Krallenspitze -- Jack Rafter Claw Tip Angle

Manfred Euchner
Handbuch der Schiftungen

Ermittlung der Klaue bei schifter
Determination of the claw at Schifter
Determination of the claw at Jack Rafter
Krallenspitze -- > Claw Tip

The math for the jack rafter claw tip. 

R5  = Hip Rafter Diamond Post Angle

R5 = arctan (tan Hip Rafter Slope Angle x cos adjacent plan angle)

Common Rafter Slope Angle - R5 = Claw Tip Angle

R5 = arctan(tan 27.50055 x cos 51.34019) = 18.01470

Claw Tip angle = 39.80557 - 18.01470 = 21.79100

R5 = arctan(tan 27.50055 x cos 38.65981) = 22.121943
Claw Tip angle = 33.69007 - 22.121943 = 11.568126

The plan angles are the opposite for valley rafter plan angles. Here we have a 8:12 & 10:12 hip roof  with the 8:12 plan angle at 51.34019° and the 10:12 plan angle at 38.65981°

In this drawing of the valley rafter you can see the plan angles are reversed.