How To: Euclidean Balustrade Layout

No tape measure! No calculator!! Euclid and his Geometry in the real world!

Old timey carpenters were not always “book learning smart” or patient enough to
read some manual or instruction sheet in the way required of modern carpenters.

But they did have a firm grasp of classical arithmetic and geometry in a way that
seems to have completely disappeared from the modern construction project.

The contemporary outdoor deck balustrade seems to be one of the most obvious
casualties of this absence of classical geometrical knowledge.

With nothing more than a piece of cardboard or 15lb felt or even sheetrock or
(now) tyvek, the old timey carpenter could take some scraps of wood and a pencil
and lay out a perfectly symmetrical, evenly spaced balustrade regardless of the
length of the interval between the railing posts in just a few minutes.

Meanwhile conventional wisdom requires the modern carpenter to use his tape measure
to start from the middle of the space between the two posts and measure to each side
in code mandated 4″ maximum intervals.

A few intrepid souls may spend some time fiddling with the spaces to achieve a
pleasing aesthetic appearance, but most of the time one of two outcomes predominate.

In first outcome, the space will be filled with the minimum number of required
balusters and the intervals closest to the posts may be just a liittttle bit larger
than code allows-maybe a quarter inch or slightly more.

In the second outcome, an extra baluster will be included and the intervals nearest
the post will be crowded in a most unpleasant asymmetric way.

This second outcome is particularly tragic because with nothing more than the old
timey carpenters pencil and stick the exact same number of balusters can be spaced
perfectly evenly and meet all code requirements!

The distance is not relevant- it can be 38 3/4 inches, 41 5/8 inches,or even 67 19/32 inches!

The pencil and stick technique will properly space the required number of
individual pickets perfectly.

To see a classroom demonstration of this technique click link here for a
terrific animation.

http://www.mathopenref.com/constdividesegment.html

The field expedient version of the technique I demonstrate in the video does
require a thorough grasp of some quirks of the process.

This can be explained in about a dozen steps:
(It takes longer to explain this than it does to do it.)

To complete this exercise you will need four (4) pieces of scrap wood.

1.A long piece to mark the interval between your handrail
posts and transfer it to paper.

2.A shorter straight edge to connect points.

3.A short piece to mark the interval between points B and
C and transfer that interval to point A and create point D.

4.And a really short piece to use as a spacer to mark
the eight (8) segments on the top angled line and the bottom angled line.

None of these pieces of scrap wood need to be any exact length just be sure the
pencil marks are accurate when you transfer dimensions.

Now, to begin:

1. Take a stick of sufficient length and pencil mark the distance between the two
posts of your balustrade (handrail).

2. Transfer that dimension to some surface –plywood, tyvek , or cardboard.

3. Important- whatever the thickness of your baluster (railing picket)
(most decks use 1 1/2 x 1 1/2 pickets) divide it by 2 and put 1/2 at each end of your line.
(A 3/4 thick board is an excellent spacer in this demonstration)

This is the length of the line you will divide into equal segments! (In another words
a 38.5 inch line will be a total of 40 inches long BEFORE you divide it)

This line will be called line A-B.

4.Draw a second line upward at any angle from point A a little longer past point B.

5. For seven pickets (balusters) divide the angled line into eight equal segments with
any short piece of wood.

6. The last segment divider mark (segment eight) on the angled line will be
labeled point C and define the end of the angled line.

7.Use a short stick of wood to mark the distance between point B
(the end of your original straight horizontal line) and the end of the angle line (point C).

8. This measurement will be used to establish a fourth point (D).

9. Use the short stick to transfer the BC distance down to point A (the beginning of your original line) and make an arc the same distance as between Point B and C.
This will become point D with addition of a second crossing arc.

10. Now take your long stick and pencil mark the distance
between Point A and the end point C of the angled line.

11. Use that long stick to duplicate the length of the line
with an arc between Point B and the first arc of Point D. The long stick arc should
intersect with the first Point D arc you made in step 9. The intersection locates the
exact point D.

12. This second angled line under the original line should now be divided into the
same eight equal segments that divided the first angled line above the original AB line. Important: Start from point B and go to point D

13. Now connect the segment points from the top angled line with the segment points
with the bottom angled line.

14. The point where these lines cross your original straight horizontal AB line will
mark the center point of your seven balusters and they will be perfectly spaced from
each other and the end posts.

Those old timey carpenters were some smart cookies even without book learning!

For another version of this video–Grandpa Builds A Handrail– click link:

CLICK THIS LINK

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