Calculating the Common, Hip & Valley Rafter Lengths.

The term "fixed ridge height" may be a bit confusing to some. You might say aren't they all a "fixed ridge height?" Well yes and no. When a ridge has a "predetermined" height or the maximum height is defined, it is said to have a fixed height. This raises the problem of "not" having a defined rafter slope to work with off the square or table, you will have to calculate all the numbers. The next section will help you do that.

Calculating the Common Rafter length (crl).

The real common rafter length can now be determined by the Pythagorean Theorem . . .c² = a² + b²  . So, if you plug in the numbers; you get (((square root) crl) = arz² + arr² )  or (((square root) crl) = 119² + 190.5² or
(((square root) crl) = 14161 + 36290.25 or (((square root) 50451.25) final crl = 223.95 (224-5/8").It's important to note that any inexpensive calculator can help you determine these numbers. It does not need any fancy sci-fi functions on it, just +, -, x, /, squared and square root. The reason for using this method is that you do not have to "adjust" your rafter lengths while marking, this was a taken care of when you made you calculation.

This is Very Important:If you were to set your rafting square to 12" on the tongue and 8" on the body to lay this rafter out, you would be using the WRONG angle. This is by far the most common error of many roof framers. If you study roofs long enough you will see this to be true. At this time you need to find what the actual roof slope angle is, this is called the inch rise. ir = (arz * 12) / arr or (119 * 12) / 190.5 or (1428 / 190.5) final ir = 7..496 (7-1/2"). You would now set the body of you rafting square to 7-1/2" to create the correct plumb angle.

Calculating the Hip/Valley Rafter length (hrl) (vrl).

Here once again is concern for much confusion. I think I've gotten this down to it's simplest form also. First let me say that about 7 years ago I gave up using "17" to set my square to cut hip or valley rafts. Actually I don't use any number other then "12", you will soon see why! If you follow a simple rule you will be able to figure any hip or valley rafter the same way as a common.

Knowing that a hip is the diagonal projection of the hypotenuse of an isosceles right triangle you can do this.  .  .  .

Using the arr in the Pythagorean Theorem . . .c² = a² + b² for both a and b you get,
(190.5²  + 190.5²) or the square root of (72580.0) which is the actual run of the hip rafter and is 269.4066 (269-7/16"). If you now use this number in the Pythagorean Theorem you can calculate the hip rafters length. Which is. . . .

(square root)hrl = (269.4077² + 119²) the roof rise doesn't change for a hip or valley just it's run changes. So, (square root)hrl = (72580.05 + 14161) or (square root)hrl = (86741.05) final hrl = 294.518(294-1/2")

You now can once again determine the ir for the hip rafter. ir = (119 * 12) / 269.4077
ir = 5.30 (5-5/16") Now set your square to this number a cut the hips.