Big drill bits take a woodsmith from amateur to more specialized tools for specific jobs. For example, Forstner Bits are much larger than the common bits, and specifically built to bore flat bottomed holes. The 1-7/8" bit that are razor sharp have a sharp price, too. You could spend in the range of $60.00 for one bit. But when it's the only tool for the job it's well worth the price.
The paddle bit, just as it's name suggests, has a flared end that looks like a flat boat paddle that becomes narrower towards the shank. These bits are fairly priced and come in a wide range of sizes from 1" to 1/8".