Answer: Timing is everything when planting onion sets. Here's why - Onions go through a process called `bulbing' to produce the onion bulb. Bulbing is affected by amount of daylight, not by plant age. Daylight necessary to initiate bulbing depends on the variety of onion and can range from 12 hours for early maturing types to 15 hours for late maturing types. Mature onion bulb size is highly correlated to the size of the onion plant at the time bulb formation begins. Thus, bulb size is influenced by the same factors which influenced plant growth prior to the beginning of bulbing, plus environmental conditions during the completion of bulbing and maturity. Factors affecting large bulb formation include early planting, space per plant, soil moisture, weed competition early in the growing season, and damage from blowing soil particles, insects and pests.
To answer your questions about breaking off the tops or partially uncovering the onion to ensure large bulbs, both are false. If you break off the tops, the plant will stop growing; if you partially uncover the onion it will be prone to sunscald. So, allow the foliage to die down naturally at the end of the season - and don't uncover the shoulders of the onion or they will sunburn.
Hope this at least heads you in the right direction! Good luck with your next crop!
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