nhyrum said:
I would say any length after your powder is completely burned is entirely useless.
No. As long as the gas pressure in the barrel is high enough to apply more force to the bullet base than is needed to overcome friction, the bullet is still accelerating and more barrel will give you more velocity. The gas pressure is still there when the powder burns out. Only when the pressure has dropped so low, due to the expanding volume it occupies behind the moving bullet, that the force it applies to the bullet base merely equals bore friction, will acceleration cease.
For the 22 LR that occurs at between 16 and 20 inches down barrel for most loads, which range from mild pistol target to hyper velocity loads. Once you pass that limit, velocity starts to drop, but it drops slowly. This is why, for calibrating a chronograph, you can generally count on match ammunition to be within 50 fps of the box stated velocity in about any rife chambered for it.
For the 22 LR the expansion ratio is huge. At 20 inches it is almost 50:1. The volume the powder is burning in grows that much before the bullet starts to slow.
For the much larger case capacities, an expansion ratio that large requires a very long barrel, indeed. A 30-06 with a 20" barrel has an expansion ratio of around 6:1. So the barrel would have to be about about 8 times longer (160") to match the 22 expansion ratio at 20". The acceleration behavior should roughly match at that point, assuming lubricated lead bullets and identical bore condition in each gun. That said, in a large chambering there are other factors involved that mess with the number, like having to push a large powder mass down the bore in the form of gas. QuickLOAD's simulator says a 170 grain lead bullet driven by H4895 at about the same peak pressure as a 22 LR would start to slow at about 120" of barrel. Due to its higher friction, it says a 165 grain jacketed bullet driven by a full load of 4350 would start to slow much earlier, at about 50" of barrel.
That seems like a reasonable estimate. We know from shooting .308 Win, that you lose about 25 fps per inch of barrel when you are near the 24" SAAMI test barrel length. But in a 30" Palma barrel it's down to 15 fps/inch due to the greater expansion causing an inch of travel to be a less significant percentage of the total volume.
Here's an approximation I worked out awhile back that comes pretty close. Note the difference in medium power and overbore due to the latter having smaller expansion ratios at any given barrel length.