Bird blocking is just blocking with a fanciful name. The intent of any blocking at the plate line is to “keep out” unwanted visitors, mainly squirrels and birds. This is going to be a brief explanation on how to calculate the angles to cut these blocks so that they fit nicely between the common and a hip/val rafters on a regular hip roof. I’ll leave the discussion of cutting these blocks for an irregular hip for another day.

For a regular hipped roof with a roof pitch of 8 at 90° to calculate the block’s cuts that go against the hip/val you would need to know the Roof Pitch Angle & Roof Counter Pitch Angle of both the common rafter and the hip/val rafter. You can determine these values with simple trigonometric functions on a scientific calculator.

Common
tan^-1(Roof Pitch/12) = {Roof Pitch Angle} 33.69°
tan^-1(12/Roof Pitch) = {Roof Counter Pitch Angle} 56.31°

Hip
tan^-1(Roof Pitch/(12*SQRT(2))) = {Roof Hip Pitch angle} 25.24°
tan^-1((12*SQRT(2))/Roof Pitch) = {Roof Hip Counter Pitch Angle} 64.76°

Once you’ve determined the basic angles you can then proceed to calculate the angles you need to apply to the block at the hip/val rafter. Below the use of the color values in red are the ones you already have determined and the ones in blue are the ones you calculate.

Calculations
(12²/Roof Pitch ) = {Counter Pitch Length}18"
tan^-1(SQRT(2)/(12/Roof Pitch)) = {Counter Hip Pitch Angle} 43.31°
tan^-1(cos(Roof Pitch Angle)) = {Fascia & Hip Miter top edge scribe} 39.76°
tan^-1(cos(Roof Counter Pitch Angle)) = {Fascia Miter wide face scribe.} 29.02°
sin^-1(cos(Roof Pitch Angle) * (SQRT(2)/2) = {Fascia & Hip Miter Saw Blade Bevel (Tilt) Angle} 36.04°
(Counter Hip Pitch Angle - Roof Hip Pitch Angle ) = {Hip Wide Face Scribe Angle}18.07°

Using a Construction Master Pro Model 4065 v3.1
{Roof Pitch Angle} 33.69° = [8] [Inch] [Pitch] [Pitch]
{Roof Counter Pitch Angle} 56.31° = [90] [-] [Pitch] [Pitch]
{Roof Hip Pitch angle} 25.24° = [12] [Inch] [Run] [Hip/V] [Hip/V]
{Roof Hip Counter Pitch Angle} 64.76° = [12] [Inch] [Run] [Hip/V] [Hip/V] [Hip/V]
{Counter Hip Pitch Angle} 43.31° = [8] [Inch] [Rise] [16.97] [÷] [2] [=] [Run] [Diag] [Diag]
{Fascia & Hip Miter top edge scribe} 39.76° = [12] [Inch] [Rise] [14] [Inch] [7/16] [Run] [Diag][Diag]
{Fascia Miter wide face scribe.} 29.02° = [8] [Inch] [Rise] [12] [Inch] [Run] [Diag] [=] [Run] [Diag] [Diag]
{Fascia & Hip Miter Saw Blade Bevel (Tilt) Angle} 36.04° = [14] [Inch] [7/16] [Diag] [16.97] [÷] [2] [=] [Rise] [Pitch] [Pitch]
{Hip Wide Face Scribe Angle}18.07° = [ 43.31] [-] [25.24]

You can easily get this information without doing any of the work by simply going to my on-line roof framing calculator. Once there enter in your information for the roof you are cutting an be sure to set the "Tail Cut Options (Plumb or Square)" to Square even if you are using plumb cuts. This will force the calculator to return the angles needed to cut the blocks. You can then recalculate with the setting to "plumb" if indeed the tail cuts are plumb.

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