>> the wider the tunnels/covers the less rigidity
That's one reason that garden fencing or cattle panels fascinate me. A semi-rigid "two dimensional mesh" has more strength than hoops with no cross-piece re-inforcement.
At one time I thought I might use one strong top-rail, plus flimsy hoops reinforced by "weaving" thin bamboo culms over and under the hoops, with some lashing of corners.
BTW, I keep forgettin g to say: I really like the thread title "Hooping"!
I'm hooping to build several small low tunnels as cold frames to hold seedlings through cold spells in February and March (next year).
And I'm hooping I can build something stordy enoguh to go over indeterminate tomatoes this Fall so they don't get starchy and nasty after one cold night.