This is a repost from another thread on the same subject:
I have never tried the potato tower method, so have no experience to share. However, based on a knowledge of plant growth I think it is a lot of un-needed effort for a set harvest. There are two controlling factors in how large a harvest you can get from a potato plant; how much nutrient solution the roots can take up, and how much leaf surface is there to convert that solution into plant usable nutrients through photosynthesis.
Growing potatoes in a tower would allow the plant to have a larger root mass due to having a taller stalk underground, so the plant could take up more nutrients. All the photos I have seen of potato towers show normal sized potato plants without any additional mass of leaves to make use of the additional nutrients. Based on that alone I would doubt that the method will increase the harvest beyond what you would get by simply ensuring that the one plant gets the nutrients it needs and the sunlight to convert them into potatoes.
If you just like fiddling with things, go for it. Or perhaps try an experiment. Plant two potato sets, one in a pot of compost and one in a tower. Ensure that they both get the same amount of sunlight and water. Just before harvest, count the leaves on both plants and then after harvest weigh the potatoes. I predict that the leaf count will be similar and so will the harvest