Leg angle vs. strength question

[Matt Campbell]

369611
My son and I recently made the footstool in the picture above, and I have a question about structural integrity. I decided to splay the two legs of the footstool at 5 degrees. Why 5 degrees? Because I decided I liked that appearance. That's all. :D Here's my question...How do you know what is the best angle for something like this? And when I say "best angle", I mean the strongest angle. Obviously, if you angle them out too far, then it gets quite unreliable to stand on. Thanks for your help.

[Steve Demuth]

The strongest in terms of ability to bear load directly on the top of the stool is 0 degrees - no splay at all, because then the entire load is straight through the leg to the floor, and wood is extremely strong under compression. Once you splay the leg, a lot of considerations come into play. A splayed leg introduces new forces into the wood and the joint between the leg and the top that are not compressive. If, for example, you splay he leg sufficiently that none of the leg's footprint is directly under the top of the stool, then you introduce a force that will want to pull the leg away from the bottom of the top of the stool, where the leg is glued or screwed to the top. You get that force because the you've introduced a rotational moment that wants to pivot the leg on the point that touches the ground nearest the stool center.

[Jerry Wright]

As long as you have a stretcher, as It appears you do, no issue. Search angled leg tables and stools. As long as you have an adequate apron, you can get away with a lot.

[Doug Garson]

+ 1 on what Steve and Jerry have said. Basically the more vertical the leg the stronger it will be and the more splayed the leg the more stable the stool will be. I built a bar stool once where I didn't splay the legs enough and it was quite unstable, had to reduce the size of the seat to make it less tippy, it's now a plant stand.

[Mike Cutler]

Stickley and Morris say 9.59 degrees, or 1 in 6.

Splaying the legs adds stability, straightening the legs adds strength.

I think you're good. ;)

[Jerry Olexa]

Agree..True vertical (no angle) is the strongest...Then wood is in compression and not being stressed in another direction.

[Bill Dufour]

It is common for the outside two edges to be 90 degrees vertical with the inside corners being slightly tapered. Starting just below the apron to make for easy 90. degree joints.
Bill d