Bruce
Herd Master
People who don't have spare old tires around also grow potatoes in wire "towers". Same as @CntryBoy777's method of adding medium. I think even just hay or straw. I ASSUME if the ground is totally worthless for growing things you would need to start the spuds in something better, maybe a bag of potting soil.
Of course this would be quite the Herculean effort for 240' of potatoes. But ... never having grown them, are they like squash where one plant can take over 50' sq feet of land so you need a lot of linear space but not all that many plants? Maybe only need 12 plants in 120' of row? If so, perhaps a much better yield per sq ft can be had with growing them "vertically". And, I think!, no weeding
I'm going to grow some white and some sweet potatoes for the first time this year, hope all goes well.
Of course this would be quite the Herculean effort for 240' of potatoes. But ... never having grown them, are they like squash where one plant can take over 50' sq feet of land so you need a lot of linear space but not all that many plants? Maybe only need 12 plants in 120' of row? If so, perhaps a much better yield per sq ft can be had with growing them "vertically". And, I think!, no weeding