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What you are referring to his commonly called dropping the hip. You do this on hip rafters to allow the sheathing to plain in correctly. An alternative to dropping the hip is to put a backing bevel on hip.
You can use this formula to determine the drop amount for any regular hip rafter:
((rise) * (1/2 thickness of the hip)) / 16.97)
You can will read a bit more about this by following the link below.
Joe and Guy, it's more than just dropping the hip to maintain the sheathing plane. Because the hip is generally 1 size wider than the jacks and commons, the seat cut must be deepened to bring the upper edge of the hip down to match the height above plate (HAP) of the jacks and commons. I don't have a formula right now, but be careful!
I hate to disagree, but dropping the hip is all about planning the sheathing. It doesn't matter what the size of the framing members are. If you use 2 x 8's to framing the commons and jacks and use 2 x 10's to framing the hips and valleys you will still need the same H.A.P. on both members. This is obvious because the H.A.P.'s are measured from the top of the building line plumb cuts down.
That does play a factor in dropping is the member thickness i.e. 1-1/2" or 3". A 3" member needs to be dropped more then an 1-1/2" member.
I agree that it's all about the sheathing. There is no other reason to drop the hip or valley.
I use the same formula you provided in your first post and have for many years. But if we have a 3" hip or valley, I simply back the two members then nail them together. In some cases I have to use 2 ply LVLs, PSLs or Paralam products or for hips or valleys. In these cases I consult the engineering dept. at Weyehouser before backing.
Joe, I'm not disagreeing with you. I've seen you post here before and I know you are an excellent framer. It's Guy I'm worried about. I was in a hurry when I posted, so I didn't explain very well.
When you wrote, "you will still need the same H.A.P. on both members", you are repeating what I was trying to say. You first measure down from the upper edge of the hip to get the same HAP as your commons and jacks, then you use your formula to go back up to make sure the sheathing planes correctly.
I could be wrong, but Guy struck me as inexperienced, so I was trying to make sure he didn't take his measurement from the lower edge of the hip. If a new framer asks me "How deep should I cut this?", I usually assume he's asking how long his kerf should be. And obviously if you measure the kerf of the bird's mouth plumb cut, you will be measuring from the lower edge of the hip, and the length of the kerf will depend on the width of the stock.