3 ms·

Yeah, there's lots of potential issues, I don't know. It's true that the air is much thinner higher up, but I'm not sure how much that will help--I think a larg

Yeah, there's lots of potential issues, I don't know. It's true that the air is much thinner higher up, but I'm not sure how much that will help--I think a large part of the sonic boom comes from air displaced by the plane to create lift, and of course the momentum imparted by the plane to the air is constant (= the weight of the plane). Also, I'm not sure the fact that the rays that forms the sonic boom are curved makes the sound itself weaker, it just takes longer to propagate down the the ground. But the fact that the sound spreads out towards the sides of the plane should help, the circumference of the shock cone at the point where it touches ground is proportional to the height of the airplane, so I'd expect things to scale down because of that? I found and skimmed this document, "Review of Sonic Boom Theory" by K.J. Plotking (http://adl.stanford.edu/aa210b/Lecture_Notes_files/AIAA-1989-1105-891.pdf http://adl.stanford.edu/aa210b/Lecture_Notes_files/AIAA-1989...), which has some helpful information. First, it notes that the shape of the wave does change while it propagates, but it turns out that the effect is in the opposite direction from what you suggested. That is, close to the aircraft the pressure forms a smooth S (the "mid-field" shape), but then as it moves further away, nonlinear effects causes the wave to bunch up to create the discontinuous N-shape. (See fig 1 and 2 on page 30.) So it seems, in this respect flying higher is actually worse---most research about reducing sonic booms tries to shape the aircraft to be long and thin, in order to make the waveform smoother, so we'd want there to less time for the wave to bunch up again. Second, the document actually has a diagram of how the over-pressure depends on altitude! In fig 10 on page 34 it plots the calculated overpressure from a hypothetical Mach 2.7 supersonic transport. As I eyeball it, the over-pressure goes from 212 pounds/ft^2 at 40,000 feet (airliner level) to 129 pounds/ft^2 at 80,000 feet (SR-71 level), so it went down by a factor of 0.6. (In a cute coincidence, that 60% is almost exactly what's predicted by the scaling law eq. 25 on page 16, even though that equation is only intended for hypersonic aircraft.)

c517402 9y ago
For an Advanced SST the quote near the end is, "Advances in aircraft technology suggest that sonic boom amplitudes for this type of aircraft, also referred to as a High Speed Civil Transport (HSCTJ or the "Orient Express". could be made substantially lower than first generation SSTs. potentially to the point that overland flight could be acceptable." I'm not sure what to make of Fig. 10. I'm sure they are accurately plotting their equations, but the impulse for the SST is a minimum at 50,000 feet and increases for higher altitudes altitudes. The impulse for the HST generally increases with altitude. OTOH they discuss the N-wave forming in the far field and maintaining its shape, but also broadening which seems like it would reduce the impulse just like the overpressure. The references 31-33 have alot of data. Here is a link to the first one: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19640014910.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/196400... PS - If you are getting three digits of accuracy eyeballing Fig. 10, you must have gotten a much cleaner copy than I did. ;)
- vilhelm_s 9y ago
  I'm not sure, but the way I read it was that the impulse is the slope of the first "vertical" bar of the N, rather than the slope of the diagonal line. So as the pulse travels, the vertical part gets compressed and steeper (I increases), and the height of the N gets smaller (Δp decreases), and the the distance between the bars gets longer (broadening). But yeah, figure 17 on page 26 of the document you linked seems to be exactly what we are looking for, great find! One can see exactly how the waveform changes with altitude. Moving from 42,100 feet to 70,700 feet reduced Δp from 1.82 to 1.13, a factor of 0.71.

c517402 9y ago

For an Advanced SST the quote near the end is, "Advances in aircraft technology suggest that sonic boom amplitudes for this type of aircraft, also referred to as a High Speed Civil Transport (HSCTJ or the "Orient Express". could be made substantially lower than first generation SSTs. potentially to the point that overland flight could be acceptable." I'm not sure what to make of Fig. 10. I'm sure they are accurately plotting their equations, but the impulse for the SST is a minimum at 50,000 feet and increases for higher altitudes altitudes. The impulse for the HST generally increases with altitude. OTOH they discuss the N-wave forming in the far field and maintaining its shape, but also broadening which seems like it would reduce the impulse just like the overpressure. The references 31-33 have alot of data. Here is a link to the first one: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19640014910.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/196400... PS - If you are getting three digits of accuracy eyeballing Fig. 10, you must have gotten a much cleaner copy than I did. ;)

vilhelm_s 9y ago
I'm not sure, but the way I read it was that the impulse is the slope of the first "vertical" bar of the N, rather than the slope of the diagonal line. So as the pulse travels, the vertical part gets compressed and steeper (I increases), and the height of the N gets smaller (Δp decreases), and the the distance between the bars gets longer (broadening). But yeah, figure 17 on page 26 of the document you linked seems to be exactly what we are looking for, great find! One can see exactly how the waveform changes with altitude. Moving from 42,100 feet to 70,700 feet reduced Δp from 1.82 to 1.13, a factor of 0.71.