How to decide stringer angle for the winder part of stairs?

[cjard]

At the moment I'm just sketching my staircase in a 3D modelling program before I turn it into a real thing. It's a wide U shape, and a double winder.. but I'll just focus on one of the winders for now

The main stair angle I'd like to be 30 degrees, but this cannot be maintained around the winder as the stringers wouldn't mitre. Most of the drawings and kits I look at for ideas have a shallower angle at the winder part..

Is ther a mathematical relationship between the two stringer angles, I wonder? should the winder stringer angle be half, a third etc? How do the factory boys pick it?

Also, am I correct in thinking that it's really hard to mitre two stringers at a 90 degree angle if the two are also sloped at 30 degrees? If a plain 45 degree mitre was cut at a complementary 30 degree angle so the two would mate, I end up with a a pyramid of wood sticking up/ just a mess:

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Is there any technique to make a mitre where two of the angles are not multiples of 90 degrees? would a butt join of one plank against the face of the other be preferable?

 

[KenGMac]

For some ideas?

Google "Dihedral Angles"

This is the really difficult angle to describe between two roof slopes [ my description runs out at this point]

if you imagine this angle is the junction of two roof slopes at a hip ?

Hope this assists, there is generally a "Formulae" on the web sites that may be of use?


Ken

 

[big-all]

the strings go into the newel post so not a problem
the string do not line up as you drop as you go around the newel more so as you have winders

 

[cjard]

The outside stringer might not enter a newel post?

 

[big-all]

it has to really as you cannot change directions unless you have a wall for support otherwise you need a newel to transfer up to the floor above or down to the ground below otherwise your string has no support

also if you have say 2 kite winders one string will not even be on the same level in fact the top off one will miss the bottom off the other