Why do aircraft radial engines always use an odd number of cylinders?

Individual rows are always an odd number of cylinders. Why is this?

Basically it’s for vibration control. Just as a straight six auto engine is inherently balanced, so are radial engines with an odd number of cylinders.

To keep the engine running smoothly.

From Wikipedia:

Pratt and Whitney engine that powered the Thunderbolt, Hellcat, Corsair, and the B-26 Marauder – 18 cylinders.

Pratt & Whitney engineused by the P-40, F4F, DC-3, B24 - 14 cylinders.

However, each of these engines had 2 rows of cylinders and each row had an odd number, but still …

Not to mention the R-4360 which had 4 rows of 7 cylinders:

Brian

Ignorance defeated! Thank you! From a lifelong motorhead…

See the F4U Corsair Bird cage. 4 rows of 9

Wow, a question so good someone else had to ask it again right away: http://boards.straightdope.com/sdmb/showthread.php?t=785150

Seriously, it was a good question. My old plane had a Continental 220 HP radial engine (7 cylinders), and that kitten could purr! “Powerful as the Nation!”

Yes, it’s important that each row has an odd number, the total doesn’t matter on multi-row engines.