This is how babies used to fly on airplanes.

How do you transport a baby on a long airline flight?

During the 1950s, engineers at the British Overseas Airways Corporation (what we now call British Airways), developed the "skycot." 

High Life, British Airways' in-flight magazine, tells us that parents would hold babies during takeoff and landing, but, while in the air, would place them in these hammocks clamped onto the overhead luggage racks.