Gabel, this is the "natural", proportional or geometric offset. The Hip/Valley rafter crosses the intersection of the eave lines. Although the eave lines in the animation are shown meeting at a right angle this corner angle can be any value.
Development of the Backing Angle ... or
C5 in the Hawkindale angle nomenclature used here.
This is looking at the same offest viewed in plumb section through the Hip rafter. The blue line being rotated is what many framers call the "Hip" drop on an unbacked Hip rafter. The offset produces equal shoulder heights on both sides of the Hip and determines the correct "plane in" point for the jack rafters on a backed or unbacked Hip rafter.
Development of the Plumb Backing Angle ... Hawkindale angle
A7The offset formulas derived from the geometry are given on the last page of
Hip Shift/Drop Analysis. A similar formula may be derived from the side cut angles on the upper shoulder of the unbacked Hip/Valley. And here are some
example Hip Shift/Drop Calculations and DiagramsThere are other offsets. The Hip/Valley can be shifted laterally or radially to produce equal overhangs ... but that's another story.
