When I was in college, I had several professors that always tried to over-explain their concepts. As mikecr pointed out, the high velocity gasses hitting a wall is what slows the rearward motion of the rifle. (your A1 acceleration) This force accounts for the greatest amount of the recoil reduction, and can be accomplished with very simple designs. (ie JP) Yes, you can increase the efficiency by redirecting the gasses after they initially impact the brake, But it usually requires a more sophisticated design, although many elegant and effective designs are out there.
I'm with johnfred and mike......and yes, I own recoil sleds and I test them all.
And more importantly, my testing agrees with all the other recoil sled guys on youtube and elsewhere.
I'ma make it real simple. Read it again from above,
the high velocity gasses hitting a wall is what slows the rearward motion of the rifle... THIS is how muzzle brakes work.
period.
To really "get it" walk around the corner of a building into the wind while carrying a sheet of plywood, or a hunk of cardboard, or just open your coat in a strong wind. In simple fact ALL OF THE RECOIL comes from accelerating the "ejecta" (bullet and powder) down the barrel and ALL OF THE BRAKING comes from the powder gas "wind" blowing on the plates of the muzzle brake. The larger the plates (sheet of plywood) the more "braking" effect.
period.
And BTW, in the real world angle has much less effect than redneck logic would seem to imply......(think carrying a satellite dish VS a sheet of plywood) there's actually very little "racetrack" or "slingshot" gas reversal effect. SIZE IS EVERYTHING in brakes and a really large (effective) commercially available brake will present 3", 4" even 6 square inches of "impingement area" (sheet of plywood)
ALL of the recoil attenuation occurs after the bullet leaves the bore and for it to work properly there must be a large wad of gas left over to make the "wind" to pull the rifle off of you....If a rifle isn't "overbore" enough to make lots of gas, the muzzle brake can't do much.
Ya want proof? Come over and shoot my 50BMG versus my subsonic 50. I have built the worlds largest muzzle brake at over 25 square inches of "plywood sheet" and it won't pull my liddle 50 off, it kicks like a MULE at over 70fp. The same brake makes a 50BMG into a pussycat, my aged grandm'ither could wakk zombies all day with it, but drop it down to 1000fps and make it burn all the powder and it'd break her neck. F'real....