It would be interesting to see a plat of the whole yard to see what you are trying to squeeze in and where sun is.
You are doing something which is not traditional. Each vine should have a support to be anchored on.
The plant will not support itself! Ex. i have one 8’ fence post per plant, ,, most vineyards seem to use rebar. Your structure looks high/ six ft? this translates into all your grape work is over head. Is this comfortable? ex. for spraying over head, or for pruning, or for having friends in the yard. Most vineyards tie the vines on wires. Some will have one vine on one post with no cross members, this makes a small plant and lower yield but is relatively easy to maintain. (There was a PVC setup in winemaker Magazine two years ago). Another maintenance treated wood has a fifteen year life. Your grapes will not start to produce any quantity for about five years. ,,, How do you maintain your wood trellis? it will look unkempt in ten years.
With three foot spacing the vine will try to fill 200% of the space you are giving it. The natural tendency for the plant will be to grow in all directions! Translation -> two vines will not stay separated if they have one spot of land. They will fight each other for water and minerals. The tendency will be to grow sideways about three feet and grow both directions on the support. To maintain separation means constant pruning. Pruning means reduced yield/ plant size. ,,, Basically I would have a post for each of the vines. The tightest spacing I have seen was in Europe with about a meter between rows and four foot plant to plant.
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I would like to start with how much space do you have for each root and then assume a circle that the roots fill with a similar circle that the canopy fills. ,,, your canopy could cantilever over the cement driveway or take over the fence.
You can make it work with two plants on one spot since grapes are weeds, ,,, BUT traditional methods do better for yield.
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