The short version of this explanation is that a muzzlebrake operates by redirecting the escaping propellant at an angle away from the bore. For example, if you have a 150 grain bullet being pushed by 50 grains of propellant (propellant/fuel doesn't lose much weight from burning, its just a chemical reaction when you look at the process) and the muzzle velocity is 3000 ft/s then you are accelerating 200gr of mass to 3000 ft/s. The muzzlebrake strips the gases off and directs them equally away from the axis of the bore, so if in our example 25gr of the propellant blows out the LH ports perpendicular to the barrel axis and 25gr of the propellant blows out the RH ports perpendicular to the barrel axis then the
actual rearward recoil (not the
felt recoil) is for the 150gr projectile only since the propellant gases were diverted in opposite directions canceling each other out.
In simple terms (I'm not going to bore you all with the acceleration and inertia equations), if your recoil equation is f=m x v^2 where
m is your total weight of projectile and propellant, then your reduction equation will be -f=m x v^2 where
m is the weight of the propellant. If you direct the muzzle blast at any angle forward of a line perpendicular to the bore axis, then there is still a rearward thrust vector since the propellant still has a forward velocity. If you direct the muzzleblast
rearward then you are imparting a net
negative velocity to the propellant which increases the recoil reduction (that's why you see a lot of angled port brakes on 50BMG rifles).
However, with that muzzleblast comes noise so you're going to have shockwaves spreading out hemispherically from the point of origin, much like ripples in a pond that spread out from a rock being dropped in it. If there is no muzzlebrake the sound spreads away from the muzzle with the higher pressure impulses directed forward. That is why a gun is much louder if you are ahead of the firing line (its even louder if you're being shot at, but that is just because you're paying undivided attention to it

). As you start redirecting the blast and the high pressure impulses further rearward, the noise level for the shooter's position is going to increase.
Basically, redirection of propellant equals redirection of noise. On most of our muzzlebrake designs we use some additional tricks to reduce recoil without having to direct blast back at the user, but there is still a distinct blast vector that you don't want to be standing in the way of. Our brakes generally sound just a little louder from the shooter's position and gets progressively louder as you move forward or to the side from the shooter's position. We had our KA-1222 on a 10" M-16 yesterday at a big shoot here in AZ and although it sounded about the same if you were the guy shooting it, if you were further down the firing line it sounded like a FAL or other large caliber rifle firing. The KA-1830 reduces recoil even more and directs the blast along a line about 6" wide running perpendicular to the bore, if you are standing on that line when it goes off it will make you wet your pants
