Question

A common belief is that a hole in a jet plane can suck a person out. On an episode of the popular TV series Myth Busters, hosts Adam and Jaime attempted to determine whether this is possible. According to the hosts' experiment, such an event cannot happen (that is, they "busted" the myth) But did they need to perform the experiment? As a science advisor to the show, Adam and Jaime ask you to perform a crude calculation to test the myth. A typical jet plane travels at 552 mph at a cruising altitude of 28500 ft. The windows on a jet plane measure 14.0 in x 14.0 in. Calculate the force exerted on such a window as the plane flies at 28500 ft. above the sea level. (Assume the density and pressure of air aft 28500 feet is 0.492 kg/m3 and 324 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm.) Number lb Calculate the fractional difference between this force and the weight Wman of a typical adult male (185 lb) Number man How would you respond to Adam and Jaime? There is no need to perform the experiment; it is impossible for a person to be sucked out of a plane. My calculation does not prove that such an event cannot happen; you will need to perform the experiment.

Answer 1

given
v = 552 mph = 246.766 m/s
h = 28500 ft = 8686.8 m
A = 14 * 14 in = 0.126451 m^2
force exerted = dP*A
dP = Pi - Po
Po = 32400 - 0.5*0.492*v^2 = 17420.209146024 Pa
hence
dP = 1.01*10^5 - Po = 83579.790853976 Pa
F = 10568.74813 N = 2375.949 lb

F/wman = 10568.748133276119176 / 822.921 = 12.8429

as this force is too large
the experiment does not show that such event cannot happen and hence the experiment needs to be performed