I plant tomatoes,cukes,peppers,onions and other salad crops in old tires. I have heavy clay soil here and nothing grows well so I had a lot of 16" and up to semi tractor tires. I cut out one sidewall(used for the top ring) and stacked them 3 high and filled them with A combination of compost and cheap potting soil. Works great. Easy on the back and putting grass clippings in as mulch smothers the weeds.You can plant potatoes in the same manner. one tire to one plant and as the plant grows put on another tire and fill with compost/potting soil mix. Cut holes in the tread around the tires (3 or 4) and you can reach in to harvest new potatoes. You can go up to 3 tires high. In the fall knock down the tires and shake out the soil and the potatoes harvest themselves. Sure beats digging!. All the dirt goes into the compost bin for the next year. The tires ,being black, really heat up in the spring fast which helps get the plants off to an early start.
Good Luck!
H.R.