I found several photos and drawing showing how potatoes grow. The eye sends roots down into the soil, the plant grows up and all the pototoes grow off the side of the plant. It looks to me like the taller the plant gets the more potatoes it will grow. The plant sends out runners in all directions and the potatoes grow on the runners.
So maybe that is why my car tire potatoe beds do better than planting in the soil with no tires. I plant the potatoes in the soil in the center of the tire. As the plants gets taller and taller I fill the tire with more and more soil. When the tire will not hold any more soil I put on another tire and keep filling it up with more soil. By the time the plant turns yellow and dies the soil is piled up about 22" high.
I am not a big fan of raised bed but today I made 3 raised beds for potatoes. I bought a scoop of garden soil from the garden center it is a mix of mushroom compost, sand, river bottom soil, and composted leaves. The raised beds have about 6" of soil in them I intend to plant the potato eyes in the garden soil then cover the plants with the compost soil.
I am going to do another car tire potato bed experement too.
I also have 3 wooden boxes 12" deep that will be potato beds.
I might try a few more experements too. Maybe wire cage. I want to know for sure how much soil depth has to do with how many potatoes the plants produce and if the soft compost soil makes larger potatoes than regular soil.
I am only planting Red Pontic potatoes this year they always do better than white potatoes. I bought 2 lbs of seed potatoes from 3 different places that might make a difference too.