The effect of barrel length on recoil.

The effect of barrel length on felt recoil:
One of the often overlooked aspects of recoil, and recoil forces, Is how much the barrel length can affect the felt, or perceived, recoil of a given firearm.
Everyone understands (I hope) that recoil is merely a force that is created by an explosion (deflagration if you want to be technical) with a bullet on one side going one direction and the firearm on the opposing side going the other direction. This force can be can be calculated with a relatively high rate of precision and applied to both actions(bullet acceleration and rifle acceleration), but I’m not going to bore you with a math class, but if you want to geek out and run the numbers on your own, the calculations are relatively easy to find. Now that we understand what starts the recoil process, we can move on to the rest of the story. The rifle, and bullet, are going to accelerate in opposing directions (but at much different rates, unless the rifle and bullet have the same weight) until either the expanding gases are released, or friction inside the barrel overrides the ability of the expanded/expanding gases to maintain acceleration, but either way, once the gases are no longer playing a part, it’s just a matter of momentum. One thing to note when you play with the various recoil calculators that are available, they don’t ask about barrel length because if all other variables remain constant, the recoil velocity will not change.
Now, to illustrate how the above information relates and brings barrel length into the equation, I’ll give a couple of examples:
a) a 12lb 308 with a 26” barrel, shooting 168s over 44.5gns of Varget. QuickLOAD predicts 2736fps, and plugging this info into a recoil calculator gives a recoil velocity of 8.12fps and using a ballpark 10ms as the barrel dwell time we get .9744” of travel under power (8.12*.01*12=.9744”)
b) same 12lb 308 with a 20” barrel shooting 168s over 44.5gns of Varget. QuickLOAD predicts 2592fps and the recoil calculator gives a recoil velocity of 7.83fps and the change in dwell time goes from 10ms to 7.692ms we now get .7227” of travel under power, in addition to the lower velocity.
c) This time it’s a 12lb 30-06 with a 20” barrel shooting 168s over 49.5gns of Varget to achieve 2736fps(to put our velocity back to what our 26” 308 could attain). And now plug this info into the recoil calculator and we get a recoil velocity of 8.42fps and with the reduced dwell time we see the recoil distance go to .777” of travel under power
So, as you can see, Keeping the rifle weight and bullet weight the same, and only changing the barrel length, you end up with a reduction of 26% driven recoil distance, and reduction of 6% of your velocity. BUT, you can go to a slightly larger capacity case (308 to 30-06) with the shorter barrel and maintain your bullet velocity while still reducing your driven recoil distance by 13% . One thing you will need to keep in mind, is that once you reach a certain point (which varies depending on the shooter, but is typically in the 7.5-8.5fps range) recoil velocity matters more than recoil distance (typically regardless of recoil velocity it takes more than about 1.5” of driven recoil to become uncomfortable) on a non-braked rifle, because the velocity/mass will continue rearward until your shoulder acts to stop it.
In conclusion, this information pertains mainly to like for like comparisons of recoil and is a based on a non-braked rifle. The calculations can also be applied across calibers to compare if you can achieve similar or better ballistics without increasing recoil. This, still, is important, even if you run a brake that sufficiently arrests the rearward momentum of the rifle, because the driven recoil distance/speed is what the rifle does before a brake can actually start working. Many of you may have no interest in the above info, but for those of you contemplating a rifle build with a particular set of parameters, you may be surprised at the options that open up when you start playing with recoil velocities, barrel dwell time, bullet weights/BCs, and bullet velocities, while still maintaining your goals for wind drift, drop, and rifle maneuverability. Sometimes its better to swing a short handled heavy hammer, than a long handled light one.