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

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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

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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 + 19.875 ) = 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




Joe Bartok 1