You have an oval shape 10 feet wide and 20 feet long in which you are interested in half of it. Your question is what is the circumference of that oval where the answer to the length of the arch should be half that. I believe the circumference of that oval would be 49.672 feet and therefore that the arch would be 24.84 feet .

Look up calculating the circumference of an ellipse where the arch is bisecting the ellipse along the short axis (the bisect line across the short axis is the floor). I think that's right but if you're doing anything important I would get a second opinion.

You guys are geniuses. Wolf has provided the theory and Charlotte has shown how to test it empirically. I'll perform the experiment later this weekend and publish the results after that.

P.S. Charlotte, I am not purchasing the supplies. I am harvesting them from a woodlot owned by a friend's ex-husband, who has kindly granted me access to his land. (More details to be provided later.)

I use to do bookkeeping for a lady that owns a nursery that sells native plants only. She also is a great old wood 'salvager'. She buys it at salvage stores but also reclaims old wood from barns and houses being torn down. If you go to her facebook page https://www.facebook.com/BoskyDellNatives/ there are pictures of what she has done and also her website page: http://www.boskydellnatives.com/random_stuff_photo_gallery.html Believe me - walking into her house is an experience. I think people come to look at what she has done architecturally as much as the plants. Great thing is - she integrates the two.

Got the trees this morning. They were on a 14-acre parcel that runs between some houses and a pond. A nice spot. One of the homeowners came out and accused my friend's ex (Jack) of stealing the trees. Threatened to call the police. Jack told homeowner that he (Jack) owned the trees and would welcome the police so he could report homeowner for dumping tires on Jack's land. (This was explained to me by my friend since it was in a language I do not speak.) Loaded the trees onto the truck and tied them down. These trees are a lot bigger than they looked in the woods. Have no idea how I am going to do this. Maybe with a little help from my friends.

Wolf, your calculations were correct. I remember that you like Robert Frost, so here's the last stanza of his poem, "Birches."

So was I once myself a swinger of birches.
And so I dream of going back to be.
It's when I'm weary of considerations,
And life is too much like a pathless wood
Where your face burns and tickles with the cobwebs
Broken across it, and one eye is weeping
From a twig's having lashed across it open.
I'd like to get away from earth awhile
And then come back to it and begin over.
May no fate willfully misunderstand me
And half grant what I wish and snatch me away
Not to return. Earth's the right place for love:
I don't know where it's likely to go better.
I'd like to go by climbing a birch tree,
And climb black branches up a snow-white trunk
Toward heaven, till the tree could bear no more,
But dipped its top and set me down again.
That would be good both going and coming back.
One could do worse than be a swinger of birches.

Hi Charlotte, No, it is at the entrance to the back yard, which is kitty-corner to "the hermitage." It will span a 9-foot space between my garage and my neighbor's fence. I always wanted to put some kind of an arbor there with climbing roses or something but it is the only way a machine (even a riding mower) can get into the back. (You should have seen it when they drove the 8-foot wide shed in there years ago.) So I wanted something that would span the whole space and that was not expensive or permanent, in case it had to be removed. Right now, I'm not sure that this is going to work. The birches do not seem to bend the way Robert Frost described in his poem. Some friends are helping me so maybe they will have some ideas.