I’ve toured a lot of historic homes and seen some extraordinary arches—door jambs, windows, passageways. In reading about historic architecture, especially Gothic and colonial styles, I’ve come across some beautiful arch work. But those once-common elements are not often incorporated into millwork today. Sure, sometimes the carpentry techniques are more difficult, and too costly, but the problem I’ve recognized is more one of design.
Combining a group of openings with segmental jambs can look awkward if the spring lines are at different elevations, if the tops of the arches vary in height, or if the spans are significantly different (see image, below, click to enlarge).
|And segmented jambs can look even worse if keystones are used improperly. Remember, you can only put a keystone in one and only one spot—at the apex of the arch (see “Parts of an Arch,” below).|
And another thing . . . segmented radius arches do not look good when they’re decorated with classical head details. Doesn’t there appear to be something missing in both of the pictures below? Yes, there is—structural support and a defined point of termination.
Certainly, there are a lot of builders and architects who aren’t reading Get Your House Right! But the real problem I found was with instructions for laying out arches—they are all terribly outdated! In fact, almost all of the information we use today has been collected and re-printed from books that were published over a century ago—illustrations filled with confusing text, multiple lines and intersections, usually with all the information compressed into one ink drawing (see image, right).
Publishing books a hundred years ago was prohibitively expensive: the cost of a single sheet of paper was so high that private letters were often written with the text running in both directions, just to save on paper. It’s no wonder book publishers never considered multiple, step-by-step illustrations.
But that’s not the case today—at least not for an e-magazine like THISisCarpentry! Now that we have paper-free publishing, it’s time to re-draw those old instructions.
The articles in this series are meant to provide a richer format for today’s “digital savvy” carpenter. There is still a fair bit of geometry involved, but fear not! All of these articles include Quick Reference Guides, or ”cheat sheets” (downloadable PDFs), with step-by-step instructions for each arch layout.
Let’s get started:
An arch is a structure that spans an opening and supports weight. Arches have been around for thousands of years, and were originally constructed out of stone. During the Roman Empire the engineering of the masonry arch was perfected and its structural element defined.
Even though decorative millwork doesn’t need to provide physical strength and support, it should do so visually. You can’t fool the eye. You might not know why, but something inside you will let you know if it doesn’t look quite right (just like the start of this next sentence!). It’s just like why choosing a terminating or supporting molding can make all the difference.
Impost: The block set into a wall or uppermost part of a column or pillar, used to support an arch.
Keystone: A wedge-shaped piece at the apex of an arch that locks the structure together and allows it to bear weight. The shape of the keystone should always be related to the center point of the arc that makes up the arch.
Spring line: The line at which an arch begins—located at or above the impost.
Stilt: The elevation of the spring line above the impost.
Voussoir: A wedge-shaped piece used to make up the curved part of an arch.
Because all of the following arch types are based on the circle, let’s review the fundamentals of circular geometry.
Arc: A curved line that is part of the circumference of a circle.
Chord: A line segment joining two points of a curve.
Circumference: The distance around the perimeter of a circle.
Diameter: The distance across a circle through its center point.
Radius: The distance from the center point of a circle to its perimeter. Equal to one half of the diameter.
Point of Tangency (tangent point): The point at which the tangent touches an arc or circle.
Tangent: A line, arc, or circle that touches an arc or circle at only one point.
Determining the radius of an arc for a given span and rise can be worked out with simple geometry, but if you have a construction calculator, you can find your radius with just a few key punches.
Finding the radius of a segmented arch
This function of a construction calculator can also be used if you need to find the radius of an existing inside curve.
1. Cut a straight piece of wood to a length that will fit inside the arch, and touch two points of its curve. The actual length of the stick is not important, but using a nice round number like 12 in. or 24 in. will make things easier. After cutting, measure and mark the midpoint along its length.
2. Place the piece of wood against the arch—it doesn’t matter where.
3. Measure the distance at a right angle from the top of the stick’s midpoint to the existing curve.
4. Enter that measurement into the calculator and press RISE.
5. Enter the length of the stick and press RUN.
6. Press the CONV key to change the ARC key to the RADIUS key.
7. Press the RADIUS Key.
For readers who don’t have a construction calculator, here is the formula you can use with a standard calculator. Unfortunately, you also have to convert any fractions to decimals.
|Download the Quick Reference Guide for Segmental Arches
While Roman architecture is known for one-centered arches, two-centered arches are fundamental to Gothic architecture and form the simplest “pointed” arches.
|The large main parlor window at Lyndhurst is framed by a two-centered arch.|
|The lancet windows surrounding this tower are typical two-centered arches. The same motif repeats itself in a crenelated pattern across the porte cochere parapet walls. (Sells Mansion, Columbus Ohio)|
There are many variations of two-centered arches, and each depends on the location of the center points. When the center points are located closer to the middle of the span, the arch flattens out; if the center points are located farther away from the middle of the span, the arch becomes sharper.
|The drop-arch on this fireplace, beneath a suspended hood, provides just the right amount of gothic flavor for an early 20th century arts-and-crafts home. (www.adamsonhouse.org)|
The following Quick Reference Guide provides step-by-step procedures for finding the required arc centers and appropriate radii for a two-centered arch that must meet a specific height and width.
|Download the Quick Reference Guide for 2-Centered Arches
Note: A recurring step found in these geometric constructions is to draw a line perpendicular to another line’s midpoint. For simplicity, a square has been used in the illustrations, but the task can also be accomplished with just a compass/trammel and a straight edge, as shown in the following Quick Reference Guide.
|Download the Quick Reference Guide for Bisecting a Line
Don’t miss the next article in this series on Three-Centered arches, where the geometry gets a little more complicated.