“Boomless” Supersonic Flight and the Mach Cut-Off
On Monday the start-up Boom Supersonic announced they had achieved supersonic flight and, not only that, none of the three sonic booms generated by their XB-1 aircraft were audible from the ground. The lack of surface disturbances is a key part of their strategy, as current US regulations prohibit supersonic flights over land due to noise concerns.
To achieve their “boomless” flights, Boom Supersonic relies on a neat bit of atmospheric physics. The speed of sound, cs, depends on the square root of temperature: sound waves travel faster in warmer air. In the troposphere (the lowest 10-15km of the atmosphere), temperature decreases with altitude – the gradient of cs with height is negative – so sound waves are preferentially refracted down to the ground.
Conversely, in the stratosphere temperature increases with height – the gradient of cs with height is positive – mostly because of absorption of solar radiation by ozone. The positive gradient in the speed of sound means that shock waves moving down from the stratosphere to the tropopause (the cold layer separating the troposphere and the stratosphere) are partially refracted away from the surface.
(From NOAA)
[Aside: without ozone and other solar radiation-absorbing gases, the stratosphere would essentially be isothermal, with a constant speed of sound!]
The refraction isn’t perfect, so the other piece of the puzzle is flying at the right speed. Supersonic flight generates a “Mach cone” of shock waves in its wake. The higher the Mach number M, the tighter this cone – simple trigonometry shows the half-angle of the cone Θ = sin-1(1/M). For Mach numbers close to 1 the cone is wide, with the energy dispersed over a large radius. Even moderate refraction near the tropopause can be enough to keep the boom from reaching the surface. This is why in Boom’s diagram they indicate Mach numbers of 1-1.3. Over the ocean they want to fly faster, at Mach number 1.7, for which they expect some sound waves to reach the surface.
From Boom’s website
This is a clever idea, but there are several practical issues. First, the tropopause is a dynamic place, which often features folds, wave breaking and other disturbances on many different scales. Moreover, small changes in temperature gradients can change the refraction angle enough to spoil the effect, and the shock wave path is also affected by interactions with other winds. To truly insulate the surface from sonic booms, the Boom aircraft will need very detailed weather forecasts. Testing over the Mojave seems easier than flying over East Coast winter storms or tropical “popcorn” convection.
It’s also notable that the test flight reached a maximum altitude of ~11km, which seems to take advantage of the tropopause being relatively low over the Mojave in winter. Looking at the nearest weather sounding for the Las Vegas airport suggests the tropopause is currently around 9.5-10km. These flights might be harder in summer.
The other problem with flying at low Mach number is transonic drag, which makes flying at speeds a little above or a little below M = 1 the most fuel-intensive way of flying. I don’t know to what extent the aircraft design, either the shape or the engine design, can compensate for this (the XB-1 looks pretty sleek), but it could be tough to keep these flights economical.
I’d be curious to learn more about how Boom is planning to address these challenges. Using the Mach cut-off to fly quietly at supersonic speeds is a fun idea, and it’s a great achievement that they have managed to do this, but it seems challenging to do this operationally across a wide range of weather regimes.
