Irregular Bay Window Solutions

Adjoining Roof Ridge Dimensioning Formulas

Links to other Diagrams and Models

Arizona Hip ... Dogleg is zero
Example Arizona Hip #1 ... footprint based on a Nonagon
Example Arizona Hip #2 ... footprint based on a Nonagon
Example Arizona Hip #3 ... Irregular Footprint

Special Cases of Bay Window ...
Doglegs terminate at intersection of Plate Line

The following style of Bay Window is not
supported by the current version of the calculator ...
Irregular Bay Windows ... Dogleg terminates at custom Working Point


Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Dogleg Valley Detail
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Plan View Dimensions

Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Plan Angles

Common and Hip Rafter Pitch Angle Check
arctan (tan 39.80557 sin 54.57597) = 34.17927
arctan (tan 34.17927 sin 80.42403) = 34.55388
arctan (tan 34.55388 sin 65.25586) = 32.02340
arctan (tan 32.02340 sin 110.25585) = 33.69007
arctan (tan 33.69007 sin 46.89006) = 25.95200
arctan (tan 25.95200 sin 43.10994) = 35.45726

Dogleg Pitch Angle Check
arctan (tan 35.45725 sin 65.18065) = 32.87819
arctan (tan 32.87819 sin 69.81935) = 34.55389

... and finally going full circle to where we began
arctan (tan 34.55389 sin 80.42403) = 34.17928
arctan (tan 34.17928 sin 54.57597) = 39.80558

A difference of only 39.80558 39.80557 = .00001 from the value we started with.

Also check the Pitches and Plan Angles with ...
Formula for Unequal Pitches at any Corner Angle

Polyhedron Modeling the intersecting Roof Planes

Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Polyhedral Model, Plan View
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Polyhedral Model, Front View
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Polyhedral Model, Oblique View

Superimposed Rafter Feet and Plates
Heel Heights are equal at Fascia


Solve the Rafter Depths, Heel Heights
and Plate Height Adjustments with ...
Rafter to Point at Fixed Height Calculator
Rafter Dimension Conversion Formulas


Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Superimposed Rafter Feet and Plates

Bird's Eye View of Polygonal Model
Rafter Depths and Plate Height Adjustments


Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Bird's Eye View: Rafter Depths and Plate Height Adjustments

Section extracted from Bay Roof
Model constructed around the Rafters


Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Rafter Model, Bird's Eye View
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Rafter Model, Worms's Eye View
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Rafter Model, Front Bay Common
Irregular Bay Roof with Equal Overhangs and Dogleg Valley ... Rafter Model, Wing Bay Hip and Valley intersect Dogleg

Joe Bartok