Yeah, you hit something with 30.06, like as not, it drops like a bag of rocks.
I guess Ive seen quite a few bags of rocks run like you poked them with a hot stick
I joke, but Ive seen bad shots made because the shooters got an all mighty "aught-six" that they have been told is lightening on game. They either take a bad shot, or the recoil is more than they are comfortable dealing with and they flinch.
The 06s is still one of my favorite cartridges, but its not infallible. Its got enough velocity to cause shallow penetration with light or soft bullets and bad angles, and dosent open the gaping holes that some of the larger cartridges using heavier for caliber projectiles will.
What it does very well is provide a good terminal performance on good hits, and gives you a much larger margin of error than a smaller cartridge, without a magnum jump in recoil. Honestly I think, in a average weight rifle, its at about the top of the recoil ladder for a lot of folks that dont shoot much.
I'm more less looking for something for my father to shoot. He can't hold a big rifle and handle recoil like he used to. I am bot a fan of AR not saying they are bad just not my cup of tea. But I would get a 556/223 in a bolt or beeak. I have seen some hunters take dear very nicely at 200 yards for a 556 and I would be shooting much smaller dear in Florida, than what most of you see. So using that round seemed we'll workable for many different games. Using a 62 great or higher bullet I would still get well over 900 ft lbs of impact.
Quick chart
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Per the OPs post there, I WOULD NOT recommend an 06.
The .223/5.56 could be made to work well, but I would opt for a slightly heavier cal/cartridge.
.243/6mm Ubiquitous reduced recoil rounds, can have a sharp recoil impulse in a lighter gun tho.
.250/.257, if you buy used, would deliver a slightly heavier bullet than the .243, but at a slower velocity reducing the slap from a lighter rifle, aint many of them around now tho.
6.5cm/260 is where i would land. plenty of bullet weights, with good bc and sectional density in 100-120gr bullets. You have the option of running those down around 2800, reducing recoil energy and velocity. These can be had in fairly light rifle, but are still easy to shoot.
7-08/7x57 Same as the 6.5s, but offering greater bullet weights, while losing some advantages at lower weights.
Again for a light gun in a reduced recoil situation, id probably not opt for anything heavier than those