My wife and daughter perform in a community theater group. The group has
decided on "Oklahoma!" for this summer's production. The biggest set
construction challenge will be the surrey, specifically the spoked
wheels. I may decide to help out with the building.

I have no familiarity with the show, but apparently the surrey will have
to carry two people on four wheels. My first thought was to cut out a
bunch of pie slice holes from a sheet of 3/4" ply, like this:

http://www.flickr.com/photos/gdguarino/11717012293/

Leaving aside that this would be a heck of a lot of tedious jigsaw work
(and routering to make the wheels round), do you think the resulting
wheel would be structurally sufficient?

We'd have to layer on some disks at the center to make a "hub", that
much I'm sure of. And I saw a video online in which a college production
(with access to a large shop, a bigger budget and a lot of free labor)
seems to have layered extra plywood circles on either side of the outer
edge to thicken the wheels. That made it look more authentic, to be
sure, but I wonder if it was structurally necessary. If not, I'm sure
"our" team would decide to forgo the extra work. Incidentally, unless
the extra layers were made in half- or quarter-circles, that's a lot of
ply to waste.

I considered other ideas as well (wooden hub and circumference, EMT
tubing for spokes), but so far the ones I've thought of seem like they
would require more precision than is likely to be available.

Any suggestions would be welcome. As an aside, does Sketchup always make
circles as such visibly-obvious polygons?