What would cause more stress the airframe of a 757/767: 550 mph at 1,500 feet, or supersonic flight at 50,000 feet?

Question

I was reading over some threads on metabunk.org about the 9/11 "Truther" Movement and it was brought up that a DC-8 was flown at supersonic speeds at 50,000 feet as an explanation for how tough planes were. The truther replies that this is not 1,500 feet, implying that ~550 mph at 1,500 is more stressful on a plane than flying above mach 1 at 50,000 ft. I have no idea what stresses the airframe more, nor do I even know how that would be measured, or how to ask that question. I appreciate any help.

My best guess is that the higher the mach number the higher the stress.

The planes in question were one Boeing 767-222, one Boeing 757-223, and one Boeing 757-222. Try to calculate for as many of these three aircraft as possible.

Answer 1

I couldn't reply with the most accuracy unless I have a detailed view of the airframe structure and rest of the specifications of the aircraft. But I will give it a try. (I will assume Mach 1 = 767.27 mph in below discussion).

So, at 50,000 ft the air density is even lower than 1/6th of the air density at 1,500 ft. This means the amount of aerodynamic forces acting on the airframe are more than 6 times at 1,500 ft than those acting on it at 50,000 ft (coming from the general equations of aerodynamic forces which are directly proportional to the air density). Now, these forces are also directly proportional to the square of incoming velocity, however the fraction: $$ \frac{{V_{50000}}^2}{{V_{1500}}^2} = \frac{{767.27}^2}{{550}^2} = 2 (almost)$$Now, this concludes that the overall aerodynamic forces should increase by approximately 3 times at the altitude of 1,500 ft. But, at the same time, at 50,000 ft, the sonic boom because of crossing the sound barrier causes the aircraft to generate a shock wave. It's this shockwave which results in dramatic increase in drag forces which can cause some serious troubles for the airframe structure. Almost all of the civil aircraft don't build the airframes by considering the shockwaves as a design criteria since none of them actually crosses this mark of 1 Mach.

What I am guessing is that even the production of shockwaves won't result in higher aerodynamic forces at 50,000 ft at 1 Mach than what the airframe would experience at 1,500 ft at 550 mph. So the ratio can be decreased from 3 to, maybe I guess, 1.5 or something. Still, 1,500 ft condition is the more critical one for the airframe structure.