Addition and Multiplication in Cutlists

Cut lists are an essential woodworking tool for calculating lumber needs.  Lumber is bought in large slabs at the lumber yard and then milled into smaller pieces that will comprise the finished piece of furniture.  Woodworkers use cut lists to calculate what size slabs they should buy at the lumber yard in order to ensure that there will be adequate supplies of wood to mill into furniture components back at their wood shops.

		Final Size	Rough Size
Part Name:	#	T x W x L	T x W x L	Board Footage
Legs	4	1.5” x 1.5” x 29.25”	2” x 2” x 30”	3.33 BF
Aprons	4	¾” x 3.5” x 12”	1” x 4” x 13”	1.44 BF
Top	1	¾” x 17” x 17”	1” x 21” x 18”	2.63 BF

(NCTM Standard: Number and Operations)

Leg Splay

The compressive strength of wood typically exceeds its tensile strength by a factor of 5.  Thus the strongest way to position wood is to have the grain aligned parallel to the force it is resisting.  To apply this principle in a chair design would result in the legs being entirely vertical.  While this design is theoretically strong, it is also very unstable.  As a compromise, chair legs are typically splayed out at 3-7 degrees in order to gain stability without compromising too much of the wood's compressive strength.

(NCTM Standard: Measurement)

Ergonomics

Human bodies come in a range of sizes.  When designing a custom piece of furniture for a unique client, a furniture maker can afford to customize all aspects of the design to the customers height and body dimensions.  When designing furniture for a restaurant or general use, furniture should suit the largest possible number of body types.  The study of the the average proportions of the human body is referred to as ergonomics.  By compiling extensive measurements of human bodies and processing those numbers into mean and average dimensions, the ergonomic studies that began in the 1960s have greatly increased the furniture designer's awareness and ability to support the human form.

                       

(NCTM Standard: Data Analysis and Probability)

Blade Duration

Factors such as dryness, density and silica content have a significant impact on the longevity of a sharp cutting edge in the tools being used upon different timbers.  Sharpening a plane blade requires a 5 minute interruption in work.  These 5 minute interruptions can accumulate to a significant loss of time in the course of a large project.  The choice to design in dense, silica rich timbers must be weighed against the added expense of additional sharpenings.  The chart below reflects the frequency of sharpening required by woods representing a range of densities.

            

Species	Density measured as Specific Gravity	Silica Content	Duration of a cutting edge
Pine	.350	None	45 minutes
Walnut	.63	None	15 minutes
Purpleheart	.750	High	2 minutes

(NCTM Standard: Data Analysis and Probability)

Time Analysis

Keeping track of the time needed for woodworking operations is an essential part of respecting customer deadlines as well as the profitability of the business.  By maintaining accurate records of how much time was required in past woodworking operations, woodworkers are capable of making accurate future estimates that ensure timely delivery and accurate pricing.

Task	Time needed	# of repetitions	Total time
Set up cross-cut saw	10 minutes	1	10 minutes
Cut lumber to length	15 seconds	20	5 minutes
Set up mortiser	30 minutes	1	30 minutes
Cut mortises	1 minute	20	20 minutes

(NCTM Standard: Measurement)

 

Analyzing Precision

The common knowledge in woodworking circles is that mortise and tenons should fit with a tolerance of 1/64”.  In Joe's experience, this tolerance is too great.  The most common type of wood glue, poly-vinyl adhesive (PVA), relies on the glued pieces of wood being in contact with each other or near enough to each other to allow for a polar attraction. The range of the attraction is less than .003”.  The glue itself has no spanning strength.  1/64” equates to .016”.  Thus if there is a 1/64” difference between the mortise and the tenon there can be up to .008” between either side of the tenon and the walls of the mortise.  While this amount of glue might seem to be insignificant, it makes a big difference in strength the finished product. Joe has seen glue fail in joints with tolerances over .01" but never in joints with tolerances of .005" or less.

(NCTM Standard: Measurement)

Working with Fractions

Most furniture is still measured in imperial measurements.  As a result, conversions between feet and inches are frequent and fractions with unlike denominators must frequently be added, subtracted, and multiplied.

(NCTM Standard: Number and Operations)