A question from my 13 yo that I can’t answer -
If you had a plane fast and solid enough to make a sonic boom and loop around and pass through the wave front a second time (no mean feat of technology and aerial acrobatics), what would happen?
Thanks!
It would take unimaginable flight parameters for a plane to fly through its own shock wave but for sake of argument let’s say a plane flys through the shock wave of a different plane. Very unlikely as pilots try to avoid wake turbulence but not impossible.
It would all depend on how close the second plane crossed the shockwave relative to the apex of the cone. The shockwave weakens exponentially as it expands due to our old friend the law of inverse squares. For anything that expands in all directions - I won’t try to illustrate the geometry of a shockwave here - the intensity is inversely proportional to the square of the radius. That means for a point close to the first plane the shockwave has an overpressure of X. If you double the distance which is still far too close for a second plane to be able to cross the overpressure would be x/4. Quadruple the distance wich is still extremely close and it’s 4/16.
Supersonic planes are made pretty sturdy because they have to create that shockwave. Since the plane is made to make its own shockwave I doubt if anything would happen other than giving plane and pilot a hell of a good slam. Maybe some less sturdy parts like the fiberglass radome might fail but that’s pretty iffy.
Most aircraft do this already, in a manner of speaking – the singular “boom” you hear on the ground is an aggregate of shocks being produced from the nose, canopy, wingtips, and tail. So, since each part of the plane is moving at the same speed, as soon as the nose shock separates and the plane begins moving through it, the canopy shock also separates, but is a slightly different shape and size. It’s not unrealistic to suppose that one of the several shocks will pass through another – realize that the canopy is still creating shocks as the nose shocks pass over it!
In short, the sonic booms stack up and become one big blurry pile of shocks. It’s interesting to imagine a plane doing this twice, but easier to imagine a formation of aircraft doing it (so that the hindmost one had to pass through the first plane’s shock while creating its own). Then you’d have stacking on the micro-scale (several shocks per plane stacking up) and on the macro-scale (each of the plane stacks stacking together briefly). There would be a “sweet spot” on the ground where this stacking effect would be noticed, but everywhere else, you’d hear two shocks, because the two major stacks would be moving relative to one another.
To put it yet another way: you hear a “boom” because all of the sound created over a period of time by that one source is reaching you nearly simultaneously. If there are two stacks of sound and they pass you at different times, you’ll hear two booms; however, if they pass you just as the two sources are merging, they become (for your purposes) one sound source, and you will hear one extremely muddy boom. There might be some cancellation effects, but there will also probably be some additive effects.
If one plane were able to loop around and drive through its own boom before the boom dissipated (not sure if this is remotely feasible) you’d get the same effect: two booms in most places, one MegaBoom at the “sweet spot” (wear earplugs).
That’s easy. the pilot would throw up. 
NASA and the Air Force studied a class of supersonic aircraft called Waveriders which directed the sonic boom under the fuselage and basically “surfed” the boom.
The way your question is worded, it seems like you’re interpreting the sonic boom as a single event, as if the aircraft created the boom when it passed the speed of sound and then it was over. In fact, once any part of the airflow around the aircraft is supersonic, there are shockwaves in the air which travel with the aircraft. You interpret these as a single boom if the shockwaves sweep past you (e.g. you’re standing on the ground and a supersonic craft passes over you), but the shockwaves are still there, travelling with the aircraft. They are almost exactly analogous to the wake of a boat in that they are a pressure disturbance in the flow which expands out from the vehicle.
An aircraft could turn abruptly and pass through it’s own shockwave in much the same way a boat can turn and pass through its own wake. In this respect, it would be much like passing through another plane’s shock (as Padeye said). A shock wave is just a discontinuity in pressure, density, and other flow parameters, so the vehicle would experience an abrupt change in ambient conditions. Whether or not that was catastrophic depends on how strong the shock and how sturdy the vehicle were.
Note that shock waves dissipate fairly quickly due to viscous effect, etc. so a shock that is very strong near a vehicle may blur out to a minor pressure increase at some distance from the vehicle. The pressure/density change across a shockwave at the leading edge of a supersonic wing is very high, but this pressure dissipates so much that we only interpret it as a loud noise unless we’re very close (making the point that sound is simply a pressure wave in air). So your plane would have to turn very quickly in order to pass through the strong part of its shock before that shock dissipates, and the stress on the airframe from turning at speed would likely be far more than the stress of passing through a weakening shock.
I really don’t want to pick nits, but thought some elaboration was in order. Waveriders are a class of hypersonic vehicles designed so that the top surface of the vehicle causes very little flow deflection. That is, they have basically a flat top aligned with the direction of flight. This minimizes the strength of the shockwave above the vehicle and maximizes (for a given body cross section) the strength of the shock below the vehicle. This causes a pressure differential between the top and bottom which contributes to lift.
They don’t really direct the shockwaves since shockwaves simply emanate from disturbances; the vehicle is designed so the shockwaves are in a beneficial configuration at certain speeds. Also, “sonic boom” is kind of a layman’s term for when we hear a shockwave pass by. It is the thunder to a shockwave’s lightning. That is, “sonic boom” is an audible effect caused by the shockwave, but the term shouldn’t be used interchangeably with shockwave.
Than you for clarifying it for me. Seems obvious now.