Calculating the radius of an arch
Sometimes it's useful to know the radius of an arch or head casing long before the shop work takes place. I have found the following formula provides precise dimensions and takes advantage of the simple calculators on the market today. Even calculators without a square-root function can handle this one:  Rise² + (Span/2)² 2 x Rise
For instance, let's assume that an arched opening leading from a dining room to the great room has 84" tall sides, the span is 96" and the center of the arch is to be 96" above the floor. The rise is calculated as 96-84=12.		Rise² + (Span/2)² 2 x Rise
Substitute the numbers :		12² + (96/2)² 2 x 12
Perform the multiplication and division:		144 + 48² 24
Further reduce expression :		144 + 2,304 24
Further reduce expression :		2,448 24
and finally:		102
The radius is 102", with no errors resulting from inadvertent stretching of chalk lines or other mechanical limitations, such as trying to lay out a curve with a 102" radius on a piece of plywood that's only 96"  in length.
Credits: The article above was first published in the Fine Homebuilding magazine, November 1997, No. 112. Taunton Press, Inc., Newtown, CT 06470.
Cabinet Assembly Table
	Select the thumbnail images for a larger view
There’s never enough bench space in a shop. At one time or another, almost every horizontal surface in a shop will get pressed into service as an ersatz assembly table. Through the years, I’ve had to improvise to come up with assembly space: at times using my workbench, a solid-core door placed over two sawhorses, my table saw and extension tables and (all too often) the shop floor. All the projects assembled on these makeshift assembly tables were completed, but there were always compromises and inconveniences. My workbench is too narrow for many projects; solid-core doors aren’t as stable as I would like and I hated to tie up the table saw from glue-up until I removed the clamps—usually the next morn­ing. Clamping around the casting on the bottom of the table saw is a pain, too, and extension tables just aren’t meant to take the weight or the pounding that assemblies often entail. I wanted a table that was large enough to stack standard sheet goods on and flat enough to screw face frames together on. I want­ed it stationary most of the time (and able to be locked in place) but capable of being moved around the shop when needed else­where, I also warned the table to support relatively large loads (I figured up to 3,000 lbs. or so), such as for stacking sheet goods at the infeed side of the table saw. Through a process of trial and er­ror, I found that a surface height of 20 in. provided comfortable access to my work and allowed me to set one foot comfortably onto the table, which makes it easier to reach the middle of the table and also relaxes my back. I mulled over the design for sever­al months; then, during a lull between jobs, I did some serious design work and began construction. The result (with a few modifica­tions) is shown in the photo at left and in the drawing on p. 40. A torsion box for a flat, strong surface Torsion box construction was really the only solution to my design dilemma. A torsion box consists of a core grid with a skin on both sides. The resulting box is stronger (especially in resisting bending or twisting forces), more stable and far lighter than a block of solid wood of equivalent size. I decided on 3/4-in. birch plywood for the torsion box's core members and for the two full sheets that would sandwich the core. I wanted a flat surface on which to build the table, so I put a sheet of Kortron (an acrylic-faced pine particle-board) on—you guessed it—the floor to smooth out any slight ir­regularities in the concrete. Kortron is more rigid than plywood, so it’s ideal for this application. Also, my floor is very nearly flat to begin with, hut if yours is not, you may need to shim beneath the Kortron to eliminate any tendency for the sheet to rock. I cut the box’s sides, ends and all core members and then marked the long core members where the short pieces would butt against them. 1 stapled together the perimeter of the box first and then proceeded from one side of the box to the other. Because I didn’t have a giant, industrial milling machine handy to surface the core and perimeter, I didn’t glue the core members to each other. The core members must be able to move slightly to come flush with the box's top and bottom when the whole is assembled. I stapled across each joint line to provide sufficient hold till the box was glued up and made sure all the staples were set below the surface of the core members. After checking corner to corner for square, I marked the box’s perimeter where the core members were stapled to it. 1 then applied glue to the top edge of all core members and, with my wife’s help, carefully laid the box’s top ~‘ place. Working quickly, 1 snapped chalk lines to define the core’s grid on the top, using the marks I’d made around the perimeter for guidance. I nailed off the perimeter first, placing a nail every 6 in. and did the same in the interior of the grid. I was careful to avoid intersections of the core members be­cause I didn’t want to hit staples or split the core members’ ends. I wanted even pressure over the entire surface until the glue set, so I placed six sheets of Kortron on top of my now half-finished tabletop. I calculated this would provide approximately 140 lbs. per square inch of “clamping” pressure on the glue joints. By now it was late afternoon, so I left the “clamps” on overnight. The next morning, I removed the sheets of Kortron, flipped the assembly over and attached the box’s bottom in the same way. To provide a means of attaching the leg assembly, I glued and screwed pairs of leg-attachment plates to the bottom of the torsion box, one over the other, at the four corners. I positioned the out­side edges of the plates directly beneath two core spacers. Besides transferring the load more directly (than if the leg were positioned over a void), this placement provides plenty of stability to the table as a whole and keeps the brake-cam lever under the table and out of the way. Although I used two pieces of plywood for the leg-attachment plates, in retrospect, using one goodly piece of Douglas-fir 2xa would have been adequate and would have saved me some time and effort. Designing the legs and brake system I’d already determined the overall height for the table, so I had a rough idea of the size of the leg assembly. I also knew about how much weight I wanted the table to be able to support. I had since revised my original goal of having the table support 3000 lbs., figuring instead on a maximum of 19 sheets of 3/4-in. stock, which would stack level with the height of my Unisaw’s tabletop. At just over 98 lbs. a sheet, 19 sheets of Kortron weigh almost 1900 lbs., and the table itself would weigh over 300 lbs. complete. Even with my reduced-load requirement, I needed a set of casters with a loadl rating of more than 500 lbs. each! After an extensive (but ultimately futile) search for rubber casters with brakes that could accommodate this load, I realized I’d have to compromise a bit. I decided I could do without the mobility when the table was fully loaded. I settled on some 4-in. casters, load-rated at 200 lbs., which had been kicking around in a dark corner of my shop ever since I’d salvaged them from a defunct dolly. They had no brakes, so I redesigned the leg assembly to incorporate a shop made, cam-operated brake, separate from the swivel casters (see the drawing on the following page and the photo above). The legs on my table consist of a core of 4x4 Douglas-fir, two L-shaped leg braces, the caster mounting plate and two filler plates that help support the caster mounting plate (see the drawing on p 40). The cores, braces and filler pieces’ are glued and nailed together with 1½-in, finish nails, and the caster mounting plates are glued and screwed to the leg braces. I bored a ½-in. hole in each of the leg assemblies for the brake-cam fulcrum, and glued and nailed the leg assemblies to the attachment plates on the table’s bottom. I used heat-treated, SAE grade 8, 1/2-20 hex head cap screws as fulcrums for the brake cam (a screw with a smaller diameter may not have been strong enough under full load, and a lower-grade steel probably would have bent). To secure the screws, I used aviation-style, nylon-insert locking nuts. These nuts permit me to keel) the brake cam in the upright “off’ position by just snugging the nuts against the leg braces, yet they don’t interfere with the cam’s operation. Getting the brake to work properly required a good deal of trial and error. Setting the brake cam has to cause the caster to rise oft the ground, but only slightly; the greater the distance, the more stress on the cam and the more difficult the brake will be to operate. I settled on a design whereby the wheel rises 1/8in. off the ground when the brake is engaged. Ensuring the stability of the leg assembly under load required that I design the cam with a flat section on both sides of the fulcrum. Arriving at an optimal length for the flat at the end of the cam (7/8 in.) and an optimal curve for the cam end required some experimentation and several trips to the band saw. The drawing detail on the facing page shows the final shape I arrived at. A couple of oversights rectified I used my table for a couple of weeks, very contentedly, but soon discovered, as often happens, that I’d overlooked a thing or two in my design. I noticed that I was always just beyond the reach of an electrical outlet. I remedied this situation by adding four outlets below the torsion box, one at the midpoint of each side and one at each end. I used metal handy-outlet boxes because both boxes and cover plates have round corners to prevent snags or cuts. I installed Leviton #5014 special-service duplex outlets into these boxes. These outlets were considerably more expensive ($2.99) than standard-service outlets ($0.39), but they’re designed to stand up better to rough conditions, such as those found in a woodworking shop. I connected a 14-gauge, Type SJ electrical-cable supply line with a nylon grounding plug to one of the boxes at the end of the table. All 115-volt outlets in my shop are protected with Ground Fault Circuit Interrupter (GFCI) breakers. If yours aren’t, you may wish to install one instead of a duplex outlet in the handy box where you have attached the supply line, and feed the power through it to the other three boxes. Select a receptacle-type GFCI device with a rating of at least 15 amperes at the receptacle and 20 amperes feed-through to the other three outlets. My shop outlets are protected with the Leviton #6599. (For more on GFCI breakers. see Fine Woodworking #93, pp. 58-62.) Working on my new assembly table was infinitely better than working on any of the previous surfaces I’d used, but I did notice that some of my face-frame joints were slightly offset. The only thing I could attribute this to, since I was using the table as reference, was a slight deflection in the tabletop. I’d screwed a sheet of 1/4in. hardboard to the top of the birch plywood after I’d finished the table (intending it to be a replaceable. smooth work surface), but, evidently, it wasn’t stiff enough. I replaced it with a 3/4-in. sheet of Kortron, and that solved the problem. I’d also noticed —especially with the Kortron—that whenever I really bore clown on a face frame, it would tend to slip. I fixed this by installing side and edge boards all around (to get the sides out beyond the 49x9” sheet of Kortron) and using temporary stop blocks whenever I’m assembling cabinets. Since completing the assembly table, over 100 sets of cabinets have moved across it on their way through my shop. The table’s low height has saved my back (as has being able to use the table at the table saw’s in-feed side); the flat, stiff reference surface has saved me untold hours of sanding; and the convenience of electrical outlets—where I need them, when I need them—has eliminated many snake-like tangles and saved me plenty of time as well.
Credits: The article above was first published in the Fine Woodworking magazine, August 1992, No. 95. Taunton Press, Inc., Newtown, CT 06470. It subsequently appeared in The Small Woodshop, ©1993 by The Taunton Press, Inc.