——————-

Be sure to read Part 1 of this series on arches: Circular-Based Arches

——————-

This depressed type of arch, like the Segmental and Drop arch, can be used when the design requires the rise—or height—of the arch to be reduced. While segmental and ‘elliptical shaped’ arches both share a rounded top, the elliptical variation provides the benefit of a clean vertical transition, and respects traditional design principles.

A three-centered arch is an elliptical approximation using three tangent arcs. (Click any image to enlarge.)

A true ellipse is the shape created by making a diagonal section-cut through a cone or cylinder. The ellipse has two focal points and a constantly changing arc radius.

It can be difficult to determine if an arch is a true ellipse, or just one composed of simple tangent arcs, swung from three centers. Either way, elliptically shaped arches are more commonly found in traditional homes based on colonial styles—though their use depends more upon the skill of the architects, millwrights, and finish carpenters.

I’ve heard some carpenters say (and I won’t mention any names!) that the popularity of segmental arches—sometimes one of the most boring and ugly forms of architecture—results more from a lack of knowledge and technique than from an understanding of classical forms—both Gothic and Colonial.

These carpenters believe that elliptical arches—or, at the very least, three-centered arches—are far more attractive, but that the technique is beyond the skill of most contemporary carpenters. I don’t necessarily agree. I don’t think the segmental arch should be completely avoided.

A segmented arch forms a pleasing and handsome frame, as long as the arches (the rise, the radius, the span) are nearly identical in size.

In the first part of this series, I shared some images of segmented arches gone wrong. But, when designed and executed properly, a segmented arch forms a pleasing and handsome frame, as long as the arches (the rise, the radius, the span) are nearly identical in size. But, if the openings have variable spans, a three-centered arch is a better answer!

At this point, I can’t help but mention Gary Striegler’s article in JLC about building an arched passage door. I’m including a PDF of that article here. It’s a critical part of this study, both because it will help readers form a better understanding of complex arches (arches with more than two centers, and elliptical arches), and because Gary’s article provides techniques for constructing a three-centered arch, which is much easier than milling elliptical molding! In fact, mill shops often use a similar technique to create their elliptical moldings, sometimes using five or more centers to create a more accurate elliptical shape.

This coffered three-centered arch passageway features raised panels and uses the Ionic capitals of the pilasters as imposts to provide visual strength and support.

Another example of where a three-centered arch is easier on the carpenter, as opposed to a true ellipse, is in a coffered passageway. The curved panels of the head only require two different radii. In the photo to the right, you can see that the panels across the top share the same curvature, and panels with a tighter radius are used as the arch terminates on each side.

Getting back to the purpose of this article—how do we layout this pseudo ellipse? Well…it all depends on what you are given to work with. Although being involved at the planning stages is ideal, most of the time it’s not a reality.

Hopefully, the following Quick Reference Guides will help you deal with any ‘curve’ you’re thrown.

The Classic Three-Centered Arch

This layout is for the classic three-centered arch. You only need to know the required width or span of the arch. The rise of the arch will be determined by proportion only.

.

Three-Centered Arches with a Known Height & Width

This layout is used when you must fit an arch within a predetermined height and width.

.

Three-Centered Arches with Known Radii

This layout is used for creating a three-centered arch when the two radii to be used are predetermined. This is the situation used in Gary Striegler’s article.

.

Keep an eye out for the last part in this series, on Four-Centered Arches!

Common circular-based arches (Note: Click any image to enlarge)

Arches in modern homes often seem slightly off—there’s frequently something wrong with them, particularly when you compare arches built in homes today to historic designs. I couldn’t put my finger on the problem, so I started researching arch designs in pattern books and on the Internet. What I discovered is more a problem of communication than technique. Mixing arch designs—like this segmented entry door jamb and 3-centered stone arch—never works (see photo, right).

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).

Segmental Openings

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:

Arch Basics

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.

Parts of an arch (click to enlarge)

Important Terminology

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.

Geometry Refresher

Because all of the following arch types are based on the circle, let’s review the fundamentals of circular geometry.

Anatomy of a circle

Important Terminology

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.

One-Centered Arches

Done correctly, segmental arches are versatile enough to even feel at home in a Craftsman style home.

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.

Here are the steps (I use BuildCalc on my iPad. If you use CMPro on your iPhone/iPad or Droid, the key locations are a little different, but steps are the same!):

1. Enter the desired span of the arch (48 inches in this example) and press RUN.		2. Enter the desired rise of the arch (6 inches in this example) and press RISE
3. Press the CONV key (when you press the convert key, the ARC key will change to the RADIUS key).		4. Press the RADIUS key to display the radius. (Note that at the completion of this calculation, BuildCalc's keys will revert back to their default settings. The Radius key becomes the Arc key again, as seen above.)

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.

Two-Centered 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)

Variations

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.

.

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.

.

Don’t miss the next article in this series on Three-Centered arches, where the geometry gets a little more complicated.

If you are tired of working out trim details on a scrap of wood or making shop drawings with graph paper and a ruler, SketchUp is your answer. Unlike most computer-aided design programs you may have tried, SketchUp is very intuitive and works the way a carpenter thinks.

SketchUp has a simple set of tools that you can use to create anything from a rough mock-up to a very detailed drawing with 1/64″ precision. How much detail you want is up to you. The ability to convey your ideas to customers quickly and to produce working shop drawings is what SketchUp can do for you. Are you intrigued? What if I told you that it’s FREE!

It’s true. SketchUp is 3-D design software available from Google. It is currently available in two versions—SketchUp 7, which is absolutely free, and SketchUp 7 Pro, which is not. The free version of SketchUp has all the power of the Pro version with the following few exceptions.

SketchUp 7 Pro includes:

Layout – additional software that works with SketchUp and allows the user to import drawings from SketchUp to create various types of presentations. You can incorporate title blocks and use standard sheet sizes for printing.

Style Builder – additional software for creating custom drawing styles.

Additional Exporting Options - PDF, DWG, DXF, as well as various vector formats.

Creation of Dynamic Components – used to make components that are interactive, such as moving doors and drawers, and to make components that will rescale or replicate, such as fence pickets or floor tiles. These components will work in the free version, but can only be created in the Pro version.

SketchUp 7 Pro currently retails for $495. A student license is available for just $49 a year to anyone who is currently enrolled in an accredited school and has an .edu email address. The terms of a student license, however, forbid commercial use. Both versions can be downloaded from http://sketchup.google.com/download/.

Before you download the software and get to work, make sure your computer’s hardware is adequate. The hardware requirements to run this program should be “no sweat” for most new computers. This link should answer any questions you may have.

http://sketchup.google.com/support/bin/answer.py?answer=36208&cbid=-x534j6yf9529&src=cb&lev=topic

The one thing Google lists as “recommended,” that I feel is ESSENTIAL, is a three-button, scroll-wheel mouse. Without this very inexpensive add-on, I can promise you nothing but frustration. Navigating in a 3-D drawing is almost impossible without one.

Drawing your way:

Once you have installed SketchUp, you have the opportunity to customize it to the way you work. SketchUp is used by architects, engineers, and designers, as well as carpenters. Different units of measurements and levels of precision are available as preset templates for the type of work you do. The first screen you see after installation will look like this. Note that tutorials are available from this screen. They are excellent for the general user.The button labeled “Choose Template” will give you  an opportunity to select the type of drawings you plan to do and will  load SketchUp with those settings every time you launch it (circled in red on right).

The template that will probably be of the most use to a finish carpenter is the “Product Design and Woodworking – Inches” template (circled in red on right). It is a 3-D template with the units of measurement set to fractional inches. The template for metric units is also available just beneath it. This is a good place to start, and as you become more familiar with the program, any personal preferences you decide to change, such as unit precision, background color, styles, etc., can be saved as a new template with a unique name.

One thing you might want to consider changing right off the bat is the unit precision in this template. It is pre-set at 1/64″. For most work, I keep the precision at 1/16″. If I’m working with veneer core plywood, I will dial it down to 1/32″ precision to get more accurate shop drawings (I still take actual measurements in the shop before I cut anything!). It is also a good idea to check the box labeled “Enable Length Snapping.” These options can be selected from Windows>Model Info, under Units.

Once you have your new preference set, create a personal template by going to File>Save As Template.

Getting your tools in order:

These are not the only tools available—just the selected tools by Google for “Getting Started.” By going to View>Toolbars, you have the ability to turn on or off the toolbars you want available. The toolbar setup I prefer to have available looks like this.

This is only my preference and what you will see in the following video tutorials.  As you become more familiar with the program and all of its different tools, you may find that a different tool suite suits your work better.

Keyboard shortcuts are great timesavers for the most commonly used tools. Instead of moving your cursor back and forth from the drawing window each time you want to select a new tool, new tools can be automatically selected by pressing an assigned key on your keyboard. If you click on the “Tools” menu at the top of the screen, a menu with a list of frequently used tools will appear. To the right of the tool name will be the assigned keystroke. A list of all assigned shortcuts can be found under Windows>Preferences>Shortcuts. There you can change any shortcuts or create new ones.

SketchUp Quick Reference Card

Many of SketchUp’s tools also have multiple functions. By hitting a modifier key on the keyboard, the selected tool will perform a different task.

You are probably starting to worry that there is too much to remember. A great help is the quick reference card that Google has available for download at: http://sketchup.google.com/support/bin/answer.py?hl=en&answer=116693

I highly recommend printing a copy of this PDF to keep handy as you start to learn SketchUp. I even laminated mine!

Navigating in 3-D:

In order to draw in 3-D, you must first understand how to navigate through the three-dimensional world of Sketchup. There are three colored axes in a SketchUp model—red, green, and blue. The blue axis is your vertical “plumb line.” The red and green lines are both “level” and run at right angles. These axes all meet at the origin. Understanding this important concept is half the battle when it comes to drawing your masterpiece.

Although all of the navigation tools are available from the toolbar and through keyboard shortcuts, using your three-button scroll-wheel mouse is the only way to draw efficiently.

	Zoom – By rolling the mouse wheel forward, you can zoom in for a closer look at the detail under your cursor. Roll the wheel backward to zoom out again.
	Orbit – Pressing down on the scroll wheel will allow you to pivot your point of view. By holding down the scroll wheel and moving the mouse left and right and forward and backward, you can orbit around your drawing to change your perspective.
	Pan – Holding down the shift key while “orbiting” with your mouse will allow you to slide your current view in any direction. This can be helpful for moving quickly to another part of your drawing.

Helpful hints:

• When zooming in or out, place you cursor over a part of your drawing instead of the background. This will speed up the process since you are zooming from a specific point and not a point in space.
• Use “Zoom Extents” on the Camera Toolbar to find yourself when you get lost in the details.
• Don’t overlook the “Pan” tool. Sometimes it’s the fastest way to get to where you want to be.

Drawing 2-D shapes:

Unlike a house that is composed of thousands of different components, a SketchUp drawing is only made up of two things—edges and faces. An edge is really just a line. When you close a loop of at least three edges (in the same plane), a face will be automatically created. The face is like a skin connecting all the edges. You can think of it like the canvas an artist might stretch across a wooden frame, and like a canvas, those surfaces can be “painted” with colors and textures to give your model a more realistic look.

With the very simple set of drawing tools SketchUp provides, you can easily create complex shapes with precision. (Shortcut keys are in parentheses.)

	Drawing Toolbar- Use the rectangle (R), line (L), circle (C), and arc (A) tools togetherto create new shapes.
	Undo – Use this to back up through your previous operations.
	Eraser (E) – Use this tool to erase unwanted edges.

Measurement Toolbar or MTB- Use the MTB, located in the bottom right corner of the screen, to give precisemeasurements to the lines and shapes you draw

Inferring – This is an internal part of SketchUp and is always available. It allows you to use points in your drawing as a reference when creating or moving new objects.

Helpful hints:

• The perspective of your view tells SketchUp which plane you want to draw in. Using an elevation or the plan view is a quick way to give SketchUp the “hint.”
• Use the inferred snapping points along an edge to quickly draw objects with precision.
• When entering numbers in the MTB for a rectangle, the length along the red axis is entered first. If the rectangle isn’t aligned with the red axis, the blue length is entered first. There are exceptions to this rule that will be covered later.
• To recreate or “heal” a face, redraw any of the face’s edges.

Drawing 3-D shapes:

The magical part of Sketchup begins when you start to extrude 3-D objects from the faces you have created. The intuitiveness of SketchUp’s patented “push/pull” technology not only makes it easy to learn but also fun to use.

	Push/Pull (P) – Like its name implies, this tool allows you to push or pull on a selected face to add or subtract volume from an object.
	Select Tool (Spacebar) – Use this to select objects for modification in your drawing.
	Move (M) - Use this tool both to move and to copy selected objects.
	Rotate (Q) – Use this tool to rotate a selected object around any axis you choose.
	Follow Me - Use this tool to extrude shapes along a path, including around corners and curves.

Helpful hints:

• Inferring to parts of your drawing while using the Push/Pull tool or the Move/Copy tool is a quick and accurate way to set dimensions.
• Double-clicking a face with the Push/Pull tool will repeat the last push/pull operation.
• Pre-selecting a path for Follow Me is faster and will often give better results.
• Creating a “selection box” by drawing a box with the Select Tool from left to right will help you select objects quickly. This will select every edge and face that is completely bound by the box. A box drawn from right to left, on the other hand, will select everything in the box as well as any line and face the box crosses.
• The Move Tool is in “copy mode” when a “+” appears next to the cursor icon. This is toggled on and off by pressing the Ctrl key (Use the Option key on a Mac).
• To move objects in an axis direction, use the arrow keys to lock the movement of the Move Tool. Pressing one of these keys will toggle the lock on and off.

↑or ↓ for the blue axis (remember: the blue axis runs up and down)

→ for the red axis (remember: right for red)

← for the green axis (remember: it’s the only one left!)

Putting it all together:

With the basics under your belt, it is time to apply them to a “real world” project. Using the previous tools and techniques, some tools from the Construction Toolbar, and an introduction to “Groups” and “Components,” we will put together a simple bookcase.

	Components (G) – An entity of edges and faces (or other components) that are separated from other objects in the drawing. All instances of a Component are automatically updated by editing a single copy.
	Groups – An entity of edges, faces, or components that are separated from other objects in the drawing.
	Tape Measure (T) – Use this tool to create guidelines and points to help layout and place desired objects.
	Dimension – Use this tool to display dimensions in your drawing.

Helpful hints:

• When creating a component, make sure the box labeled “Replace selection with component” is checked.
• When drawing rectangles connected to endpoints or on the face of another object, the dimension entries in the MTB will list the longest dimension first.
• Use Flip along from the context menu to create mirrored copies of objects.
• Use the Outliner to hide and unhide groups and components in your drawing to view details.
• When using Follow Me on a group or component, make sure to draw the path within the group/component by double clicking on the entity to edit it.

When you are finished with your drawing, you can save it by going to the File menu and choosing Save. You can choose to share your drawing in several ways. You can print the current view in the drawing window by selecting the Print option from the File menu, or you can create a JPEG file from the File>Export> 2D Graphic option. The JPEG file that is created can be printed or sent in an e-mail. You can share the 3-D version of your drawing by sending the saved SKP file to anyone who has SketchUp on his or her computer. Clients can easily view your designs in 3-D with the SketchUp viewer available from Google’s SketchUp website. This software only allows users to view the drawing, they cannot edit it! http://sketchup.google.com/download/gsuviewer.html

Honestly, this article has only scratched the surface of what SketchUp can do. There are many other tools available and even more ways to use the tools that I have introduced. I hope I have been able to dispel the myth that all computer-aided design software is complicated and has a steep learning curve. In future articles, I hope to share some more advanced techniques, which will help you make your drawing more efficient.   Learning to make your own personal component library, and using the “Paint Bucket” tool to give your drawings a more realistic look, will take your drawings to the “next level.” It’s easier than you think.

I truly hope this brief introduction to SketchUp has made you consider using it in your work. I promise it will save you time, impress your customers, and most importantly, make you even more successful in your career.

Additional resources:

Books:

Google SketchUp 7 for Dummies by Aidan Chopra:

An excellent book that I always keep nearby for reference. Whenever I go to look up a question I have, I find myself engrossed and come away learning something I hadn’t even planned on.

On the Web:

http://www.aidanchopra.com/ — The companion website to Google SketchUp 7 for Dummies. Includes video tutorials that follow the book, chapter by chapter.

http://sketchup.google.com/training/videos.html — Straight from the source. Includes great video tutorials for the beginner through advanced user.

http://www.go-2-school.com/ — The definitive website for SketchUp education. Offers training material for purchase, as well as a blog and free “webisodes” of their fantastic webcast, “The SketchUp Show.”

http://finewoodworking.taunton.com/blog/design-click-build — A blog from Fine Woodworking magazine dedicated to the use of SketchUp for the woodworker. Tends to cover more advanced techniques, and I am always amazed by their work.

http://garymkatz.com/ — A great website for the finish carpenter and where I was first introduced to SketchUp.  There are two SketchUp tutorials located on the Charts & Drawings page that I highly recommend.

http://www.youtube.com/user/toddmurdoc — My YouTube channel. A collection of short videos, covering some timesaving techniques for the carpenter who uses SketchUp.

Read this article in its original format (with more images) at TiC Issue 4!

AUTHOR BIO

Todd is a fourth-generation carpenter/woodworker who is currently employed as a corporate pilot. His schedule alternates between a week “on the road,” flying all over North America and the Caribbean, and a week at home in Northern Virginia.

While at home he enjoys spending time with his wife Jennifer and their three children.  The time at home also allows him to “escape” to his shop where he builds custom furniture and cabinets. Most of his work is for pleasure these days, doing only one or two paying jobs a year.

He began learning SketchUp as a way to kill time on layovers and quickly discovered he could use it to continue progress on projects back home. Having a detailed model completed ahead of time also makes his limited time in the shop more efficient, since all the details have already been worked out in a “virtual” prototype.

During college, while working for a local contractor, Todd vividly remembers shingling a roof one VERY hot summer day. He paused for a moment to watch a jet flying high over head and thought to himself, “Boy, I wish I were up there flying.” Ironically, he now finds himself occasionally looking out the cockpit window from 35,000 feet and thinking, “I wish I were down there making sawdust.”