Flying with kids or infants can be stressful. An easy way to calm your child is to book seats that are near the plane's engine so the noise puts them to sleep.
You should still take the usual precautions to make travelling with kids less of a nightmare. Buy your child a separate seat, keep some earplugs handy for pressure changes and noise, and have a few toys to distract them. But The Art of Manliness has a new, sound tip from a flight attendant:
The golden recommendation I got from a flight attendant is to seat your kids wherever the plane's engines are. The engines create a din of white noise that will help knock your kids out. It may seem loud, but the womb was incredibly loud too -- they will think they're back in their happy place. The placement of the engines varies from plane to plane. Figure out the type of plane you'll be flying in, and then do a google search to see where the aircraft's engines are located.
The blog recommends checking SeatGuru for seating arrangements of the plane.
There is one caveat. Some planes have engines at the back, and if you choose the last seat, you'll be next to the lavatory. That means the constant noise of the door and people, as well as the smell. You're better off sitting a few rows ahead in that case.
The Complete Guide to Flying With Babies and Toddlers (While Avoiding a Defcon 1 Meltdown) [The Art of Manliness]