@fanfare while form 2210 and 2210ai are complicated and in effect you have to complete your tax return 4 times (one for each period of the year), it is the way to indicate to the IRS that the taxpayer's income is "lumpy".
if your income is quite low from Jan 1 - Dec 30 and then on Dec 31 you do a large Roth conversion (or hit the lottery or whatever that generates a boatload of income), making the estimated payment by Jan 15 and then completing 2210 and 2210ai informs the IRS that you were not required to make estimated payments for the first 3 payments, but made the appropriate payment for Jan 15 estimate and therefore no penalty may be necessary.
without form 2210 and 2210ai, the IRS really doesn't know the income was "lumpy" and they otherwise assume 1/4 of the income occurred each quarter. The penalty is then determined based on smooth income by quarters and the timing of any estimated payments.
