## Sunday, February 23, 2014

### Tréteaux Angles Trigonometry Formulas

```Tréteaux Angles Trigonometry Formulas
```
`Link to Online Script to check the Tréteaux Angles`

`Input Variables`

`Works for any Roof Eave Angle with equal or unequal rafter slope angles.`

```Roof Eave Angle
SS = Main Rafter Slope Angle
S = Adjacent Rafter Slope Angle

DD = Main Plan Angle

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

P2m = Main Jack Rafter Side Cut Angle
90° - P2m = Main Roof Sheathing Angle
P2a = Adjacent Jack Rafter Side Cut Angle
90° - P2a = Adjacent Roof Sheathing Angle

Tréteaux Angles```
```tréteau à devers

R8-DP = Tilted Hip Rafter Slope Angle on DP Side = arctan( tan ( Hip Rafter Backing Angle) ÷ tan (Jack Rafter Side Cut Angle ))
R8-DP = arctan( tan ( C5m )  ÷  tan ( P2m ))

R9-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line
R9-DP = arctan( sin ( R1 ) × tan ( C5m ))

D-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line from Eave Line
D-DP = D - R9

R10-DP = Vertical Plane Rotation for Tilted Hip Rafter on DP Line
R10-DP = arctan((cos(R1) × tan(R9)) / sin(R1));

PSB-DP = Prism Saw Blade Bevel Angle Along side of Hip Rafter Rotated into the Roof Surface Plane
PSB-DP = arctan( sin(90° - P2m) ÷ tan(R8))

SR4Bm-DP = Prism Footprint Angle Along side of Hip Rafter Rotated into the Roof Surface Plane
SR4Bm-DP = arccos( cos(90° - P2m) × cos(R8))

SR4Ba-DP = Prism Footprint Angle Along side of Hip Rafter on Main Plan Angle
SR4Ba-DP = arccos( cos(90° + P2m) × cos(R8))

R11m-DP = Hip Rafter Miter Angle on Side Of Hip Rafter at Peak
R11m-DP = arctan( (sin (90° - P2m ) ÷ tan ( C8 )) ÷ cos (90° - P2m ))

P7m-DP = Purlin Rafter Bevel Angle on Side Face Parallel To Roof Surface
P7m-DP = 90° + P2m
P7m-DP = 90° + 19.01633 = 109.01633
P8m-DP = Purlin Rafter Miter Angle On Top Edge Face Perpendicular to Roof Surface = 90.00°
P9m-DP = Purlin Rafter Saw Blade Bevel Angle Along Miter Angle on Side Face = 0.00°

P10m-DP = Jack Rafter Miter Angle on Side Face Perpendicular to Roof Surface at Hip Rafter Rotated Into Roof Surface
P10m-DP = 90°
P11m-DP = Jack Rafter Bevel Angle On Top Edge Face Set in Roof Surface = P2m
P12m-DP = Jack Rafter Saw Blade Bevel Angle Along Miter Angle on Side Face = P2m ```
```P13a-DP = Purlin Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Lower Claw Angle
P13a-DP = arctan( sin (90° - P2a ) ÷ tan ( Valley Sleeper Saw Blade Bevel Angle ))

P14a-DP = Purlin Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Upper Claw Angle
P14a-DP = arctan( cos ( P2a ) ÷ tan ( 90° -  Valley Sleeper Saw Blade Bevel Angle ))

P15a-DP = Purlin Rafter Bevel Angle on DP Side Of Hip Rafter on Face Set in Roof Surface
P15a-DP = 90° - P2a```
```
P16a-DP = Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Lower Claw Angle
P16a-DP = arctan( sin ( P2a ) × tan (90° - Valley Sleeper Saw Blade Bevel Angle ))

P17a-DP = Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Upper Claw Angle
P17a-DP = arctan( sin ( P2a ) × tan ( Valley Sleeper Saw Blade Bevel Angle ))

```
```P18a-DP = Jack Rafter Bevel Angle on DP Side Of Hip Rafter on Face Set in Roof Surface
P18a-DP = P2a```

```Control files for Roof Eave Angle = 90° , 7:12 & 10:12 roof pitch
```

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`Control files for Roof Eave Angle = 120° , 7:12 & 10:12 roof pitch`