Here’s a how-to from (http://www.backwoodshome.com/articles2/sanders98.html):
Potato stacks
When I was a youngster, I used a hoe to ridge up rows and rows of potatoes, pulling the soil up around the plants to help increase their yield. I have since learned of an easier way to grow potatoes that doesn’t require any hoeing—just plant a vertical potato patch. If you are limited in space, then this method is especially beneficial. You can grow a nice crop of spuds in just a few tires. Here’s how:
Generally, a stack of four or five tires that are progressively filled with some good compost and a couple of pounds of seed potatoes will produce around 25 pounds of potatoes. A few of these stacks can provide your winter’s supply of potatoes with no problem.
Use a utility knife to cut the sidewall completely out of the upper side.
To begin, pick a spot that is out of the way and perhaps out of sight where you can stack your tires. Loosen the soil just enough to allow for some drainage and place the first tire. Fill it with soil, being sure to fill the inside of the tire casing as well. Take your seed potatoes and cut them into pieces that have at least two “eyes,” or sprout buds in each piece. It doesn’t hurt to let each piece dry for a day or two before planting it. Plant three or four cut potato sets into the soil in the tire center. Cover the sets with enough soil to bring it level with the top of the opening.
Once the new potato plants get to be about eight inches tall, add another tire and add soil around the plants until just a couple of inches of the tops are above the soil. Repeat this process for the third and subsequent tires. As you add tires and soil to the ‘tater stack, the plant stalk is covered with soil. As you do this, the existing stalk will send off roots as well as grow upward to once again find the sunlight it needs. Since you are gradually raising the soil level eight inches or so at a time, the plant is able to keep growing without suffocating. At the same time, you are creating a 24- to 36-inch tap root off of which many lateral roots will develop. Each of the lateral roots can produce additional potatoes at three or four levels instead of only one. When you water the plant, be sure that the soil is thoroughly moistened all the way down to the base of the pile.
Since the tires also act as an insulator and heat sink for your potatoes, the added warmth will stimulate the lateral roots to multiply more quickly, giving you more potatoes. To harvest your crop, wait until the top dries up and begin to remove the tires, working your way down the stack and harvesting the potatoes as you go.
