The stored energy in the spring is also used to drive the BCG forward and load the next round.
True, but not relevant to the backward recoil impulse. The bolt/BCG being driven forward introduces a new impulsive force which further drags the whole business out in time.
BTW, you've just given me an idea for suggestion to "Ballistic High Speed" or "The Slow-Mo Guys" ... their kind of high-speed video of an AR-15 (or some such) firing when shouldered, and when hanging freely. I'd like to actually SEE (at ridiculous frame rate) the recoil motion of a rifle. A gas-operated semiauto should be very different from a bolt-action.
Agreed, but...
The bolt/BCG being driven forward introduces a new impulsive force
using the stored energy from taken from the recoil before it could be transferred to the operator, thus reduced recoil at the operators shoulder.
Energy is a scalar value, not a vector value. And energy is only conserved in a perfectly elastic collision, which the impact of a bullet never is.
I think it was Roy Whetherby, the first evangelist of Kinetic Energy, who put that bee in everybody's bonnet. KE/ME is exactly the wrong tool for assessing the lethality of a cartridge, but that doesn't stop gazillions from using it.
And old acquaintance of mine (who obviously was well more more science-literate that your average shooter) used to say, "The Gospel of Kinetic Energy: proposed by the ignorant, parroted by the unknowing, evangelized by those who failed high school physics.
It bears mention that none of the more credible lethality calculators (Hatcher's relative stopping power, Taylor's knock-out factor, Thorniley stopping power, etc) used velocity factored exponentially, yet KE does.
In the world of science, this is what's known as "a clue."
To put a point on it, kinetic energy never killed nobody.