# This lesson begins at a stoplight when a truck with a standard load of logs pulls up

Subject:

Math

8, 9, 10, 11, 12

Title – Logging Truck Loads ~ Lumber
By – Jim Connelly
Primary Subject – Math

As you sit at a stoplight, up rolls a logging truck with a full load of logs headed for the nearby mill………

OBJECT:

Determine the number of:

a) board feet and

b) cubic feet of lumber of a “standard load of logs” on a passing logging truck.
(In a follow-up lesson), we use this lesson to determine the value of the load to:

a) The owner of the trees

b) The lumberjack who falls, limbs, and bucks the trees

c) The logging enterprise that skids and loads the logs

d) The trucker hauling the logs to the mill

*sometimes the driver is paid by the load

*sometimes the driver owns the rig and is paid by

volume

e) The mill

f) The wholesaler

g) The retailer

h) The customer at Lowe’s, Home Depot, Lumberman’s, ..

You can take one, all, or pick and choose any strand you wish. Be creative, as lumber is a commodity that makes the nation go hum, hum, hum.

Given:

1. A hand-out with photograph (I used my digital camera, snapped a picture of the truck from the rear as it passed me, copied and pasted it to a sheet of 8.5 x 11 sheet of paper). Bingo — an instant load of logs.
2. Written on the butt of each log (in the photo), is the approximate diameter of the log/s, each log being a standard log length of 33 feet. You can hand write the numbers on the logs, or if you have Adobe or some other program, you can insert numbers from the computer…..
The bunk of the truck is just under 8 feet wide. Typically, the load is approximately 8 feet high and 33 feet long. Let’s say the load measures 7′ x 7′ x 33′ giving us 1617 cubic feet. There are 12 board feet in each cubic foot, therefore this load would have 19,404 board feet.
We know that NOT to be true. We know that the load should be in the 4,000 board foot category. This 7x7x33 figure is a perfect, voidless, rectangular prism, and equals an erroneous figure when trying to determine board feet in a log, which is round, air space between each log and is tapered. Some of the old logging trucks, with 10 and 12 foot bunks, hauling off road, could carry a load of that size, called “Three Log Loads” and they were HUGE, but not today’s highway rigs with weight limitations).

3. For today’s lesson plan and to simplify the math for a 60 minute math class, I have given the logs the same diameter at each end, a true cylinder if you will. In the real world, trees DO NOT grow in a perfect cylinder and the students need to be reminded of that fact.
The formula for finding the board feet in a log is cumbersome and most students make simple errors in the math calculations attempting to find the end resultant. They are frustrated before they begin.
I will include the true formula here, but unless you are in a forestry class or a science class and have a great deal of time, or want to do this, the true formula is FYI only.
The true formula is as follows:

V = .(005454 (L + 0.67)*

X [ (DS + 0.7)sq’d + (DL = 0.7)sq’d + (DS + 0.7)(DL = 0.7)] (all this is divided by 3) and equals cubic feet ………….
WHERE: V = volume (cubic feet)

L = scaled length (feet)

DS = scaled small-end diameter (inches)

DL = scaled large-end diameter (inches)

* When logs are 17 feet and longer in length substitute (L + 1.00) for (L + 0.67) …………..

This equation will give you CUBIC FEET. Again. One cubic foot of lumber equals 12 board feet. ( A board foot equals the value of 1″ x 12″ x 12″ or 144 cubic inches. i.e. A board that measures 1″ x 12″ x 10 ft long is figured at 10 board feet).
4. Formula to be used (very simplistic): Volume = pi r squared x height.
5. Species of wood is Douglas Fir (Psuedotsuga menziesii), cut on the west side of the Cascade Range, state of Oregon, therefore giving each log the value of, let’s say, 35 pounds per cubic foot. That’s not perfect, but it’s close enough.

As each truck is only allowed to carry so many pounds on the highway, we know that there will be approximately 4,000 board feet in the load, so your answers should come close to that figure. If not….. modify your butt measurements until your numbers come close to 3500.

Q: “How many pounds does the load weigh?”
Q: “How many board feet are in the load?”

*** In the “Real World,” using the “Scribner Log Rules,” “Rules for taking log scaling measurements,” which takes defects, taper, where cut, and more into consideration, at the mill 15 miles from here, here’s what a true log will issue:

Measuring 15 inches in diameter (diameter of small end) and having a length of 33 feet, this log will scale out at 290 board feet. To get a “thousand foot log”, it would have to measure 26 inches in diameter (small end) and be 32 feet long…….

Draw the picture. Do the math. Have fun.

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