Surprised by hip roof trigonometry.

[epsilonGreedy]

Most of my main hipped roof trusses are up and this morning I was going to trim the hip rafter ends so that the top of the hip rafters seated flat against the ridge end truss.

 

My roof pitch is 30 degrees and I assumed the settings for my compound mitre saw would be a 45 degree bevel because the hip rafters bisect 90 degrees and the other setting would be 30 degrees matching the pitch.

 

The hip rafters were supplied with angled cut off ends which I assumed were 30 degrees. My expectation was that with the mitre saw configured for a 30+45 compound cut I would slide the hip rafter end along to the cutting point and just slice off the 45 degree bevel. It turns out the hip after ends are cut to 24 degrees and not 30. I decided to double check and offered up the hip rafter to the roof trusses already erected and it turns out 24 degrees is correct.

 

Before trimming my hip rafters I thought it best to check here that I am not seeing things.

 

I have tried to visualize the trigonometry by imagining sweeping a rafter through 90 degrees at the hip end. The angle of intersection must start and end at 30 degrees but half way through the sweep the pitch angle is 24 degrees. Part way through this visualization my head explodes.    

[ToughButterCup]

Here's a link to the sections of the Skillbuilder YooChube site which might just help you.  I am afraid I didn't understand your problem statement.

https://www.youtube.com/c/SkillBuilder/search?query=hip

Discussion of hips in our family usually centres on the amounts of Paracetamol and Anti Inflamatory pills taken. 

Edited November 1, 2020 by ToughButterCup

[Oz07]

Doesn't sound right to me are you sure its not just a dodgy cut the manufacturer has put on the ends? I've sent monos back before as have been supplied an inch out of square in the distance of a framing square. To be fair i had the remade ones on the driveway at 8am the next day - can't complain about that service

[Oz07]

Oh sorry just looked at my cheat sheet. Your hip will be on a 22 deg angle as it's over a longer distance. Your jack rafters at 600 c/c will reduce by 693mm in length each time

[Construction Channel]

Wait until you put a protractor on the angle you just cut at 45deg....... It's not 45 ? mind blown..... 

 

Hips and cripples are fairly straightforward if your chopsaw can accommodate the timber. They get a lot more complicated when you need to cut them by hand and mark them with a bevel.

 

The first few pages of the ready reconer are fairly good at explaining why the angles are what they are.

 

https://onlinelibrary.wiley.com/doi/book/10.1002/9780470697788

[joe90]

I gave up on rafter cutting with a chop saw, reverted to a https://www.thesafetysupplycompany.co.uk/p/9356377/silverline---aluminium-alloy-roofing-square-7---trsl-si-734100.html?gclid=Cj0KCQjwufn8BRCwARIsAKzP6945bXaQ31o0XoyRcr_ib9CZXivkC965n8wT-WZ7DLhsw0qxLLtxVwwaAkXeEALw_wcB and did it with a handsaw, much better IMO.