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Breaking the sound barrier

Illustration of the effects of breaking the sound barrier using Java

When an object passes through the air, it creates a series of pressure waves in front of it and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound, and as the speed of the object increases, the waves are forced together, or compressed, because they cannot "get out of the way" of each other, eventually merging into a single shock wave at the speed of sound. This critical speed is known as Mach 1 and is approximately 1,225 kilometers per hour (761 mph) at sea level. In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. Because directions around the aircraft's direction of travel are equivalent, the shock forms a cone with the aircraft at its tip. The half-angle (between direction of flight and the shock wave ) A is given by sin(A) = 1/M, where M is the plane's Mach number. So the faster it goes, the finer, more pointed the cone. There is a sudden rise in pressure at the nose, decreasing steadily to a negative pressure at the tail, followed by a sudden return to normal pressure after the object passes. This "overpressure profile" is known as an N-wave because of its shape. The "boom" is experienced when there is a sudden change in pressure, so the N-wave causes two booms, one when the initial pressure rise from the nose hits, and another when the tail passes and the pressure suddenly returns to normal. This leads to a distinctive "double boom" from supersonic aircraft. When maneuvering, the pressure distribution changes into different forms, with a characteristic U-wave shape.

Since the boom is being generated continually as long as the aircraft is supersonic, it fills out a narrow path on the ground following the aircraft's flight path, a bit like an unrolling celebrity carpet and hence known as the boom carpet. Its width depends on the altitude of the aircraft.

(Source: Sonic boom at Wikipedia)

Implementation details

The applet is based on my wave equation applet. I solve the wave equation but this time i move the whole grid with a certain velocity in order to get the impression of a plane moving through air. By doing this an advection term is added to the equation.

You can manipulate the speed of the airplane by moving the mouse inside the applet. if the mouse is at the right border the speed is maximized if it is left it is minimized. Once you reach a certain point you see the cone like shape emerging from the wave fronts. When this happens you have broken the sound barrier.

In order to use the applet add the following lines to your html code:

```    <object classid="java:MachNumber.class" type="application/x-java-applet" width="800" height="600">
<param name="code" value="MachNumber.class"/>
<param name="archive" value="JMachNumber.jar"/>
<param name="sleep" value="1"/>
<param name="preview" value="false"/>
</object>
```

The following table lists the applet parameters and their meaning.

Parameter Meaning
sleep time to wait after each frame (in milli seconds)
preview If this value is true the applet looks like an image only moving when the mouse is over the applet.