What is a reasonable group for 30-06

Pheroze,

Stocky has an excellent suggestion.
When I was hunting ground squirrels, prairie dogs, and such, (many rounds being fired all summer long) I had found my screws loose once in awhile (!)
But when it was not in my head and actually pertained to whatever rifle that began producing unacceptable groups, I had my best luck tightening the screw just in front of the trigger guard very tight, and then the other one/s, depending on make and model.

It is worth mentioning though, that my scope mount screws/scope ring screws were often loosening long before the stock screws vibrated loose from much firing.
None of the above happened to me very often (and I have owned a pile of rifles) but it has happened and as Stocky suggested, check those screws, tighter groups might just be that easy.

Likewise, in small bore rifles, bore fouling was usually the culprit more often than me or the rifle having our screws loose.
But you are not bringing a small bore to Africa so, bore fouling, though still worth cleaning out for accuracy sake, is not quite as critical.

Best Regards,
Velo Dog.
 
A couple of words of advice. First learn to "call your shots" Even when you think you're doing good you should be able to tell if it's off and in which direction, everytime. Practice by dry firing, make doubly sure it's clear (unloaded), point it at something safe, even do it at the range. If the bullseye is still centered after you pull the trigger on a dry fire you're ready for the range. I learned this from a decorated Marine sniper I used to shoot with in Montana (it was always a humbling experience).
 
Constant and conscient shooting is the master of the accuracy with any gun!...
The 30-06 an every caliber, in any rifle (GOOD rifle, i mean) is capable to put three shots in an inch at 100 yards...
But... the question is... IS THE SHOOTER CAPABLE TO DO THIS?
If we look a pic like the "grumulkin" group, and shows admiration, incredulity, or shame... there is a long way to learn, fellows!!(y)
In the hunt field, however, there is not "bench rest".... so, te practice make masters...
It´s my humildy thinking!
 
Most of what I shoot will group one inch at a 150 yds, I set them all to shoot 3" high. That should get the job done on anything with 4 legs on either continent
 
All of my loads will shoot under 1" consistently from one day to the next. However, what I'm most interested in is where the first two shots go. I want them to hit exactly where I intend every time. Even if the first two are in the same hole and the 3rd is off 0.75-1.0", I'm happy. Why? Usually that third shot is at a fleeing critter in which the objective is merely to hit fleeing critter and not to be nearly as accurate. Sometimes it takes a lot of work and time at the range to find the right combination for a rifle.

One other thing to watch with rifles is the mood of the rifle regarding a clean or dirty bore. I have a 300 WM that prefers having a dirty barrel when it comes to accuracy. The groups really start to shrink when I get to around 20 rounds down the tube. So, I clean and plan on shooting milk jugs filled with water prior to hitting the hunting fields with this particular rifle.

Good luck finding the combination that works for you!
 

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