Totally Hypothetical, probably incorrect, Shock Wave Generation Mechanism

[aseylys]

So I was sitting around pondering about forces, and I found myself thinking about shock-waves. Whether they're caused by supersonic travel, or explosions, the pressure at the front of the wave-bow shock pressure is a force.

So I started thinking of a way to generate them without having to go Mach 1 or detonate something. And here is what I came up with, and please be as brutal as you want with the criticism. This is all hypothetical and done out of curiosity.

So imagine, if you will, a block .1 m x .1 m x .1 m of some super dense metal and this block weighs about .5 lbs (.2267 kg). Now imagine this block is at the end of a .1 m rod and this whole contraption rotates around the other end of the rod. (Hoping that you're still with me) This rod will need to rotate at least at 33422 RPM to go 350 m/s which is a little more than Mach 1 (v=r*RPM*.10472). Which isn't hard for today's electric motors, so let's bump it up to Mach 1.1 (so 17905 RPM).

That's the setup. Now for some more math. So going off some math off a great technical paper (linked at the bottom), I was able to calculate the bow shock pressure with some generous assumptions.

Bow Shock Pressure:
Δp=K_p*K_R*√[p_v*p_g](M²-1)^1/8h_e^-3/4L^3/4*K_s

K_p: Pressure Amplification Factor
K_R: Reflection Factor (assumed 2.0)
p_v: Atmospheric pressure of aircraft (Pa)
p_g: Atmospheric pressure of ground (101325 Pa)
M: Mach number
h_e: Altitude
L: Length of object
K_s: Object shape factor

To find K_s, we have this equation:
K_s=.685*√[A_e]/(L^¾*L_e^¼)

A_e: Effective area
L: Length
L_e: Effective length

Because it's a cube, L=L_e

So we get
K_s=2.166 (In that ballpark)

Now onto our assumptions, as crazy as they may be. I'm assuming that the whole system is sealed and the environment is pressurized to 3atm and we have some technology (magic?) to transfer the pressure generated in the system to the outside to be measured.

I think I've assigned all the variables except K_p and h_e. So without doing those we get
Δp=111244*K_p/h_e^¾

Now, K_p is usually in the ballpark of .8-2.1 for supersonic aircraft, so that factor won't have much affect on the order of magnitude of the pressure.
h_e affects how the bow shock travels through the air s it's really not relevant to my system because it's closed. Unless someone can give me an idea of what to assign it, I'll just ignore it, because like K_p, it won't affect the order of magnitude much.

Wrapping this up, we have somewhere in the vicinity of 110000 Pa, which is 110000 N/m². Supersonic aircraft are usually within 50-100 Pa, and I was trying to get as large of a pressure as possible.

Can someone comment on this, or just tell me that this idea is completely ludicrous and shut me up?

http://www.pdas.com/refs/tp1122.pdf

 

[Dr. Courtney]

How about a bb gun from Walmart and a $4 piece of pipe from the hardware store?

See: http://arxiv.org/ftp/arxiv/papers/1502/1502.06112.pdf

 

[aseylys]

Now where's the hypothetical fun in that?

 

[Dr. Courtney]

We've done a lot of work inventing several shock wave and simulated blast wave generators.

One idea we tested was simply shooting a bullet into water. It gives a true shock wave with a repeatable peak pressure, but the shape is too poor to serve as a simulated blast wave in any practical application. It will kill fish though. It will also burst old Igloo ice chests requiring the need to mop the lab.

Most of our better simulated air blast waves use oxy-acetylene based devices. I still think projectile based devices have potential in water.