## Thursday, February 7, 2013

### Quad Tetrahedra Analytic Algorithm Technology

One of the problems with roof framing trigonometry, is unconstructable roof framing. Without geometrically drawing out the roof framing,  it's hard to tell if the roof framing  trigonometry calculated lengths and angles are construct-able. I'm using Quad Tetrahedra Analytic Algorithm Technology in my Rafter Tools for Android app, to hopefully catch the roof framing  trigonometry calculated lengths and angles that most likely fall into the unconstructable roof framing category.

Unconstructable roof framing is usually a roof with an eave angle greater than 120° with unequal rafter slope angles that have 10° or more difference  in the roof slope angle. It's not to say that the roof can't be framed correctly, but the roof framing trigonometry is prone to errors without a lot of error checking. The easiest way to tell if the roof framing falls into the unconstructable roof framing category is with the hip rafter backing angles. If either of the hip rafter backing angles are less than 0°, like -5.02145, than the roof falls into the unconstructable roof framing category.  One side of the hip rafter becomes an valley rafter. Another way to tell if the roof falls into the unconstructable roof framing category are the jack rafter side cut angles and the roof sheathing angles that are less than 0°. On the  unconstructable roof framing  the hip jack rafter becomes valley jack rafters on one side of the hip rafter.

Here's an example of the Rafter Tools app using the Quad Tetrahedra Analytic Algorithm Technology.
Roof Eave Angle = 140.00°
Major Roof Pitch  = 8:12
Minor Roof Pitch  = 12:12

Roof Eave Angle = 140.00°
Major Pitch Angle = 33.69007°
Minor Pitch Angle = 45.00000°

Major Plan Angle = 98.78859°
Minor Plan Angle = 41.21140°

Major Run = 17.99999°
Minor Run = 12.00000°
Major Rise = 12.00000°

Hip Rafter Slope Angle = 33.37846°
Major Quad Tetrahedra Hip Rafter Backing Angle = -4.861770°
Minor Quad Tetrahedra Hip Rafter Backing Angle = 32.1369599175

Here's a couple of drawings showing the  roof framing geometrically drawn out  to check the roof framing trigonometry used in the Rafter Tools App.

Here's a drawing showing how the hip rafter backing angle becomes a negative angle. The 29.12189° hip rafter backing angle is in it's usual location. However, the 5.09957° hip rafter backing angle is sloping up rather than down. Resulting in an negative hip rafter backing angle. So the right side of this hip rafter becomes a valley rafter.

Euclidean geometry, without the use of numbers, is the only way to make all roof framing construct-able. In Euclidean geometry there are only whole numbers like 1,2,3,4,5 etc... and there are no fractions or decimal point numbers. With Euclidean geometry you would use a bevel square to transfer the roof framing angles to the roof framing members. However, the Quad Tetrahedra Analytic Algorithm Technology in the Rafter Tools app will help you when the Euclidean geometry is not an option.