When are chair stretchers important?

I am making 4 chairs to go with a dining room table I just finished. I posted a question and a couple people suggested getting Jeff Miller's "Chairmaking & Design".
Miller talks about how important stretchers are, but most of his chairs don't have any. And the ones that do seem to be more robustly built than the ones that don't. At one point he implies that he leaves them out of curving designs because they are a challenge to fit. That doesn't seem like an adequate reason.
Under what circumstances are stretcher's important? Presumably they are less important when there are arms.
I am going to try to take elements from his "Captain's Chair" and his "Slat-Back Chair".
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Toller said:

No expert, but do have an observation to share. We have a few old maple chairs without stretchers. The legs are fairly beefy, and are wedged tenons. They make me a little nervous, but are still solid. But the long, unrestrained legs have splayed at varying angles, depending on the grain direction, which makes them rock slightly on a solid floor. And we definitely don't tip them back as 8 year olds are wont to do.
FWIW
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My grandfather built many chairs some singles, some sets, large and small. I recall his thought that stretchers were typically added to compensate for poor structural integrity. Of course, in some cases a stretcher would be a valid aspect of the design.
J
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Toller wrote:

One consideration is how weight is transmitted to the bottom of the legs...is it straight down or do the legs curve/slope toward the back/front? In the latter case, the downward force acts a bit like a wedge and will want to pull them off the seat aprons.
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"Toller" wrote in message

Important for what?
Some folks build for art/appearance, and some build for structural integrity/longevity. For the former, whenever you think they are; for the latter, when you have any angle on the legs.
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Wouldn't there be a minimum angle where the stretchers aren't necessary? If you're designing the legs as individual structural members there's no need for stretchers. If you're trying to lighten the look of the chair by using more slender legs, having the legs act in concert, as a system, would require stretchers.
R
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Chair stretchers add a lot of structural integrity, especially when heavy-set people use the chair or if the chair is abused. If stretchers are not used I will put in what's called a "ships knee" made from bent wood or laminated strips. The ship's knee is attached to the legs and underside of the seat with screws.
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I googled on "ship's knee" but didn't find anything. Can you either reference it or explain it more fully?
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It looks like an upside down "U," with the top fastened to the bottom of the seat and each leg screwed into the chair legs. You need two ship's knees for each side of the chair. It acts like a brace. Most of the ones I've seen were made from steam-bent dowels. This gives incredible strength to the legs and eliminated the need for stretchers.
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Phisherman wrote:

This may help. http://www.newmansknees.com /
Sonny
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Stretchers help reinforce strength to legs by transferring some of the load to the other legs. This really makes sense when some one leans back on two legs and the angle of the applied weight changes.
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Toller wrote:

Grandmom did antique collecting, and the best old chairs (some very comfy, others elaborately decorated) all had stretchers. Chairs without stretchers, that I've seen, are generally broken before they reach a century.
Elegance and style matter somewhat, but I get uncomfortable in a chair that looks like it'd break. And I always expect the long legs of a chair to act as levers and break their joints at the seat. The historical record of grandma's collection says stretchers are valuable. So does my stress analysis.
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