Small disturbances in air cannot propagate faster than the speed of sound,  , where  is 1.4, T is in Kelvins, and R is the gas constant of air. Example: T= 300K . Then a = 347 m/s (776 mph) because R =287.04. At T= 216K, a is 294 m/s (658mph). Mach number is u/a.

Consider a tiny point flying faster than the speed of sound (i.e., supersonic). The flight Mach number is thus greater than 1. In one second the point moves from A to B. In the same time, the disturbance from A has travelled everywhere inside a circle of diameter a. The cone half-angle m is called the Mach angle. Note that  . Thus,  . The disturbance due to the source can only be felt within the Mach cone. The air immediately in front cannot feel the oncoming disturbance, and so it cannot start moving out of the way. The above results are for "infinitesimal" disturbances; so small in amplitude that they don't change the temperature of the flow. If the disturbance is big, the temperature will change appreciably, so the speed of sound at the new temperature will be different.

The shock pattern over the front of a sharp wedge is the simplest to consider. The shock formed is called an "oblique shock", for obvious reasons. The shock angle B is greater than the Mach angle m, because the shock is a disturbance formed when many Mach waves, corresponding to many tiny disturbances, all run into each other and coalesce. In the process, the pressure and temperature behind the shock are appreciably greater than those in front, and hence the speed of sound in the shock is greater than that in front of it. Hence the larger inclination of the shock. Now we can also see that the shock angle has to be less than 90 degrees: disturbances cannot propagate upstream in a supersonic flow!

Across a shock there is a large pressure increase. As the flight Mach number increases beyond 4 or 5, we enter what is called the "hypersonic" regime. Here the Mach angle, and the shock angle, are extremely small (as you can verify using the Mach angle expression above). In fact the shock angle is so small that the shock lies very close to the surface, and is almost not distinguishable from the disturned boundary layer near the surface. The temperature rise across this layer is so large that the flow (and the vehicle surface) glows orange, or even white-hot, as the molecules get excited enough to emit a large amount of radiation at all wavelengths. So, when we calculate forces on the vehicle, we see that the large pressure rise below the lower surface produces a large force component along the lift direction. Thus it appears that the vehicle is "riding" on this shock wave: it almost does not need wings!

Now we can also consider what happens when an asteroid (or an alien spaceship) enters the earth's atmosphere, traveling at velocities high enough to be in orbits around the sun (or whatever). A very strong shock develops in front of the object, causing temperatures and pressures that are only seen on earth during nuclear explosions. The gas molecules get so excited (bounce around at such high speeds and run into each other) that they break up, and even the atoms break up and electrons fly off. These are called, respectively, "dissociation", and "ionization". Fortunately these processes soak up a lot of heat, or else the objects would vaporize instantly. As it is, most re-entering objects break up and melt due to the terrible pressures and temperatures. They glow brightly, and may leave glowing trails of gases with various colors, depending on the chemicals present in the objects and their reactions with the air. The ionization is the reason why radio communication is impossible with the crew of a re-entering spacecraft.

Now most of the time our Atmosphere does a terrific job of protecting us from these falling objects. In fact thousands and thousands of such objects fall into the atmosphere every day, and get vaporized with no fuss. A theory which has gained a lot of followers recently says that most of the water on our planet comes from little comets which melt and vaporize in the upper atmosphere. Comets are supposed to be composed of ice, among other things, a result of what must have been quite an ice storm in the Solar System at some time.

If an asteroid is so big that it still remains as a solid object when it nears the ground (i.e., comes down to a few thousand feet), the shock waves can hit the ground with terrible strength. This can flatten trees, forests, and buildings (happened in Siberia just around the time that the Wright Brothers were getting off the ground). When the objects finally reaches the ground, the shock in front blasts a huge crater in the earth's surface. The crater is huge, even though the object that actually reaches the ground may be quite small. See Meteor Crater in Arizona for an example of such a crater which has survived for centuries since the event. There is a growing belief that an immense object hit the Gulf of Mexico during the Age of Dinosaurs, and the havoc  was such that it caused the extinction of the dinosaurs, worldwide.
 

Flight at high Subsonic and Transonic Speeds

The Critical Mach Number

Supersonic Transports

. So if "getting there quickly" is important (and it is, after more than 5 hours in a cramped seat!), there are benefits to designing airliners for flight Mach numbers upto about 3.5. In the 1960s, SuperSonic Transports (SSTs) were developed by the Soviet Union (Tupolev Tu-144), a British-French consortium (Concorde) and by the United States (Boeing SST). The Soviet aircraft went into operation in a limited manner, soon being relegated to official flights and urgent cross-continental missions. The American effort was canceled after it was decided that there were no good solutions to the problems of Sonic Boom (shock-induced noise reaching the ground and causing large impulsive pressure changes which were believed to be dangerous enough to break windows), and pollution in the upper atmosphere. Also, fuel prices started rising so that the SST was considered to be economically not viable. The Concorde was built, and several of them operate even today, flying Mach 2 at over 50,000 feet on regular airline flights between New York, London, Paris, and Sydney. When flying over land, the Concorde has to fly subsonic to avoid the sonic boom problem. Today, interest in supersonic transports is rising again, with more efficient engines, better materials, and lower sonic boom "footprints". The High Speed Civil Transport (HSCT) is one such effort, with Boeing believed to be developing an aircraft in collaboration with NASA. Several tough problems remain, and are being solved through advanced research and development. The target for sonic boom is to reduce it below 1psf. This requires flight at altitudes of 50,000 to 60,000 feet. Unfortunately, this is far above the region where there are strong winds, so any pollutants deposited there, tend to stay there, with bad consequences for the ozone layer which protects us from solar ultraviolet radiation, among other problems. Even though engines have become highly efficient compared to those in the 1960s and 1970s, they still operate at very high temperatures, where oxides of nitrogen are formed. Another problem is the heating of the aircraft skin due to skin friction. One curious aspect of this is that the skin may remain so hot after landing that it may be dangerous to open the doors for an hour after landing: this will hardly be acceptable to people who pay premium airfares to zip across the oceans in 5 hours. Another issue is that the aircraft will have to land at a speed which is higher than that of current airliners, since its low-speed performance is not likely to be as efficient as that of slower airliners. This landing speed demands better landing gear and tires (not to mention pilots who won't close their eyes as the ground comes up at them?) Until these problems are solved, the HSCT may be designed for lower Mach numbers, in the range of 1.4 to 1.7, rather than 2.2 to 2.5.

Some Useful Facts About High-Speed Flight

Subsonic flight: Prandtl-Glauert Correction

. So, to get the same lift coefficient at a higher Mach number, one requires a smaller angle of attack. Which is good, because the drag coefficient also increases like this. This expression is valid for Mach numbers which are lower than the critical Mach number.

Note that the exponent has the value 3.5 for air.

Aerodynamic Noise from a jet exhaust is proportional, roughly, to the sixth power of the jet exhaust velocity. This is why modern engines, where the jet exhaust velocity is kept as low as possible using high bypass ratio and mixing with cold air, are so much quieter than older turbojet engines. However, this also explains why aircraft designed for high-speed flight, which usually must have a high jet exhaust velocity, are bound to be noisier than aircraft meant for low speed flight.

The intensity of the Sonic Boom caused by a supersonic aircraft is proportional to the wing loading, W/S.