If you want to talk about the actual physical profile of the recoil energy, the impulse curve, then just think of it in terms of delivered impulse to the projectile. That is the easiest way to look at it, because we can take a slice of the curve during any given time frame to determine how much impulse and thus total energy has been delivered in recoil. The recoil curve is essentially directly relative to the impulse curve delivered by the propellant energy release into the projectile.
The true recoil curve at hand is entirely dependent upon the burn time and energy release of the propellant. The impulse curve shapes and peak pressure times can vary widely between calibers and powders. The problem trying to quantify felt recoil this way is that it truly means diddily squat to a human perception of it. The reason is quite simple. We feel the total impulse curve of energy delivered to us in only a couple of milliseconds, making it impossible for us to distinguish the actual impulse profile itself when referring to two like total energy amounts with different pressure curves. However, what we can account for ourselves is the total impulse energy delivered by that event, as it hangs around much longer as it dissipates and decelerates in our hand and arms. Because of this human limitation, we must speak in terms of total impulse delivered as the basic means of our perception and comparison.
Think of two rocket motors.
One burns over the course of 1 second, and generates a steady 10lbs of thrust for that time duration.
The second rocket motor burns for 2 seconds, and generates a steady 5lbs of thrust for that duration.
At this point, we know that both rocket motors deliver the same total impulse, they just burn for different durations.
Now, if you had to hold each one in your hand, the motor burning for only 1 second is going to seem like it gives you more of a kick. If gunshots took 1 second for the pressure event to complete, this motor would represent a high pressure load with a very fast pressure rise time.
The second rocket motor is going to feel like a much more modest push, as its duration is longer. It would similarly represent a low-pressure load, with longer pressure event.
At these amounts of time for the events to occur, we ourselves can easily distinguish a difference in feel between the pressure events of the rocket motors.
OK, lets try something interesting. Speed the rocket engines' burnrates up, but keep them at the same total impulse. The 1 second rocket motor now burns for 1/20 of a second, and the 2 second motor is increased to 1/10 of a second, still twice as slow as the first motor. What do you think you will feel at this point? The rocket engines are getting much closer together in feel, both lasting for just a very quick burst of energy, instead of the large difference they had before.
Now, push those times even faster, down to the level of firearms. Down to the point where both of these events each occur over only a few thousandths of a second. Our "high-pressure" rocket motor #1 now lasts for a duration of 0.002 seconds, and our slower rocket #2 now lasts for a duration of 0.004 seconds.
Now imagine holding the two in your hand at these speeds, and trying to tell the 2/1000s of a second difference in pressure profile between them. Do you think you could distinguish the difference?
This is why the true pressure profiles themselves are far less relevant than the total impulse delivered by the energy involved.
I get what 1911Tuner was saying about "muzzle velocity", and I agree. The simple fact is that recoil calculators assume that the bullet is still accelerating, and has not lost any acceleration before muzzle exit. Otherwise, it's not really about muzzle velocity, it is rather about total impulse delivered during any given time frame. But, from muzzle velocity we can determine energy involved which had to occur at some point before the muzzle exit to achieve that projectile speed. Then, from that total impulse value we can then approximate feel, hence my example of why true profile curves are irrelevant.
Here is a little graph I drew to attempt and illustrate what the recoil on the bolt face or breech of the gun would look like over time and, as you would imagine, bullet travel:
Also do notice the shape of the impulse curve in the graph. Since this profile is directly proportional to the shape of the acceleration curve on the projectile, each 1" of barrel removed will never do the same as any other inch of barrel. Think of printing that graph out on a piece of paper, and then taking scissors and cutting vertical slices off from the right side, making it shorter. Each slice, you would have a different amount of blue area, or pressure. This is the way you would be removing acceleration impulse as you cut the barrel shorter, closer to its maximum pressure point.
