I have a JP brake.  It is loud.  I was thinking about having a blast shield machined for it.  My thought was a two inch diameter tube with small holes drilled in it.

The question I have is will the shield negate the brake's effect on muzzle rise and recoil.  I would appreciate your input.

I would imagine so. Wish I had proof/further information but my (very lacking) knowledge of physics would incline me to believe so.

My college physics classes were a long time ago, so I no confidence in my analysis.  My initial thought would be that the brake would offset recoil and rise as normal.  Then as the gas hits the shield it would be cooler and have an increase in volume.  The shield would allow part of the gas to go through the holes, and would direct some of the gas forward.  

The gas that passes through the holes should not have an effect, since they are equal on each side.  The gas going forward will cause the rifle to move back.  My thinking is that since the gas has expanded, the force to the rear would be negligible.  

Another potential issue would be the gas moving forward would have effect the bullet leaving the barrel.  My guess is that the bullet would be down range, before the gas would get to the front of the barrel.  However, I have no scientific basis for this belief.

Maybe the answer is, don't worry about it.  5.56 doesn't recoil enough to matter.  lol

I am having one made.  I will report back on my impressions.

Sorry that you didn't get a ton of feedback. I'm not sure anyone really has a solid answer to give you.

There are quite a few blast shields on the market...why are you trying to reinvent the wheel?

First, they are expensive.  Two they require a specific brake.  I want to stick with what I have.  I can also have it made for a bottle of wine.

Griffin QD blast shield and vg6 cage can be used on a2 and brakes/comps/hiders that use the same profile used at the "two notched" part of the device.

If cost is your limiting factor, use an old mag light  Cut the barrel of the light to whatever length, drill hole in back end cap and install it like an oversized washer behind the flash hider (can even reinstall crush washer over it).  Then you can screw on and off a shroud over the brake whenever you want.  As long as you don't close off the front end that reduces sound, you'll be fine.

I don't get how that would stay on

The mag light end cap is held in place by the flash hider.  Like a giant washer with threads at the rim.  Then the mag light body is slipped over everything and threaded on to the end cap.

Yes blast shields ruin the brake/comp effectiveness. The amount it is ruined is directly proportional to the effectiveness of the blast shield. That is why a silencer gets increased recoil vs the bare muzzle brake attachment. Also a silencer over a very effective flash hider  gives increased flash over the flash hider alone.