Tuesday, September 9, 2014

Trigonometric Formulas Geometrically

Trigonometry comes from the Greek trigōnon ("triangle") and metron ("measurement").
Geometry comes from the Greek geo ("earth") and metron ("measurement"). 

The Greek mathematicians Euclid and Archimedes in the 3rd century BC were the first to prove trigonometric formulas geometrically. You can find the values of sine, cosine and tangent functions, by using a unit circle with a radius = 1. This article will explain how to develop Hip -Valley Rafter Roof Ratios using  Trigonometric Formulas geometrically drawn using Tetrahedrons or Trirectangular Tetrahedrons for the Trigonometric Ratios we use in roof framing. The tetrahedron unfolded is the same as the roof framing kernel. The trirectangular tetrahedron unfolded is a tetrahedron slice from a compound joint. 

The "Unit Circle" is a circle with a radius of 1.



For a triangle with an angle θ, the trigonometric ratios functions are calculated this way:
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
For a triangle with an angle θ, the trigonometric ratios functions are calculated this way for roof framing:
Sine Function:
sin(θ) = Rafter Rise / Rafter Length
Cosine Function:
cos(θ) = Rafter Run / Rafter Length
Tangent Function:
tan(θ) = Rafter Rise / Rafter Run


Because the radius is 1, you can directly measure sine, cosine and tangent.



Because the radius is 1, you can also directly measure cosecant, secant and cotangent.
Because the radius is 1, you can also directly measure the Trigonometric Ratios of an polygon. An Octagon in this example.

Basic Roof Framing Tetrahedron unfolded.
D Angle = Plan Angle
A Angle = Roof Slope Angle
C Angle = Hip Rafter Slope Angle
E Angle = Jack Rafter Side Cut Angle
B Angle = Hip Rafter Backing Angle


In this example the triangle in blue has the following properties:
Roof Slope Angle = ß  = 33.69007°
Plan Angle = α = 45.00°
Radius = 1

The altitude of the triangle can be found by multiplying the sine of the triangle by the cosine of the triangle. 
Altitude of Triangle =  sin ß × cos ß
sin ß = 0.5547
cos ß  = 0.8321
Altitude of Triangle =  sin ß × cos ß = 0.5547 × 0.8321 = 0.4615





In this example the triangle in blue has the following properties:
Hip Rafter Slope Angle = ß  = 25.23940°
Plan Angle = α = 45.00°
Radius = 1
 Again, the altitude of the triangle can be found by multiplying the sine of the triangle by the cosine of the triangle. 
Altitude of Triangle =  sin ß × cos ß
sin ß =0.4264
cos ß  =  0.9045 
Altitude of Triangle =  sin ß × cos ß = 0.4264 × 0.9045 = 0.3857




If were studying tetrahedrons for roof framing trigonometric ratios we could also use following trigonometric ratios to find the base length of the plan angle triangle or the height of the plan angle triangle.
cos α × cos ß =  base length of the plan angle triangle
cos α × cos ß = 0.6396
0.7071 × 0.9045 = 0.6396

sin α × cos ß = height of the plan angle triangle
sin α × cos ß = 0.6396
0.7071 × 0.9045 =0.6396


Since the Altitude of Triangle =  sin ß × cos ß
we can use the following Trigonometric Ratios to write an formula for the hip rafter backing angle when the plan angle is equal to 45.00°.

Hip Rafter Backing Angle = 
arctan((sin ß × cos ß) ÷ cos ß) =
arctan((sin ß × cos ß) ÷ cos ß) =
arctan(sin ß)  =

arctan(sin 25.23940°) = 23.09347°
arctan(sin(Hip Rafter Slope Angle)) = Hip Rafter Backing Angle



When the plan angle is not equal to 45.00° you need to use the tan of the plan angle in the trigonometric formula for the hip rafter backing angle.

Hip Slope Angle = ß  =  27.50055°
Plan Angle = α = 51.34019°
Radius = 1

Hip Rafter Backing Angle = 
arctan((sin ß × cos ß) ÷ (cos ß × tan α)) =
arctan((sin ß × cos ß) ÷ (cos ß × tan α)) =
arctan(sin ß ÷ tan α) =
arctan(sin 27.50055° ÷ tan 51.34019) = 20.27452°
arctan(sin Hip Rafter Slope Angle ÷ tan Plan Angle)= Hip Rafter Backing Angle



In this example you can find the trigonometric ratios to write a formula for the Hip Rafter Slope Angle, angle C in the unfolded tetrahedron.  You have to extend the base of triangle A, Rafter Slope Angle Triangle, so the Hypotenuse (Rafter Length) is equal to 1. So, you can dimension the correct length of the cosine of the Rafter Slope Angle.

Angle C = arccos( cos( A ) ÷ cos ( B ))
or
Hip Rafter Slope Angle = arccos( cos( Roof Slope Angle ) ÷ cos (Hip Rafter Backing Angle ))
cos A = 0.83205
cos B = 0.93804
cos C = ( 0.83205 ÷ 0.93804)
cos C = ( 0.88701)
Angle C = arccos( 0.83205 ÷ 0.93804) =27.50055
Angle C = arccos(0.88701) =27.50055



It's useful to print out the Unit Circle Trigonometric Functions-Ratios for the triangles you're studying, when you're trying to write roof framing formulas.  This way you can try different combinations of the trigonometric ratios using multiplication or division. 
Example using   multiplication of the cosine of D and the values of angle A:
0.62470 × 0.83205 = 0.51978 ...no match
0.62470 ×  0.55470 = 0.34652 ...matches the sin of the angle B
0.62470 ×  0.66667 = 0.41647 ...no match

From these matches we can write
Angle B = arcsin(cos(D) × sin(A))
Hip Rafter Backing Angle = arcsin(cos(Plan Angle) × sin(Roof Slope Angle)) 


D Angle = 51.34019 = Plan Angle
cos = 0.62470
sin = 0.78087
tan = 1.24999

A Angle = 33.69007 = Roof Slope Angle
cos = 0.83205
sin = 0.55470
tan = 0.66667

C Angle = 27.50055 = Hip Rafter Slope Angle
cos = 0.88701
sin = 0.46176
tan = 0.52058

E Angle = 33.64933 = Jack Rafter Side Cut Angle
cos = 0.83244
sin = 0.55411
tan = 0.66564

B Angle = 20.27452 = Hip Rafter Backing Angle
cos = 0.93804
sin = 0.34652
tan = 0.36941


Here's an example for writing an trigonometric formula for the tetrahedron angle E, jack rafter side cut angle.
Angle E = arctan(cos(A) ÷ tan(D))
Angle E = arctan(0.83205 ÷ 1.24999)
Angle E = arctan(0.66564) = 33.64933 
Jack Rafter Side Cut Angle = arctan(cos(Roof Slope Angle) ÷ tan( Plan Angle))



Here's an example of using the values of tan, cosine and sine of a tetrahedron to write a trigonometric for the Angle D in the tetrahedron. (D = Plan Angle)
Angle D = arccos(sin(E) ÷ cos(C))
Angle D = arccos(0.55411 ÷ 0.88701)
Angle D = arccos(0.62470) = 51.34019
Plan Angle = arccos(sin(Jack Rafter Side Cut Angle) ÷ cos( Hip Rafter Slope Angle))


Saturday, September 6, 2014

Layover Cuts #2

Purlin Rafters, Roof Sheathing or Dormer Square Tail Fascia Layover Cuts
(Cutting Roof Sheathing with an Edge Bevel)

I was asked to elaborate on roof framing layover cuts. Using the same valley sleeper angle to cut the valley sleeper bevel angle and the layover roof sheathing seems wrong, but it is correct.

Always make some type of test model while you're studying roof framing angles.
Layover cut with an irregular valley. 6:12 & 8:12 roof pitches.


Layover cut with an regular valley. 8:12 roof pitch. 


Trirectangular Tetrahedron example for irregular hip roof layover cuts.

C5m Main Hip Rafter Backing Angle = 26.34404
C5a Adjacent Hip Rafter Backing Angle = 15.56481
P2m = Main Jack Rafter Side Cut Angle = 47.96889
90° - P2m = Main Roof Sheathing Angle = 42.03111
P2a = Adjacent Jack Rafter Side Cut Angle = 33.85451
90° - P2a = Adjacent Roof Sheathing Angle = 56.14549

Bevel Angle = arctan(tan(C5m + C5a) × sin(90° - P2a))
Bevel Angle = arctan(tan(26.34404 + 15.56481) × sin(90° - 33.85451°))
Bevel Angle = arctan(tan(41.90885°) × sin(56.14549)) = 36.69923°

Bevel Line Side = Cut Perpendicular to Roof Surface = 36.69923°
Saw Blade Bevel Angle From Bevel Line Side =arctan(sin(Bevel Angle on Stick) ÷ tan(Miter Angle on Stick)
Saw Blade Bevel Angle From Bevel Line Side = arctan(sin(36.69923°) ÷ tan(56.14549°) = 21.84545°

Bevel Line Side = Cut in Roof Surface Plane = 56.14549°
Saw Blade Bevel Angle From Bevel Line Side =arctan(sin(Bevel Angle on Stick) ÷ tan(Miter Angle on Stick)
Saw Blade Bevel Angle From Bevel Line Side = arctan(sin(56.14549°) ÷ tan(36.69923°) = 48.0911487°





Monday, September 1, 2014

Napa EarthQuake Structural

Here's some pictures of the buildings I visited on August 31 2014. 7 days after the 6.0 Earthquake in Napa California. The structural damage I viewed suggested that it was a unreinforced masonry - brick tension tie failure, or lack of tension ties. Unreinforced masonry was banned in California in 1930, due to its vulnerability during earthquakes. Downtown Napa is open for business and the earthquake damage is a new tourist attraction. Walking around Napa, it looks like there's only about 1% of the buildings in Napa there were damaged by the earthquake. The Historic Napa Mill and RiverFront Inn looked like it had no exterior damage to the 3 story building.

Extreme Danger
Stay Back 100 Feet

This National Disaster Team didn't read the Extreme Danger sign. 
So, what is in those two trucks? Or are they there just for advertising?


I was in this building 6 years ago. I remember seeing the tension ties running thru the building. The main damage to this building was the front of the building where there are no tension ties.

Here's the famous dangling roof that was part of a recent retrofit. Apparently the tubular steel with rods 16" O.C. should had the rods protrude thru the exterior wall with plate washers. It probably needed an steel uplift post at the corner as well.


This church with the exterior parapet wall detached from the roof framing needed some type of wall to roof connection. This is a lot of weight leaning towards the street. It needs some raker bracing.


Wood frame structure

Wood is one of the best materials for earthquake-resistant construction since it is lightweight and more flexible than masonry.  This Victorian house and 100's more are right across the street from the church with the leaning rake wall. These Victorian homes didn't appear to have any exterior wall framing damage from the earthquake. I had forgotten how many Victorian houses are in downtown Napa. 



The GoodMan Library, historical society, needed bigger tension ties to hold the exterior brick-stone walls together in an earthquake.Again it should of had tension ties with plate washers on the outside of the building.


This church had stain glass windows blown out in the earthquake. However, the exterior framing looked pretty good.

I stayed in the Church Hill Manor bed & breakfast Inn 6 years ago and it didn't appear to have any damage from the earthquake.

The United States Post Office in Napa definitely needs some repair. Again it could've used some tension ties with plate washers to prevent this crack in the exterior wall of the building. Right across the street from the post office is a newer building with all glass exterior walls and some brick veneer. This building looked completely unaffected by the earthquake.

The castle, Napa State Hospital -- Asylum for the Insane, was torn down after world war II. However, it represents the love affair with building with bricks in the 19th century. I researched to see why it was torn down, but never found an answer. This brick building was doomed from the time the first brick was laid.

Link to all of my pictures of the Napa Earthquake.


Saturday, August 30, 2014

Purlin - Roof Sheathing - Dormer Square Tail Fascia Layover Cuts

Purlin Rafters, Roof Sheathing or Dormer Square Tail Fascia Layover Cuts
(Cutting Roof Sheathing with an Edge Bevel)

Cutting Purlin Rafters from the Face Set in the Roof Surface
Saw Blade Miter = arctan (sin Dormer Pitch Angle ÷ tan Main Pitch Angle)
Saw Blade Miter = arctan (sin 26.56505 ÷ tan 33.69007) = 33.85451°
Saw Blade Bevel = arcsin (cos Main Pitch Angle × cos Dormer Pitch Angle)
Saw Blade Bevel = arcsin (cos 33.69007 × cos 26.56505) = 48.09115°
or use
Jack Rafter Side Cut Angle for the Miter Angle
Valley Sleeper Saw Blade Bevel Angle  for the Saw Blade Bevel Angle

Example
Roof Eave Angle = 90.00000
SS = Main Rafter Slope Angle = 33.69007 -- 8:12
S = Adjacent Rafter Slope Angle = 26.56505 -- 6:12

DD = Main Plan Angle = 36.86990
D = Adjacent Plan Angle = 53.13010

R1 = Hip Rafter Slope Angle = 21.80141
C5m Main Hip Rafter Backing Angle = 26.34404
C5a Adjacent Hip Rafter Backing Angle = 15.56481
Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 48.09115

P2m = Main Jack Rafter Side Cut Angle = 47.96889
90° - P2m = Main Roof Sheathing Angle = 42.03111
P2a = Adjacent Jack Rafter Side Cut Angle = 33.85451
90° - P2a = Adjacent Roof Sheathing Angle = 56.14549

Cutting Purlin Rafters from the Face Set in the Roof Surface
or
Cutting Roof Sheathing with an Edge Bevel

Jack Rafter Side Cut Angle for the Miter Angle -- 33.85451°
Valley Sleeper Saw Blade Bevel Angle  for the Saw Blade Bevel Angle -- 48.09115°



Cutting Purlin Rafters from Face perpendicular to Roof
Saw Blade Miter = arctan (cos Dormer Pitch Angle ÷ tan Main Roof Pitch Angle)
Saw Blade Miter = arctan (cos 26.56505 ÷ tan 33.69007) = 53.30077°
Saw Blade Bevel = arcsin (cos Main Roof Pitch Angle × sin Dormer Pitch Angle)
Saw Blade Bevel = arcsin (cos 33.69007 × sin 26.56505) = 21.84545°








Friday, August 29, 2014

Twisted Steeple Geometry

Here's my first attempt for developing the geometry of the twisted steeple. This twisted steeple has an Octagonal base  for the rotation of the twist. It also sets on top of a square base for the connection to a church roof.




Clocher tors -- Twisted Steeples -- Belfray



I started off with an Octagon, 36" diameter for the circumscribed radius.  


Then I used a height of 50" for the peak of the steeple and drew in the hip rafters.


Then I divided the roof peak height into 5 equal heights. For the 5 Octagonal platforms.


Draw in the Octagonal platforms and rotate each Octagonal platform by 22.5°.


Octagonal platforms rotated 22.5°.



With the Octagonal platforms drawn in I added the hip rafters.

Here's the plan view the twisted steeple.


Hip Rafter Slope Angles and plan Angles for each of the Octagonal platforms.





Here's the plan view of the twisted steeple with the plan view of the square base.


In the next post I'll develop the geometry for the hip rafter backing angle for each of the Octagonal platforms.



Sunday, August 17, 2014

Plywood Roof Sheathing Stick

Most of the time we just snap a chalk line down the hip rafter to cut the plywood roof sheathing. However, when the roof slope angle is steeper than an 8:12 pitched roof, 33.69007°, we will cut the plywood roof sheathing that attaches to the hip or valley rafter on the ground.  The easiest way to make an Roof Sheathing Stick is to lay the first plywood sheathe across the hip rafter and lay a stick parallel with the hip rafter and drive two nails next to the hip rafter.   AKA -- Okie Roof Stick,  something my father taught me. No math, just a couple of nails.







To make an Roof Sheathing Stick on the ground you can use the plywood cut off dimension, included in both of my Android and iPhone RafterTools apps. Simply mark off the plywood cut off, offset, dimension and snap a line for the plywood sheathing diagonal. Then lay a stick next to the diagonal line and drive two nails next to the edge of the plywood.

You can also use a framing square to layout the roof sheathing angle on the plywood using 12" and the length of the common rafter per 12" of run. Not very accurate on a 48" wide piece of plywood, but it works.



Math or Trigonometry for the Roof Sheathing Stick.


For Unequal -- Irregular -- Bastard pitched roofs.

Sheathing Angle = arctan(tan(Plan Angle) ÷ cos(Roof Slope Angle))
Plywood Offset Dimension = 48 / tan(Sheathing Angle)
Roof Sheathing Stick (Diagonal) = 48 / sin(Sheathing Angle)


For Equal Pitched Roofs:

Roof Slope Angles for Roof Pitch
1:12 = 4.76364°
2:12 = 9.46232°
3:12 = 14.03624°
4:12 = 18.43495°
5:12 = 22.61986°
6:12 = 26.56505°
7:12 = 30.25644°
8:12 = 33.69007°
9:12 = 36.86990°
10:12 = 39.80557°
11:12 = 42.51045°
12:12 = 45.00000°
13:12 = 47.29061°
14:12 = 49.39871°
15:12 = 51.34019°
16:12 = 53.13010°
17:12 = 54.78241°
18:12 = 56.30993°
19:12 = 57.72436°
20:12 = 59.03624°
21:12 = 60.25512°
22:12 = 61.38954°
23:12 = 62.44719°
24:12 = 63.43495°

Roof Sheathing Angles for Equal Roof Pitch
1:12 = 45.09913°
2:12 = 45.39245°
3:12 = 45.86825°
4:12 = 46.50848°
5:12 = 47.29061°
6:12 = 48.18969°
7:12 = 49.18024°
8:12 = 50.23784°
9:12 = 51.34019°
10:12 = 52.46776°
11:12 = 53.60406°
12:12 = 54.73561°
13:12 = 55.85174°
14:12 = 56.94427°
15:12 = 58.00718°
16:12 = 59.03624°
17:12 = 60.02867°
18:12 = 60.98286°
19:12 = 61.89810°
20:12 = 62.77437°
21:12 = 63.61220°
22:12 = 64.41247°
23:12 = 65.17634°
24:12 = 65.90516°

Roof Sheathing Plywood Offset for Equal Roof Pitch
1:12 = 3'-11 7/8''
2:12 = 3'-11 3/8''
3:12 = 3'-10 5/8''
4:12 = 3'-9 9/16''
5:12 = 3'-8 5/16''
6:12 = 3'-6 15/16''
7:12 = 3'-5 1/2''
8:12 = 3'-3 15/16''
9:12 = 3'-2 7/16''
10:12 = 3'-0 7/8''
11:12 = 2'-11 7/16''
12:12 = 2'-9 15/16''
13:12 = 2'-8 9/16''
14:12 = 2'-7 1/4''
15:12 = 2'-6''
16:12 = 2'-4 13/16''
17:12 = 2'-3 11/16''
18:12 = 2'-2 11/16''
19:12 = 2'-1 11/16''
20:12 = 2'-0 3/4''
21:12 = 1'-11 7/8''
22:12 = 1'-11''
23:12 = 1'-10 1/4''
24:12 = 1'-9 1/2''

Roof Sheathing Plywood Marking Stick for Equal Roof Pitch(diagonal--hip length)
1:12 = 5'-7 13/16''
2:12 = 5'-7 7/16''
3:12 = 5'-6 15/16''
4:12 = 5'-6 3/16''
5:12 = 5'-5 3/8''
6:12 = 5'-4 7/16''
7:12 = 5'-3 7/16''
8:12 = 5'-2 1/2''
9:12 = 5'-1 1/2''
10:12 = 5'-0 9/16''
11:12 = 4'-11 11/16''
12:12 = 4'-10 13/16''
13:12 = 4'-10''
14:12 = 4'-9 5/16''
15:12 = 4'-8 5/8''
16:12 = 4'-7 15/16''
17:12 = 4'-7 7/16''
18:12 = 4'-6 15/16''
19:12 = 4'-6 7/16''
20:12 = 4'-6''
21:12 = 4'-5 5/8''
22:12 = 4'-5 1/4''
23:12 = 4'-4 15/16''
24:12 = 4'-4 5/8''


Roof Sheathing Plywood Offset for Irregular Roof Pitches
Main Plywood Offset -- Adjacent Plywood Offset

Main Pitch 1:12
Adjacent Pitch 1:12 = 3'-11 7/8'' -- 3'-11 7/8''
Adjacent Pitch 2:12 = 1'-11 15/16'' -- 7'-10 3/4''
Adjacent Pitch 3:12 = 1'-3 15/16'' -- 11'-7 3/4''
Adjacent Pitch 4:12 = 0'-11 15/16'' -- 15'-2 3/16''
Adjacent Pitch 5:12 = 0'-9 5/8'' -- 18'-5 9/16''
Adjacent Pitch 6:12 = 0'-7 15/16'' -- 21'-5 5/8''
Adjacent Pitch 7:12 = 0'-6 7/8'' -- 24'-2 1/4''
Adjacent Pitch 8:12 = 0'-6'' -- 26'-7 9/16''
Adjacent Pitch 9:12 = 0'-5 3/8'' -- 28'-9 5/8''
Adjacent Pitch 10:12 = 0'-4 13/16'' -- 30'-8 3/4''
Adjacent Pitch 11:12 = 0'-4 3/8'' -- 32'-5 1/4''
Adjacent Pitch 12:12 = 0'-4'' -- 33'-11 5/16''
Adjacent Pitch 13:12 = 0'-3 11/16'' -- 35'-3 1/4''
Adjacent Pitch 14:12 = 0'-3 7/16'' -- 36'-5 3/8''
Adjacent Pitch 15:12 = 0'-3 1/4'' -- 37'-5 13/16''
Adjacent Pitch 16:12 = 0'-3'' -- 38'-4 13/16''

Main Pitch 2:12
Adjacent Pitch 1:12 = 7'-10 3/4'' -- 1'-11 15/16''
Adjacent Pitch 2:12 = 3'-11 3/8'' -- 3'-11 3/8''
Adjacent Pitch 3:12 = 2'-7 5/8'' -- 5'-9 7/8''
Adjacent Pitch 4:12 = 1'-11 11/16'' -- 7'-7 1/8''
Adjacent Pitch 5:12 = 1'-6 15/16'' -- 9'-2 13/16''
Adjacent Pitch 6:12 = 1'-3 13/16'' -- 10'-8 13/16''
Adjacent Pitch 7:12 = 1'-1 9/16'' -- 12'-1 1/8''
Adjacent Pitch 8:12 = 0'-11 7/8'' -- 13'-3 13/16''
Adjacent Pitch 9:12 = 0'-10 9/16'' -- 14'-4 13/16''
Adjacent Pitch 10:12 = 0'-9 1/2'' -- 15'-4 3/8''
Adjacent Pitch 11:12 = 0'-8 5/8'' -- 16'-2 5/8''
Adjacent Pitch 12:12 = 0'-7 15/16'' -- 16'-11 11/16''
Adjacent Pitch 13:12 = 0'-7 5/16'' -- 17'-7 5/8''
Adjacent Pitch 14:12 = 0'-6 13/16'' -- 18'-2 11/16''
Adjacent Pitch 15:12 = 0'-6 3/8'' -- 18'-8 15/16''
Adjacent Pitch 16:12 = 0'-5 15/16'' -- 19'-2 7/16''

Main Pitch 3:12
Adjacent Pitch 1:12 = 11'-7 3/4'' -- 1'-3 15/16''
Adjacent Pitch 2:12 = 5'-9 7/8'' -- 2'-7 5/8''
Adjacent Pitch 3:12 = 3'-10 5/8'' -- 3'-10 5/8''
Adjacent Pitch 4:12 = 2'-10 15/16'' -- 5'-0 3/4''
Adjacent Pitch 5:12 = 2'-3 15/16'' -- 6'-1 7/8''
Adjacent Pitch 6:12 = 1'-11 5/16'' -- 7'-1 7/8''
Adjacent Pitch 7:12 = 1'-7 15/16'' -- 8'-0 3/4''
Adjacent Pitch 8:12 = 1'-5 1/2'' -- 8'-10 9/16''
Adjacent Pitch 9:12 = 1'-3 9/16'' -- 9'-7 1/4''
Adjacent Pitch 10:12 = 1'-1 15/16'' -- 10'-2 15/16''
Adjacent Pitch 11:12 = 1'-0 3/4'' -- 10'-9 3/4''
Adjacent Pitch 12:12 = 0'-11 11/16'' -- 11'-3 13/16''
Adjacent Pitch 13:12 = 0'-10 3/4'' -- 11'-9 1/8''
Adjacent Pitch 14:12 = 0'-10'' -- 12'-1 13/16''
Adjacent Pitch 15:12 = 0'-9 3/8'' -- 12'-5 15/16''
Adjacent Pitch 16:12 = 0'-8 3/4'' -- 12'-9 5/8''

Main Pitch 4:12
Adjacent Pitch 1:12 = 15'-2 3/16'' -- 0'-11 15/16''
Adjacent Pitch 2:12 = 7'-7 1/8'' -- 1'-11 11/16''
Adjacent Pitch 3:12 = 5'-0 3/4'' -- 2'-10 15/16''
Adjacent Pitch 4:12 = 3'-9 9/16'' -- 3'-9 9/16''
Adjacent Pitch 5:12 = 3'-0 7/16'' -- 4'-7 7/16''
Adjacent Pitch 6:12 = 2'-6 3/8'' -- 5'-4 7/16''
Adjacent Pitch 7:12 = 2'-2 1/16'' -- 6'-0 9/16''
Adjacent Pitch 8:12 = 1'-10 13/16'' -- 6'-7 15/16''
Adjacent Pitch 9:12 = 1'-8 1/4'' -- 7'-2 7/16''
Adjacent Pitch 10:12 = 1'-6 1/4'' -- 7'-8 3/16''
Adjacent Pitch 11:12 = 1'-4 9/16'' -- 8'-1 5/16''
Adjacent Pitch 12:12 = 1'-3 3/16'' -- 8'-5 7/8''
Adjacent Pitch 13:12 = 1'-2 1/16'' -- 8'-9 13/16''
Adjacent Pitch 14:12 = 1'-1 1/16'' -- 9'-1 3/8''
Adjacent Pitch 15:12 = 1'-0 3/16'' -- 9'-4 1/2''
Adjacent Pitch 16:12 = 0'-11 7/16'' -- 9'-7 1/4''

Main Pitch 5:12
Adjacent Pitch 1:12 = 18'-5 9/16'' -- 0'-9 5/8''
Adjacent Pitch 2:12 = 9'-2 13/16'' -- 1'-6 15/16''
Adjacent Pitch 3:12 = 6'-1 7/8'' -- 2'-3 15/16''
Adjacent Pitch 4:12 = 4'-7 7/16'' -- 3'-0 7/16''
Adjacent Pitch 5:12 = 3'-8 5/16'' -- 3'-8 5/16''
Adjacent Pitch 6:12 = 3'-0 15/16'' -- 4'-3 9/16''
Adjacent Pitch 7:12 = 2'-7 11/16'' -- 4'-10 1/16''
Adjacent Pitch 8:12 = 2'-3 3/4'' -- 5'-3 15/16''
Adjacent Pitch 9:12 = 2'-0 5/8'' -- 5'-9 1/8''
Adjacent Pitch 10:12 = 1'-10 3/16'' -- 6'-1 3/4''
Adjacent Pitch 11:12 = 1'-8 3/16'' -- 6'-5 7/8''
Adjacent Pitch 12:12 = 1'-6 1/2'' -- 6'-9 1/2''
Adjacent Pitch 13:12 = 1'-5 1/16'' -- 7'-0 11/16''
Adjacent Pitch 14:12 = 1'-3 7/8'' -- 7'-3 1/2''
Adjacent Pitch 15:12 = 1'-2 13/16'' -- 7'-5 15/16''
Adjacent Pitch 16:12 = 1'-1 7/8'' -- 7'-8 3/16''

Main Pitch 6:12
Adjacent Pitch 1:12 = 21'-5 5/8'' -- 0'-7 15/16''
Adjacent Pitch 2:12 = 10'-8 13/16'' -- 1'-3 13/16''
Adjacent Pitch 3:12 = 7'-1 7/8'' -- 1'-11 5/16''
Adjacent Pitch 4:12 = 5'-4 7/16'' -- 2'-6 3/8''
Adjacent Pitch 5:12 = 4'-3 9/16'' -- 3'-0 15/16''
Adjacent Pitch 6:12 = 3'-6 15/16'' -- 3'-6 15/16''
Adjacent Pitch 7:12 = 3'-0 13/16'' -- 4'-0 3/8''
Adjacent Pitch 8:12 = 2'-8 1/4'' -- 4'-5 5/16''
Adjacent Pitch 9:12 = 2'-4 5/8'' -- 4'-9 5/8''
Adjacent Pitch 10:12 = 2'-1 13/16'' -- 5'-1 1/2''
Adjacent Pitch 11:12 = 1'-11 7/16'' -- 5'-4 7/8''
Adjacent Pitch 12:12 = 1'-9 1/2'' -- 5'-7 15/16''
Adjacent Pitch 13:12 = 1'-7 7/8'' -- 5'-10 9/16''
Adjacent Pitch 14:12 = 1'-6 7/16'' -- 6'-0 15/16''
Adjacent Pitch 15:12 = 1'-5 3/16'' -- 6'-2 15/16''
Adjacent Pitch 16:12 = 1'-4 1/8'' -- 6'-4 13/16''

Main Pitch 7:12
Adjacent Pitch 1:12 = 24'-2 1/4'' -- 0'-6 7/8''
Adjacent Pitch 2:12 = 12'-1 1/8'' -- 1'-1 9/16''
Adjacent Pitch 3:12 = 8'-0 3/4'' -- 1'-7 15/16''
Adjacent Pitch 4:12 = 6'-0 9/16'' -- 2'-2 1/16''
Adjacent Pitch 5:12 = 4'-10 1/16'' -- 2'-7 11/16''
Adjacent Pitch 6:12 = 4'-0 3/8'' -- 3'-0 13/16''
Adjacent Pitch 7:12 = 3'-5 1/2'' -- 3'-5 1/2''
Adjacent Pitch 8:12 = 3'-0 5/16'' -- 3'-9 11/16''
Adjacent Pitch 9:12 = 2'-8 1/4'' -- 4'-1 3/8''
Adjacent Pitch 10:12 = 2'-5 1/16'' -- 4'-4 11/16''
Adjacent Pitch 11:12 = 2'-2 7/16'' -- 4'-7 5/8''
Adjacent Pitch 12:12 = 2'-0 3/16'' -- 4'-10 3/16''
Adjacent Pitch 13:12 = 1'-10 3/8'' -- 5'-0 1/2''
Adjacent Pitch 14:12 = 1'-8 3/4'' -- 5'-2 1/2''
Adjacent Pitch 15:12 = 1'-7 3/8'' -- 5'-4 5/16''
Adjacent Pitch 16:12 = 1'-6 3/16'' -- 5'-5 7/8''

Main Pitch 8:12
Adjacent Pitch 1:12 = 26'-7 9/16'' -- 0'-6''
Adjacent Pitch 2:12 = 13'-3 13/16'' -- 0'-11 7/8''
Adjacent Pitch 3:12 = 8'-10 9/16'' -- 1'-5 1/2''
Adjacent Pitch 4:12 = 6'-7 15/16'' -- 1'-10 13/16''
Adjacent Pitch 5:12 = 5'-3 15/16'' -- 2'-3 3/4''
Adjacent Pitch 6:12 = 4'-5 5/16'' -- 2'-8 1/4''
Adjacent Pitch 7:12 = 3'-9 11/16'' -- 3'-0 5/16''
Adjacent Pitch 8:12 = 3'-3 15/16'' -- 3'-3 15/16''
Adjacent Pitch 9:12 = 2'-11 9/16'' -- 3'-7 1/4''
Adjacent Pitch 10:12 = 2'-7 15/16'' -- 3'-10 1/8''
Adjacent Pitch 11:12 = 2'-5 1/16'' -- 4'-0 11/16''
Adjacent Pitch 12:12 = 2'-2 11/16'' -- 4'-2 15/16''
Adjacent Pitch 13:12 = 2'-0 5/8'' -- 4'-4 15/16''
Adjacent Pitch 14:12 = 1'-10 7/8'' -- 4'-6 11/16''
Adjacent Pitch 15:12 = 1'-9 5/16'' -- 4'-8 1/4''
Adjacent Pitch 16:12 = 1'-7 15/16'' -- 4'-9 5/8''

Main Pitch 9:12
Adjacent Pitch 1:12 = 28'-9 5/8'' -- 0'-5 3/8''
Adjacent Pitch 2:12 = 14'-4 13/16'' -- 0'-10 9/16''
Adjacent Pitch 3:12 = 9'-7 1/4'' -- 1'-3 9/16''
Adjacent Pitch 4:12 = 7'-2 7/16'' -- 1'-8 1/4''
Adjacent Pitch 5:12 = 5'-9 1/8'' -- 2'-0 5/8''
Adjacent Pitch 6:12 = 4'-9 5/8'' -- 2'-4 5/8''
Adjacent Pitch 7:12 = 4'-1 3/8'' -- 2'-8 1/4''
Adjacent Pitch 8:12 = 3'-7 1/4'' -- 2'-11 9/16''
Adjacent Pitch 9:12 = 3'-2 7/16'' -- 3'-2 7/16''
Adjacent Pitch 10:12 = 2'-10 9/16'' -- 3'-4 15/16''
Adjacent Pitch 11:12 = 2'-7 7/16'' -- 3'-7 1/4''
Adjacent Pitch 12:12 = 2'-4 13/16'' -- 3'-9 5/16''
Adjacent Pitch 13:12 = 2'-2 5/8'' -- 3'-11 1/16''
Adjacent Pitch 14:12 = 2'-0 11/16'' -- 4'-0 5/8''
Adjacent Pitch 15:12 = 1'-11 1/16'' -- 4'-1 15/16''
Adjacent Pitch 16:12 = 1'-9 5/8'' -- 4'-3 1/4''

Main Pitch 10:12
Adjacent Pitch 1:12 = 30'-8 3/4'' -- 0'-4 13/16''
Adjacent Pitch 2:12 = 15'-4 3/8'' -- 0'-9 1/2''
Adjacent Pitch 3:12 = 10'-2 15/16'' -- 1'-1 15/16''
Adjacent Pitch 4:12 = 7'-8 3/16'' -- 1'-6 1/4''
Adjacent Pitch 5:12 = 6'-1 3/4'' -- 1'-10 3/16''
Adjacent Pitch 6:12 = 5'-1 1/2'' -- 2'-1 13/16''
Adjacent Pitch 7:12 = 4'-4 11/16'' -- 2'-5 1/16''
Adjacent Pitch 8:12 = 3'-10 1/8'' -- 2'-7 15/16''
Adjacent Pitch 9:12 = 3'-4 15/16'' -- 2'-10 9/16''
Adjacent Pitch 10:12 = 3'-0 7/8'' -- 3'-0 7/8''
Adjacent Pitch 11:12 = 2'-9 9/16'' -- 3'-2 15/16''
Adjacent Pitch 12:12 = 2'-6 3/4'' -- 3'-4 3/4''
Adjacent Pitch 13:12 = 2'-4 3/8'' -- 3'-6 3/8''
Adjacent Pitch 14:12 = 2'-2 3/8'' -- 3'-7 3/4''
Adjacent Pitch 15:12 = 2'-0 5/8'' -- 3'-9''
Adjacent Pitch 16:12 = 1'-11 1/16'' -- 3'-10 1/8''

Main Pitch 11:12
Adjacent Pitch 1:12 = 32'-5 1/4'' -- 0'-4 3/8''
Adjacent Pitch 2:12 = 16'-2 5/8'' -- 0'-8 5/8''
Adjacent Pitch 3:12 = 10'-9 3/4'' -- 1'-0 3/4''
Adjacent Pitch 4:12 = 8'-1 5/16'' -- 1'-4 9/16''
Adjacent Pitch 5:12 = 6'-5 7/8'' -- 1'-8 3/16''
Adjacent Pitch 6:12 = 5'-4 7/8'' -- 1'-11 7/16''
Adjacent Pitch 7:12 = 4'-7 5/8'' -- 2'-2 7/16''
Adjacent Pitch 8:12 = 4'-0 11/16'' -- 2'-5 1/16''
Adjacent Pitch 9:12 = 3'-7 1/4'' -- 2'-7 7/16''
Adjacent Pitch 10:12 = 3'-2 15/16'' -- 2'-9 9/16''
Adjacent Pitch 11:12 = 2'-11 7/16'' -- 2'-11 7/16''
Adjacent Pitch 12:12 = 2'-8 7/16'' -- 3'-1 1/16''
Adjacent Pitch 13:12 = 2'-5 15/16'' -- 3'-2 1/2''
Adjacent Pitch 14:12 = 2'-3 13/16'' -- 3'-3 13/16''
Adjacent Pitch 15:12 = 2'-1 15/16'' -- 3'-4 15/16''
Adjacent Pitch 16:12 = 2'-0 3/8'' -- 3'-5 15/16''

Main Pitch 12:12
Adjacent Pitch 1:12 = 33'-11 5/16'' -- 0'-4''
Adjacent Pitch 2:12 = 16'-11 11/16'' -- 0'-7 15/16''
Adjacent Pitch 3:12 = 11'-3 13/16'' -- 0'-11 11/16''
Adjacent Pitch 4:12 = 8'-5 7/8'' -- 1'-3 3/16''
Adjacent Pitch 5:12 = 6'-9 1/2'' -- 1'-6 1/2''
Adjacent Pitch 6:12 = 5'-7 15/16'' -- 1'-9 1/2''
Adjacent Pitch 7:12 = 4'-10 3/16'' -- 2'-0 3/16''
Adjacent Pitch 8:12 = 4'-2 15/16'' -- 2'-2 11/16''
Adjacent Pitch 9:12 = 3'-9 5/16'' -- 2'-4 13/16''
Adjacent Pitch 10:12 = 3'-4 3/4'' -- 2'-6 3/4''
Adjacent Pitch 11:12 = 3'-1 1/16'' -- 2'-8 7/16''
Adjacent Pitch 12:12 = 2'-9 15/16'' -- 2'-9 15/16''
Adjacent Pitch 13:12 = 2'-7 3/8'' -- 2'-11 5/16''
Adjacent Pitch 14:12 = 2'-5 1/8'' -- 3'-0 1/2''
Adjacent Pitch 15:12 = 2'-3 3/16'' -- 3'-1 1/2''
Adjacent Pitch 16:12 = 2'-1 1/2'' -- 3'-2 7/16''

Main Pitch 13:12
Adjacent Pitch 1:12 = 35'-3 1/4'' -- 0'-3 11/16''
Adjacent Pitch 2:12 = 17'-7 5/8'' -- 0'-7 5/16''
Adjacent Pitch 3:12 = 11'-9 1/8'' -- 0'-10 3/4''
Adjacent Pitch 4:12 = 8'-9 13/16'' -- 1'-2 1/16''
Adjacent Pitch 5:12 = 7'-0 11/16'' -- 1'-5 1/16''
Adjacent Pitch 6:12 = 5'-10 9/16'' -- 1'-7 7/8''
Adjacent Pitch 7:12 = 5'-0 1/2'' -- 1'-10 3/8''
Adjacent Pitch 8:12 = 4'-4 15/16'' -- 2'-0 5/8''
Adjacent Pitch 9:12 = 3'-11 1/16'' -- 2'-2 5/8''
Adjacent Pitch 10:12 = 3'-6 3/8'' -- 2'-4 3/8''
Adjacent Pitch 11:12 = 3'-2 1/2'' -- 2'-5 15/16''
Adjacent Pitch 12:12 = 2'-11 5/16'' -- 2'-7 3/8''
Adjacent Pitch 13:12 = 2'-8 9/16'' -- 2'-8 9/16''
Adjacent Pitch 14:12 = 2'-6 1/4'' -- 2'-9 11/16''
Adjacent Pitch 15:12 = 2'-4 1/4'' -- 2'-10 5/8''
Adjacent Pitch 16:12 = 2'-2 1/2'' -- 2'-11 1/2''

Main Pitch 14:12
Adjacent Pitch 1:12 = 36'-5 3/8'' -- 0'-3 7/16''
Adjacent Pitch 2:12 = 18'-2 11/16'' -- 0'-6 13/16''
Adjacent Pitch 3:12 = 12'-1 13/16'' -- 0'-10''
Adjacent Pitch 4:12 = 9'-1 3/8'' -- 1'-1 1/16''
Adjacent Pitch 5:12 = 7'-3 1/2'' -- 1'-3 7/8''
Adjacent Pitch 6:12 = 6'-0 15/16'' -- 1'-6 7/16''
Adjacent Pitch 7:12 = 5'-2 1/2'' -- 1'-8 3/4''
Adjacent Pitch 8:12 = 4'-6 11/16'' -- 1'-10 7/8''
Adjacent Pitch 9:12 = 4'-0 5/8'' -- 2'-0 11/16''
Adjacent Pitch 10:12 = 3'-7 3/4'' -- 2'-2 3/8''
Adjacent Pitch 11:12 = 3'-3 13/16'' -- 2'-3 13/16''
Adjacent Pitch 12:12 = 3'-0 1/2'' -- 2'-5 1/8''
Adjacent Pitch 13:12 = 2'-9 11/16'' -- 2'-6 1/4''
Adjacent Pitch 14:12 = 2'-7 1/4'' -- 2'-7 1/4''
Adjacent Pitch 15:12 = 2'-5 3/16'' -- 2'-8 3/16''
Adjacent Pitch 16:12 = 2'-3 3/8'' -- 2'-8 15/16''

Main Pitch 15:12
Adjacent Pitch 1:12 = 37'-5 13/16'' -- 0'-3 1/4''
Adjacent Pitch 2:12 = 18'-8 15/16'' -- 0'-6 3/8''
Adjacent Pitch 3:12 = 12'-5 15/16'' -- 0'-9 3/8''
Adjacent Pitch 4:12 = 9'-4 1/2'' -- 1'-0 3/16''
Adjacent Pitch 5:12 = 7'-5 15/16'' -- 1'-2 13/16''
Adjacent Pitch 6:12 = 6'-2 15/16'' -- 1'-5 3/16''
Adjacent Pitch 7:12 = 5'-4 5/16'' -- 1'-7 3/8''
Adjacent Pitch 8:12 = 4'-8 1/4'' -- 1'-9 5/16''
Adjacent Pitch 9:12 = 4'-1 15/16'' -- 1'-11 1/16''
Adjacent Pitch 10:12 = 3'-9'' -- 2'-0 5/8''
Adjacent Pitch 11:12 = 3'-4 15/16'' -- 2'-1 15/16''
Adjacent Pitch 12:12 = 3'-1 1/2'' -- 2'-3 3/16''
Adjacent Pitch 13:12 = 2'-10 5/8'' -- 2'-4 1/4''
Adjacent Pitch 14:12 = 2'-8 3/16'' -- 2'-5 3/16''
Adjacent Pitch 15:12 = 2'-6'' -- 2'-6''
Adjacent Pitch 16:12 = 2'-4 1/8'' -- 2'-6 3/4''

Main Pitch 16:12
Adjacent Pitch 1:12 = 38'-4 13/16'' -- 0'-3''
Adjacent Pitch 2:12 = 19'-2 7/16'' -- 0'-5 15/16''
Adjacent Pitch 3:12 = 12'-9 5/8'' -- 0'-8 3/4''
Adjacent Pitch 4:12 = 9'-7 1/4'' -- 0'-11 7/16''
Adjacent Pitch 5:12 = 7'-8 3/16'' -- 1'-1 7/8''
Adjacent Pitch 6:12 = 6'-4 13/16'' -- 1'-4 1/8''
Adjacent Pitch 7:12 = 5'-5 7/8'' -- 1'-6 3/16''
Adjacent Pitch 8:12 = 4'-9 5/8'' -- 1'-7 15/16''
Adjacent Pitch 9:12 = 4'-3 1/4'' -- 1'-9 5/8''
Adjacent Pitch 10:12 = 3'-10 1/8'' -- 1'-11 1/16''
Adjacent Pitch 11:12 = 3'-5 15/16'' -- 2'-0 3/8''
Adjacent Pitch 12:12 = 3'-2 7/16'' -- 2'-1 1/2''
Adjacent Pitch 13:12 = 2'-11 1/2'' -- 2'-2 1/2''
Adjacent Pitch 14:12 = 2'-8 15/16'' -- 2'-3 3/8''
Adjacent Pitch 15:12 = 2'-6 3/4'' -- 2'-4 1/8''
Adjacent Pitch 16:12 = 2'-4 13/16'' -- 2'-4 13/16''

Roof Sheathing Plywood Diagonal for Irregular Roof Pitches
Main Plywood Diagonal -- Adjacent Plywood Diagonal

Main Pitch 1:12
Adjacent Pitch 1:12 = 5'-7 13/16'' -- 5'-7 13/16''
Adjacent Pitch 2:12 = 4'-5 11/16'' -- 8'-10 3/16''
Adjacent Pitch 3:12 = 4'-2 5/8'' -- 12'-3 3/4''
Adjacent Pitch 4:12 = 4'-1 1/2'' -- 15'-8 3/8''
Adjacent Pitch 5:12 = 4'-0 15/16'' -- 18'-10 11/16''
Adjacent Pitch 6:12 = 4'-0 11/16'' -- 21'-10 1/16''
Adjacent Pitch 7:12 = 4'-0 1/2'' -- 24'-6 3/16''
Adjacent Pitch 8:12 = 4'-0 3/8'' -- 26'-11 1/8''
Adjacent Pitch 9:12 = 4'-0 5/16'' -- 29'-0 15/16''
Adjacent Pitch 10:12 = 4'-0 1/4'' -- 30'-11 7/8''
Adjacent Pitch 11:12 = 4'-0 1/4'' -- 32'-8 3/16''
Adjacent Pitch 12:12 = 4'-0 3/16'' -- 34'-2 1/8''
Adjacent Pitch 13:12 = 4'-0 3/16'' -- 35'-5 15/16''
Adjacent Pitch 14:12 = 4'-0 1/8'' -- 36'-7 15/16''
Adjacent Pitch 15:12 = 4'-0 1/8'' -- 37'-8 3/8''
Adjacent Pitch 16:12 = 4'-0 1/8'' -- 38'-7 5/16''

Main Pitch 2:12
Adjacent Pitch 1:12 = 8'-10 3/16'' -- 4'-5 11/16''
Adjacent Pitch 2:12 = 5'-7 7/16'' -- 5'-7 7/16''
Adjacent Pitch 3:12 = 4'-9 1/2'' -- 7'-0 13/16''
Adjacent Pitch 4:12 = 4'-5 9/16'' -- 8'-6 15/16''
Adjacent Pitch 5:12 = 4'-3 5/8'' -- 10'-0 3/4''
Adjacent Pitch 6:12 = 4'-2 9/16'' -- 11'-5 1/2''
Adjacent Pitch 7:12 = 4'-1 7/8'' -- 12'-8 7/8''
Adjacent Pitch 8:12 = 4'-1 1/2'' -- 13'-10 13/16''
Adjacent Pitch 9:12 = 4'-1 3/16'' -- 14'-11 3/8''
Adjacent Pitch 10:12 = 4'-0 15/16'' -- 15'-10 9/16''
Adjacent Pitch 11:12 = 4'-0 13/16'' -- 16'-8 1/2''
Adjacent Pitch 12:12 = 4'-0 11/16'' -- 17'-5 1/4''
Adjacent Pitch 13:12 = 4'-0 9/16'' -- 18'-1''
Adjacent Pitch 14:12 = 4'-0 1/2'' -- 18'-7 7/8''
Adjacent Pitch 15:12 = 4'-0 7/16'' -- 19'-1 15/16''
Adjacent Pitch 16:12 = 4'-0 3/8'' -- 19'-7 3/8''

Main Pitch 3:12
Adjacent Pitch 1:12 = 12'-3 3/4'' -- 4'-2 5/8''
Adjacent Pitch 2:12 = 7'-0 13/16'' -- 4'-9 1/2''
Adjacent Pitch 3:12 = 5'-6 15/16'' -- 5'-6 15/16''
Adjacent Pitch 4:12 = 4'-11 3/8'' -- 6'-5 7/16''
Adjacent Pitch 5:12 = 4'-7 9/16'' -- 7'-4 1/8''
Adjacent Pitch 6:12 = 4'-5 3/8'' -- 8'-2 3/8''
Adjacent Pitch 7:12 = 4'-4'' -- 9'-0''
Adjacent Pitch 8:12 = 4'-3 1/8'' -- 9'-8 7/8''
Adjacent Pitch 9:12 = 4'-2 1/2'' -- 10'-4 13/16''
Adjacent Pitch 10:12 = 4'-2'' -- 10'-11 15/16''
Adjacent Pitch 11:12 = 4'-1 11/16'' -- 11'-6 3/8''
Adjacent Pitch 12:12 = 4'-1 7/16'' -- 12'-0''
Adjacent Pitch 13:12 = 4'-1 1/4'' -- 12'-5 1/16''
Adjacent Pitch 14:12 = 4'-1 1/16'' -- 12'-9 1/2''
Adjacent Pitch 15:12 = 4'-0 15/16'' -- 13'-1 7/16''
Adjacent Pitch 16:12 = 4'-0 13/16'' -- 13'-4 15/16''

Main Pitch 4:12
Adjacent Pitch 1:12 = 15'-8 3/8'' -- 4'-1 1/2''
Adjacent Pitch 2:12 = 8'-6 15/16'' -- 4'-5 9/16''
Adjacent Pitch 3:12 = 6'-5 7/16'' -- 4'-11 3/8''
Adjacent Pitch 4:12 = 5'-6 3/16'' -- 5'-6 3/16''
Adjacent Pitch 5:12 = 5'-0 5/16'' -- 6'-1 5/16''
Adjacent Pitch 6:12 = 4'-8 13/16'' -- 6'-8 3/8''
Adjacent Pitch 7:12 = 4'-6 5/8'' -- 7'-3''
Adjacent Pitch 8:12 = 4'-5 3/16'' -- 7'-9 1/4''
Adjacent Pitch 9:12 = 4'-4 1/8'' -- 8'-2 7/8''
Adjacent Pitch 10:12 = 4'-3 3/8'' -- 8'-7 15/16''
Adjacent Pitch 11:12 = 4'-2 13/16'' -- 9'-0 1/2''
Adjacent Pitch 12:12 = 4'-2 3/8'' -- 9'-4 5/8''
Adjacent Pitch 13:12 = 4'-2 1/16'' -- 9'-8 1/4''
Adjacent Pitch 14:12 = 4'-1 3/4'' -- 9'-11 7/16''
Adjacent Pitch 15:12 = 4'-1 9/16'' -- 10'-2 5/16''
Adjacent Pitch 16:12 = 4'-1 3/8'' -- 10'-4 13/16''

Main Pitch 5:12
Adjacent Pitch 1:12 = 18'-10 11/16'' -- 4'-0 15/16''
Adjacent Pitch 2:12 = 10'-0 3/4'' -- 4'-3 5/8''
Adjacent Pitch 3:12 = 7'-4 1/8'' -- 4'-7 9/16''
Adjacent Pitch 4:12 = 6'-1 5/16'' -- 5'-0 5/16''
Adjacent Pitch 5:12 = 5'-5 3/8'' -- 5'-5 3/8''
Adjacent Pitch 6:12 = 5'-0 9/16'' -- 5'-10 7/16''
Adjacent Pitch 7:12 = 4'-9 1/2'' -- 6'-3 3/8''
Adjacent Pitch 8:12 = 4'-7 7/16'' -- 6'-7 15/16''
Adjacent Pitch 9:12 = 4'-5 15/16'' -- 7'-0 3/16''
Adjacent Pitch 10:12 = 4'-4 7/8'' -- 7'-4''
Adjacent Pitch 11:12 = 4'-4 1/16'' -- 7'-7 1/2''
Adjacent Pitch 12:12 = 4'-3 7/16'' -- 7'-10 9/16''
Adjacent Pitch 13:12 = 4'-2 15/16'' -- 8'-1 5/16''
Adjacent Pitch 14:12 = 4'-2 9/16'' -- 8'-3 13/16''
Adjacent Pitch 15:12 = 4'-2 1/4'' -- 8'-5 15/16''
Adjacent Pitch 16:12 = 4'-1 15/16'' -- 8'-7 15/16''

Main Pitch 6:12
Adjacent Pitch 1:12 = 21'-10 1/16'' -- 4'-0 11/16''
Adjacent Pitch 2:12 = 11'-5 1/2'' -- 4'-2 9/16''
Adjacent Pitch 3:12 = 8'-2 3/8'' -- 4'-5 3/8''
Adjacent Pitch 4:12 = 6'-8 3/8'' -- 4'-8 13/16''
Adjacent Pitch 5:12 = 5'-10 7/16'' -- 5'-0 9/16''
Adjacent Pitch 6:12 = 5'-4 7/16'' -- 5'-4 7/16''
Adjacent Pitch 7:12 = 5'-0 1/2'' -- 5'-8 3/16''
Adjacent Pitch 8:12 = 4'-9 13/16'' -- 5'-11 3/4''
Adjacent Pitch 9:12 = 4'-7 15/16'' -- 6'-3''
Adjacent Pitch 10:12 = 4'-6 1/2'' -- 6'-6''
Adjacent Pitch 11:12 = 4'-5 7/16'' -- 6'-8 3/4''
Adjacent Pitch 12:12 = 4'-4 5/8'' -- 6'-11 3/16''
Adjacent Pitch 13:12 = 4'-3 15/16'' -- 7'-1 3/8''
Adjacent Pitch 14:12 = 4'-3 7/16'' -- 7'-3 5/16''
Adjacent Pitch 15:12 = 4'-3'' -- 7'-5 1/16''
Adjacent Pitch 16:12 = 4'-2 11/16'' -- 7'-6 5/8''

Main Pitch 7:12
Adjacent Pitch 1:12 = 24'-6 3/16'' -- 4'-0 1/2''
Adjacent Pitch 2:12 = 12'-8 7/8'' -- 4'-1 7/8''
Adjacent Pitch 3:12 = 9'-0'' -- 4'-4''
Adjacent Pitch 4:12 = 7'-3'' -- 4'-6 5/8''
Adjacent Pitch 5:12 = 6'-3 3/8'' -- 4'-9 1/2''
Adjacent Pitch 6:12 = 5'-8 3/16'' -- 5'-0 1/2''
Adjacent Pitch 7:12 = 5'-3 7/16'' -- 5'-3 7/16''
Adjacent Pitch 8:12 = 5'-0 3/16'' -- 5'-6 1/4''
Adjacent Pitch 9:12 = 4'-9 7/8'' -- 5'-8 7/8''
Adjacent Pitch 10:12 = 4'-8 1/8'' -- 5'-11 5/16''
Adjacent Pitch 11:12 = 4'-6 13/16'' -- 6'-1 1/2''
Adjacent Pitch 12:12 = 4'-5 3/4'' -- 6'-3 7/16''
Adjacent Pitch 13:12 = 4'-4 15/16'' -- 6'-5 1/4''
Adjacent Pitch 14:12 = 4'-4 5/16'' -- 6'-6 13/16''
Adjacent Pitch 15:12 = 4'-3 13/16'' -- 6'-8 1/4''
Adjacent Pitch 16:12 = 4'-3 3/8'' -- 6'-9 1/2''

Main Pitch 8:12
Adjacent Pitch 1:12 = 26'-11 1/8'' -- 4'-0 3/8''
Adjacent Pitch 2:12 = 13'-10 13/16'' -- 4'-1 1/2''
Adjacent Pitch 3:12 = 9'-8 7/8'' -- 4'-3 1/8''
Adjacent Pitch 4:12 = 7'-9 1/4'' -- 4'-5 3/16''
Adjacent Pitch 5:12 = 6'-7 15/16'' -- 4'-7 7/16''
Adjacent Pitch 6:12 = 5'-11 3/4'' -- 4'-9 13/16''
Adjacent Pitch 7:12 = 5'-6 1/4'' -- 5'-0 3/16''
Adjacent Pitch 8:12 = 5'-2 1/2'' -- 5'-2 1/2''
Adjacent Pitch 9:12 = 4'-11 3/4'' -- 5'-4 5/8''
Adjacent Pitch 10:12 = 4'-9 11/16'' -- 5'-6 9/16''
Adjacent Pitch 11:12 = 4'-8 1/8'' -- 5'-8 3/8''
Adjacent Pitch 12:12 = 4'-6 15/16'' -- 5'-9 15/16''
Adjacent Pitch 13:12 = 4'-5 15/16'' -- 5'-11 7/16''
Adjacent Pitch 14:12 = 4'-5 3/16'' -- 6'-0 3/4''
Adjacent Pitch 15:12 = 4'-4 9/16'' -- 6'-1 15/16''
Adjacent Pitch 16:12 = 4'-4'' -- 6'-3''

Main Pitch 9:12
Adjacent Pitch 1:12 = 29'-0 15/16'' -- 4'-0 5/16''
Adjacent Pitch 2:12 = 14'-11 3/8'' -- 4'-1 3/16''
Adjacent Pitch 3:12 = 10'-4 13/16'' -- 4'-2 1/2''
Adjacent Pitch 4:12 = 8'-2 7/8'' -- 4'-4 1/8''
Adjacent Pitch 5:12 = 7'-0 3/16'' -- 4'-5 15/16''
Adjacent Pitch 6:12 = 6'-3'' -- 4'-7 15/16''
Adjacent Pitch 7:12 = 5'-8 7/8'' -- 4'-9 7/8''
Adjacent Pitch 8:12 = 5'-4 5/8'' -- 4'-11 3/4''
Adjacent Pitch 9:12 = 5'-1 1/2'' -- 5'-1 1/2''
Adjacent Pitch 10:12 = 4'-11 3/16'' -- 5'-3 1/8''
Adjacent Pitch 11:12 = 4'-9 3/8'' -- 5'-4 5/8''
Adjacent Pitch 12:12 = 4'-7 15/16'' -- 5'-5 15/16''
Adjacent Pitch 13:12 = 4'-6 7/8'' -- 5'-7 1/4''
Adjacent Pitch 14:12 = 4'-5 15/16'' -- 5'-8 5/16''
Adjacent Pitch 15:12 = 4'-5 1/4'' -- 5'-9 5/16''
Adjacent Pitch 16:12 = 4'-4 11/16'' -- 5'-10 3/16''

Main Pitch 10:12
Adjacent Pitch 1:12 = 30'-11 7/8'' -- 4'-0 1/4''
Adjacent Pitch 2:12 = 15'-10 9/16'' -- 4'-0 15/16''
Adjacent Pitch 3:12 = 10'-11 15/16'' -- 4'-2''
Adjacent Pitch 4:12 = 8'-7 15/16'' -- 4'-3 3/8''
Adjacent Pitch 5:12 = 7'-4'' -- 4'-4 7/8''
Adjacent Pitch 6:12 = 6'-6'' -- 4'-6 1/2''
Adjacent Pitch 7:12 = 5'-11 5/16'' -- 4'-8 1/8''
Adjacent Pitch 8:12 = 5'-6 9/16'' -- 4'-9 11/16''
Adjacent Pitch 9:12 = 5'-3 1/8'' -- 4'-11 3/16''
Adjacent Pitch 10:12 = 5'-0 9/16'' -- 5'-0 9/16''
Adjacent Pitch 11:12 = 4'-10 9/16'' -- 5'-1 13/16''
Adjacent Pitch 12:12 = 4'-9'' -- 5'-2 15/16''
Adjacent Pitch 13:12 = 4'-7 13/16'' -- 5'-4''
Adjacent Pitch 14:12 = 4'-6 13/16'' -- 5'-4 15/16''
Adjacent Pitch 15:12 = 4'-5 15/16'' -- 5'-5 13/16''
Adjacent Pitch 16:12 = 4'-5 1/4'' -- 5'-6 9/16''

Main Pitch 11:12
Adjacent Pitch 1:12 = 32'-8 3/16'' -- 4'-0 1/4''
Adjacent Pitch 2:12 = 16'-8 1/2'' -- 4'-0 13/16''
Adjacent Pitch 3:12 = 11'-6 3/8'' -- 4'-1 11/16''
Adjacent Pitch 4:12 = 9'-0 1/2'' -- 4'-2 13/16''
Adjacent Pitch 5:12 = 7'-7 1/2'' -- 4'-4 1/16''
Adjacent Pitch 6:12 = 6'-8 3/4'' -- 4'-5 7/16''
Adjacent Pitch 7:12 = 6'-1 1/2'' -- 4'-6 13/16''
Adjacent Pitch 8:12 = 5'-8 3/8'' -- 4'-8 1/8''
Adjacent Pitch 9:12 = 5'-4 5/8'' -- 4'-9 3/8''
Adjacent Pitch 10:12 = 5'-1 13/16'' -- 4'-10 9/16''
Adjacent Pitch 11:12 = 4'-11 11/16'' -- 4'-11 11/16''
Adjacent Pitch 12:12 = 4'-9 15/16'' -- 5'-0 5/8''
Adjacent Pitch 13:12 = 4'-8 5/8'' -- 5'-1 9/16''
Adjacent Pitch 14:12 = 4'-7 1/2'' -- 5'-2 3/8''
Adjacent Pitch 15:12 = 4'-6 5/8'' -- 5'-3 1/16''
Adjacent Pitch 16:12 = 4'-5 13/16'' -- 5'-3 3/4''

Main Pitch 12:12
Adjacent Pitch 1:12 = 34'-2 1/8'' -- 4'-0 3/16''
Adjacent Pitch 2:12 = 17'-5 1/4'' -- 4'-0 11/16''
Adjacent Pitch 3:12 = 12'-0'' -- 4'-1 7/16''
Adjacent Pitch 4:12 = 9'-4 5/8'' -- 4'-2 3/8''
Adjacent Pitch 5:12 = 7'-10 9/16'' -- 4'-3 7/16''
Adjacent Pitch 6:12 = 6'-11 3/16'' -- 4'-4 5/8''
Adjacent Pitch 7:12 = 6'-3 7/16'' -- 4'-5 3/4''
Adjacent Pitch 8:12 = 5'-9 15/16'' -- 4'-6 15/16''
Adjacent Pitch 9:12 = 5'-5 15/16'' -- 4'-7 15/16''
Adjacent Pitch 10:12 = 5'-2 15/16'' -- 4'-9''
Adjacent Pitch 11:12 = 5'-0 5/8'' -- 4'-9 15/16''
Adjacent Pitch 12:12 = 4'-10 13/16'' -- 4'-10 13/16''
Adjacent Pitch 13:12 = 4'-9 3/8'' -- 4'-11 5/8''
Adjacent Pitch 14:12 = 4'-8 3/16'' -- 5'-0 5/16''
Adjacent Pitch 15:12 = 4'-7 3/16'' -- 5'-0 15/16''
Adjacent Pitch 16:12 = 4'-6 3/8'' -- 5'-1 1/2''

Main Pitch 13:12
Adjacent Pitch 1:12 = 35'-5 15/16'' -- 4'-0 3/16''
Adjacent Pitch 2:12 = 18'-1'' -- 4'-0 9/16''
Adjacent Pitch 3:12 = 12'-5 1/16'' -- 4'-1 1/4''
Adjacent Pitch 4:12 = 9'-8 1/4'' -- 4'-2 1/16''
Adjacent Pitch 5:12 = 8'-1 5/16'' -- 4'-2 15/16''
Adjacent Pitch 6:12 = 7'-1 3/8'' -- 4'-3 15/16''
Adjacent Pitch 7:12 = 6'-5 1/4'' -- 4'-4 15/16''
Adjacent Pitch 8:12 = 5'-11 7/16'' -- 4'-5 15/16''
Adjacent Pitch 9:12 = 5'-7 1/4'' -- 4'-6 7/8''
Adjacent Pitch 10:12 = 5'-4'' -- 4'-7 13/16''
Adjacent Pitch 11:12 = 5'-1 9/16'' -- 4'-8 5/8''
Adjacent Pitch 12:12 = 4'-11 5/8'' -- 4'-9 3/8''
Adjacent Pitch 13:12 = 4'-10'' -- 4'-10''
Adjacent Pitch 14:12 = 4'-8 3/4'' -- 4'-10 5/8''
Adjacent Pitch 15:12 = 4'-7 11/16'' -- 4'-11 3/16''
Adjacent Pitch 16:12 = 4'-6 13/16'' -- 4'-11 11/16''

Main Pitch 14:12
Adjacent Pitch 1:12 = 36'-7 15/16'' -- 4'-0 1/8''
Adjacent Pitch 2:12 = 18'-7 7/8'' -- 4'-0 1/2''
Adjacent Pitch 3:12 = 12'-9 1/2'' -- 4'-1 1/16''
Adjacent Pitch 4:12 = 9'-11 7/16'' -- 4'-1 3/4''
Adjacent Pitch 5:12 = 8'-3 13/16'' -- 4'-2 9/16''
Adjacent Pitch 6:12 = 7'-3 5/16'' -- 4'-3 7/16''
Adjacent Pitch 7:12 = 6'-6 13/16'' -- 4'-4 5/16''
Adjacent Pitch 8:12 = 6'-0 3/4'' -- 4'-5 3/16''
Adjacent Pitch 9:12 = 5'-8 5/16'' -- 4'-5 15/16''
Adjacent Pitch 10:12 = 5'-4 15/16'' -- 4'-6 13/16''
Adjacent Pitch 11:12 = 5'-2 3/8'' -- 4'-7 1/2''
Adjacent Pitch 12:12 = 5'-0 5/16'' -- 4'-8 3/16''
Adjacent Pitch 13:12 = 4'-10 5/8'' -- 4'-8 3/4''
Adjacent Pitch 14:12 = 4'-9 5/16'' -- 4'-9 5/16''
Adjacent Pitch 15:12 = 4'-8 3/16'' -- 4'-9 13/16''
Adjacent Pitch 16:12 = 4'-7 1/4'' -- 4'-10 1/4''

Main Pitch 15:12
Adjacent Pitch 1:12 = 37'-8 3/8'' -- 4'-0 1/8''
Adjacent Pitch 2:12 = 19'-1 15/16'' -- 4'-0 7/16''
Adjacent Pitch 3:12 = 13'-1 7/16'' -- 4'-0 15/16''
Adjacent Pitch 4:12 = 10'-2 5/16'' -- 4'-1 9/16''
Adjacent Pitch 5:12 = 8'-5 15/16'' -- 4'-2 1/4''
Adjacent Pitch 6:12 = 7'-5 1/16'' -- 4'-3''
Adjacent Pitch 7:12 = 6'-8 1/4'' -- 4'-3 13/16''
Adjacent Pitch 8:12 = 6'-1 15/16'' -- 4'-4 9/16''
Adjacent Pitch 9:12 = 5'-9 5/16'' -- 4'-5 1/4''
Adjacent Pitch 10:12 = 5'-5 13/16'' -- 4'-5 15/16''
Adjacent Pitch 11:12 = 5'-3 1/16'' -- 4'-6 5/8''
Adjacent Pitch 12:12 = 5'-0 15/16'' -- 4'-7 3/16''
Adjacent Pitch 13:12 = 4'-11 3/16'' -- 4'-7 11/16''
Adjacent Pitch 14:12 = 4'-9 13/16'' -- 4'-8 3/16''
Adjacent Pitch 15:12 = 4'-8 5/8'' -- 4'-8 5/8''
Adjacent Pitch 16:12 = 4'-7 11/16'' -- 4'-9''

Main Pitch 16:12
Adjacent Pitch 1:12 = 38'-7 5/16'' -- 4'-0 1/8''
Adjacent Pitch 2:12 = 19'-7 3/8'' -- 4'-0 3/8''
Adjacent Pitch 3:12 = 13'-4 15/16'' -- 4'-0 13/16''
Adjacent Pitch 4:12 = 10'-4 13/16'' -- 4'-1 3/8''
Adjacent Pitch 5:12 = 8'-7 15/16'' -- 4'-1 15/16''
Adjacent Pitch 6:12 = 7'-6 5/8'' -- 4'-2 11/16''
Adjacent Pitch 7:12 = 6'-9 1/2'' -- 4'-3 3/8''
Adjacent Pitch 8:12 = 6'-3'' -- 4'-4''
Adjacent Pitch 9:12 = 5'-10 3/16'' -- 4'-4 11/16''
Adjacent Pitch 10:12 = 5'-6 9/16'' -- 4'-5 1/4''
Adjacent Pitch 11:12 = 5'-3 3/4'' -- 4'-5 13/16''
Adjacent Pitch 12:12 = 5'-1 1/2'' -- 4'-6 3/8''
Adjacent Pitch 13:12 = 4'-11 11/16'' -- 4'-6 13/16''
Adjacent Pitch 14:12 = 4'-10 1/4'' -- 4'-7 1/4''
Adjacent Pitch 15:12 = 4'-9'' -- 4'-7 11/16''
Adjacent Pitch 16:12 = 4'-7 15/16'' -- 4'-7 15/16''