Ah - gotcha. If mangels are allowed, you're really going to have a giant beet contest!
Unfortunately, I don't grow vegetables for size, so I probably can't give you much advice. We do grow mangels and occasionally get them almost to soccer ball size. It seems that they do the best following potatoes, which means that they are growing in soil that was amended with duck manure and deeply worked the year prior. A long, cool season with plenty of water seems to help as well. Too much water toward the end of growth and they tend to split. None of that is probably news to a competition grower though.
Don't forget to make some mangel beer
with the runners up.