You do not have to use a car seat on an airplane. But you might want to. First, the background information. I know it is expensive to buy the seat, but would you regret it if something should happen?
"The US Federal Aviation Administration, the US National Transportation Safety Board, the American Academy of Pediatrics, and the Australian Civil Aviation Safety Authority all appear to agree on the following basic principles:
All passengers are always safer on an airplane when properly restrained, period. Being properly restrained will make a baby significantly safer on an airplane.
Unrestrained babies in airplanes are subject to more risks than unrestrained adults. It takes less turbulence to fling them around the cabin, and once they have gotten misplaced in the cabin, they cannot find themselves and can get trapped under seats and in small spaces, making them hard to evacuate. (There isn't good data on this because adults are usually belted. However, this article suggests that unrestrained babies are up to 9.6 times as likely to die in an airplane accident than restrained adults.)
A baby in a bassinet is an unrestrained baby.
Restraining babies with an adult seatbelt is simply unacceptable and drastically increases the chance of injuring the baby.
Restraining babies with an addition to an adult seatbelt (an extra loop) keeps them from flying around the cabin, which is good, but significantly increases the chance of other injuries to the baby, which is bad. [The US and Australia differ on whether this tradeoff is acceptable, but agree that it will result in some babies that would have died of head injuries living with abdominal injuries and also some babies that would have had no injuries having abdominal injuries.]
The best possible way to restrain a baby on an airplane is an aviation-approved child restraint (that is, a car seat certified for airplane use). This should be installed according to the manufacturer's label, even if that means facing the rear of the airplane. Aviation-approved child restraints are tested for airplane safety as well as car safety."
Quote from parentsknow.com:
The reasons for the proposed regulations are clear-cut: More than 90 percent of injuries on airplanes occur in-flight during turbulence, so when parents hold infants or toddlers on their laps, they are putting themselves and their children at risk for injury. Between 1987 and 1994, three children on the laps of adults died (and others received injuries) in plane crashes in Denver, Colo., Sioux City, Iowa, and Charlotte, N.C. Five children were aboard American Airlines Flight 587 when it crashed into the Belle Harbor section of Queens on Veteran's Day.