Flying and Physics

This weekend I flew down to Washington D.C.. Given my dislike of flying I was not thrilled when I saw the tiny plane I was flying down in. For some reason, big planes always seemed safer than small planes. Something about the small planes always made me wonder how they are able to stay in the air given how small the engines are. Given our recent discussion of momentum, I figured I could use that information to show that the size of the plane is more or less irrelevant. A small plane is considered 12,500 lbs or less and a large plane (ex Boeing 747) weighs 735,000 lbs. Momentum (p)= mv and given momentum in a system is conserved, the mgasvgas=mplanevplane. So although the small plane (12,500 lbs → 56.7 x10^5 g) is lighter it also then requires the engine to shoot out less gas or gas at a lower velocity, to reach the necessary take off speed of ~250km/hr). Meanwhile, the Boeing 747 (735,000 lbs → 33.3 x10^7g) requires more gas leaving the plane at a higher velocity to reach the same take off speed of ~250km/hr. 250km/hr *(1hr/3600sec)*(1000m/1km) = 69m/sec. Therefore, the small plane requires a momentum of (56.7x10^5g)(69m/sec) = 391,230,000 gm/sec. The large plane requires (33.3 x10^7g)(69m/sec) = 22,977,000,000 gm/sec which is more than 50 times the amount of momentum. So now it makes a bit more sense why some of the engines on large planes like the Boeing747 may be the same size as some of these tiny planes, but that’s just to make up for the larger mass and that each size plane would be equally as safe and should be able to safely take off!