Post on 05-Jan-2016
description
Planting Trees: How many in 10 acres?
What do we need to know?
A. How closely should the trees be planted?
1 tree every 6 feet in each direction.
B. How big is an acre?
220 yards by 22 yards = 4840 square yards.
So, we can get 11 x 110 = 1210 trees in an acre, or 12,100 trees in 10 acres.
How long a log for a rafter?
What do you need to know?
8ft
10:12 pitch – goes up 10” rise for every 12” of run
8 ft
80”
96”
802 + 962 = (rafter length)2
125”
David is making two cuts on a large piece of wood.He’s going to cut a 2” thick piece and a 1” thick piece off and leave an 8” beam.How thick should the beam be before the cuts, if the blade takes out 1/8th of an inchOn each cut?
2”
He’ll make another cut that is 1” thick, leaving 8” behind.
How thick should the whole piece be?
8 + 2 + 1 + (2 x 1/8) = 11 ¼
1”
Remember, each cut removes 1/8” of wood.
$170 x 5 =
We have almost this many 1000 board feet of 1” boards.
$850
Let’s estimate to see if he did this right.
225
90
50
250
Calculating acreage
80,000 ft2
43,560 ft2/acre
How many yards of sand do I need to mix mortar for this wall?
Let’s see. A bag of cement is 1 cubic foot, and a “yard” of sand is
really a cube of sand one yard on a side (yd3).
Mortar Mix 1:3
cement sand
I have 18 bags of cement.
18 ft3 of cement would require
18 x 3 = 54 ft3 of sand.
And a cubic yard of sand is 27ft3. So I
need to order 2 “yards” of sand.
3 ft
3 ft
3 ft
Cubic yard
?
26 ½ 28 ¼ 28 13/16
3 ½”
What’s the total length?
How wide is one board?
33 1/16 + 3 ½ = 36 9/16
1 ¾
$597.65 x .7 = $418.36$597.65 x .7 = ?
Try it in your head: estimate!
What information is necessary to define these shapes?
What’s the best way to define these curves?
Roofing!
What is the angle here?
What math is behind a set of stairs?
For stairs to be comfortable, they should be proportioned by the formula:
2 x (riser height) + (tread length) = between 24 and 26 inches
I got 3 rises out of a set of triangular (turning) steps at the bottom
RISERS
With 10 more rises on the straightaway, I would have 13 rises total.
RISERS
My total height was 8’ 6 ¾” so each of 13 risers would be
102.75/ 13 = 7.9
= a little less than 7 29/32
RISERS
I had 8 feet of floor space to put in 10 stairs on the straight run
TREADS
So the tread for each stair would be:
8 feet96 inches / 10 = 9.6 inches per stair
= a little more than 9 19/32
TREADS
How did I do with the formula for comfort?
2 x (riser height) + (tread length) = between 24 and 26 inches
Risers = 7.9 inchesTreads = 9.6 inches
(2 x 7.9) + 9.6 = 25.4
Must go somewhere…
Sink drains into the bowels of the earth
3” x 2” x 3” Y
2” x 1 ½” x 2” T
What is the naming convention for T’s and Y’s?
A waste pipe should be sloped 1% - 2%. How much should it slope per foot?
x
12=.01
x =.12
I know that 1/8” is .125”, so a 1% slope is a little bit less than 1/8 inch per foot.
We burn about 3 cords of wood a year to heat our house.cords
A cord is a 4’ x 4’ x 8’ stack
Approximately what fraction of our yearly supply of wood is this stack?
12 ft
4 ft
Each piece of wood is 18 inches long
Remember, we need 3 cords (each 4’x4’x8’) for the winter.
A cord is 4 feet x 4 feet x 8 feet
The stack is 4 feet x 12 feet x 18 inches
72 ft3
384 ft3
= .1875 = About 19%
= 72 cubic feet1.5 feet
= 128 cubic feet (128 ft3).
So we will need 128 ft3 x 3 = 384 ft3 for the winter.
or about one fifth (1/5th) of a year’s supply
= 72 ft3 stack
Problems• Trees per acre• Rafter length• Timber milling• Milling price• Acreage• Mortar Mix• Length• Window price• Arch• Roof• Stairs• Plumbing• Firewood