Sub-Sonic, Sonic, Supersonic — Bullet Traces at Three Velocities
On the Applied Ballistics Facebook Page, there is a fascinating series of posts showing traces of bullets at various speeds from Mach 0.86 to Mach 3.0. At the slowest speed, Mach 0.86, i.e. 962 FPS, there is turbulence behind the bullet, but no clear shockwave. At the highest velocity, Mach 3.0 (3375 FPS at sea level, 68° F), there is a dramatic double nose and tail wave formation.
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Mach 3.00 Bullet Flight Image
At Mach 3 (3355 FPS) this bullet now has a strong and well established shock wave forming at the tip, and at the base. Unlike the transition through Mach 1.0, nothing really interesting happens to the aerodynamics or shock waves meaning the aerodynamics and stability are: continuous, easy to predict, and model. As you go faster, the shockwaves make a shallower angle because the bullet is moving forward 3X faster than the shock wave is moving away from it. So the shock wave makes an angle that has a rise/run ratio of 1/3.
If a bullet flew within 10 feet of you traveling this fast, it would be about as loud as a 22 magnum. You’d certainly want hearing protection as the energy contained in a Mach 3 shock wave is high! How high…? Well, in 10 yards, this bullet slows from 3355 FPS to 3334 FPS in a time of 0.0090 seconds. The 55 ft-lb of kinetic energy lost during this 10 yards is due to aerodynamic drag on the bullet, which is comprised of wave, base, and skin friction drag components with the majority of the drag being due to shock wave formation. Expending 55 ft-lb of energy in 0.0090 seconds requires a power output of 6111 ft-lb/sec = 11.1 horsepower, most of which goes into creating the shock wave. Remember it’s a 3-D cone that travels great distance, and it gets its energy by stealing velocity from your bullet!
Mach 1.00 Bullet Flight Image
Many shots were fired to capture an image of the transonic shockwave structure at exactly Mach 1.00. With the bullet now moving at the speed of sound, the local airflow on some parts of the bullet exceeds Mach 1.0. Anytime something is moving thru the air faster than the air can get out of the way, you get a compression wave, aka “shock wave”. That’s what’s visible in this image — the areas where the air density changes rapidly (in the compression wave) are visible as near vertical lines and a detached bow wave out front. As the bullet progresses through transonic speed, this shockwave structure develops which has strong effects on the drag (wind sensitivity) and stability of the bullet.
The exact development of the shockwaves and the resulting effects are unique and sensitive to the bullet geometry, and become very difficult to predict through the transition from subsonic (incompressible flow without shock waves) to supersonic (compressible flow with shock waves). Each bullet geometry does this differently which is why it’s difficult to determine transonic stability criteria for bullets of different shapes.
Mach 0.86 Bullet Flight Image
Here’s a bullet at Mach 0.86 (86% the speed of sound, which is 962 FPS at 61° F). As you can see, this 0.86 Mach is not fast enough to make any discernable waves but you can see turbulence in the bullet wake (right side in photo). The beginning of small shock waves can be seen on the bullet tip, and at the bearing surface/boat tail juncture. For the most part, all of the airflow around this bullet is subsonic. You wouldn’t hear a supersonic ‘crack’ from this bullet flying past the observer.
