Living in TN I have never been able to grow any root crops. When I lived in Illinios they all grew great. The soil here is pretty bad lots of clay. I have put 4 bales of peat moss in the garden for the past 3 years. My garden is about 20 ft by 45 ft. I put sand in the garden last year. I put my wood ashes in the garden too. I have a compose too.
My potatoes are usually the size of golf balls. Red potatoes do better than white potatoes.
Onions sprout roots but never get any larger than the day they were planted.
Garlic will sprout roots too but it just sets there never gets any larger.
Carrots grow 2 inch long pencil diameter.
Beets are about the size of marbles.
Last summer I saved all the ash from the wood stove and put it in the potato row. I fertilized the row with 15/15/15 too. My potatoes were a little larger than gold balls but the crop was very very small for some reason a whole row of potatoes produced only about 20 potatoes.
This year I hauled 2 tons of sand for the carrot, onion, garlic, potato patch. I also tilled in 2 large bales of 3.8 cu ft peat moss and 2 5 gallon buckets of wood ash. I bought 4 lbs. of Super Phosphate and 4 lbs of Murate of Potash and 5 lbs of Sulfur to make the potato patch acid.