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
5 comments:
Firewood is wedge shaped, not round, rounds are not yet firewood
Where can we buy this fire wood ?
Where can we buy this fire wood ?
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