Monday, December 10, 2012

Firewood By The Truck-load: Volume & Per Unit Pricing





Let's assume you got behind on your firewood splitting and needed to purchase some firewood for a week till you get caught up. You check you local paper and see they have prices of $80 per truck-load. What can one expect from a truck-load of wood? How many units? How much is this per unit? We will be using some basic volume to get the number of units and use this number to get a per unit price. We could then decide how long it will last based on types of wood, etc (Note: The purpose of this activity is for the application more so than for the usefulness. As anyone whose ever split wood knows, quality has more to do with density and how well the wood is seasoned..see below)

Measurements Used
Full Size F-150 Long-bed Truck

Length = 8ft
Width = 6.5ft
Height = 1.6ft

Piece of Firewood (We will assume the average log length is 18inches and has a radius of 8 inches which will be cut into 8 pieces for firewood)



Units of Firewood by Volume

For the sake of ease, let us assume that a truckload of firewood will be neatly stacked but not higher than the sides of the truck.

Volume of truck bed

8x6.5x1.6 = 83.2ft^3

Volume of Firewood Log

Changing Our Units to feet

length = 18 inches = 1.5ft
radius = 8 inches = 0.66ft

Volume of a cylinder equals

V = (pi)(r^2)(h)
V = (3.14)(0.44)(1.5) = 2.05ft^3

Volume of Firewood Piece (once split into 8 pieces)

2.05ft^3 / 8 = 0.26ft^3


Units of Firewood Per Truckload


Now that we know the volume of both the truck-bed and for a piece of fire wood we can simply divide them to see how much firewood should stack neatly into the truck-bed

83.2 / 0.26 = 320 pieces of firewood

Adjusting For The Odd Shapes

Since the pieces of firewood are not cubic, they are circle-sections. They will not stack neatly together. There will be added spacing between them. The seller could compensate for this by stacking the firewood above the walls of their truck, but we will assume they didn't.

This spacing could be compensated with a little optimization. But, from stacking wood I think it would be safe to say that four every 10 pieces you will loose one to spacing. Thus we will loose 1/10th of our total to spacing. 1/10 of 320 = 32

320 – 32 = 288pieces of firewood.



Prices Per Unit

At the rate of $80 per truck-load. We have $80 per 288 pieces of wood

80/288 = $0.28 per unit.
The Calculations Are Quite Arbitrary

These calculations are quite arbitrary in their usefulness. Most firewood comes in different sizes. A true calculation of how good the deal on firewood would to compare volume to density as well as how seasoned. The purpose of this posting was simply to serve as an application.


From Here We Could

From here we could ask questions like.

1) If we use 40 pieces of firewood per night, how long will this last us?
2) If you wanted to, you could make a step-function based on how cold it is outside.

At 40 degrees we use 10 pieces of firewood per night
At 30 degrees we use 30 pieces of firewood per night
etc.

3) Could recalculate based on the volume questions for different size truck-beds or different materials



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