Sample HAP Calculations

PLUMB LINE DEPTH = RAFTER DEPTH / cos PITCH ANGLE

       Diagram detailing the relationship between rafter depth, rafter pitch angle, and total plumb line depth. The pitch angle, given as 45° on the diagram, may actually assume any value. For a rafter depth of 11.25, and a pitch angle of 45°:
(1) PLUMB LINE DEPTH = 11.25 / cos 45° = 15.9099
(2) Factoring by 2/3 gives a HAP of 10.6066.

Value for the HAP returned by CAD

The sum of the angles is the rafter pitch angle, 45°
Angle A = 27.84943°
Angle B = 17.15057°

Sample Calculations

(1) Length along bottom = RAFTER DEPTH / sin PITCH ANGLE
(2) Subtract the plate width
(3) Multiply this result by tan PITCH ANGLE

       Substituting the numbers in the diagram above:
(1) 11.25 / sin 45° = 15.9099
(2) 15.9099 - 5.5 = 10.4099
(3) 10.4099 (tan 45°) = 10.4099

Changing the variables:

       Another example, using a rafter depth of 13.25, and a pitch of 8/12, giving a pitch angle of arctan (8/12) = 33.69007°.
(1) 13.25 / sin 33.69007° = 23.88678
(2) 23.88678 - 5.5 = 18.38678
(3) 18.38678 (tan 33.69007°) = 12.25785

       Same initial variables as the last calculation, but this time solving for the plumb line depth, and factoring by 2/3.
(1) 13.25 / cos 33.69007° = 15.92452
(2) 15.92452 (2/3) = 10.61635

Triangle lengths instead of trig functions:

       The final pair of calculations repeated using the lengths of the 8/12 pitch triangle. This is exactly the same as using the trig functions of 33.69007°.
(1) Since the rise is 13.25, the run = 13.25 (12/8) = 19.875
(2) Hypotenuse = Square Root ( 13.25 ² + 19.875 ² ) = 23.88678
(3) 23.88678 - 5.5 = 18.38678
(4) 18.38678 (8/12) = 12.25785

       Solving for the plumb line depth, and factoring by 2/3.
(1) 13.25 (23.88678 / 19.875) = 15.92452
(2) 15.92452 (2/3) = 10.61635