Momentum matters:
Assume no spring for the moment, we'll add that in later.
M1 is the buffer mass
M2 is the bolt carrier mass
M3 is the bolt mass
Before the cam pin bottoms out in the cam track (bolt velocity is zero) the momentum of the system is:
momentum = (M1 + M2) x v1
-or-
= (M1 x v1) + (M2 x v1)
What is going to happen when the bolt carrier (M2) picks up the bolt (M3)?
M1 will continue back at v1, but M2 will have to slow down because of the conservation of momentum.[1]
M2 x v1 = (M2 + M1) x v2
with v2 being the new velocity of the bolt carrier, something less than v1.
Since the energy = 1/2 x mass x velocity squared, the energy of the bolt carrier/bolt combination will be less that the energy of the bolt carrier before picking up the bolt.
E1 = 1/2 x M2 x (v1)^2 - before picking up the bolt
E2 = (1/2 x M1 + M2) x (v2)^2 - after picking up the bolt
E1 > E2
Note that E2 is completely independent of M1, the buffer mass.
Since the energy available to operate the system (E2) is independent of the buffer mass, the energy tied up in the buffer is lost to the system. The bolt carrier/bolt combination alone, must have sufficient momentum (which is proportional to velocity and thus energy) to operate the system. If we are dealing with a 'standard" AR system the mass of the carrier (M2), bolt (M3) and spring are fixed.
So, no matter what mass buffer you put it, the momentum of the bolt carrier/bolt combination (which is proportional to velocity and thus energy) required to operate the system is fixed, therefore , no matter what buffer you chose, the minimum bolt carrier/bolt velocity required to operate the system is the same. And since increasing the buffer mass can only decrease the initial velocity (v1), it can only decrease the energy of the system (E2). This is why when we put in the super heavy buffer, we needed to increase the gas pressure to restore the velocity.
And, the minimum velocity required is a lot closer to what the rifle runs than what you might think, note the number of "my rifle won't lock back..." threads here and elsewhere on the web. Also, I'll wager about 20% -25% of the perfect running, 3:00 ejecting, smooth shooting, ARs out there will fail the lock back on an empty magazine when fired straight down. Gravity retards the system just enough to reduce the velocity below minimum.
Now the spring.
The spring only acts on the back of the buffer (M1), but before the bolt carrier picks up the bolt the bolt carrier and buffer travel as one and the spring provides a retarding force to both, but when the bolt carrier picks up the bolt the spring will now only act on the buffer alone. If the energy in the spring is equal to or greater than the energy of the buffer alone the buffer will maintain contact with the bolt carrier, if not the buffer will separate from the bolt carrier.
Spring energy = 1/2 x k x (d)^2
Buffer energy= 1/2 x m1 x (v1)^2
with
k = spring constant
d = spring compression
In either case, the spring/buffer combination cannot add energy to the bolt carrier/bolt combination.
EDIT: Obviously, if you change the weight of the bolt carrier you will get a different minimum velocity requirement, but it will still be independent of the buffer used. Since the system being discussed in this thread does use a non-standard carrier weight, that might make a "kinder, gentler" rifle.....
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NOTES:
1. Let's keep it simple and assume a completely inelastic collision.
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