# I What happens if two moving shock waves collide?

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1. Mar 22, 2016

### DigedyDan

Say there were to be two normal shock waves that were moving towards each other at different speeds. What would happen when they collide with each other? Would the shock waves flow past each other or would they be reflected back from the direction they came from? Also how would you be able to determine how the shock waves would change in velocity after passing through each other, reflecting, or whatever it is that they do?

I'm not sure if I'm describing it well enough, so I'll try to draw it out.
shock @ speed X air moving at speed Y shock @ speed Z
|->x ( -->y ) z<-|

which then becomes

a<-| ( -->b ) |->c

Last edited: Mar 22, 2016
2. Mar 22, 2016

### TheQuietOne

Logically speaking, it doesn't seem that the air movement would make much difference (depending on the strength of the waves)

3. Mar 22, 2016

### DigedyDan

So the velocity of the air in the middle would only change the reference frame? As in if you were to make Y=0m/s, then the two shocks would be X-Y and Z+Y respectively?

EDIT: This seemed to have worked, and it matched with given calculations for before the shocks collide with each other. However, I still do not know what happens when the shocks do collide.

Last edited: Mar 22, 2016
4. Mar 23, 2016

### Staff: Mentor

What happens when supersonic warplanes fly past each other on opposite courses? Photographic evidence probably exists somewhere.

5. Mar 30, 2016

### caz

Look up the rankine-hugoniot jump conditions. Treat air as a perfect gas with P=(gamma-1)E/V. Using the jump conditions, rewrite the eos as a function of pressure and change in particle velocity (P-u space). Center this eos on each of your shocks. Since pressure and particle velocity need to be identical after the shocks pass, where the two eos's intersect is the final state. You can then use the jump conditions to calculate the two new shock velocities. A compressible flow book should tell you how to do this using mach numbers.

This method is slightly incorrect. As I descibed it, the eos (hugoniot) describing the second shock is identical to the eos for the first shock (principal hugoniot), i.e, it is a little too hard, i.e. the pressure and shock velocity calculated will be a little high. If you want to correct for this, recalculate the hugoniot using the shocked as opposed to ambient state for the region connecting the first shocked state to the final shocked state.

Last edited: Mar 30, 2016
6. Mar 30, 2016

### caz

If you do not want to do the math, you can do the above graphically. If you overlay plots of the eos in P-u space over the initial shock conditions, where they intersect will be the final state, subject to the limitations of the second paragraph above.

Regardless, you will end up with shocks with different shock velocities propagating in both directions.

Last edited: Mar 30, 2016