didn't think to round the corners until AFTER I took these pix).

PivotScrewCloseup
Pivot Screw Closeup
(Photograph by and © 2013 S. Berliner, III - all rights reserved)

I really DID file down those strap ends:   added (03 Sep 2013)

StrapEnds
Strap Ends
(Photographs by and © 2013 S. Berliner, III - all rights reserved)

I marked an 8' long x 6" wide piece of ⅜" plywood (for stability) with 11" index marks, plus 42" marks from the center, and used it to lay out the longitudinal reference marks and will use it as a straight edge for painting the lines in the rectangular center section:

O'llView/Plank
Overall View with 8'Plank
(Photograph by and © 2013 S. Berliner, III - all rights reserved)

Note the heavy concrete paving block I use to hold the outer end of the strap in place while I make my marker markings.

When the measuring strap is not in use, the machine screws can be screwed down fully so they sit flush with the concrete (just like the pool cover anchors) and won't trip up anyone.

PivotScrewFlush
Pivot Screw Flush with Concrete
(Photograph by and © 2013 S. Berliner, III - all rights reserved)

Another gimmick is to use mini poly paint pads and drill the handle for a stub ¼" rod and paint the arcs by inserting the rod in the appropriate center hole in the strap and just walk the pad around:   rev (09 Dec 2014)

paintpad
Modified Paint Pad Handle
(Altered photograph by and © 2014 S. Berliner, III - all rights reserved)
[Temporary illustration to give you the idea.]

I've drawn a template (stencil, really) for a half rosette tip, extending from the inner labyrinth circle (the outer rosette circle) to the inner tip; it fits on 8½" x 14" legal-size card stock.  Make one also for the lunations on the arcs and on the straight segments.

HalfTipTemplate
Half Tip Template
(CAD drawing by and © 2013 S. Berliner, III)

Be sure to add a half-linewidth semicircle to the ends of your arcs and straight lines at each turn; this allows a neat finish by painting a semi-circle of half-linewidth radius at each ending

LineEndTemplate
(CAD drawing by and © 2013 S. Berliner, III)
Line End Template

Make templates (stencils) for the arc and straight line labryses:

LabrysesTemplate
(CAD drawing by and © 2013 S. Berliner, III)
Labryses Template

[Note 2 - a word to the wise - while we're on the subject of templates and exactitude, do NOT make my mistake of assuming that your base (asphalt or concrete or whatever) is rectangular.  In my case, the joints in the concrete pad turned out to be neither parallel to each other nor perpendicular to the back wall!  Pick the straightest line you can find (or create one), mark an end point or center, and then bank all dimensioning off that.]

On Continuation Page 1, under NOMINAL DIMENSIONS and PRECISION, did I really write, "No uneven lunations for me!"?  HA!  How the mighty have fallen!  I awoke much too early on 05 Sep 2013 to the realization that I had never recalculated the lunations and that they had little projections on them (in the design drawings).  Some number crunching and some CAD time later, I had amazingly precise lunations and, no, they are NOT all identical,  Those on the ends (the original outer circle) have a 2.181" radius while those in the center (on the inserted rectangular section) have a 2.1" radius.  This is because, at the juncture between the circle and the straight outer center lines, the geometry gets a tad weird and the number of lunations must be even and exact to fit properly.  Thus, also because of the 11" path width at the entry (proportionately MUCH wider than Chartres), I end up with 57 lunations on the left (half of the prototypical 114) and 54 on the right, plus 20 each top and bottom on the straight section, for a grand total of 151 lunations (that could mean a LOT of candles/tea lights)!  Now, if your eyeballs aren't crossed, here's how it worked out (05 Sep 2013):0

RecalcLuns
RECALCULATED LUNATIONS
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

Looney?  Lunatic (but they fit exactly)!

Here's a revised detail of the lunations to be used as a template (based on Nominal Dimensions and Precision and the preceding write-up) (05 Sep 2013):

ExtLabyIIIPath
Revised LABYRINTH III Lunations
(CAD drawing by and © 2013 S. Berliner, III - all rights reserved)

Another example of unwonted exactitude: - it occurred to me, early one morning, that I had no idea how the intersecting lines meet at the entry, those of the outer circle (inboard of the lunations) and those of the entry "walls".  Are they sharp cornered or rounded (radiused)?   new (02 Oct 2013)

EntryCorners
Entry Corners
(Diagram by and © 2013 S. Berliner, III - all rights reserved)

A quick look at detailed photos of Chartres shows unequivocally that the corners are sharp:

ChartresEntry
Detail of Chartres Entry Stonework


Here's an intermediate stage; markings are down for the entry, the inner circle (outer circle of rosette), and the "goal", the end of the path as it enters the rosette:

PrelimMarkings
Markings as of 31 Aug 2013
(Photograph by and © 2013 S. Berliner, III - all rights reserved)

As a guide to infilling the labryses and the lunations, I whipped up this diagram:   new (17 Sep 2013)

InfillDiagr
Infill Guide
(2013 Diagram revised 07 Jun 2015 by and © 2015/2013 S. Berliner, III - all rights reserved)

It's easy to fill missed areas but I sure don't want to fill the wrong areas!

- - - * - - -

{to be continued when the painting is started or even finished!}


Continued from main Labyrinth page and Labyrinth Continuation Page 1.



LEGACY

  What happens to all this when I DIE or (heaven forfend!) lose interest?  See LEGACY.

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