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I read that the "cone" of the sonic boom is a cone of angle 25 degrees extending from the nose of the aircraft, centred on the axis of the aircraft.

I also read that the English Electric Lightning (and no doubt many another jet since) could break the sound barrier while climbing near-vertically.

If Concorde could have climbed at 45 degrees (or less) when it was accelerating through Mach 1 would that have solved the problems associated with sonic boom over land? The idea being that at that angle the cone would usually not intercept the ground (subject to mountainous terrain).

Edit

Following Bianfable's comment I now see the problem: you have to be at this angle from the point you are just about to hit Mach 1 to the point you get to the ocean ... and climbing at that angle would probably reach your operational ceiling fairly fast (and no doubt the thinner the air the more difficult it is to maintain).

So the obvious thing would be to dip down to, ooh, 2,000 feet as you approach Mach 0.95 and then pivot upwards! (To clarify, I do realise Mach 0.95 is trickier at lower altitudes... and also that it's quite noisy...).

And/or use rocket motors to get to a more satisfactory ceiling, perhaps.

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  • $\begingroup$ Are you aware that the sonic boom is created continuously above Mach 1 and not just when breaking through the sound barrier? $\endgroup$
    – Bianfable
    Feb 26, 2023 at 14:30
  • $\begingroup$ In fact I wasn't, no. Although it makes sense, since sound has a near-constant speed. But the question still stands... if you can continue climbing at 27 degrees until you get over the ocean... does that work? $\endgroup$ Feb 26, 2023 at 14:31

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When flying at Mach 2, the Mach cone will look like this:

Mach cone at Mach 2

The opening angle of the cone $\mu$ at a given Mach number $M$ is given by

$$ \mu = \arcsin \left( \frac{1}{M} \right) $$

I added the red arrows to indicate the direction in which the wavefronts forming the cone will expand as time passes. The lower one will eventually hit the ground and can then be heard as a sonic boom.

When flying upwards at an angle higher than $90^\circ - \mu$, the cone will never hit the ground. For Mach 2 this would be a climb angle of more than 60°:

Mach cone upwards

The individual waves (grey circles) will still eventually hit the ground, but never more than one circle at a time. The wavefronts forming the cone do not hit the ground anymore, therefore no sonic boom can be heard. Note that the cone only extends backwards up to the moment where the aircraft first reached supersonic speeds and therefore does not continue backwards into the ground (because the aircraft obviously wasn't in the ground when flying).

It goes without saying that Concorde was not nearly capable of climbing at 60°, especially not while flying at Mach 2. The required angle is a bit less when going slower (about 45° at Mach 1.4), but this does not seem to be realistic for any supersonic airliner.

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  • $\begingroup$ Thanks, this has given me a different perspective to the problem. I have a question though: even with a climb angle of <60°, won't the intensity of the boom phenomenon be mitigated (for those on the ground I mean)? Surely the phenomenon can't be the same between an aircraft climbing and an aircraft which is flying level? Not least because, as these wave fronts "move", mustn't they reduce in intensity accordingly? $\endgroup$ Feb 26, 2023 at 16:39
  • $\begingroup$ @mikerodent Good point, yes, the sonic boom reduces in intensity the longer it travels through air and the higher angle should spread the energy over a larger area, so I would expect reduced intensity. $\endgroup$
    – Bianfable
    Feb 26, 2023 at 17:00
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    $\begingroup$ This is why rocket launches appear to not have sonic booms, but Falcon 9 landings (as well as X-37B) do, and Shuttle landings did. $\endgroup$ Feb 26, 2023 at 21:20
  • $\begingroup$ @Bianfable you're right, I totally got the question wrong, very good answer indeed 👍 $\endgroup$
    – sophit
    Feb 27, 2023 at 4:14

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